Kinematics of the Diffuse Ionized Gas in
Spiral Galaxy Disk-Halo Interactions
by
George Herbert Heald, Jr.
B.A., Thiel College, 2000
M.S., University of New Mexico, 2003
THESIS
Submitted in Partial Fulfillment of the
Requirements for the Degree of
Doctor of Philosophy
Physics
The University of New Mexico
Albuquerque, New Mexico
July, 2006
c
2006,
George Herbert Heald, Jr.
iii
iv
Kinematics of the Diffuse Ionized Gas in
Spiral Galaxy Disk-Halo Interactions
by
George Herbert Heald, Jr.
ABSTRACT OF THESIS
Submitted in Partial Fulfillment of the
Requirements for the Degree of
Doctor of Philosophy
Physics
The University of New Mexico
Albuquerque, New Mexico
July, 2006
Kinematics of the Diffuse Ionized Gas in
Spiral Galaxy Disk-Halo Interactions
by
George Herbert Heald, Jr.
B.A., Thiel College, 2000
M.S., University of New Mexico, 2003
Ph.D., Physics, University of New Mexico, 2006
Abstract
Multiphase gas has been observed in the halos of the Milky Way and some external
spiral galaxies. The origin of this gas is still unknown, but observational evidence
indicates that star formation-driven disk-halo flows likely play an important role:
a correlation is observed between more prominent gaseous halos and higher disk
star formation rates; moreover, loop and filamentary structures, often rooted in disk
H II regions, extend well into some halos. Whether this process is characterized
by hydrodynamic flows of diffuse gas, or ballistic motion of denser clouds, may be
addressed by examining the kinematics of the gaseous halos. Accretion of material
from the surrounding environment may also be important in driving the kinematics
of halo gas. In this thesis, I present an investigation into the kinematics of the warm
ionized phase of halo gas in three external edge-on, late type spiral galaxies: NGC
5775, NGC 891, and NGC 4302.
vii
The extraction of rotation curves from edge-on systems is a non-trivial task, particularly in the faint halo region, and requires detailed analysis of position-velocity
(PV) diagrams. Spectra covering two-dimensional areas of each galaxy have been
obtained using Fabry-Perot imaging spectroscopy in the case of NGC 5775, and
multi-fiber spectroscopy in the cases of NGC 891 and NGC 4302. PV diagrams constructed from the data are analyzed to investigate whether the rotation speed of the
halo gas varies with height above the disk. In each case, a gradient in rotational
velocity with height is revealed, with approximate magnitudes 8 km s−1 kpc−1 (NGC
5775), 15 km s−1 kpc−1 (NGC 891), and 30 km s−1 kpc−1 (NGC 4302). All three gradients represent a decrease in rotation speed with increasing distance from the star
forming disk. The gradient measured in NGC 891 agrees with an earlier H I study.
These three results, together with the H I result, are the first robust measurements
of rotation speeds in gaseous halos and their variation with height above the disk.
A model of disk-halo flow which considers pure ballistic motion of gas clouds
through a galactic gravitational potential is utilized in an attempt to match the
results for each galaxy. In each case, the change in rotation speed with height
predicted by the ballistic model is found to be significantly lower than the measured
value from the data. The model also predicts a large amount of radial redistribution
of halo gas, which is not seen in the data. The discrepancy between the kinematics in
the data and model is most severe in NGC 4302, and least severe in NGC 5775. The
magnitude of the discrepancy decreases as the prominence of filamentary structures in
each halo increases, suggesting that the motion of gas in halos of smoother appearance
may be intrinsically less ballistic in nature. Evidence from other modeling studies
indicates that a hydrodynamic treatment may be more successful. The variation in
the observed gradient in rotational velocity appears to be related to the morphology
of the gaseous halo, and to the level of star formation in the underlying disk.
viii
Contents
List of Figures
xiii
List of Tables
xvii
1 Introduction
1.1
1.2
1
Gaseous Halos in Spiral Galaxies . . . . . . . . . . . . . . . . . . . .
3
1.1.1
The Milky Way . . . . . . . . . . . . . . . . . . . . . . . . . .
4
1.1.2
External Galaxies . . . . . . . . . . . . . . . . . . . . . . . . .
11
Role of Gaseous Halos in Galaxy Evolution . . . . . . . . . . . . . . .
16
1.2.1
Galactic Fountain . . . . . . . . . . . . . . . . . . . . . . . . .
17
1.2.2
Accretion . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
21
1.3
Halo Kinematics
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
24
1.4
Observational Techniques . . . . . . . . . . . . . . . . . . . . . . . . .
27
1.4.1
Fabry-Perot Imaging Spectroscopy . . . . . . . . . . . . . . .
27
1.4.2
Multi-Fiber Spectroscopy . . . . . . . . . . . . . . . . . . . . .
31
ix
Contents
2 DIG Halo Kinematics in NGC 5775
35
2.1
Chapter Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35
2.2
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
36
2.3
Observations and Data Reduction . . . . . . . . . . . . . . . . . . . .
42
2.4
Analysis and Modeling . . . . . . . . . . . . . . . . . . . . . . . . . .
48
2.4.1
The velocity field . . . . . . . . . . . . . . . . . . . . . . . . .
48
2.4.2
Disk rotation curves . . . . . . . . . . . . . . . . . . . . . . .
53
2.4.2.1
The envelope tracing method . . . . . . . . . . . . .
54
2.4.2.2
The iteration method
. . . . . . . . . . . . . . . . .
55
Halo rotation . . . . . . . . . . . . . . . . . . . . . . . . . . .
61
2.4.3.1
Azimuthal velocity gradient . . . . . . . . . . . . . .
67
2.4.3.2
Systemic velocity shift . . . . . . . . . . . . . . . . .
68
2.4.3.3
Modification of the halo radial density profile . . . .
70
2.4.3.4
Modification of the halo rotation curve . . . . . . . .
71
2.4.3.5
Modification of halo position angle and inclination .
74
2.5
The Ballistic Model . . . . . . . . . . . . . . . . . . . . . . . . . . . .
75
2.6
H I Loops . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
88
2.6.1
F1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
90
2.6.2
F2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
93
2.6.3
F3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
96
2.4.3
x
Contents
2.7
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3 DIG Halo Kinematics in NGC 891
98
101
3.1
Chapter Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
3.2
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
3.3
Observations and Data Reduction . . . . . . . . . . . . . . . . . . . . 106
3.4
Halo Kinematics
3.5
3.6
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
3.4.1
Envelope Tracing Method . . . . . . . . . . . . . . . . . . . . 113
3.4.2
PV Diagram Modeling . . . . . . . . . . . . . . . . . . . . . . 115
The Ballistic Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
3.5.1
Rotation velocity gradient . . . . . . . . . . . . . . . . . . . . 123
3.5.2
Emission profiles . . . . . . . . . . . . . . . . . . . . . . . . . 124
3.5.3
Minor-axis velocity dispersion . . . . . . . . . . . . . . . . . . 127
3.5.4
Halo potential . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
4 DIG Halo Kinematics in NGC 4302
137
4.1
Chapter Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
4.2
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
4.3
Observations and Data Reduction . . . . . . . . . . . . . . . . . . . . 142
4.4
Halo Kinematics
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
xi
Contents
4.4.1
Envelope Tracing Method . . . . . . . . . . . . . . . . . . . . 147
4.4.2
PV Diagram Modeling . . . . . . . . . . . . . . . . . . . . . . 151
4.5
The Ballistic Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
4.6
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
5 Future Work
171
5.1
Exploring the Cause of the Velocity Gradient
5.2
Putting Extraplanar DIG in a Cosmological Perspective . . . . . . . . 173
5.3
Testing the Galactic Fountain Model . . . . . . . . . . . . . . . . . . 174
xii
. . . . . . . . . . . . . 171
List of Figures
1.1
Schematic of the Milky Way Galaxy . . . . . . . . . . . . . . . . . .
6
1.2
High Velocity Clouds in the Milky Way . . . . . . . . . . . . . . . .
7
1.3
The Wisconsin H-Alpha Mapper Northern Sky Survey . . . . . . . .
9
1.4
Radio continuum observations of NGC 5775 . . . . . . . . . . . . . .
12
1.5
Dust absorption features in NGC 891 . . . . . . . . . . . . . . . . .
18
1.6
Schematic representation of a galactic fountain . . . . . . . . . . . .
19
1.7
Schematic representation of the chimney model . . . . . . . . . . . .
22
1.8
Major and minor galaxy interactions . . . . . . . . . . . . . . . . . .
23
1.9
Mapping of gas density and kinematics on to the position-velocity
plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
28
1.10
Sketch of a Fabry-Perot etalon . . . . . . . . . . . . . . . . . . . . .
30
1.11
Transmission of an etalon as a function of wavelength . . . . . . . .
32
1.12
Layout of SparsePak fibers . . . . . . . . . . . . . . . . . . . . . . .
34
2.1
Sky subtraction of a Fabry-Perot image of NGC 5775 . . . . . . . .
49
xiii
List of Figures
2.2
Hα, H I, and CO 2–1 NGC 5775 major axis PV diagrams . . . . . .
50
2.3
NGC 5775 Fabry-Perot moment maps . . . . . . . . . . . . . . . . .
51
2.4
Comparison between output of GIPSY task RADIAL and NGC 5775
major axis intensities . . . . . . . . . . . . . . . . . . . . . . . . . .
59
2.5
Hα and best-fit model major axis PV diagrams for NGC 5775 . . . .
60
2.6
Best-fit radial density profiles and rotation curves for NGC 5775 . .
61
2.7
CO 2–1 and best-fit model major axis PV diagrams for NGC 5775 .
64
2.8
Vertical intensity profile in NGC 5775 . . . . . . . . . . . . . . . . .
65
2.9
NGC 5775 Hα and CR model PV diagrams . . . . . . . . . . . . . .
66
2.10
Hα and model with vertical velocity gradient PV diagrams for NGC
5775 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.11
Hα and model with vertical velocity gradient and systemic velocity
shift PV diagrams for NGC 5775 . . . . . . . . . . . . . . . . . . . .
2.12
72
Hα and model with modified radial density profile PV diagrams for
NGC 5775 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.14
70
Modified radial density profiles and rotation curves for NGC 5775
halo models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.13
69
73
Hα and model with modified rotation curve PV diagrams for NGC
5775 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
74
2.15
Cloud density contour plots for NGC 5775 ballistic base model . . .
78
2.16
Azimuthal velocity curves for NGC 5775 ballistic base model . . . .
80
2.17
Meridional plots for NGC 5775 ballistic base model
83
xiv
. . . . . . . . .
List of Figures
2.18
Vertical mean velocity profiles for NGC 5775 ballistic base model . .
85
2.19
Hα and ballistic base model PV diagrams for NGC 5775 . . . . . . .
87
2.20
Hα and ballistic base model moment-0 cuts for NGC 5775 . . . . . .
91
2.21
NGC 5775 F1 PV diagrams . . . . . . . . . . . . . . . . . . . . . . .
92
2.22
NGC 5775 F2 PV diagrams . . . . . . . . . . . . . . . . . . . . . . .
94
2.23
NGC 5775 F3 PV diagrams . . . . . . . . . . . . . . . . . . . . . . .
97
3.1
SparsePak pointings overlaid on an Hα image of NGC 891 . . . . . . 107
3.2
Envelope-tracing rotation curves for NGC 891 (pointing H) . . . . . 117
3.3
Density profiles used as model inputs for NGC 891 (pointing H) . . 120
3.4
Grid of comparisons between PV diagrams constructed from data
and from models for NGC 891 (pointing H) . . . . . . . . . . . . . . 122
3.5
Comparison between PV diagrams constructed from data and from
models for NGC 891 (pointing L3) . . . . . . . . . . . . . . . . . . . 123
3.6
NGC 891 ballistic model azimuthal velocity curves . . . . . . . . . . 126
3.7
Comparison between intensity cuts parallel to the major axis from
an Hα image of NGC 891 and the ballistic model . . . . . . . . . . . 128
3.8
Comparison between minor-axis velocity dispersions in NGC 891 and
the best fit model described in the text . . . . . . . . . . . . . . . . 130
3.9
NGC 891 ballistic model radial velocity curves . . . . . . . . . . . . 131
3.10
Regions dominated by the bulge, disk, and halo potentials in the
ballistic model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
xv
List of Figures
4.1
SparsePak pointings overlaid on an Hα image of NGC 4302 . . . . . 157
4.2
NGC 4302 major axis H I and DIG rotation curves . . . . . . . . . . 158
4.3
Azimuthal velocity curves on the west side of NGC 4302 . . . . . . . 159
4.4
Comparison of east and west side rotation curves in NGC 4302 . . . 160
4.5
Comparison between western PV diagrams from the NGC 4302 data
and models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
4.6
Difference PV diagram statistics . . . . . . . . . . . . . . . . . . . . 163
4.7
Comparison between eastern PV diagrams from the NGC 4302 data
and models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
4.8
NGC 4302 ballistic model azimuthal velocities . . . . . . . . . . . . 167
4.9
NGC 4302 and ballistic model intensity cuts . . . . . . . . . . . . . 170
xvi
List of Tables
2.1
Galaxy Parameters for NGC 5775 . . . . . . . . . . . . . . . . . . .
41
2.2
Ballistic Base Model Characteristics for NGC 5775 . . . . . . . . . .
76
2.3
Properties of NGC 5775 H I Loops . . . . . . . . . . . . . . . . . . .
89
3.1
NGC 891 SparsePak Observing Log . . . . . . . . . . . . . . . . . . 108
4.1
NGC 4302 SparsePak Observing Log . . . . . . . . . . . . . . . . . . 143
4.2
Summary of dV /dz Values for the West Side, using Envelope Tracing
Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
4.3
Summary of Determinations of dV /dz using PV Diagram Modeling
Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
4.4
Summary of Galaxy Parameters . . . . . . . . . . . . . . . . . . . . 168
5.1
Tentative LSB Sample for WSRT Observations . . . . . . . . . . . . 176
xvii
List of Tables
xviii
Chapter 1
Introduction
“These curious objects [Nebulae], not only on account of their number,
but also in consideration of their great consequence,
. . . we may hope, will in future engage
the attention of Astronomers.”
— William Herschel, 1789, in
“Catalogue of a Second Thousand of New Nebulae and Clusters of Stars”
By the middle of the twentieth century, the attention of astronomers was indeed
engaged by Herschel’s “curious objects,” and the study of spiral galaxies was developing rapidly. Although the field had until that time been dominated by optical
observations, exciting discoveries were beginning to be made in the radio portion of
the electromagnetic spectrum. Ewen & Purcell (1951) famously made the first detection of Milky Way (MW) emission of the 21-cm (1420 MHz) neutral hydrogen (H I1 )
ground state hyperfine transition line2 . Neutral hydrogen was observed outside of
1 Astronomers
refer to ionic species using the number of missing electrons plus one; for
example, neutral helium is He I, and singly-ionized helium is He II.
2 The hyperfine transition occurs when the spin vector of the electron flips from being
1
Chapter 1. Introduction
the MW soon thereafter, for example in the Coma cluster (Heeschen 1956), as well
as the external galaxies M33 (Dieter 1957), M32, M51, and M81 (Heeschen 1957).
Meanwhile, radio continuum observations of M31 at a wavelength of 3.7 meters
(Baldwin 1954) revealed what appeared to be a spherical corona surrounding the
spiral disk to a radius of approximately 10 kpc; in the MW, similar observations
indicated a similar structure, again with a radius of order 10 kpc (Baldwin 1957).
Neutral clouds were detected at large vertical distances above the spiral arms via
Ca II and Na I absorption lines in the spectra of several early-type main sequence
stars3 (Münch 1957). Motivated by these observational results, Spitzer (1956) postulated the presence of a spherical corona of hot (T ∼ 106 K), diffuse (electron number
density ne = 5 × 10−4 cm−3 ) gas, enveloping the disk of the MW. Such a halo would
provide the ambient pressure necessary to prevent the neutral clouds in the halo from
dissolving, and would account for the observed spherical radio-emitting regions. An
independent theory was put forward by Pickelner & Shklovsky (1958), who hypothesized that instead of a high gas temperature, the halo gas could instead have a large
dispersion velocity (∼ 70 km s−1 ) and higher density by about an order of magnitude,
and thereby maintain the observed neutral clouds at a lower ambient temperature
(T ∼ 104 K). Spitzer (1956) argued, however, that the turbulent energy in such a
halo would dissipate too rapidly, and that a large energy input would be required to
maintain it. We return to this question later.
The years following Spitzer’s seminal 1956 paper have been fruitful in developing
our understanding of the nature of gaseous halos. Surveys at different wavelengths
have revealed the presence of hot ionized gas, warm and cold neutral gas, and warm
aligned to anti-aligned with the spin vector of the proton. The timescale for this transition
is about ten million years, so the density and temperature of the gas must be rather low
to prevent collisional de-excitation of the atom.
3 Main sequence stars are normal stars in the hydrogen-burning phase of their lifetime.
Early-type main sequence stars are the most massive of these, with the highest temperatures; they do not normally show Ca II or Na I lines in their spectra.
2
1.1. Gaseous Halos in Spiral Galaxies
ionized gas surrounding the MW (see § 1.1.1). Observations of external galaxies
have been crucial to combat the difficulties inherent in studying a system of which
we are a part. Theoretical work has progressed to incorporate the multiphase nature
of gaseous halos. However, there remain unanswered questions regarding the origins
and properties of the halo gas. Our picture of the multiphase gaseous halos is still
incomplete, and while we are aware that gaseous halos must play a critical role in
the evolution of galaxies, the processes involved are still poorly understood.
With this thesis, I present an investigation into the kinematics of the warm ionized
gas that populates the halos of three external edge-on spiral galaxies. A census of
the material content of gaseous halos is merited before discussing its motion, and is
given in § 1.1. I will then summarize the current ideas regarding the role of gaseous
halos in the dynamical evolution of galaxies in § 1.2. In § 1.3, I will briefly describe
the historical development of the study of gaseous halo kinematics, leading up to the
work presented in the later chapters of this thesis. Before presenting the observational
data, a summary of the observational techniques is provided in § 1.4. The bulk of
the thesis describes the observations and analysis of NGC 5775 (Chapter 2), NGC
891 (Chapter 3), and NGC 4302 (Chapter 4). I conclude the thesis in Chapter 5 by
outlining some research topics to consider in the future.
1.1
Gaseous Halos in Spiral Galaxies
Our location within the MW (see Figure 1.1) has both advantages and disadvantages
for learning about the structure of galaxies. Because we are completely surrounded
by the Galaxy, there are a great many lines of sight available to us that pass through
the medium we are trying to study. The halo gas is also very nearby, and we are
therefore able to investigate small-scale, and faint, structures. Yet our location in
the disk does not allow us to step outside and observe the overall structure of the
3
Chapter 1. Introduction
Galaxy; instead, we must rely on surveys conducted from within. Worse, in order to
get as complete a picture as possible, the entire sky must be surveyed – a significant
undertaking. The distances to structures are often unknown, greatly complicating
interpretation of survey results. Moreover, obscuration in our own Galactic disk (see,
e.g., Henning 1990) can blind us to distant regions of the Galaxy.
Observations of external galaxies, on the other hand, allow us to view the overall
structure of galaxies in a relatively short period of time. There are many nearby
galaxies at different inclinations to the line of sight, so we can investigate the structure
from different viewpoints. However, their distance precludes observation of small
scale structures, and faint diffuse components are often extremely difficult to detect.
Hence, observations both of the MW and external galaxies are required to take
advantages of the strengths of each approach.
1.1.1
The Milky Way
A great deal of the available data regarding the MW’s gaseous halo come from surveys
that cover a large portion of the sky. Surveys have detected halo gas in the radio,
optical, ultraviolet, and X-ray bands. Perhaps the most prominent features in the
halo of the MW are the so-called high-velocity clouds (HVCs), which are gas clouds
observed to have large local standard of rest (LSR) velocities (vLSR )4 . The definition
of HVCs (and sometimes intermediate velocity clouds or IVCs) is arbitrary, but the
condition |vLSR | & 90 km s−1 is typical (Wakker & van Woerden 1997). The essential
point is that the gas clouds do not fit into the standard model of galactic rotation.
Most have negative vLSR , but while it is likely that many of these clouds are falling
onto the disk, it should be remembered that other situations can result in a negative
velocity in the LSR frame. For example, a cloud moving away from the disk, but with
4 The
local standard of rest is a coordinate frame centered on the Sun as it travels around
the Galaxy in an idealized circular orbit.
4
1.1. Gaseous Halos in Spiral Galaxies
the projection of its velocity vector onto the line connecting it to the Sun pointing
toward the Sun, would have a negative vLSR .
HVCs were first discovered in the halo of the Milky Way, via 21-cm line emission,
by Muller et al. (1963). Current estimates of the fraction of the sky covered by
HVCs varies anywhere from approximately 0.1 to 0.4, depending on the brightness
cutoff and whether one considers the Magellanic Stream5 , for example, to be an
HVC (Wakker & van Woerden 1997, and see Figure 1.2). Cloud properties have
often proved difficult to determine because of a lack of knowledge of the distances to
the clouds, but progress has recently been made along those lines (see the discussion
by Wakker et al. 1999, for example).
But HVCs are not the whole story. Observations of H I can also directly reveal
the disk-halo interface in our Galaxy. Lockman & Pidopryhora (2005) illustrate some
recent results obtained using the 100 × 110 − meter Green Bank Telescope (GBT).
The observations reveal multiple cloud structures in the inner MW, some of which
are connected to the disk and each other in long, kpc-scale filamentary structures.
Others are more isolated, but all are observed to be approximately rotating with
the underlying disk (and are therefore not considered to be a part of the HVC
population). Of the ∼ 40 clouds studied by Lockman (2002), the median diameter
is 24 pc, the median density 0.25 cm−3 , and the median H I mass 50 M (though the
mass distribution is skewed to the low-mass end). Lockman estimates that in the
area studied, half of the extraplanar H I mass may be contained in these clouds.
A diffuse component of the extraplanar H I is also observed. The Leiden/Dwingeloo
Survey (LDS; Hartmann & Burton 1997) was performed over ∼ 5 yr using the
Dwingeloo 25-m radio telescope, covering the entire northern sky accessible from
the Netherlands (δ < −30◦ ), and was carefully corrected for stray radiation (Hart5 The
Magellanic Stream is a tidal stream of material that has been stripped out of the
Large Magellanic Cloud (LMC) as it orbits the MW. It is clearly visible in Figure 1.2, in
the ranges (l = 90◦ , b < −30◦ ) and (270◦ < l < 315◦ , b < −30◦ ).
5
Chapter 1. Introduction
Figure 1.1 Schematic of the Galaxy showing the four spiral arms as mapped by H II
regions and the dust (bold lines), the sheared arms in the K band (stars), and the
arms in the two-arm logarithmic model for J- and K-band fit (dashed ) and the Kband fit alone (solid ) (Drimmel & Spergel 2001a). The H II spirals are incomplete
on the opposite side of the Galaxy owing to lack of data. From Drimmel & Spergel
(2001b). The center of the Galaxy is marked with a plus, and the location of the
Sun is also marked ().
6
1.1. Gaseous Halos in Spiral Galaxies
Figure 1.2 Brightness temperature map of HVCs (H I with |vLSR | > 90 km s−1 ). Contours at 0.04, 0.5, and 1.5 K. Common names of some complexes are indicated.
Background sources in which high-velocity absorption has been detected or claimed
are indicated. From Wakker & van Woerden (1997). The coordinates in this Mercator Equal-Area projection are Galactic longitude (l) and latitude (b).
mann et al. 1996). Kalberla et al. (1998) heavily averaged the data to enhance the
weakly detected, faint H I emission. The resulting vertical profiles (i.e., the distribution of emission perpendicular to the Galactic plane) revealed faint extended wings,
with exponential scale height h = 4.4 ± 0.3 kpc. The velocity dispersion of this gas is
approximately 60 km s−1 at the north galactic pole. Thus, the cooler, high dispersion
medium suggested by Pickelner & Shklovsky (1958) is present in the halo, in addition
to the hot component (see below).
Radio continuum emission is also observed in the halo of the MW (e.g., Mills
1959; Price 1974; Beuermann et al. 1985). At long (i.e., meter) wavelengths, the
radio continuum is dominated by nonthermal emission, predominantly in the form of
synchrotron radiation. This emission is generated by cosmic-ray electrons6 spiraling
6 Cosmic
rays are relativistic charged particles. Supernova remnants such as the Crab
7
Chapter 1. Introduction
around magnetic field lines. A large fraction of the nonthermal emission takes the
form of loops and spurs. But there is again a diffuse component, with an equivalent
width at 408 MHz of ∼ 4 kpc near the Sun (Beuermann et al. 1985), suggesting that
the magnetic field and cosmic-ray electrons are coupled in some way to an extended
hot halo like the one proposed by Spitzer (1956).
In the optical, emission lines such as Hα (the n = 3 − 2 transition in neutral hy-
drogen) trace warm ionized gas, which has temperatures T ∼ 104 K, and is the main
focus of this thesis. In the disk, this phase of the ISM is known as the warm ionized
medium (WIM) or the Reynolds Layer, has a mean density of hne i ∼ 0.1 cm−3 , and
a scale height of about 1 kpc (Reynolds 1993). A recent Hα survey, the Wisconsin
H-Alpha Mapper (WHAM; Tufte 1997; Haffner et al. 2003), has been completed in
the northern sky (WHAM-NSS; see Figure 1.3), and is currently being extended to
the southern sky. The results of this survey reveal large-scale, faint, ionized structures in the halo up to 1 − 2 kpc (see Madsen 2005; Reynolds et al. 2005). A faint
Hα background flux (IHα > 5.6 × 10−19 erg cm−2 s−1 arcsec−2 ) is observed in nearly
all directions.
Ionized components of HVCs have also been detected with WHAM (e.g., Tufte
et al. 1998). In general, the positions and mean velocities of the ionized and neutral
components of the HVCs are strongly correlated, but a trend for some of the Hα
emission to be slightly offset in velocity from the neutral component has been noticed
(e.g., Haffner 2005). The integrated Hα intensity and H I column density along any
given line of sight are not strongly correlated, but the hint of a weak relationship
may be present (from observations of HVC Complex L; Haffner 2005).
Returning full circle to the hot halo postulated by Spitzer (1956), the first tentative detection of such a hot diffuse medium surrounding the MW was reported
by Bowyer et al. (1968), but it was not clear whether the observed flux instead
Nebula emit electrons traveling very close to the speed of light.
8
1.1. Gaseous Halos in Spiral Galaxies
Figure 1.3 WHAM-NSS: total intensity. The integrated Hα intensity between vLSR =
−80 and +80 km s−1 is mapped as a function of Galactic coordinates. These three
Hammer-Aitoff projections are centered at b = 0◦ and l = 120◦ . Dashed lines are
spaced 30◦ apart in longitude and 15◦ apart in latitude. From Haffner et al. (2003).
originated in the Solar neighborhood. Later observations, however, have provided
convincing support for a hot phase of the Galactic halo. First, spectra of QSOs7
and distant stars obtained using the Far-Ultraviolet Spectroscopic Explorer (FUSE;
Moos et al. 2000), for example, reveal absorption lines from species such as C IV and
O VI. The presence of these highly ionized atoms implies a very hot gas temperature
(the ionization potential needed to convert O V to O VI is 113.9 eV, corresponding
to a temperature T ∼ 106 K). The observed O VI absorption is widespread in the
9
Chapter 1. Introduction
MW halo, but very patchy (e.g., Savage et al. 2003).
Further evidence for a hot halo surrounding the MW comes from X-ray observatories. The Röntgen Satellite (ROSAT; see for example Snowden & Schmitt 1990) was
the first to detect X-ray “shadows” – regions where the X-ray background has been
obscured by foreground absorption. An X-ray shadow associated with the Draco
Nebula was reported by Snowden et al. (1991), who showed that the 1/4-keV background was suppressed at the same location of an H I cloud. The amount of apparent
absorption indicated that about half of the X-ray background in that energy band
originated behind the Draco Nebula, which is located more than about 200 pc above
the plane. Later, Snowden et al. (1994) investigated sensitive H I observations of a
low NH I 8 region in Ursa Major, and compared the 1/4-keV X-ray flux with the H I
column density. An anticorrelation was found between the two quantities, but the
amount of background X-ray flux was much lower than in the Draco study, implying that the hot coronal gas is spatially clumped, with the brightness doubling over
scales of a few degrees.
All together, these observations indicate that gas exists in many different phases
within the Galactic halo. Yet our ability to describe how all of these components fit
together to create a (presumably) steady-state multiphase halo is diminished by our
inability to measure the distances to many of the observed features, and confusion
between emission sources along the line of sight. To resolve some of these issues, we
must appeal to observations of external galaxies, where we can hope to see the “big
picture” of how the gas phases coexist.
7 QSO
is short for Quasi-Stellar Object, and refers to strong radio sources which have
an unresolved optical counterpart; they are now thought to be the cores of distant (high
cosmological redshift) active galaxies.
8 The symbol N is used to refer to the column density, which is the line integral of the
volume density in a column along the line of sight, resulting in dimensions of length−2 .
10
1.1. Gaseous Halos in Spiral Galaxies
1.1.2
External Galaxies
To be clear, I will consider only normal, late-type spiral galaxies in this section.
Other types of galaxies have large effects on their surrounding medium, such as
galaxies with large-scale energetic winds (e.g., M82, NGC 253; Heckman et al. 1990)
or kiloparsec-scale jets (e.g., M87 Owen et al. 1989; Sparks et al. 1996). But this
discussion is focussed on galaxies similar to our own, whose effects on the extraplanar
regions are more subtle.
The vertical structure of disk galaxies can be investigated by performing deep
observations of spirals highly inclined to the line of sight. The earliest suggestion that
galaxy disks were surrounded by gaseous coronae was, as described above, revealed
by 3.7 meter radio continuum images of M31 (Baldwin 1954). Twenty years later, a
review of radio continuum morphology in spiral galaxies (van der Kruit & Allen 1976)
included a short section discussing halos and thick disks. The radio halo of M31 was
tentatively confirmed, with the caveat that its brightness is not well constrained.
Only in two other spirals were detections confirmed: NGC 4631 (see Ekers & Sancisi
1977) and NGC 891 (e.g., Baldwin & Pooley 1973; Allen et al. 1978). More recently,
Dahlem et al. (1994) obtained new VLA radio continuum data to study the halo of
NGC 891.
Because the source of the radio continuum emission, synchrotron radiation, traces
the presence of magnetic fields and cosmic-ray electrons, critical information about
their distribution and properties can be gleaned from the observations. An important
property of synchrotron radiation is that it is polarized along the magnetic field lines.
Thus, by observing the polarization of the synchrotron radiation, the magnetic field
structure of halos can be investigated. This has been done, for example, by Tüllmann
et al. (2000), who used VLA observations of NGC 5775 to derive magnetic field
vectors in the halo (see Figure 1.4). Note that the magnetic field lines tend to line
11
Chapter 1. Introduction
Figure 1.4 VLA radio-continuum maps with total power (TP; left), polarized intensity (PI; right) and resulting B-vectors overlaid on an Hα image of NGC 5775.
Contours are at 3, 8, 21, 55, 144, 377, and 610 × 16 µJy/beam for TP and 3, 5, 8,
13, 21, and 34 × 7 µJy/beam for PI, for the B-vectors a length of 100 corresponds to
10 µJy. From Tüllmann et al. (2000). Note that a flux density of 1 Jansky (Jy) is
equivalent to 10−26 W m−2 Hz−1 .
up perpendicular to the disk.
Synchrotron radiation can also teach us about the cosmic-ray electron energy
distribution in the halo. Because these are relativistic particles, we will express their
velocity (v) in terms of the Lorentz factor, γ = (1 − v 2 /c2 )−1/2 , where c is the speed
of light. Consider a population of electrons with a power-law distribution of Lorentz
factors: N(γ) ∼ γ −x . The emissivity of the emitted synchrotron radiation will
be jν ∼ ν −(x−1)/2 , again a power law (Binney & Merrifield 1998, p. 479). Multiwavelength observations of radio continuum halos have shown a steeper power law
index (higher x) in the halo than in the disk, meaning that there is a decreasing
number of electrons with high γ as height above the disk (z) increases (see, e.g.,
Hummel et al. 1991). This is consistent with the source of relativistic electrons
12
1.1. Gaseous Halos in Spiral Galaxies
being supernovae in the disk; as the electrons propagate upward they lose energy by
emitting synchrotron and inverse Compton9 radiation.
Neutral hydrogen has also been found in the halos of spiral galaxies. An excellent
example is one of the best-studied external galaxies, NGC 891. Swaters et al. (1997)
observed NGC 891 for a total of 12 × 12 hr with the Westerbork Synthesis Radio
Telescope (WSRT) and detected H I up to z ≈ 5 kpc. This extraplanar H I emission
had previously been noted by Sancisi & Allen (1979), who interpreted the emission
as a flare in the outer disk, and Rupen (1991). Even deeper WSRT observations of
NGC 891 have recently been performed (an additional 200 hours!), and while the
edge of the H I disk seems to have been reached, the new data now show that the
halo emission reaches up to about z ∼ 10 kpc (Fraternali et al. 2005). We return to
H I halos, in this and other galaxies, in § 1.3, where they are used to investigate the
kinematics of halo gas.
Recently, searches have been made for HVC analogues in external galaxies (e.g.,
Thilker et al. 2004; Miller & Bregman 2005; Westmeier et al. 2005). These studies
have been successful in uncovering clouds surrounding a handful of nearby galaxies.
The cloud masses are typically of the order 105−6 M . These detections are probably
a combination of infalling clouds and segments of tidal streams. If these objects are
truly distant counterparts to the MW’s HVCs, then this population of clouds will
provide extremely valuable information.
Although the focus of this discussion is the gas in halos, it seems appropriate to
mention an exciting recent discovery made using archival Infrared Space Observatory
(ISO) data. Recent analysis of infrared spectra in NGC 5907 by Irwin & Madden
(2006) has revealed the presence of polycyclic aromatic hydrocarbons (PAHs) above
the disk. Although dust has been observed above spiral disks in the past (see below),
9 Compton
scattering occurs when a photon scatters off of an electron and imparts
energy to the electron; inverse Compton radiation occurs the same way, except that the
photon gains energy, and the electron loses energy.
13
Chapter 1. Introduction
this is the first detection of PAH emission above the plane. The PAH emission is
detected up to z ≈ 6.5 kpc; the characteristic scale height is 3.5 − 5 kpc. This raises
the question of how the PAHs came to be located so far from the disk.
As mentioned above, dust has been detected above the disks of some spirals,
in both absorption and emission. Studies by Howk & Savage (1999, 2000) and
Thompson et al. (2004) have revealed beautiful filamentary structures (see Figure
1.5) extending well above the disk in several edge-ons. In some of the galaxies, dust
extinction is observed up to 1 − 2 kpc. Also, thermal continuum emission from dust
has been detected in the submillimeter (e.g., Alton et al. 1998) and in the infrared
(e.g., Popescu et al. 2004).
In external galaxies, the analogue of the MW’s WIM or Reynolds Layer is more
commonly referred to as diffuse ionized gas (DIG). Extraplanar DIG (EDIG) has
been detected in many edge-on galaxies. The first detections of Hα emission above
the plane of an external spiral were made via narrowband images of NGC 891 by
Rand et al. (1990) and Dettmar (1990). In the years since those studies, multiple
surveys for EDIG in edge-on spirals have been undertaken (among them, Rand et al.
1992; Pildis et al. 1994; Rand 1996; Hoopes et al. 1999; Rossa & Dettmar 2000,
2003a; Miller & Veilleux 2003a). There is a large variation in EDIG morphology,
brightness, and scale height from galaxy to galaxy. A connection between the scale
height of the EDIG and the star formation rate (SFR) in the underlying disk has
been found (see, e.g., Rand 1996; Rossa & Dettmar 2000).
EDIG in external spirals will be discussed in more detail in § 1.3 and in later
chapters. Before moving on, however, it is important to discuss some observational
results which can help us understand how the gas is ionized at such a large distance
from the disk. Spectroscopic observations of forbidden transition10 emission lines, in
10 Forbidden
transitions are so called because they violate angular momentum selection
rules for dipole transitions; however, they have nonzero transition rates (via quadrupole
14
1.1. Gaseous Halos in Spiral Galaxies
addition to Balmer hydrogen emission lines, are commonly used as diagnostic tools.
For example, the ratio of two sulfur lines, [S II] λ 6731 to [S II] λ 6716, can be used as
a tracer of the gas density in some cases.
In studies of EDIG, among the most commonly used line ratios are [N II]/Hα,
[S II]/Hα, and [S II]/[N II]. The values of [N II]/Hα and [S II]/Hα are consistently
observed to increase with z, as expected from photoionization models. As z increases,
the radiation field becomes more dilute, and, for example, S III is increasingly able
to recombine to form S II, increasing the value of [S II]/Hα (e.g., Collins & Rand
2001, and references therein). So far, the picture is consistent with OB associations
in the disk being the ionizing source of the EDIG. But there are a few line ratios
that are consistently not in line with the photoionization model. For example, the
ratio [S II]/[N II] should increase with z (for the same reason described above, plus,
nitrogen has a higher second ionization potential and is rarely in the form of N III
even in H II regions). Instead, the ratio is sometimes observed to be roughly constant
with z. The values of the ratio [O III]/Hα are also inconsistent with the models in
some halos. These pieces of information tend to suggest either a secondary source of
ionization, such as shocks (Shull & McKee 1979) or turbulent mixing layers (Slavin
et al. 1993), or a variation in gas temperature with z (e.g., Haffner et al. 1999).
Hot X-ray halos have now been observed in several external galaxies. Bregman
& Pildis (1994) reported the first detection of an X-ray halo surrounding a (normal)
spiral, NGC 891. Their ROSAT observations implied a gas temperature T ∼ 3−4 ×
106 K, a density of about 10−3 cm−3 , and a total mass ∼ 108 M . Since then, more
recent surveys using Chandra (Strickland et al. 2004) and XMM-Newton (Tüllmann
et al. 2006) have greatly increased the sample of edge-on spirals with known hot
halos. With the newer telescopes, enough photons are collected that spectra may be
obtained, revealing additional information about the physical conditions of the halo
transitions, for example). Forbidden lines are indicated with brackets, e.g. [N II].
15
Chapter 1. Introduction
gas. In the XMM-Newton survey, for example, the spectra indicated a decrease in
gas temperature with increasing distance from the disk, and perhaps a need for a
two-temperature component of the hot halo. Additional observations are required to
investigate these issues further.
For a final piece of the puzzle, we briefly move away from the local Universe.
Gaseous envelopes surrounding moderate to high redshift galaxies can be studied
in absorption against background QSOs. Churchill et al. (2000), for example, have
catalogued 45 systems detected via metal absorption lines (in that case, Mg II) in
QSO spectra. The impact parameters (i.e., distances from the line of sight to the
center of the candidate absorbing galaxy) can be quite large (up to ∼ 30 kpc at the
distances of the absorbers). This calls into question whether the galaxy observed
to be near the line of sight is actually associated with the absorbing medium. But
a relationship has emerged (Steidel 1995) between the luminosity of the absorbing
galaxy, and the maximum impact parameter for which absorption is detected, indicating that intermediate redshift galaxies are indeed surrounded by large, extended
gaseous envelopes. Preliminary studies relating the velocity of the absorption line to
the rotation curve of the absorbing galaxy have been performed (e.g., Steidel et al.
2002), and the results imply that there is a kinematic connection between them.
With all of these observational results in hand, the picture of multiphase halos is
becoming increasingly clear, both in our Galaxy and in external galaxies. In the next
section, I will address some of the physical mechanisms that have been suggested to
be responsible for creating and sustaining these multiphase halos.
1.2
Role of Gaseous Halos in Galaxy Evolution
I now move on to a brief overview of the current status of theoretical work involving
galaxy evolution, and, in particular, the role of gaseous halos therein. I will discuss
16
1.2. Role of Gaseous Halos in Galaxy Evolution
the two models which are of particular relevance to this thesis: the galactic fountain (and the related chimney model), and accretion of gas from companions or the
intergalactic medium (IGM).
1.2.1
Galactic Fountain
The “galactic fountain” model was first put forward by Shapiro & Field (1976), in
an attempt to fit observations of MW ISM gas into one coherent picture. A model
of the hot ionized medium, constrained by two observational results (the diffuse
soft X-ray background flux, and the O VI absorption lines, both described above),
suggested that the pressure of that component was an order of magnitude higher
than the pressure that had been measured earlier in the cool neutral clouds of the
ISM. Because of this pressure imbalance, Shapiro & Field argued that the hot gas
must convect upward (away from the plane). The rising gas radiatively cools, and
travels upward for a distance vτcool , where v is the velocity of rising gas and τcool is
the time required for the hot gas to cool. At that height (≈ 1 kpc if v is ∼ the sound
speed), the cooling gas undergoes thermal instabilities (Field 1965) and forms cool,
condensed clouds, which then return to the disk ballistically.
Over the years, this model has been updated by other researchers. Of particular
relevance to the present discussion is the work done by Bregman (1980). His model
was targeted more toward a description of the HVCs. Bregman points out that
at the current infall rate of HVCs (he quotes 1 M yr−1 ; the value may actually be
somewhat greater), the infalling material would outweigh the original disk gas within
a Hubble time11 , unless the original source of the HVCs is the disk gas. This model,
too, describes hot gas rising upward out of the disk, cooling into clouds and raining
back down, but adds the additional feature that the rising gas will move upward and
11 The
“Hubble time” is the inverse of the Hubble constant, the rate at which the Universe
is expanding. The Hubble time is typically used as a characteristic cosmological time scale.
17
Chapter 1. Introduction
Figure 1.5 WIYN V -band images of NGC 891. The top panel shows the V -band
image, while the bottom panel shows the unsharp masked version of this image. The
display is inverted such that darker regions represent brighter emission. Regions of
dust extinction are lighter than their surroundings. This image covers 60 .4 × 20 .8
(17.3 kpc × 7.6 kpc); a scale bar denoting 1 kpc is shown. North and east are marked.
From Howk & Savage (2000).
18
1.2. Role of Gaseous Halos in Galaxy Evolution
Figure 1.6 Hot gas rising from the disk is denoted by dotted lines with an arrow. The
solid and dashed lines illustrate the cycle in which gas moves upward and radially
outward before suffering a thermal instability and forming into a cloud which falls
toward its point of origin. From Bregman (1980).
radially outward due to the decreasing gravitational potential (see Figure 1.6).
To see that this radially outward movement is expected, we follow the derivation
given by Breitschwerdt & Komossa (2000). For gas leaving the disk at an initial
radius r = Ri , where the rotational frequency of the disk is θ̇(Ri ), the specific angular
momentum is li = Ri2 θ̇(Ri ). The centrifugal acceleration balances the gravitational
acceleration r θ̇2 = geff (r, z), and together with conservation of angular momentum
[Ri2 θ̇(Ri ) = r 2 θ̇(r)], we obtain
"
Ri4 θ̇2 (Ri )
r=
geff (r, z)
#1/3
(1.1)
so that as the gas moves upward and geff (r, z) decreases, r must also increase.
As r increases, conservation of angular momentum dictates that θ̇ decrease, i.e.,
that the rotation speed drops. Several different models were calculated, for different
hydrodynamical situations. Bregman states that for one of the models considered,
19
Chapter 1. Introduction
the vertical gradient in rotation speed takes the values 13.5 km s−1 kpc−1 at a radius
of 15 kpc, 10.4 km s−1 kpc−1 at 12.4 kpc, and ∼ 8 km s−1 kpc−1 at radii less than
9 kpc. Often, clouds do not return to their initial radius in the disk after falling back
down ballistically; the cycle time is typically of the order 107−8 yr.
Another revised treatment of the fountain model was given by Norman & Ikeuchi
(1989), and is called the chimney model. They acknowledged that supernovae tend
to be spatially and temporally clustered in star forming disks, and considered the
implications of the formation of superbubbles12 in the disk. The model is similar to
the fountain model, but has localized regions of upward gas movement (corresponding
to the superbubbles), rather than ubiquitous upward gas flow throughout the disk.
The basic picture, illustrated in Figure 1.7, is that of an OB association13 blowing a superbubble, which expands roughly spherically in the disk until an edge of
the bubble reaches the point where the surrounding density is low enough that the
bubble can burst. At that point, hot gas (observable via hard X-rays) begins flowing
upwards. A “chimney” will form (hence the name of the model), with the hot gas
flowing up within the chimney walls, which are made of dense, cool, neutral gas.
The hot gas reaches an average height of several kpc. As in the fountain model, the
hot gas cools and condenses after a characteristic time scale of order 107 yr, at which
point the clouds fall back down to the disk. The chimneys in this model would be
located primarily along the spiral arms in the disk, which is where most of the star
formation takes place.
One of the important features of both the fountain model and the chimney model
is the radial redistribution of matter, especially metals, throughout the disk of the
12 Superbubbles
are expanding pockets of hot ionized gas, embedded in the disk, surrounded by H I gas, and energized by multiple supernovae. An example is the Cygnus
superbubble (Cash et al. 1980), which is 450 pc in diameter and contains approximately
6 × 1051 erg of thermal energy.
13 An OB association is a cluster of early type (very hot, energetic, and short-lived) stars,
all of which form at roughly the same time.
20
1.2. Role of Gaseous Halos in Galaxy Evolution
galaxy. The metal content of the ISM has consequences for the evolution of the stars
that form from that gas (see Binney & Merrifield 1998, p. 276), and therefore for the
evolution of the host galaxy. Also, as indicated in Figure 1.7, the return flow may
be the source of the HVCs observed in this and other galaxies.
1.2.2
Accretion
Another process which may be of critical importance in the evolution of galaxies
is accretion of material, either from the IGM or from companions. Accretion from
companions certainly plays a major role in the evolution of some galaxies, as in the
case of the Antennae (Figure 1.8, left panel). This type of interaction, where the
masses of the two galaxies are roughly equal, can be labeled a major interaction (as
does Sancisi 1999) in order to distinguish from the case where one galaxy is much
more massive than the other. Although examples of major interactions provide
beautiful images, they are of lesser interest in the present context.
A minor interaction, as defined by Sancisi (1999), is one in which the smaller
galaxy has less than about 10% of the mass of the larger one. This case is more
interesting with respect to this thesis because the external signs of interaction will in
general be much more subtle, and can lead to a relatively slow trickle of material onto
the existing (more massive) galaxy. For example, the Sagittarius dwarf (Ibata et al.
1994) is in the process of being tidally torn apart and accreted by the Milky Way.
Based on counts of planetary nebulae and globular clusters in the halo, and their
association with the Sagittarius dwarf, it has been estimated that about ten percent
of the Milky Way halo is debris from the merger (Zijlstra et al. 2006). Evidence for
a similar tidal merger of a dwarf with M31 has also been recently discovered (e.g.,
Ferguson et al. 2002). Deep H I observations often reveal faint distortions, tidal
streams, and other signs of interactions (see Figure 1.8, right panel). A mulitude of
21
Chapter 1. Introduction
Figure 1.7 A sketch of some of the obvious qualitative aspects of the halo structure in
the chimney model. The observational characteristics and effects on galaxy evolution
of these disk-halo connections are discussed in §§ IV and V [of Norman & Ikeuchi
(1989)]. From Norman & Ikeuchi (1989).
22
1.2. Role of Gaseous Halos in Galaxy Evolution
Figure 1.8 Examples of major and minor galaxy interactions. Left panel: NGC
4038/4039 – the Antennae. This optical image was obtained from the STScI Digitized
Sky Survey. The black smudge near the center is an artifact. Right panel: H I
emission at four velocities between 1256 and 1287 km s−1 superposed on the DSS
image of NGC 4565 at a resolution of 1300 × 3300 . These channels clearly show the
interaction between the companion and NGC 4565. Contours are -2.0 -1.0 1.0 2.0
4.0 8.0 16.0 32.0 64.0 120.0 mJy/beam. From van der Hulst & Sancisi (2005).
examples of these are discussed by Sancisi (1999).
To date, a clear picture of the effects of minor interactions does not exist. Gas
accretion from mergers can induce star formation, and influence the structure of the
outer parts of the main galaxy (van der Hulst & Sancisi 2005), by generating warps
and flares, for example. Weinberg & Blitz (2006) show how the warp of the Milky
Way could have been caused by interactions with the Magellanic Clouds.
Accretion of primordial material from the IGM may also be important. Oort
(1970) estimated the current accretion rate onto the Milky Way to be equivalent to an
increase in mass of about 1% per gigayear. The model of galaxy formation developed
by White & Rees (1978) predicts that present-day galaxies should still be gaining
23
Chapter 1. Introduction
primordial gas from the IGM. The accreting gas may undergo thermal instabilities
(see Field 1965), cool and collapse into dense, warm, pressure confined clouds before
falling onto the disk (e.g., Maller & Bullock 2004). The low metallicity of some
HVCs (e.g., Tripp et al. 2003) may indicate that at least part of the HVC population
consists of such infalling primordial gas. Furthermore, accretion of primordial gas
may help solve the “G-dwarf problem” (e.g., Pagel 1997), a phrase which refers to
the fact that there are too few stars in the solar neighborhood with low metallicity
(see Binney & Tremaine 1987, pp. 571-574).
1.3
Halo Kinematics
One line of evidence which may shed light on the relative importance of star formationdriven disk-halo cycling, and accretion of external material, is the kinematics of
gaseous halos. Attention has only recently been paid to this topic. Models incorporating different physical pictures are just beginning to make predictions for their
kinematic signature. Here, I would like to summarize the work that has been done
to characterize the rotation of halo gas in external spirals.
The first galaxy in which the vertical variation in rotation speed was addressed
was NGC 891. Both the ionized and neutral components were analyzed. In the case
of the DIG, Rand (1997) analyzed the variation of mean velocity as a function of
slit position (the slit was oriented perpendicular to the plane). Above the height
at which the effects of dust extinction and projection effects from the disk are no
longer important, the mean velocities are seen to decrease with z. This was taken
as an indication that the rotation speed was dropping, but Rand pointed out that
the effect could also be caused by a change in the radial density profile with height,
or a combination of both density and velocity variations. This point is extremely
important.
24
1.3. Halo Kinematics
The importance of the gas density along the line of sight (LOS) in edge-on observations can be seen by inspection of Figure 1.9, from Kregel & van der Kruit (2004).
In Fig. 1.9a, a face-on view of a modeled galaxy disk is displayed. The disk consists
of a series of concentric rings, each with a different gas density. The galaxy is to
be viewed from an edge-on perspective; one of the lines of sight is indicated by the
dashed vertical line. Because the galaxy is circularly rotating, the projection of the
velocity vector onto the LOS varies along the LOS. For example, at the outermost
ring, the component of the rotational velocity vector along the LOS is minimized,
while at the innermost ring, the rotational velocity vector is parallel to the LOS,
and thus the projection is maximized. The contributions to the observed velocity
profile along that LOS from each ring are depicted in Fig. 1.9c. It is clear that
modifications of the density profile of the disk would alter the mean velocity derived
from the velocity profile, although the rotational velocity of the disk remains the
same. This demonstrates not only that mean velocities cannot be considered alone,
but furthermore that densities and velocities must be considered in tandem.
In the neutral component, Swaters et al. (1997) analyzed deep WSRT observations of the disk, and also saw an apparent decrease in rotation speed with height.
They created several models in an attempt to exclude effects which could disguise
themselves as a changing rotation curve with z, for example flares and warps, both of
which can weight the observed velocity profiles toward the systemic velocity simply
because of projection effects. Analysis of channel maps showed that the best explanation was a lagging halo, and they concluded that the halo of NGC 891 is rotating
approximately 25 km s−1 slower than the disk.
Additional studies of the kinematics of EDIG came from long-slit spectra of NGC
5775 (Rand 2000; Tüllmann et al. 2000). In each of the three slit positions analyzed
by the two groups, the mean radial velocity is observed to drop with increasing z. At
the highest z, the mean velocities drop to almost systemic. Again, the results were
25
Chapter 1. Introduction
taken as an indication of a changing rotation speed with height, but the possible
projection effects were not modeled.
The H I component of the low surface brightness galaxy UGC 7321 was observed
by Matthews & Wood (2003), and was found to be vertically extended. The authors
modeled the gas distribution, and found that the disk is both warped and flared.
They tentatively concluded that a decrease in rotation speed was also necessary to
provide the best match to the data, but were not able to make a firm statement
either way.
Further H I results, this time for the moderately inclined NGC 2403, were obtained by Schaap et al. (2000) using WSRT data, and enhanced later by Fraternali
et al. (2002b) using data from the Very Large Array (VLA). The results indicated a
slowly rotating halo (about 25 to 50 km s−1 slower than the disk), as well as radial
inflow at about 10 to 20 km s−1 . The ionized component of the same galaxy was
studied using long-slit spectra (Fraternali et al. 2004), with similar results to the H I
study. In that case, position-velocity (PV) diagrams, rather than mean velocities,
were analyzed. In NGC 4559, too, H I observations reveal a slowly rotating halo,
about 25 − 50 km s−1 slower than the disk (Barbieri et al. 2005).
Additional WSRT time was devoted to H I observations of NGC 891, resulting in
a remarkably deep data set. Fraternali et al. (2005) present an analysis of the density
and velocity structure of the neutral halo, and show that it is essential to take both
into account before conclusions can be drawn regarding the variation in rotation
speed with z. It is clear that in order to properly analyze the EDIG rotation speeds,
spectra should be obtained with two-dimensional spatial coverage, rather than a long
slit, in order to estimate the density distribution of ionized gas.
The remainder of this thesis is concerned with this type of investigation into both
the density and velocity structure of the EDIG in three edge-on spirals, using two
26
1.4. Observational Techniques
different observational techniques for obtaining spectra with two dimensional spatial
coverage. Comparisons between data obtained with these techniques and physical
models may help elucidate the origin and nature of the halo gas.
1.4
Observational Techniques
In this section, I describe the instruments used to perform the observations presented
in this thesis. Both allow the collection of optical spectra over a relatively large solid
angle (of order square arcminutes) simultaneously, which is far more powerful for
this thesis work than the more traditional long-slit spectroscopy.
1.4.1
Fabry-Perot Imaging Spectroscopy
The first galaxy, NGC 5775 (Chapter 2), was observed using the TAURUS-II FabryPerot interferometer, which was installed on the Anglo-Australian Telescope (AAT),
but has since been decommissioned. A Fabry-Perot interferometer takes advantage of
wave interference to selectively filter light at finely tunable wavelengths. TAURUS-II
operated in two modes; in the first, it was effectively a tunable narrowband filter,
and the second enabled the creation of a three-dimensional data cube (two spatial
dimensions and one velocity dimension, after some data reduction steps described
in Chapter 2). For these observations, it was used in the second mode. A sketch
of an etalon, the heart of the Fabry-Perot interferometer, is shown in Figure 1.10.
Light collected and focussed by the telescope passes through the etalon before being
imaged on a CCD.
The etalon is constructed of two partially reflective glass plates, which are parallel
to one another, perpendicular to the optical axis, and separated by a distance d.
Light rays enter the interferometer from the telescope at multiple angles. The angle
27
Chapter 1. Introduction
Figure 1.9 The mapping of the gas density and kinematics on to the position-velocity
plane, illustrated for a simulated edge-on view of the H I in NGC 2403 (adopted
distance 3.2 Mpc). (a) Spider diagram showing the line-of-sight velocities in the
disc plane (receding side only). Contours range from 10 to 130 km s−1 in steps of
20 km s−1 . The greyscale divides the plane into a set of five rings, uniformly spaced
in radius. (b) The integrated major axis positionvelocity diagram in contours. The
greyscale indicates the rings in the disc plane from which the H I originates. (c) A
velocity profile (solid line) at a projected radius of 7 kpc (the hatched region in the
other panels) and the contributions from the different rings (greyscale). From Kregel
& van der Kruit (2004).
28
1.4. Observational Techniques
of each ray with respect to the optical axis corresponds to the position on the sky
of the object that emitted the ray. Consider a collection of rays that enter at a field
angle θ, one of which is shown in the figure. Between the plates, the rays reflect back
and forth multiple times, and interfere with each other. The interference condition
is
2d cos θ = nλ,
(1.2)
where n is the order of interference (an order-blocking filter is used to ensure that
only one value of n is permitted), and λ is the wavelength of the light. The free
spectral range (∆λ) of the etalon refers to the range of wavelength between orders.
Figures of merit for the etalon are the reflective finesse,
√
π R
,
NR =
1−R
(1.3)
where R is the reflectivity of the coating on the glass plates (0 ≤ R < 1), and the
effective finesse,
NE =
∆λ
,
δλ
(1.4)
where δλ is the spectral resolution (Bland & Tully 1989). The spectral resolution is
effectively set by R; see below.
For a fixed value of θ, the interference condition dictates that only one wavelength
λ constructively interferes, and is therefore allowed to pass through the interferometer
to be imaged. In practice, the interference condition is satisfied by a range of λ
(see Figure 1.11); the full width at half maximum (FWHM) of the distribution of
constructively interfering λ is called δλ above. The reflectivity R effectively sets the
value of δλ, because higher reflectivity leads to more reflections, on average, within
the etalon. Thus, higher R not only gives a higher value of NR , but also leads to a
lower value of δλ, and therefore a higher NE .
29
Chapter 1. Introduction
Figure 1.10 Schematic of a Fabry-Perot etalon. Light enters at an angle θ with respect
to the optical axis (dashed line), and interferes between the partially reflective glass
plates, which are separated by a distance d.
30
1.4. Observational Techniques
Now consider the situation where θ is allowed to vary. When λ is held fixed,
the constructive interference only occurs at a single field angle θ, so monochromatic
light passes through in a ring (θ = constant). More generally, when broadband light
passes through the etalon, the output can be described as a series of concentric rings,
each of constant wavelength. If the distance d between the plates is varied, the field
angle at which each λ constructively interferes changes. In practice, an image is
taken at several values d, such that every λ constructively interferes at every θ at
least once. The set of images obtained in the end can be used to create a data cube
(see § 2.3).
1.4.2
Multi-Fiber Spectroscopy
The other two galaxies, NGC 891 and NGC 4302, were observed using the SparsePak
multi-fiber integral field unit (IFU) on the WIYN Telescope at the Kitt Peak National
Observatory. SparsePak is an array of optical fibers, arranged in the pattern shown
in Figure 1.12.
The fiber array is located at the focal plane of the telescope, so that an image
forms on the ends of the fibers. Each fiber can be thought of as a giant pixel on a
detector. The fibers all simultaneously feed a spectrograph, so that one spectrum is
obtained from each of the 82 fibers.
Traditionally, instead of fibers, the spectrometer would be fed by a long slit
located in the imaging plane of the telescope. The observer can usually change
the width of the slit to allow more light to pass though, but at the expense of
spectral resolution. Therefore, long slit observations are often a compromise between
sensitivity and spectral resolution. The benefit of SparsePak is that its fibers, which
are 4.700 in diameter, allow a large amount of light to enter the system at each location,
31
Chapter 1. Introduction
Figure 1.11 The transmission of an etalon as a function of wavelength. An etalon with
higher finesse (NR = 25; dashed line) shows sharper peaks and lower transmission
minima than an etalon with lower finesse (NR = 5; solid line). The free spectral
range (∆λ) and spectral resolution (δλ) are shown.
32
1.4. Observational Techniques
with little degradation of spectral resolution (due to large anamorphic factors14 at the
grating). A further advantage for observations like the ones described in Chapters 3
and 4 is the large spatial coverage of the entire fiber array (approximately 8000 × 8000 ).
This allows the observer to cover the spatial extent of a relatively nearby galaxy with
only a few pointings of the telescope. With a long slit, the spatial coverage obtained
with SparsePak could never be achieved in practice.
14 Anamorphic
magnification refers to the change in the apparent width (along the dispersion direction) of the fiber with increasing angle between the incident light and a line
normal to the grating; larger angles lead to smaller projected fiber widths (e.g., Schweizer
1979).
33
Chapter 1. Introduction
Figure 1.12 The arrangement of fibers in the SparsePak array. Dark circles correspond to inactive fibers, and the white numbered fibers are the active fibers that
feed the spectrograph, as described in the text. In this image, east is to the left, and
north is up.
34
Chapter 2
DIG Halo Kinematics in NGC
5775
2.1
Chapter Overview
We present imaging Fabry-Perot observations of Hα emission in the nearly edge-on
spiral galaxy NGC 5775. We have derived a rotation curve and a radial density profile
along the major axis by examining position-velocity (PV) diagrams from the FabryPerot data cube as well as a CO 2–1 data cube from the literature. PV diagrams
constructed parallel to the major axis are used to examine changes in azimuthal
velocity as a function of height above the midplane. The results of this analysis
reveal the presence of a vertical gradient in azimuthal velocity. The magnitude of
this gradient is approximately 1 km s−1 arcsec−1 , or about 8 km s−1 kpc−1 , though a
higher value of the gradient may be appropriate in localized regions of the halo. The
evidence for an azimuthal velocity gradient is much stronger for the approaching
half of the galaxy, although earlier slit spectra are consistent with a gradient on
both sides. There is evidence for an outward radial redistribution of gas in the halo.
35
Chapter 2. DIG Halo Kinematics in NGC 5775
The form of the rotation curve may also change with height, but this is not certain.
We compare these results with those of an entirely ballistic model of a disk-halo
flow. The model predicts a vertical gradient in azimuthal velocity which is shallower
than the observed gradient, indicating that an additional mechanism is required to
further slow the rotation speeds in the halo. We have also examined PV diagrams
constructed within regions known to contain H I loops, and find that the structure
of the ionized and neutral distributions is consistent with a chimney-type picture.
This chapter has been published, with significant omissions, in the Astrophysical
Journal (Heald, G. H., Rand, R. J., Benjamin, R. A., Collins, J. A., & BlandHawthorn, J. 2006, ApJ, 636, 181).
2.2
Introduction
Gaseous thick disks are observed in the Milky Way and in some external edge-on
spirals. In the Milky Way, the layer of vertically extended ionized emission is known
as the Reynolds Layer or the warm ionized medium (WIM). This phase consists of
gas with T ∼ 104 K and ne ∼ 0.1 cm−3 , and has a scale height of about 1 kpc
(Reynolds 1993).
In external galaxies, these diffuse ionized gas (DIG) layers are observed to have
widely varying morphologies (e.g., Rand et al. 1990; Dettmar 1990; Hoopes et al.
1999; Miller & Veilleux 2003a). Not all edge-on spirals show detectable extraplanar
(i.e., above the layer of H II regions) DIG (EDIG) emission (e.g., Rand 1996; Rossa
& Dettmar 2003a,b). Two notable extremes are NGC 891 and NGC 5775, which
show bright, diffuse EDIG emission in addition to shell-like structures and filaments.
EDIG emission has been detected in these two galaxies surprisingly high off of the
midplane (5 and 13 kpc, respectively; Rand 1997, 2000; Hoopes et al. 1999; Tüllmann
et al. 2000). The prominence of a galaxy’s EDIG layer is now known to correlate
36
2.2. Introduction
with tracers of star formation in the disk, such as the surface density of FIR emission,
the star formation rate as determined by Hα luminosity, and the dust temperature
(e.g., Rand 1996; Rossa & Dettmar 2000, 2003a,b).
Observations outside of the optical spectrum have also revealed the presence of
gas and dust high above the midplane. A rapidly growing set of observations have
been made of extraplanar neutral hydrogen (e.g., Swaters et al. 1997; Fraternali
et al. 2002b; Matthews & Wood 2003), X-ray emitting gas (e.g., Wang et al. 2001;
Fraternali et al. 2002a; Wang et al. 2003; Strickland et al. 2004), radio continuum
emission (e.g., Dahlem et al. 1994), and dust absorption (e.g., Howk & Savage 1999;
Alton et al. 2000; Rossa & Dettmar 2003a,b).
Distinct linear and arc-like features embedded in the general EDIG distribution
are thought to be associated with the structures predicted within the framework of
the chimney model described by Norman & Ikeuchi (1989). The model explains how
superbubbles, like those seen in the Milky Way (e.g., Cash et al. 1980), may burst
open and inject material into the halo via flows resembling chimneys. In this picture,
the outer chimney walls would consist of neutral gas, the inner walls of warm ionized
gas, and the inside of the chimney would be filled with X-ray emitting gas (Lee et al.
2001). Thus, the observed Hα filaments and arcs may be indicative of the presence
of bubbles and chimney walls. Correlations with observations in other wavebands
(e.g., Lee et al. 2001; Collins et al. 2000) support this interpretation.
In a general picture of disk-halo flow such as that described by the chimney
or galactic fountain (e.g., Shapiro & Field 1976; Bregman 1980) model, gas should
rise into the halo and cool as it returns to the disk. Rising hot gas may originate in
chimneys but warm, swept up ambient gas may also be pushed upwards to significant
heights. The evolution of such gas and the interaction of different extraplanar phases
is not at all well understood. However, the observations described above strongly
suggest that such flows exist.
37
Chapter 2. DIG Halo Kinematics in NGC 5775
To date, the bulk of research into EDIG layers has focused on the method of energization (e.g., Tüllmann & Dettmar 2000; Collins & Rand 2001). It has been found
that in most cases, photoionization probably contributes most of the energy to DIG
layers. However, effects such as shocks (e.g., Shull & McKee 1979), turbulent mixing
layers (Slavin et al. 1993), and/or an additional mechanism of raising the electron
temperature (Reynolds et al. 1999) are likely necessary to explain the observed emission line intensity ratios in many cases. In any case, a good understanding of the
gas kinematics may also be important for understanding the ionization mechanism.
Mass flow rates of certain phases have been estimated from observations under
some simple assumptions. In the case of NGC 891, Bregman & Pildis (1994) estimate
that the cooling rate of the hot X-ray emitting gas in the halo implies that ∼ 0.12
M yr−1 may be falling back down to the disk as cooled gas. Wang et al. (1995)
estimate a mass outflow rate of ∼ 1.4 M yr−1 from X-ray observations of NGC 4631.
Fraternali et al. (2002a) combine X-ray and neutral hydrogen observations of NGC
2403 to estimate an outward flow of ∼ 0.1 – 0.2 M yr−1 in the hot X-ray component,
and an inward flow of ∼ 0.3 – 0.6 M yr−1 in the cooled, neutral component.
A likely effect of disk-halo cycling is redistribution of gas in the disk. The mass
flux rates determined thus far imply that this process is responsible for moving a
large amount of gas. Whether the cycling process is dominated by ballistic motion,
(magneto-) hydrodynamic effects, or both, is still an open question. But the cycling
may affect the distribution and rate of star formation in the disk, and may result
in extraplanar star formation (e.g., Tüllmann et al. 2003). That a disk-halo flow is
responsible for some of the observed high-velocity clouds (HVCs) is also a possibility
(e.g., Wakker & van Woerden 1997). For these reasons, it is important to understand
the kinematics of this disk-halo cycling.
Studies of extraplanar H I emission have so far provided the most spatially complete velocity information about gas which may be participating in disk-halo inter-
38
2.2. Introduction
actions. Halo gas is seen to lag the underlying disk rotation in NGC 891 (Swaters
et al. 1997; Fraternali et al. 2005), NGC 5775 (Lee et al. 2001), and NGC 2403
(Schaap et al. 2000; Fraternali et al. 2001). This result is expected in a disk-halo
flow model because as gas is lifted into the halo, it feels a weaker gravitational potential, migrates radially outward, and thus its rotation speed drops in order to conserve
angular momentum. Since DIG has turned out to be an excellent tracer of disk-halo
cycling, its kinematics may shed significant light on the nature of such flows.
Limited studies of EDIG kinematics have been performed to date. Fraternali
et al. (2004) use spectra from slits along the major and minor axes of NGC 2403
to detect a rotational lag in the extraplanar ionized gas component. Spectra have
also been obtained along slits perpendicular to the major axes of NGC 891 (one slit;
Rand 1997) and NGC 5775 (three slits; Rand 2000; Tüllmann et al. 2000). In both
galaxies, the mean velocities are seen to approach the systemic velocity as height
above the midplane (z) increases. Models representing two distinct physical regimes
have been generated to try to understand the apparent drop-off in rotation speed
with z in NGC 891 and NGC 5775. Benjamin (2000) describes a purely hydrostatic
model which includes gravity, pressure gradients, and magnetic tension, though it
neglects turbulent viscosity and ram pressure. Barnabè et al. (2005) describe a fluid
model which considers temperature and pressure in addition to the gravitational potential; their approach is based on the so-called baroclinic solutions to hydrodynamic
equilibria, and has so far been shown to be successful in matching the halo lag inferred via H I observations of NGC 891 (Fraternali et al. 2005). Collins et al. (2002,
hereafter CBR) describe a model which treats the halo gas as non-interacting, ballistic particles launched from the disk in the absence of pressure, drag, and magnetic
effects. More detail regarding the specifics of the ballistic model is provided in §4.
Note that these models represent opposite extremes of physical possibilities: either
the gas is completely dynamically coupled, or it does not self-interact at all.
39
Chapter 2. DIG Halo Kinematics in NGC 5775
The hydrostatic model of Benjamin (2000) predicts a steeper dropoff in rotation
velocity with height than is observed in NGC 891, to the extent that mean velocities
from the spectra are indicative of rotation speeds. Mean velocities are observed to
drop by 20 – 30 km s−1 from z = 1 to 4 kpc, whereas the model predicts a drop
in rotation speed of 80 km s−1 . The ballistic model of CBR also overpredicts the
falloff in mean velocity for NGC 891 (prompting the authors to suggest that an
outwardly directed radial pressure gradient or magnetic coupling may provide extra
support to the gas, but the behavior of the model may be explained in our §4). It
performs somewhat better for NGC 5775, though while the observations indicate that
mean velocities at the largest projected z-heights approach the systemic velocity, this
behavior cannot be replicated with the model. The fact that the EDIG emission in
NGC 5775 is brighter, more vertically extended, and more filamentary in nature than
in NGC 891 may indicate that a more active, possibly more ballistic disk-halo flow
is taking place. In that case, the fact that the ballistic model is more successful in
predicting the kinematics of NGC 5775 may be understood.
The studies of EDIG kinematics described above were limited by the poor velocity
resolution and the one-dimensional spatial coverage of the long-slit spectroscopy. The
mean velocities used are affected by both the rotation speed and the distribution
of emission along the line of sight. A full analysis of how gaseous halos rotate
requires that these effects be separated as has been done with H I observations of
NGC 891 (e.g., Fraternali et al. 2005), and this can only be achieved with high
spectral resolution and two-dimensional spatial coverage. The work described in this
paper represents an extension of the previous optical studies, in that high spectral
resolution velocity information is obtained and analyzed for the full two-dimensional
extent of NGC 5775.
NGC 5775 is classified as an SBc galaxy. It is undergoing an interaction with its
neighbor, NGC 5774, and a tidal stream of H I connects the two galaxies (see Irwin
40
2.2. Introduction
Table 2.1. Galaxy Parameters for NGC 5775
Parameter
Value
RA (J2000.0)
14h53m 57.s 57
Decl. (J2000.0)
03d32m 40.s 1
Adopted Distancea 24.8 Mpc
Inclination
86◦
Position Angle
145.7◦
Systemic Velocity
1681.1 km s−1
a
Assuming H0 = 75 km s−1 Mpc−1
Note. — All values are from Irwin (1994).
1994). Collins et al. (2000) cite a high far-infrared luminosity determined from the
IRAS satellite, LFIR = 7.9 × 1043 erg s−1 , and a “far-infrared surface brightness” of
2
LFIR /D25
= 8.4 × 1040 erg s−1 kpc−2 (where D25 is the optical isophotal diameter at
25th magnitude), which is typical of mild starbursts (Rossa & Dettmar 2003a). The
EDIG layer is bright, with a large scale height and filamentary structures (Collins
et al. 2000). A summary of galaxy parameters for NGC 5775 is presented in Table
2.1.
This paper is organized as follows. We describe the observations and the data
reduction steps in §2.3. In §2.4, we present an analysis of disk and halo rotation. We
compare the data with the ballistic model of CBR in §2.5. The velocity structure of
the ionized component of some H I loops studied by e.g. Lee et al. (2001) is examined
41
Chapter 2. DIG Halo Kinematics in NGC 5775
in §2.6. We conclude the paper in §2.7.
2.3
Observations and Data Reduction
Data were obtained during the nights of 2001 April 11–13 at the Anglo-Australian
Telescope (AAT). The TAURUS-II Fabry-Perot interferometer, which is placed at the
Cassegrain focus (f/8) of the AAT, was used in conjunction with the MIT/LL 2k×4k
CCD. Design, theory, and data reduction techniques of Fabry-Perot interferometers
are well described in the literature; see e.g. Bland & Tully (1989); Jones et al. (2002);
Gordon et al. (2000). An order blocking filter (6601/15) isolated Hα emission at
order 379 over a 9 arcminute field of view. At this order, the spectral resolution is
quite high (FWHM ' 0.5Å = 22.9 km s−1 ), but the wavelength satisfying the etalon
interference condition varies radially across a given image (each of which corresponds
to a given etalon spacing, h). Over the course of the observing run, the etalon spacing
was changed to sample the full free spectral range (FSR = 17.4Å) at each CCD pixel.
It should be noted, however, that telescope pointing variations resulted in the FSR
being incompletely sampled at some spatial locations, resulting in blank pixels later
in the reduction process. The exposure time at each of the 72 etalon spacings was
12 minutes. To avoid confusion from ghost images, the galaxy was placed away from
the optical center (a faint ghost image can be seen in the upper-left corner of Fig.
2.1a).
Bias frames, taken during the observing run, were averaged and subtracted from
each image. Flat fields were averaged and applied to the images. A “white light”
cube was also obtained. This reduction step is used to remove any wavelengthdependent flat field structure. However, the white light cube was found everywhere
to vary by 2 percent or less. A test application of the white light cube yielded
little difference; therefore, this correction was deemed unnecessary. The individual
42
2.3. Observations and Data Reduction
images were arranged in order of etalon spacing and stacked into a data cube. To
increase signal-to-noise, the images were spatially binned 2×2 in software. Cosmic
ray removal was performed by hand using the IRAF1 task CREDIT.
The resulting cube contains planes of constant etalon spacing rather than wavelength. The surfaces of constant wavelength are paraboloids, centered on the optical
axis and with a curvature constant Kλ which is dependent on instrumental parameters (see Bland & Tully 1989, and our equation 2.2). In addition, the position of
the optical axis on the detector is not known a priori; indeed, the position was found
to vary over the course of the observing run, distorting the shape of the constantwavelength paraboloids. Moreover, telescope pointing variations result in shifts of
object locations with respect to both the detector and optical centers. The process
of aligning the optical axis and transforming the surfaces of constant wavelength to
planes is called the phase correction.
Unfortunately, an arc-lamp cube was not obtained during the observing run.
Therefore, night-sky emission lines were used for the wavelength calibration. Because
the wavelength satisfying the etalon interference condition varies radially across each
image, the night-sky emission lines appear as rings in the images (see Fig. 2.1a), with
radii dictated by the wavelength of the line, the etalon spacing, and Kλ . Thus, by
measuring the properties of a ring (center and radius) in each frame so that it may be
subtracted, the phase correction solution is also obtained. A first attempt at finding
the optical center of each image was made by fitting a circle to three points on an
individual ring, as described by Bland & Tully (1989). However, the rings appear
at about the 3.5σ level in the images, and because the widths of the ring profiles
increase with decreasing ring radius it was often difficult to select appropriate points
for a good fit. As noted by Jones et al. (2002), the azimuthal symmetry of the ring
1 IRAF
is distributed by the National Optical Astronomy Observatories, which are operated by the Association of Universities for Research in Astronomy, Inc., under cooperative
agreement with the National Science Foundation.
43
Chapter 2. DIG Halo Kinematics in NGC 5775
images may be exploited to find the optical center and subtract the sky rings. The
location of the optical center in each plane was found with the following algorithm:
1. First, the location of the optical center is approximated by fitting a circle to
three points on an individual ring. This step yields a point close to the true
optical center.
2. Next, object signal is masked, and an azimuthal average is performed about
the fiducial center selected in step (1). This results in a radial profile with clear
ring signatures. An example is shown in Fig. 2.1b.
3. Next, a non-linear least-squares algorithm is used to fit a gaussian to the most
prominent ring profile.
4. The fiducial center point is then varied over a search grid. At each grid point,
a new azimuthal average is calculated, and a gaussian is fit to the new ring
profile. At the end of this step, the width of the line profile has been calculated
at each fiducial optical center location.
5. Because of the azimuthal symmetry, the profile width is minimized at the
true optical center. The grid of line widths obtained in step (4) is therefore
interpolated, and the location of the minimum on the interpolated grid is taken
to be the true optical center.
The azimuthal profile corresponding to our choice of optical center is used to form
a two-dimensional image of the sky rings (Fig. 2.1c), which is then subtracted from
the original, resulting in a sky-subtracted image (Fig. 2.1d). Azimuthal variations in
ring intensity and any non-circularity of the rings will result in incomplete subtraction
of the sky emission. The residual emission was minimized by limiting the image area
to a 4.6 arcminute square, inside of which the azimuthal variations were greatly
44
2.3. Observations and Data Reduction
reduced. The calculation of the azimuthal average was limited to this area in each
step, and the sky-subtracted image was cropped to the same region.
The ring fitting algorithm also yields the radii of the sky rings in each image.
The two brightest sky lines were identified as OH λ6596.64 and the unresolved pair
OH λλ6603.99, 6604.28 (see Osterbrock et al. 1996). We used a central wavelength
of 6604.12Å for the unresolved pair. For each image, the sky-line wavelengths λ and
radii r are inserted in
λ = λ 0 + Kλ r 2
(2.1)
to determine λ0 , the wavelength at the optical center. The curvature constant, Kλ ,
is dependent solely on instrumental parameters:
2
Kλ = (n/2)∆λ0 (p2µ /fcam
),
(2.2)
where n is the etalon order, ∆λ0 is the on-axis free spectral range, pµ is the CCD
pixel size, and fcam is the focal length of the camera lens (Bland & Tully 1989). Once
λ0 is known for each image, equation 2.1 can be used to determine the value of λ at
every pixel (using its distance, r, from the optical center). The value of Kλ [actually,
2
its counterpart expressed in terms of etalon spacing, Kh = (n/2)∆h0 (p2µ /fcam
)],
was verified by inserting the nominal values for the instrumental parameters and
comparing to the curvature value obtained by fitting a simple parabola to a plot of
night-sky emission ring radius versus etalon spacing. The values of Kh obtained with
these two methods were found to differ by only 0.2 per cent; therefore, the nominal
instrumental parameters were used to specify Kλ .
Relative intensity variations between the sky-subtracted images were measured
and corrected for using field stars. The IRAF task GAUSS was used to convolve
each image to a common beam corresponding to the worst seeing conditions from
the observing run (3.5500 ). Because we are primarily looking for diffuse emission, the
45
Chapter 2. DIG Halo Kinematics in NGC 5775
poor seeing is not harmful; rather, the faint diffuse structure is brought out by the
convolution.
Astrometric solutions for each image were calculated with the IRAF task CCMAP,
using six relatively bright stars included in the HST Guide Star Catalog2 . With these
astrometric solutions, and the wavelength solutions described above, the phase correction was completed by sorting each intensity value into the correct pixel in the
final data cube. In cases where multiple intensity values were assigned to a single
pixel, the average value was used. The pixels in the final data cube are 200 square,
and the channel width is 11.428 km s−1 .
With a FSR of only 17.4Å, corresponding to ∼800 km s−1 at Hα, the rotational
velocity of the galaxy (198 km s−1 ; Irwin 1994) together with the broad emission
profiles (σgas ≈ 32.5 − 42.5 km s−1 ; see §2.4.2) causes real Hα emission to appear
in nearly all planes of the data cube. Thus, there are few continuum channels in
our data set and the continuum must be removed locally. To remove the continuum
emission, a median-filtering algorithm was implemented, using intensity values along
the spectral axis at a particular spatial location and those along the four nearestneighbor spectra. Taking the intensity values from all five spectra together, the
median and standard deviation were calculated. Values differing from the median
value by more than two standard deviations were excluded (thus eliminating the
part of the spectrum containing Hα emission), and new statistics were calculated.
This procedure was repeated until no more statistical outliers were found, or for a
maximum of five iterations. The resulting median was taken as a measure of the
continuum level at that location, and was subtracted from the spectrum.
To enhance faint emission far from the galaxy midplane, the data cube was further
smoothed to an 800 beam. Blank (unsampled) pixels in the final cube, caused by
2 The
Guide Star Catalog was produced at the Space Telescope Science Institute under
U.S. Government grant. These data are based on photographic data obtained using the
Oschin Schmidt Telescope on Palomar Mountain and the UK Schmidt Telescope.
46
2.3. Observations and Data Reduction
variations in telescope pointing, were replaced before smoothing by interpolating
over adjacent pixels. In the region of the data cube containing emission from NGC
5775, approximately 3 per cent of the pixels were initially blank.
To obtain a rough intensity calibration, a major axis cut through the moment-0
map shown in Fig 2.3a was compared to a major axis cut through the Hα image
from Collins et al. (2000), smoothed to the same resolution as in the moment-0 map.
The noise in the channel maps was thus measured to be 1.38 × 10−19 ergs cm−2 s−1
arcsec−2 channel−1 . Assuming a gas temperature T=104 K, this corresponds to an
emission measure (EM) per channel of 0.0688 pc cm−6 channel−1 .
Because the wavelength solution was based on night-sky emission lines rather
than observations of a standard wavelength calibration lamp, the velocity scale was
verified by comparing with existing data. H I data (see Irwin 1994) and CO 2–1
data (see Lee et al. 2001) were kindly provided by J. Irwin and S.-W. Lee for this
purpose. The beam size of the H I data is 13.600 × 13.400 at position angle −33.7◦ ,
and the channel width is 41.67 km s−1 . The beam size of the CO 2–1 data is 2100 ,
and the channel width is 8.08 km s−1 . Overlays of major axis position-velocity (PV)
diagrams were generated to compare both data sets to the Hα data. The H I PV
diagram differs substantially from the Hα PV diagram in that it shows a slower rise
in velocity at low R (see Fig. 2.2a). This is due to the H I being less centrally
concentrated than the ionized gas, as found through modeling of the H I data cube
by Irwin (1994). The H I diagram is therefore not optimal as a check on the velocity
scale. On the other hand, the CO emission is expected to follow the ionized gas
distribution more closely (e.g., Rownd & Young 1999; Wong & Blitz 2002), except
where extinction may affect the Hα profiles. Indeed, the shapes of the PV diagrams
are more similar (see Fig. 2.2b). Based on the comparison between the CO and Hα
PV diagrams (after converting the Hα velocities to the LSR frame), a constant 9
km s−1 offset was added to the velocity axis of the Hα data cube. This correction is
47
Chapter 2. DIG Halo Kinematics in NGC 5775
smaller than the channel width of the data cube. In all presentations of kinematic
data in this paper, velocities are relative to the systemic velocity of NGC 5775 (see
Table 2.1).
Moment maps were generated with the Groningen Image Processing System
(GIPSY) task MOMENTS by requiring that emission appears above the 3σ level
in at least three velocity channels. The moment-0 (total intensity) map is displayed
in Fig. 2.3a, and the moment-1 (mean velocity) map is displayed in Fig. 2.3b.
2.4
Analysis and Modeling
The primary goal of this work is to study the kinematics of the ionized halo of
NGC 5775. In this Section, we first present the velocity field and point out some
interesting features and trends. Next, major axis rotation curves are obtained for
both the ionized and molecular gas components from PV diagrams. Our analysis of
the kinematic structure is then extended by modeling the halo component to search
for a change in the rotation curve with height above the midplane.
2.4.1
The velocity field
Some insight into the global kinematic characteristics of the ionized component of
NGC 5775 can be obtained by examining the velocity field. Figure 2.3b shows the
moment-1 map calculated from the data cube. The following features are observed:
• In all four galaxy quadrants, mean velocities are seen to decrease with increasing distance from the major axis (up to ∼ 1000 ). This initial decrease is
attributed to viewing a rotating disk in projection, and is not indicative of a
halo lag. To determine the location of the edge of the projected disk, we as-
48
2.4. Analysis and Modeling
Figure 2.1 (a) An original image at an individual etalon spacing. Note the prominent
sky rings, and the faint ghost image in the upper-left corner. (b) Azimuthal average
of the image displayed in a, with the object pixels masked out. (c) The azimuthal
average has been used to generate an image of the sky rings. (d) To generate this
image, the image displayed in c has been subtracted from that in a. The same
grayscale values have been used to display each image.
49
Chapter 2. DIG Halo Kinematics in NGC 5775
Figure 2.2 (a) Overlay of H I (white contours) and Hα (black contours) major axis
PV diagrams. H I contours run from 3.36 to 43.7 K in increments of 6.72 K. Hα
contours run from 8.28 × 10−18 to 7.04 × 10−17 erg cm−2 s−1 arcsec−2 channel−1 , in
increments of 6.90 × 10−18 erg cm−2 s−1 arcsec−2 channel−1 . (b) Overlay of CO 2–1
(white contours) and Hα (black contours) major axis PV diagrams. CO contours
run from 0.03 to 0.33 K in increments of 0.05 K. Hα contours are the same as in (a).
Positive values of the major axis distance R correspond to the southeast side of the
disk. The 9 km s−1 offset described in the text has already been applied to the Hα
velocity scale.
50
2.4. Analysis and Modeling
Figure 2.3 (a) Moment-0 map of the Fabry-Perot data cube. Contours illustrate the
appearance of the brighter structures in the disk. The positions of the H I loops
listed in Table 2.3 are indicated by arrows. (b) Moment-1 map of the Fabry-Perot
data cube. Velocities are relative to the systemic velocity of 1681.1 km s−1 . Contours
run from -210 to 210 km s−1 in increments of 30 km s−1 (the SE and SW quadrants
constitute the receding side). The systemic velocity contour is darkened. The morphological major and minor axes, determined using the center and position angle
listed in Table 2.1, are indicated by dashed lines.
sume that the disk is axially symmetric, with a radius equal to the semi-major
axis length of ≈ 10000. Beyond this distance, the emission is observed to fall
sharply, and we therefore assume that the disk has a sharp radial cutoff.
• In the southwest and northeast quadrants (labeled SW and NE in Fig. 2.3b),
for most contours the mean velocities continue to decrease beyond the extent
of the projected disk. The EDIG in these regions is dominated by filamentary
structures (see Collins et al. 2000).
• In the southeast quadrant (labeled SE in Fig. 2.3b), the velocity contours
show an increase in mean velocity above the edge of the projected disk. The
contours then appear to run roughly parallel to the minor axis. In the northwest
51
Chapter 2. DIG Halo Kinematics in NGC 5775
quadrant (labeled NW in Fig. 2.3b), the behavior of the mean velocities is
confused by the presence of a closed contour structure, but it appears that
some of the contours show a continued drop in mean velocity above the edge
of the projected disk, while other contours run parallel to the minor axis.
• The asymmetry of the velocity contours along the major axis, particularly in
the southern (receding) side, is likely caused by significant dust extinction in
the disk. The dust lane, which runs parallel to, but offset to the northeast
from the major axis, preferentially obscures emission from gas more distant
from the observer along those lines of sight. Because the velocity projections
along the line of sight are minimized at the near edge of the disk, we observe
lower mean velocities to the northeast of the major axis than to the southwest,
where extinction is not as extreme. In other words, extinction in the dust lane
results in little or no emission reaching us from near the line of nodes.
• The kinematic and morphological minor axes are not parallel in the projected
disk [also noted in H I by Irwin (1994)]. We assume that the emission in the
projected disk locations is in fact dominated by disk emission. The sense of the
offset, together with the inclination angle of the galaxy and the assumption that
the near side is tilted to the northeast with respect to the morphological major
axis (based on the appearance of the dust lane), is consistent with a radial
inflow of gas in the disk, or may indicate the presence of a bar. If the former,
there is no clear indication that it extends beyond the projected disk into the
halo. NGC 5775 is classified as barred in the Third Reference Catalogue of
Bright Galaxies (RC3; de Vaucouleurs et al. 1991), although an examination
of the Two Micron All Sky Survey (2MASS; Kleinmann et al. 1994) K-band
survey image does not suggest bar signatures such as a box- or peanut-shaped
bulge.
52
2.4. Analysis and Modeling
Though the moment-1 map is useful for viewing overall trends, it cannot be used
to derive rotation speeds for a nearly edge-on galaxy. Intensity-weighted velocities
are affected by the rotation curve, varying projections of the rotation-velocity vector,
and the gas distribution along any line of sight and thus are not indicative of rotation
speed. A full consideration of the line profile shapes and three-dimensional density
distribution (as well as an assessment of extinction) is necessary to derive robust
rotation curves in the case of high inclination.
2.4.2
Disk rotation curves
Here, we wish to construct disk rotation curves from major axis PV diagrams generated from both the Hα and CO 2–1 data sets. Several methods have been suggested
for recovering the rotation curve of a galaxy. In particular, two useful methods in the
study of edge-on spirals are the “envelope tracing” method (Sancisi & Allen 1979;
Sofue & Rubin 2001) and the “iteration method” (Takamiya & Sofue 2002). The
envelope tracing method calculates the rotation curve using the high-velocity edge of
a PV diagram. The iteration method automates the procedure of generating a model
galaxy (with specified radial density profile and rotation curve) that best matches
the major axis PV diagram of the observed galaxy. The benefit of using the iteration method is a more accurate recovery of the rotation curve at small radii, which,
because of beam smearing and rapidly changing densities and velocities, is typically
underestimated by the envelope tracing method. However, our implementation of
the iteration method employs the envelope tracing method as part of its fitting procedure; hence, we describe here the specifics of the algorithms used in both methods,
which we have written as MATLAB scripts. For reasons discussed in §2.4.2.2, the
iteration method was unable to accurately determine the major axis rotation curve
of NGC 5775, but the results of the method were used as a starting point for a visual
determination.
53
Chapter 2. DIG Halo Kinematics in NGC 5775
Throughout this Section, the disk is assumed to consist of a series of concentric,
axisymmetric rings, each of which is allowed to have a different gas density, rotational
velocity, and velocity dispersion. We do not allow the disk to be warped, under the
assumption that the Hα emission traces the star forming disk and not the outer
parts. An examination of the channel maps did not reveal the signature of a warp
along the line of sight (see, e.g., Swaters et al. 1997), and the moment-0 map does
not show evidence for a warp across the line of sight. Here, we briefly describe the
specifics of the algorithms used.
2.4.2.1
The envelope tracing method
After the description of Sofue & Rubin (2001), we use the following algorithm. A PV
diagram is generated, and the velocity dispersion (σgas ) is estimated by measuring the
width of the line profile at the highest radius. It is assumed that at the highest radius,
only one ring of emission is being sampled, so velocity projections from additional
rings do not broaden the profile. At each radius, the value of the rotation curve
is taken to be the velocity at the edge of the line profile, with a correction for the
velocity dispersion, the channel width, and the inclination angle of the galaxy.
Mathematically, the intensity of the envelope on the line profile is defined to be
(Sofue & Rubin 2001)
q
Ienv = (ηImax )2 + Ilc2 ,
(2.3)
where Imax is the maximum intensity in the line profile, Ilc is the lowest contour
value, typically taken to be 3 times the rms noise in the PV diagram, and η is a
constant, normally taken to be in the range 0.2–0.5. On the side of the line profile
farthest from the systemic velocity, the rotational velocity is taken to be (Sofue &
Rubin 2001)
vr = (venv − vsys )/ sin(i) −
q
2
2 ,
σinst
+ σgas
54
(2.4)
2.4. Analysis and Modeling
where venv is the velocity at which I = Ienv , vsys is the systemic velocity, i is the
inclination angle, and σinst is the instrumental velocity resolution.
2.4.2.2
The iteration method
Our implementation of the iteration method makes use of the envelope tracing
method, as described in §2.4.2.1, and the suite of GIPSY tasks. Most importantly,
the task GALMOD is used to generate a model data cube using user-specified radial
and vertical density profiles, rotation curve, velocity dispersion, and viewing angle.
To create the initial model, we specify: the velocity dispersion, which is estimated
in the same way as for the iteration method; the radial density profile, which is estimated using the GIPSY task RADIAL; and the initial guess for the rotation curve,
which is estimated by using the envelope tracing method on the observed data set.
RADIAL solves the inverse problem of calculating a radial density profile from a
major axis intensity distribution using the method of Warmels (1988). The radial
profile must be well matched to the data because both the density distribution and
the rotation curve affect the shape of the line profiles. The scale of the input radial
density profile is fixed such that the signal-to-noise in the model is approximately
that measured in the data. To measure the noise in the model, the same inputs
are used with two different random number seeds, and the standard deviation of the
difference between the two runs of the model is calculated.
Once the initial model has been generated, we follow a procedure based on that
detailed by Takamiya & Sofue (2002). The envelope tracing method is used to derive
a rotation curve from the initial model. That rotation curve is compared to the one
that was derived from the data, and the differences between the two are added to
the input rotation curve to generate a new model. This procedure is repeated until
the difference between the rotation curves derived from the data and the most recent
model (using the envelope tracing method in the same way for both) is smaller
55
Chapter 2. DIG Halo Kinematics in NGC 5775
than an arbitrary value such as the channel width (or until a maximum number of
iterations have been performed).
This procedure amounts to iterating toward a model galaxy which returns the
same rotation curve (as found by the envelope tracing method) as the data. Note
that it is not the result of the envelope tracing method that is taken to be the rotation
curve of the galaxy. Rather, the rotation curve that was used as an input for the
best model is accepted. The results of the envelope tracing method are simply used
as a convergence criterion.
The degree of success of this method is dependent on how well the other galaxy
parameters (radial density profile, velocity dispersion, signal-to-noise ratio) are reproduced in the model. If these parameters are poorly specified, the iteration method
will not be able to correctly reproduce the observed PV diagram. The iteration
method will assure that in the data and model PV diagrams, at the location of each
velocity profile where I = Ienv , the velocity will be equal (except for differences allowed by the convergence criterion). If the model inputs are correct, this condition
will force the rest of the velocity profile to be matched, but if the inputs are not
correct, only the velocities at the location of Ienv will match.
The problem with this requirement is that GALMOD (or any ring-based galaxy
model) relies on circular symmetry. Spiral structure, clumpiness, and extinction all
lead to the violation of this assumption. We have found that NGC 5775 is not well
represented by a circularly symmetric disk. By matching bright clumps of emission
at large radii (see, for example, the bright knot of emission at R = +9000 in Fig. 2.5),
the corresponding outer rings are forced to contain high gas density at all azimuthal
angles. Because the galaxy is nearly edge-on, these rings of high gas density are
superposed on lower projected radii. Thus, matching bright clumps of emission at
large R by increasing the radial density profile at that radius often precludes matching
fainter emission at smaller R. In this example, when the velocity profiles at the lower
56
2.4. Analysis and Modeling
radii have overly high amplitudes, the locations of Ienv will be located too far from
the systemic velocity, and the rotation curve will be overestimated. The failure of the
assumption of circular symmetry can be seen most simply by inspecting the output
of RADIAL. In Figure 2.4, we display a comparison between the observed major axis
total intensity profile in NGC 5775 and the total intensity profile that would result
from the (azimuthally constant) radial density profile fitted by RADIAL. To obtain
these results with RADIAL, halo emission was excluded from the construction of the
integrated major axis intensity profile. The program considered the approaching and
receding sides separately, performing 25 iterations on each side (additional iterations
made little difference). Although the match appears quite good in the upper panels,
the fitted distribution is seen to differ from the observed distribution by typically
10 to 20 per cent. This level of accuracy, though quite good considering the clumpy
nature of the Hα distribution, is insufficient for our purposes, as it was found to
prevent the iteration method from converging. Nevertheless, the use of RADIAL
and the iteration method together provides a good initial estimate of the radial
density profile and rotation curve, each of which can then be adjusted by hand. We
also note that the assumptions built into RADIAL make it unreliable for regions
which do not include the major axis; therefore, we do not use it to estimate radial
density profiles in the halo.
The failure of the assumption of circular symmetry means that the PV diagrams
cannot be perfectly matched by any ring model, and that the iteration method is
unable to converge toward the correct rotation curve. We therefore abandon the use
of RADIAL and the iteration method as a means of directly obtaining the rotation
curve, and attempt to mitigate some of the effects of the clumpy density distribution.
Better results are obtained (though less efficiently) by starting with the converged
radial density profile obtained with RADIAL and a rough rotation curve obtained
with the iteration method after a few iterations. These results are used to generate
a modeled major axis PV diagram. The observed and modeled PV diagrams are
57
Chapter 2. DIG Halo Kinematics in NGC 5775
compared by eye, and first the radial density profile is adjusted so that observed
and modeled major axis intensity distributions are reasonably well matched except
in regions of obvious clumpiness. Then, the rotation curve is modified until a good
match is achieved.
A major-axis rotation curve and a radial density profile have been obtained in
this way from the Fabry-Perot data. Fig. 2.5 shows an overlay of the major axis PV
diagrams obtained from the data and the best-fit model. Fig. 2.6 shows the radial
density profile and rotation curve in the best-fit model. To achieve the best match,
the velocity dispersion in the model was set to 32.5 km s−1 on the approaching side,
and 42.5 km s−1 on the receding side. The kinematic center and systemic velocity
listed in Table 2.1 were used, and provided good agreement.
To check that the radial density profile and rotation curve are reasonable and
that our results are not biased by, for example, extinction, we have repeated this
procedure for the CO 2–1 data. Fig. 2.7 shows an overlay of the major axis PV
diagrams obtained from the data and the best-fit model. Fig. 2.6 shows the radial
density profile and rotation curve in the best-fit model. A velocity dispersion of 15
km s−1 was required to obtain the best match. Good agreement was obtained without
modifying either the systemic velocity or the kinematic center listed in Table 2.1. In
order to match the low signal-to-noise ratio of the CO data, the modeled emission is
quite faint; the apparent asymmetry between the approaching and receding sides of
the model contours in Fig. 2.7 is due to the noise in the model.
Despite the fact that our Hα and CO radial profiles differ, the rotation curves
are very similar. The mean difference between the Hα and CO rotation curves is 1.5
per cent, the maximum difference is 29.5 per cent (at low R, where the CO rotation
curve rises more slowly than does the Hα rotation curve), and the rms difference is
11.5 km s−1 . This correspondence implies that our procedure works well. We note
that the match between the Hα PV diagram and the corresponding model is worse
58
2.4. Analysis and Modeling
Figure 2.4 Upper panels: Comparison between the fitted major axis brightness distribution returned by RADIAL (solid lines) and the integrated major axis brightness
distribution from the data (squares) on the west side (left) and east side (right) of the
disk. Lower panels: Percent difference between the fitted and observed brightness
distributions.
59
Chapter 2. DIG Halo Kinematics in NGC 5775
Figure 2.5 Overlay of Hα (white contours) and best-fit model (black contours) major
axis PV diagrams. Contour levels for both are 10σ to 1010σ in increments of 100σ.
Positive values of the major axis distance R correspond to the southeast side of the
disk.
60
2.4. Analysis and Modeling
Figure 2.6 (a) Profile of density versus galactocentric radius R for the best-fit models
– Hα (squares) and CO 2–1 (diamonds). (b) Rotation curve for the best-fit models –
Hα (squares) and CO 2–1 (diamonds). The rotation curve of Irwin (1994) is plotted
(dashed line) for reference.
in the inner parts (R . 2000 ) than for the CO PV diagram. In the former, the data
appear to rise more slowly with a higher velocity dispersion.
2.4.3
Halo rotation
Having recovered a radial density profile and rotation curve for the major axis, we
now move on to modeling the halo Hα emission. PV diagrams are constructed along
cuts parallel to the major axis, at various heights above the midplane z (in this paper,
z is positive to the southwest of the major axis). To calculate model PV diagrams,
we have made a modification to the GIPSY task GALMOD to allow for a vertical
gradient in azimuthal velocity:

 v(R, z = 0) −
v(R, z) =
 v(R, z = 0)
dv
[|z|
dz
− z0 ] for z > z0
for z ≤ z0 ,
61
(2.5)
Chapter 2. DIG Halo Kinematics in NGC 5775
where dv/dz is a constant parameter in the model, with units [km s−1 arcsec−1 ]. Note
that this model fixes the shape of the rotation curve as a function of height, and only
changes the amplitude. We include a parameter (z0 ) that specifies the height at which
the rotational lag begins in order to be consistent with Fraternali et al. (2005), who
find that the neutral halo of NGC 891 co-rotates with the disk up to z = 1.3 kpc,
and shows a vertical gradient in azimuthal velocity above that height (although the
authors state that it is possible that the observed corotation at this height is an
effect of beam smearing). Limited information is available to constrain whether z0
differs from zero in our model. For NGC 5775, a height of 1.3 kpc corresponds to
z = 1100 . However, evidence discussed in this Section indicates that a gradient is
already present at z = 1000 . We therefore set z0 to be the (exponential) scale height
of the galaxy model (of order 500 ; see below), and show later that a choice of z0 = 000
does not change the derived gradient significantly.
Such a vertical gradient in azimuthal velocity is considered in §2.4.3.1. In §2.4.3.2,
an offset in the systemic velocity of the halo is added. We also consider the effects of
modifying the shape of the halo radial density profile (§2.4.3.3), the shape of the halo
rotation curve (§2.4.3.4), and the position angle and inclination of the halo (§2.4.3.5).
Assuming a circularly symmetric disk with a sharp optical cutoff radius of 10000
(see Figure 2.20d) and an inclination angle of 86◦ , the edge of the projected disk
along the minor axis is located at a distance of 700 . Collins et al. (2000) report that,
based on the modeling of Byun et al. (1994), extinction effects should be negligible at
z ≥ 600 pc = 500 . Therefore, at minor axis distances greater than 1000 , we assume the
effects of the projected disk and extinction are negligible. After smoothing the data
to an 800 beam, reasonable PV diagrams can be constructed up to a height |z| ≈ 3000 ,
but beyond that point there is not enough reliably detected emission. Thus, the
range of modeled heights is 1000 ≤ |z| ≤ 3000 (1.2 kpc ≤ |z| ≤ 3.6 kpc).
Another effect which must be taken into account is that at a given angular dis-
62
2.4. Analysis and Modeling
tance above the major axis, a range of z-heights in the galaxy frame lie along the
line of sight due to the galaxy not being perfectly edge-on. If a vertical gradient in
azimuthal velocity is present, the line of sight will cross a corresponding range of
rotation speeds, complicating the analysis. Assuming a cylindrical halo with a radial
density profile that has a constant shape as a function of height, the importance
of this effect can be determined by creating PV diagrams at a certain height above
the plane from two models: one with a non-zero vertical gradient of the rotation
curve (as described by equation 2.5), and another with no such gradient, but with
a rotation curve that matches that of the first model at the specified height. This
procedure was followed using the major axis radial density profile and rotation curve,
and a vertical gradient in azimuthal velocity of 2 km s−1 arcsec−1 . The PV diagrams
were created at a height 2000 above the plane, and were found to differ by a negligible
amount. Hence, this effect of inclination can be ignored.
First, the model described in §2.4.2.2 is considered with no vertical gradient in
azimuthal velocity. We call this the cylindrical rotation (CR) model. The scale
height is adjusted to match the minor axis intensity distributions, but the radial
density distribution and rotation curve derived for the major axis are unchanged.
The necessary scale heights are 5.800 for the southwest side of the disk (z > 0) and
4.500 for the northeast side of the disk (except for the z = −3000 PV diagram, for
which the 5.800 scale height was retained). The observed vertical emission profile is
compared to the model in Figure 2.8. Fig. 2.9 displays overlays of the observed PV
diagrams and the CR model PV diagrams for slices at heights z = ±1000 , ±2000 , ±3000 .
Upon examining these diagrams, some clear features are:
• A rotation velocity gradient appears to be necessary primarily on the northwest
side (R < 0). We attempt to model this gradient in §2.4.3.1. In some panels,
a shift in systemic velocity seems to be necessary. We present a model with
such an offset in §2.4.3.2. The kinematics appear different on the positive-z
63
Chapter 2. DIG Halo Kinematics in NGC 5775
Figure 2.7 Overlay of CO 2–1 (white contours) and best-fit model (black contours)
major axis PV diagrams. Contour levels for both are 3σ to 18σ in increments of 3σ.
Positive values of the major axis distance R correspond to the southeast side of the
disk.
64
2.4. Analysis and Modeling
Figure 2.8 Comparison of the observed (squares) and modeled (solid line) vertical
intensity profiles. Both profiles were obtained by averaging the vertical distribution
of emission along the length of the disk. The modeled profile is normalized to the
observed profile at z = 0. The exponential scale heights (as described in the text) are
5.800 on the southwest side and 4.500 on the northeast side. At z = −3000 , the model
is significantly lower than the data; hence the 5.800 scale height is used to generate
PV diagrams at that particular height.
65
Chapter 2. DIG Halo Kinematics in NGC 5775
Figure 2.9 PV diagram overlays of Hα (white contours) and CR model (black contours). PV diagrams are displayed at (a) z = +1000 , with contour levels 10σ to 210σ
in increments of 40σ; (b) z = +2000 , with contours levels 10σ to 50σ in increments of
10σ; (c) z = +3000 , with contour levels 3σ to 18σ in increments of 3σ; (d) z = −1000 ,
with contour levels 10σ to 210σ in increments of 40σ; (e) z = −2000 , with contour
levels 6σ to 36σ in increments of 6σ; (f) z = −3000 , with contour levels 3σ to 18σ in
increments of 3σ. Positive values of galactocentric radius R and z correspond to the
southeast side of the disk and the southwest side of the halo, respectively.
and negative-z sides of the halo.
• The “knee” in the model PV diagrams, caused by a combination of high gas
density and rotational velocity, appears to be unnecessary in some panels, but
in most, it appears that this knee moves further from R = 000 with increasing
z. The shift in this knee may be explained either by a change in the radial
density profile (demonstrated in §2.4.3.3), perhaps due to a radial migration,
or by a change in the shape of the rotation curve with height (demonstrated
66
2.4. Analysis and Modeling
in §2.4.3.4), as might be expected as the influence of the bulge potential diminishes. The knee could also be a signature of non-circular disk motions
associated with a bar potential, although as mentioned in 2.4.1, there is little
evidence for a bar in 2MASS images.
• In panel f, the bright knot of emission at R ≈ +10000 and v ≈ 150 km s−1
corresponds to a known (Collins et al. 2000; Lee et al. 2001) Hα extension of
possibly tidal origin. This emission is clearly visible in the moment-0 map in
Fig. 2.3, extending to the east away from the southeast edge of the disk. That
the radial velocity of this complex appears to be significantly lower than that
of the surrounding gas either means that the rotational velocity has dropped
significantly or that the complex does not lie along the line of nodes.
2.4.3.1
Azimuthal velocity gradient
The slit spectra presented by Rand (2000) and Tüllmann et al. (2000) were examined to provide a first estimate of the magnitude of a possible vertical gradient in
azimuthal velocity. Three slits are available, each measuring gas velocities on both
sides of the midplane, so that the gradient may be estimated in six regions. Based
solely on the mean velocities, the vertical gradient in azimuthal velocity was estimated to be ∼ 1 − 2 km s−1 arcsec−1 .
To test for the existence of a vertical gradient in azimuthal velocity of the form
described by equation 2.5, we have added a 1 km s−1 arcsec−1 (or, equivalently,
about 8 km s−1 kpc−1 ) gradient to the CR model (Figure 2.10). The flat part of the
approaching side appears to be better matched. However, there is still an apparent
problem matching the shape of the PV diagrams for R . 6000 in the halo (see §2.4.3.3
and §2.4.3.4 for possible explanations). It is not clear that adding the gradient to
the receding side has improved the model. An adjustment of the systemic velocity
67
Chapter 2. DIG Halo Kinematics in NGC 5775
appears to be necessary as well in most panels. We consider such an adjustment in
§2.4.3.2.
We have also generated models with different values of the azimuthal velocity
gradient. A gradient as low as 0.5 km s−1 arcsec−1 is found to be too small to match
the observed PV diagrams. Gradients with higher amplitude (in particular, dv/dz =
2 km s−1 arcsec−1 ) are able to better match some individual regions (primarily the
flat part of the PV diagrams on the approaching side for z = ±2000 ), but provide
poor agreement at z = ±3000 . We conclude that dv/dz = 1 km s−1 arcsec−1 provides
the best overall agreement with the data, but that higher values of the azimuthal
velocity gradient may be appropriate in localized regions of the halo. We note that
for a model with this gradient but with z0 = 000 , the azimuthal velocities would be
approximately 5 km s−1 lower at all locations above one scale height, corresponding
to a 3 per cent decrease at z = 3000 for a flat rotation curve at v(R, z = 0) = 200 km
s−1 .
2.4.3.2
Systemic velocity shift
We now modify the CR model by retaining the 1 km s−1 arcsec−1 gradient (on both
the approaching and receding sides), and adding a +10 km s−1 offset to the systemic
velocity. PV diagrams generated from this model are compared to the data in Fig.
2.11. This offset, while smaller than the channel width of the Fabry-Perot data cube,
seems to improve the match between model and data (for all regions of the halo).
Note that this adjustment was not indicated by the major axis PV diagrams; it is
only added to improve the agreement between data and model PV diagrams in the
halo. We also note that applying a shift in the systemic velocity without retaining
the gradient in azimuthal velocity is not sufficient to match the shape of the PV
diagrams in the halo.
68
2.4. Analysis and Modeling
Figure 2.10 PV diagram overlays of Hα (white contours) and model (black contours)
where a vertical gradient in azimuthal velocity of 1 km s−1 arcsec−1 has been added
to both sides of the disk. Contour levels are as in Fig. 2.9.
69
Chapter 2. DIG Halo Kinematics in NGC 5775
Figure 2.11 PV diagram overlays of Hα (white contours) and model (black contours)
where a vertical gradient in azimuthal velocity of 1 km s−1 arcsec−1 has been added
to both sides of the disk, and the systemic velocity has been increased by 10 km s−1 .
Contour levels are as in Fig. 2.9.
2.4.3.3
Modification of the halo radial density profile
In Figs. 2.9 - 2.11, the “knee” in the modeled PV diagrams is too prominent when
compared with the data (except at z = +1000 , for R < 000 ). We next make an attempt
to match the shape of the PV diagrams in the halo, retaining the features of our best
halo model thus far. The shape of the rotation curve is unchanged; only the radial
density profile is modified (in the same way for each height z), as shown in Figure
2.12a, by the introduction of a central depression. We have not attempted to recover
the actual radial density profile in the halo. Rather, we mean to illustrate that a
radial density profile different from that obtained for the major axis better reproduces
70
2.4. Analysis and Modeling
the changing shape of the PV diagrams with height. The PV diagram overlays are
shown in Fig. 2.13. We note that the z = −3000 panel suggests a central depression
even more severe than we have modeled. Further evidence for a change in the radial
gas distribution with height will be discussed in §2.5: cuts through the moment-0
map (shown in Figure 2.20) suggest that such a central hole may well be present in
the halo, especially on the negative-z side. Moreover, comparisons with PV diagrams
constructed from the ballistic base model (discussed in §2.5; see Figure 2.19) suggest
that the changing shape of the observed PV diagrams is strongly affected by radial
redistribution of matter in the halo.
2.4.3.4
Modification of the halo rotation curve
Because the radial density profile and rotation curve are partially coupled in the PV
diagrams, the density profile may not be responsible for the change in shape of the
halo PV diagrams. We next attempt to modify the form of the rotation curve such
that the shape of the halo PV diagrams is better matched. In this case, the CR
model radial density profile is unchanged. The 1 km s−1 arcsec−1 vertical gradient
in azimuthal velocity and +10 km s−1 systemic velocity offset are also still included.
We have not attempted to recover the exact shape of the rotation curve in the halo.
Rather, we illustrate how a change in the shape of the rotation curve changes the
shape of the PV diagrams in the halo. The modification to the rotation curve is
shown in Figure 2.12b. The rotation speed rises roughly linearly for R < 5000 , as
would be the case for a less centrally condensed potential. Figure 2.14 shows the PV
diagram overlays. The modification to the radial density profile (§2.4.3.3) appears
to match the data somewhat better than changing the shape of the rotation curve,
but we cannot exclude the latter possibility.
71
Chapter 2. DIG Halo Kinematics in NGC 5775
Figure 2.12 (a) Comparison between the profile of density versus galactocentric radius
R in the CR model (dotted line) and the modification presented in §2.4.3.3 (solid
line). (b) Comparison between the rotation curve in the CR model (dotted line) and
the modification presented in §2.4.3.4 (solid line).
72
2.4. Analysis and Modeling
Figure 2.13 PV diagram overlays of Hα (white contours) and model (black contours)
where the radial density profile has been varied as shown in Figure 2.12a. Contour
levels are as in Fig. 2.9.
73
Chapter 2. DIG Halo Kinematics in NGC 5775
Figure 2.14 PV diagram overlays of Hα (white contours) and model (black contours)
where the shape of the rotation curve has been varied as shown in Figure 2.12b.
Contour levels are as in Fig. 2.9.
2.4.3.5
Modification of halo position angle and inclination
In Figure 2.3b, the appearance of the velocity contours in the SW and SE quadrants
could be interpreted as resulting from the halo being oriented at a slightly different
position angle relative to the disk. The effect is not clearly visible in the NE and
NW quadrants, although the mean velocities in both spectra of Rand (2000) are
consistent with this asymmetry in all four quadrants. Such a shift in the position
angle in a lagging halo would make the contours run more perpendicular to the
major axis in two opposite quadrants (e.g., NW and SE in Fig. 2.3b), and increase
the angle between the contours and the minor axis in the other two quadrants (e.g.,
NE and SW in Fig. 2.3b). Examination of the velocity contours indicates that the
74
2.5. The Ballistic Model
magnitude of such an offset in position angle necessary to produce the observed effect
would be on the order of 20◦ , but it should be noted that clumpiness in the halo gas
distribution and peculiar velocities may confuse the situation.
On a similar note, if we allow the inclination of the halo to vary relative to that
of the disk, it is possible that an apparent lag in halo rotation could be simply an
indication that the halo is viewed from a more face-on perspective than the disk. If
we assume a disk rotation speed of 200 km s−1 and a vertical gradient in azimuthal
velocity of 1 km s−1 arcsec−1 beginning at a height of 500 , then at a height z = 3000 ,
the azimuthal velocities in the halo would be about 175 km s−1 . To mimic this effect
with a variation in inclination angle, an offset between the disk and halo of about
30◦ would be required. We consider such an offset very unlikely. An offset in the
position angle or inclination of the halo relative to the orientation of the disk could
occur if the extraplanar gas were accreted. This possibility is interesting given the
interaction between NGC 5775 and its neighbor, but it is uncertain how long such a
configuration might last.
2.5
The Ballistic Model
We next utilize the ballistic model of CBR to attempt to understand what vertical
gradient in azimuthal velocity would be expected if the disk-halo flow in NGC 5775
is purely ballistic in nature. The full details of the model are described by CBR,
who compared mean velocities from this model to those obtained from slit spectra
for NGC 5775 and NGC 891. Basically, clouds are launched from the disk with an
initial velocity selected from a constant probability distribution between zero and a
maximum “kick velocity”, Vk , along a unit vector at an angle γ from a line normal to
the midplane. The cloud ejection cone angle γ is selected from a gaussian probability
distribution of the form P (γ) ∝ exp(−γ 2 /2γ02 ). The clouds are then allowed to orbit
75
Chapter 2. DIG Halo Kinematics in NGC 5775
Table 2.2. Ballistic Base Model Characteristics for NGC 5775
Parameter
Value
R0
6 kpc
z0
200 pc
Rhole
0 kpc
Vk
160 km s−1
γ0
0◦
Vc
198 km s−1
ballistically in the galactic gravitational potential of Wolfire et al. (1995), which is
parameterized by the circular velocity, Vc (the bulge, disk, and halo components each
scale linearly with Vc2 ). Whenever a cloud leaves the simulation or returns to the
disk, it is replaced by another cloud. Initial locations of the clouds are randomly
selected from a distribution with a radial exponential scale length R0 and a vertical
gaussian scale height z0 = 0.2 kpc. The disk is allowed to have a central hole of radius
Rhole . The clouds do not interact with each other, and are assumed to have constant
temperature, density, and size (and therefore equal Hα intensities) throughout the
course of their orbits. After the simulation is run for 1 Gyr, at which time the
system has reached a condition of steady state, positions and velocities of each cloud
are extracted from the model. These outputs can be examined directly or used to
generate an artificial data cube at any inclination, from which, e.g. PV diagrams or
runs of mean velocity versus projected height above the midplane can be created.
The most influential parameter in the model is the ratio of the maximum kick
velocity to the rotational velocity of the disk, Vk /Vc . For a given value of the circular
velocity and initial R, increasing kick velocities result in more radial movement,
76
2.5. The Ballistic Model
larger maximum height of the orbit, and increased drop in azimuthal velocity at the
peak height of the orbit. The circular velocity is determined observationally, and
the kick velocity is set such that the resulting scale height of cloud density matches
the scale height of EDIG emission (determined by CBR). This critical parameter is
thus reasonably well constrained by observations. The other parameters were found
to have little effect on the model outputs. The characteristics of the so-called base
model for NGC 5775 from CBR are summarized in Table 2.2. With these parameters
set in the model, CBR compared the mean velocities obtained from the model viewed
at i = 86◦ with those measured along their two slits for NGC 5775. They found that
the mean velocities from the model were roughly the same as the measured ones, but
the model could not reproduce the observed mean velocities at the largest heights,
which are seen to approach the systemic velocity (see their Figure 8).
We have performed an analysis of the variation in azimuthal velocity as a function
of z in the ballistic model. This analysis shows that in the model that best matches
the mean velocities from the slit spectra of CBR, the vertical gradient in azimuthal
velocity is shallower than the corresponding variation in mean velocity. The reason
for this discrepancy is the large-scale radial redistribution of clouds in the ballistic
model. Figure 2.15 displays contour plots of cloud density in the ballistic model as
a function of R and z, and Figure 2.16 shows the azimuthal velocity curves of the
ballistic model clouds as a function of height. Most of the clouds at high z are also
found at large R. Therefore, most of the decrease in mean velocity in the model is
caused by velocity projection, and the magnitude of the vertical azimuthal velocity
gradient is of lesser importance in setting the mean velocity gradient. For this reason,
the results of the ballistic model cannot be relied upon to explain variations in mean
velocity unless the observed radial density profiles are found to be similar to those
in the model. In the present study, our spectral resolution is sufficient to allow the
density distribution to be modeled, thus allowing azimuthal velocities to be measured
as a function of z and compared directly with azimuthal velocities from the ballistic
77
Chapter 2. DIG Halo Kinematics in NGC 5775
Figure 2.15 Contours plots of cloud density as a function of galactocentric radius R
and z in the ballistic “base model” (see text), for clouds (a) moving up, (b) moving
down, and (c) all clouds. Contours levels correspond to 80, 400, 880, 1520, 2320,
and 3280 clouds kpc−2 in (a) and (b). In (c), contour levels correspond to 160, 800,
1760, 3040, 4640, and 6560 clouds kpc−2 .
78
2.5. The Ballistic Model
model.
As an aside, we point out how the azimuthal velocities to be extracted from the
model may depend on the physical nature of the disk-halo flow. In Figure 2.17, we
display meridional plots of cloud orbits in the ballistic model at various initial radii.
The ballistic model predicts that the radial motion during the majority of a cloud’s
orbit is radially outward. Only at the highest initial radii and kick velocities do the
ends of the orbits show a radially inward motion. Because the radius of a given
cloud is nearly always increasing, conservation of angular momentum dictates that
the azimuthal velocity of the same cloud is nearly always decreasing. The azimuthal
velocities of upward-moving clouds are thus always higher than those of downwardmoving clouds. The vertical gradient in azimuthal velocity extracted from the model
will therefore be dependent on the assumption of the dynamics of the disk-halo flow.
In a scenario where the gas begins in the ionized state, cools and condenses into
neutral clouds somewhere near the top of the clouds’ orbits, the azimuthal velocities
will be relatively high. On the other hand, if the flow begins as hot gas and cools
to a warm ionized gas for the downward portion of the flow, the azimuthal velocities
will be lower. In the latter case, the assumption of ballistic motion is likely violated
for the upward portion of the flow, and simply associating the warm ionized gas with
the downward moving clouds in our model may not be accurate. The fact that the
structure of the EDIG emission resembles shells and filaments implies that at least
part of the ionized distribution is upward moving, but additional evidence is required
to determine how much of the flow is ionized.
Clearly, the vertical gradient in azimuthal velocity in Figure 2.16 is not as simple
as that described by equation 2.5, which assumes a constant rotation curve shape as
a function of height. Nevertheless, an approximate value of dv/dz can be obtained
by inspecting the plots. In the interest of comparison with the velocity gradient
modeled from the data, we only report here the gradient seen in the ballistic model
79
Chapter 2. DIG Halo Kinematics in NGC 5775
Figure 2.16 Plots of average azimuthal velocity versus galactocentric radius R in the
ballistic base model, for clouds (a) moving up, (b) moving down, and (c) all clouds.
Points are plotted in (a) for z = 0 kpc (diamonds), z = 2 kpc (circles), z = 4 kpc
(crosses), z = 6 kpc (squares), z = 8 kpc (triangles), and z = 10 kpc (plus signs).
The same symbols are plotted in (b) and (c), except that the z = 8 kpc and z = 10
kpc points are left out for clarity (the azimuthal velocities at those heights are very
similar to the ones at z = 6 kpc).
80
2.5. The Ballistic Model
for 0 kpc ≤ z ≤ 4 kpc, which is a slightly larger vertical range than we have modeled
in this work (§2.4), and for 5 kpc ≤ R ≤ 12 kpc. (No clouds in the model reach z = 4
kpc for R < 5 kpc, so azimuthal velocities cannot be extracted at those locations.
The upper limit, 12 kpc, corresponds approximately to the optical radius of NGC
5775.) For the upward-moving clouds, the average gradient over the indicated ranges
of R and z is approximately 2.4 km s−1 kpc−1 ; for the downward-moving clouds, 4.3
km s−1 kpc−1 ; for all clouds considered together, 2.6 km s−1 kpc−1 . Even the highest
value, 4.3 km s−1 kpc−1 (appropriate if all of the observed Hα emission is from clouds
returning to the disk), is approximately a factor of 2 lower than the vertical gradient
modeled from the data [about 8 km s−1 kpc−1 ; recall that a galaxy model using
dv/dz ≈ 4 km s−1 kpc−1 was examined and rejected (see §2.4.3.1)].
The base model of CBR includes a ratio of Vk /Vc = 0.81 in order to match the observed scale height of EDIG emission. To understand how the maximum kick velocity
affects the vertical gradient in azimuthal velocity, and thereby to examine whether
a model with a different value of Vk might better match the gradient estimated from
the data, we have generated models with Vk = 100 km s−1 (Vk /Vc = 0.51) and
Vk = 220 km s−1 (Vk /Vc = 1.11). In those cases, the gradients in azimuthal velocity
were found to be approximately 1.9 km s−1 kpc−1 and 6.8 km s−1 kpc−1 , respectively,
for downward-moving clouds only. The approximately linear relationship thus determined between the gradient in azimuthal velocity and Vk /Vc implies that a maximum
kick velocity of 255 km s−1 (Vk /Vc = 1.29) is required to match the observed gradient
even when only downward-moving clouds are considered. Unfortunately, this value
of Vk /Vc yields a DIG layer with a vertical exponential scale height of approximately
6.3 kpc, or about a factor of 3 higher than the values derived from the two slit spectra
used by CBR of 2.1 − 2.2 kpc. We conclude that it is unlikely that any value of Vk
will result in a model that reproduces the observed gradient in azimuthal velocity.
CBR also consider two galactic potential models (2 and 2i) from Dehnen & Binney
81
Chapter 2. DIG Halo Kinematics in NGC 5775
(1998). They find that model 2i, which has an oblate, flattened halo (axial ratio
q = 0.3 rather than q = 0.8 as in model 2; see Dehnen & Binney 1998), produces a
steeper change in radial migration with the ratio Vk /Vc compared to their base model.
We might therefore expect a steeper gradient in azimuthal velocities with height if
we use this potential. Referring to Figures 4 and 5 of CBR, we select Vk = 200 km
s−1 for model 2i, which should give roughly the same radial redistribution as the
base model with Vk = 255 km s−1 , for radii R & 5 kpc. The gradients in azimuthal
velocity generated by this model are approximately 3.2 km s−1 kpc−1 for downwardmoving clouds, 1.0 km s−1 kpc−1 for upward-moving clouds, and 1.6 km s−1 kpc−1 for
all clouds considered together. This model produces a disk with an average vertical
scale height of about 3.5 kpc (considerably higher than the observed scale height,
2.1 − 2.2 kpc). Increasing the maximum kick velocity still higher to increase the
azimuthal velocity gradient will only make the scale height larger. Thus, a flattened
dark halo is not likely to be more successful in explaining the observed gradient in
azimuthal velocity.
Figure 2.18 demonstrates how the gradient in mean velocity in the model is affected not only by the gradient in azimuthal velocity but also by the radial redistribution of clouds. The gradient in mean velocity versus height in the model is shown
for R = 4 kpc and R = 12 kpc. Figure 2.18a (R = 4 kpc) shows a much steeper
gradient in mean velocity with height than Figure 2.18b (R = 12 kpc). The average
gradients over the range 0 kpc ≤ z ≤ 4 kpc are approximately 14 km s−1 kpc−1 in the
former case and 6 km s−1 kpc−1 in the latter, despite the gradient in azimuthal ve-
locity being roughly the same at these two radii. In Fig. 2.15, the cloud distribution
reaches 3 − 4 times higher at R = 12 kpc than at R = 4 kpc. Thus, the only clouds
encountered along a line of sight at low radius and high z are concentrated at the
edges of the disk, whereas a line of sight at higher radius and the same z encounters
more clouds closer to the line of nodes, keeping the mean velocity closer to the actual
rotation speed at that height. At both radii, the gradient in mean velocity is much
82
2.5. The Ballistic Model
Figure 2.17 Meridional plots of clouds in the ballistic base model with kick velocities
equal to the maximum value, Vk = 160 km s−1 , starting at galactocentric radii (a)
R = 4 kpc; (b) R = 8 kpc; (c) R = 12 kpc; and (d) R = 16 kpc. Cloud positions are
plotted at 20 Myr intervals. Azimuthal velocities (in km s−1 ) are noted above the
cloud’s plotted position for most time steps (some omissions are made for clarity).
83
Chapter 2. DIG Halo Kinematics in NGC 5775
larger than that of azimuthal velocity because of radial redistribution.
PV diagrams constructed from the output of the ballistic base model and displayed in Figure 2.19 clearly illustrate the points previously discussed and may be
directly compared to the data. Along the major axis (Fig. 2.19a), the appearance
of the “knee” in the ballistic model PV diagram is roughly matched to that in the
data. We note that the radial density profile and major axis rotation curve in the
ballistic model have not been adjusted to the extent described in §2.4, and that the
ballistic model does not simulate noise, so signal-to-noise contours may not be plotted and directly compared to the data. As in the observations, the “knee” in the
ballistic model PV diagrams moves radially outward with increasing height above
the midplane. Simultaneously, the velocity profile peak at a given R shifts away
from the local azimuthal velocity and closer to the systemic velocity. Both effects
are caused primarily by the radial redistribution of clouds in the halo, and appear
more striking in the ballistic model than in the data (see also Figure 2.20). The PV
diagrams in Fig. 2.19 make clear that, at least in the ballistic model, most of the
changes are caused by radial motions reshaping the velocity profiles. A gradient in
azimuthal velocity is present in the model, and, though clearly evident by inspecting
the shape of the PV diagrams, produces relatively minor modifications. That the
effects described above are also seen in the observed PV diagrams provides further
evidence for radial redistribution in NGC 5775.
Whether the large-scale radial redistribution of gas predicted by the ballistic
model is actually observed in NGC 5775 is a very important question. Such a redistribution may be apparent in cuts taken parallel to the major axis through moment-0
maps at various heights above the plane. Figure 2.20 shows such cuts for moment-0
maps made from the ballistic base model and the Hα data cube. At most heights, it
appears that the data cuts may follow the shape of the model cuts fairly well, apart
from the complication of filamentary structures. This correspondence is better for
84
2.5. The Ballistic Model
Figure 2.18 Plots of mean velocity as a function of height above the midplane (z)
in the ballistic base model for clouds at major axis distances (a) R = 4 kpc and
(b) R = 12 kpc. Mean velocities are shown for clouds moving up (squares), moving
down (diamonds), and all clouds (solid lines). All mean velocities were calculated
assuming an inclination angle of 86◦ .
85
Chapter 2. DIG Halo Kinematics in NGC 5775
z < 000 . At heights greater than 3000 , the moment-0 cuts from the ballistic model
show a much clearer signature of radial redistribution, but our data are not sensitive
enough to make a comparison at those heights. We conclude, then, that there is
moderate morphological evidence for radial redistribution at the level predicted by
the ballistic model.
CBR have previously compared the results of this ballistic model to mean velocities obtained with slit spectra for NGC 891 and NGC 5775. In NGC 891, the
authors find that the observed mean velocities drop more slowly as a function of
height than the mean velocities derived from the ballistic model. The authors concluded from this that (magneto-) hydrodynamical effects are probably at work. For
instance, the radial migration could be modified by a gas pressure gradient in the
halo. However if, as seems reasonable, halo gas pressure decreases with radius, the
discrepancy would be worse because outward radial migration would be larger and
modeled mean velocities even closer to systemic. It is possible that one major reason
for the difference between mean velocities from the data and the model is that the
radial density distribution in the halo of NGC 891 is more centrally concentrated
than the prediction of the ballistic model. That outward radial migration occurs at
some level in the halo is indicated by Figure 11 of Rand (1997). However, to properly examine halo rotation, azimuthal velocities must be estimated from data and
the density distribution modeled, as in the present study. In a forthcoming paper,
we attempt such an analysis from high spectral resolution data of the DIG halo of
NGC 891 with two-dimensional spatial coverage.
In the case of NGC 5775, CBR find a better overall agreement between the mean
velocities obtained from the slit data and those from the ballistic model. However,
the ballistic model does not reproduce all of the observed features. Of particular
interest with respect to the present study, the modeled mean velocities in the range
z = 0 − 4 kpc (the same range considered here) show a markedly steeper gradient
86
2.5. The Ballistic Model
Figure 2.19 PV diagrams constructed from the output of the ballistic base model
(black contours), which has been projected to the distance of NGC 5775, smoothed
to an 800 beam, and viewed at i = 86◦ . PV diagrams were created at heights of (a)
z = 000 , (b) z = 1000 , (c) z = 2000 , and (d) z = 3000 . Contour levels correspond to 0.5,
2, 3.5, 5, 6.5, and 8 clouds arcsec−2 channel−1 in (a); 0.5, 1.5, 2.5, 3.5, 4.5, and 5.5
clouds arcsec−2 channel−1 in (b); 0.5, 1, 1.5, 2, and 2.5 clouds arcsec−2 channel−1 in
(c); 0.5, 0.75, and 1 clouds arcsec−2 channel−1 in (d). Also plotted in each frame are
PV diagrams constructed from the Hα data cube (white contours) on the positive-z
(southwest) side of the halo. Contour levels correspond to 20σ to 520σ in increments
of 50σ in (a); 20σ to 200σ in increments of 30σ in (b); 5σ to 35σ in increments of
6σ in (c); 2σ to 11σ in increments of 3σ in (d). The channel width in the ballistic
model is the same as that of the Hα data cube, 11.428 km s−1 . Positive values of
the major axis distance R correspond to the southeast side of the disk.
87
Chapter 2. DIG Halo Kinematics in NGC 5775
than the data. Mean velocities calculated from the Fabry-Perot data cube show a
similar lack of agreement with those from the ballistic model. In both cases, smallscale velocity and density variations are likely significantly affecting the observed
mean velocities.
2.6
H I Loops
In order to understand the method by which matter and energy are injected into the
halo in NGC 5775, the kinematics and morphology of specific sites of input are of
interest. In a general fountain-type model of disk-halo circulation, in which hot gas
rises into the halo, cools, and returns to the disk (Shapiro & Field 1976; Bregman
1980), sites of significant mass transfer into the halo should be marked by concentrations of supernovae. If the disk-halo flow is well described by a chimney-type
picture (Norman & Ikeuchi 1989), these sites will be characterized by the presence of
superbubbles and chimneys. Thus, regardless of the favored model of disk-halo flow,
to understand how mass and energy are injected into the halo, one should search for
loop and filamentary structures that may indicate a high level of supernova activity.
Three extraplanar H I loops have been identified by Irwin (1994) and analyzed
in detail by Lee et al. (2001). In the latter work, PV diagrams were generated from
H I data so that the velocity structure of these regions can be inspected. We now
examine Hα emission in similar PV diagrams to investigate the morphology and
kinematics of their ionized components. Table 2.3 summarizes some properties of
these H I loops.
To compare the H I and Hα emission in the regions of interest, both cubes were
converted to units of column density (per unit velocity interval). The values of
flux density in the H I cube were converted to brightness temperatures and then
to column densities in the usual way. In the Hα cube, the brightnesses were first
88
2.6. H I Loops
Table 2.3. Properties of NGC 5775 H I Loops
F1
RAa(J2000.0)
F2
F3
14 54 00.54 14 53 57.77 14 53 57.39
Decl.a(J2000.0) 03 32 25.7
03 31 48.1
03 33 52.6
Rsh b(kpc)
2.0
1.7
a
2.2
Coordinates were obtained by examining the H I moment-0 map and estimating
the locations of the loop centers.
b
Radii of shells from Lee et al. (2001).
converted to emission measure (EM) by assuming a gas temperature T = 104 K. To
proceed further, a path length must be assumed. Using the radii provided by Lee
et al. (2001), and assuming that the H I shells are spherical, mean path lengths L0
were calculated for each location at which a PV diagram was created. This allows
p
us to calculate the rms density with hn2e i ≈ EM/L0 . Using hne i = f hn2e i, where f
is the filling factor of the gas along the path length (we scale our results to f = 0.1),
and Ne ≈ hne i L0 , rough column densities were obtained. We express all Hα column
p
densities in units of (f /0.1)(L/L0 ) to facilitate calculations of column densities
using different filling factors [for example, Reynolds (1991) determined f & 0.2 for
|z| ≤ 1 kpc in the Milky Way] and path lengths (values of L in the disk will be much
longer than the values L0 determined for the H I loops).
In Figures 2.21, 2.22, and 2.23, we present overlays of H I and Hα PV diagrams
of the regions containing F1, F2, and F3. Note that our definition of the sign of z is
opposite that of Lee et al. (2001). Contours are plotted in units of column density
per channel (recall that the H I and Hα cubes have unequal channel widths of 41.67
89
Chapter 2. DIG Halo Kinematics in NGC 5775
and 11.428 km s−1 respectively). We now compare H I and Hα PV diagrams for each
region individually.
2.6.1
F1
The Hα moment-0 map in this region appears smooth and slightly more vertically
extended than the surrounding emission. An Hα filament extends upwards from
a location in the disk at a slightly lower radius, and reaches to approximately our
estimated center of F1. Another, fainter extension can be seen approximately 1500 to
the southeast. The H I emission has the appearance of a loop.
In Figure 2.21, it can be seen that the extraplanar H I emission is blueshifted
(closer to systemic) relative to the midplane gas. The Hα emission does not appear
to be as vertically extended, except in Fig. 2.21a, where the two phases are detected
to approximately the same height. The ionized gas is predominantly redshifted
relative to the H I emission, and does not show a gradient relative to the midplane
velocities. Above z ≈ 2000 , the Hα profiles are singly peaked (except at the very
largest z-heights), as are the H I profiles, but they are significantly broader than
the neutral profiles. For example, at z = −3200 , the full width at half-maximum
(FWHM) of the H I and Hα profiles are roughly: 125 and 195 km s−1 in Fig. 2.21a;
55 and 245 km s−1 in Fig. 2.21b; 90 and 200 km s−1 in Fig. 2.21c. The FWHM of
these Hα profiles is significantly higher than of profiles in regions lacking filamentary
structures, where characteristic FWHM values are ∼ 100 − 140 km s−1 . In all three
panels, there is a hint of an Hα filament at the highest velocities (vLSR ≈ 200 − 250
km s−1 ; the faint extension above v ≈ 250 km s−1 is due to residual sky emission). An
H I extension may also be present (see Figs. 2.21b and c), but it is not as vertically
extended. The appearance of these features suggests that this portion of the shell is
ionized at the highest z.
90
2.6. H I Loops
Figure 2.20 Comparison between moment-0 cuts generated from the Hα data
(squares) and the ballistic base model (solid lines), at heights of (a) z = −3000 ,
(b) z = −2000 , (c) z = −1000 , (d) z = 000 , (e) z = +1000 , (f) z = +2000, and (g)
z = +3000 . In each panel, the mean of the model profile is scaled to the mean of the
data. The major axis distance R is positive on the receding (southeast) side of the
disk, and z is positive to the southwest.
91
Chapter 2. DIG Halo Kinematics in NGC 5775
Figure 2.21 Overlays of H I (white contours) and Hα (black contours) column density
PV diagrams for the region containing F1, at offset distances parallel to the major
axis relative to the coordinates in Table 2.3: (a) 1300 southeast; (b) 000 ; (c) 1300
northwest. In all cases, the H I contour levels are 1.53, 2.04, 3.06, 4.59, 7.14, 12.8,
17.9, and 25.5×1020 cm−2 (H I channel)−1 . The noise level in the H I data corresponds
to 1.28 × 1020 cm−2 (Hp
I channel)−1 . The Hα contour levels are 1.89, 2.52, 3.78, 5.66,
8.81, and 15.8 × 1019 (f /0.1)(L/L0 ) cm−2 (Hα channel)−1 , where L0 is (a) 2500
pc, (b) 3500 pc, and (c) p
2400 pc. The noise level in the Hα data corresponds to
19
1.28, 1.51, and 1.25 × 10
(f /0.1)(L/L0 ) cm−2 (Hα channel)−1 in (a), (b), and (c),
respectively. All velocities are relative to Vsys . The H I and Hα channel widths are
41.67 km s−1 and 11.428 km s−1 respectively.
Lee et al. (2001) interpret this feature as an open-topped H I loop, filled with
ionized gas (some of which also extends vertically above the neutral gas). The large
Hα line width may indicate that this feature is still expanding, and that only the
low-vLSR edge (closer to the observer in this scenario) is neutral. Assuming that the
broad profiles are due to expansion, we can estimate the required energy input, under
the assumption that the loop is a result of multiple supernova explosions in the star
forming layer. Integrating all of the Hα emission above z = 1000 up to the maximum
height displayed in Fig. 2.21 in all velocity channels shown, assuming a cylindrical
geometry so that the average path length is Lav = 3500 pc, and using a filling factor of
92
2.6. H I Loops
0.1, a total mass in ionized gas of Mtot = 1.46×106
p
(f /0.1)(L/Lav ) M is obtained.
2
The kinetic energy of the expansion is then estimated to be KE ' Mtot vFWHM
/2 =
p
1.74 × 1054 (f /0.1)(L/Lav ) erg. Modeling of supernova remnants indicates that less
than 10 per cent of the initial total energy of the supernova explosion is converted to
kinetic energy (Chevalier 1974). Thus, our estimated kinetic energy suggests that at
least 1.7 × 1055 erg are required to provide the observed expansion of ionized gas. To
produce the observed expansion of the neutral component, Lee et al. (2001) estimate
an input energy of 1.9×1055 erg. The total energy required to generate the expansion
of the neutral and ionized gas is the sum of these estimates, approximately 3.6 × 1055
erg.
2.6.2
F2
In the region of F2, the Hα moment-0 map shows a bright vertical plume. This
extension, which is clearly seen in Figure 1b of Collins et al. (2000), appears to
extend slightly radially outward as it reaches up into the halo. The H I emission has
the appearance of a loop.
F2 was described by Lee et al. (2001) as the only one of these features which has
a clear-cut expanding shell profile. In particular, the 21-cm velocity profiles near
the center of the shell are characterized by a double-peak shape, and a single-peak
shape (at least in Figures 2.22a and b) at the highest location. This structure is
most obvious in Figure 2.22a, where, between z ≈ 30 − 4000 , the closed contours at
vLSR = 50 km s−1 and 175 km s−1 represent local maxima, and the closed contour at
vLSR = 125 km s−1 represents a local minimum (the same velocity profile structure is
present in Fig. 2.22b, except that the local minimum is not represented by a closed
contour). When we compare the Hα emission (Figure 2.22), we see that in locations
where the H I profiles are split, the Hα line center is approximately between the H I
93
Chapter 2. DIG Halo Kinematics in NGC 5775
Figure 2.22 Overlays of H I (white contours) and Hα (black contours) column density
PV diagrams for the region containing F2, at offset distances parallel to the major
axis relative to the coordinates in Table 2.3: (a) 600 southeast; (b) 000 ; (c) 400 northwest.
The H I contour values and noise level are the same as in p
Fig. 2.21. The Hα contour
19
(f /0.1)(L/L0 ) cm−2 (Hα
levels are 1.89, 2.52, 3.78, 5.66, 8.81, 15.8, and 22.1 × 10
−1
channel) , where L0 is (a) 2800 pc, (b) 3200 pc, and (c)
level
p3000 pc. The noise
19
−2
in the Hα data corresponds to 1.35, 1.45, and 1.40 × 10
(f /0.1)(L/L0 ) cm (Hα
channel)−1 in (a), (b), and (c), respectively. All velocities are relative to Vsys . The
H I and Hα channel widths are 41.67 km s−1 and 11.428 km s−1 respectively.
velocity peaks. The Hα emission continues to greater heights, beyond where the
H I profiles again become singly peaked in Figures 2.22a and b, but with a gradient
toward lower values of vLSR , reaching the systemic velocity at z ≈ 10000 . We note that
this height corresponds to about 12 kpc, and represents the most vertically extended
Hα emission detected in the galaxy in this study. Because this feature appears to
the southeast of the shell center, and the shell itself is located to the southeast of
the rotation center of the galaxy, the velocity gradient does not necessarily indicate
an expansive motion, but may simply indicate ionized gas moving radially outward
from the location of the H I shell and experiencing a concordant decrease in azimuthal
velocity. The magnitude of the gradient is approximately 1 km s−1 arcsec−1 , and is
94
2.6. H I Loops
thus consistent with the general velocity gradient observed for the entire halo (which
was determined for lower z than is reached by the filament). It should be noted
that this is a gradient in mean velocity; therefore, if the filament does not remain
at a constant azimuthal angle (in the galaxy frame) as it extends into the halo, the
observed gradient is misleading. At the very largest heights, the mean velocity seems
to cross to the other side of systemic.
The Hα velocity profiles are rather broad in this region as well. At z = +4000 ,
the FWHM are roughly: 125 km s−1 in Fig. 2.22a; 175 km s−1 in Fig. 2.22b; 185
km s−1 in Fig. 2.22c. We estimate the total mass in ionized gas in this region (using
the same method as for F1, but with Lav = 3200 pc) to be roughly Mtot = 2.25 ×
p
106 (f /0.1)(L/Lav ) M . Assuming that the velocity widths are due to expansion,
p
2
the kinetic energy is then KE ' Mtot vFWHM
/2 = 1.53 × 1054 (f /0.1)(L/Lav ) erg.
This suggests that an initial total energy of at least 1.5 × 1055 erg was required
to provide the observed expansion of the ionized gas component. Lee et al. (2001)
estimate that an input energy of 2.1 × 1055 erg is required to produce the observed
expansion of neutral gas. The total energy required to provide the expansion of both
the neutral and ionized gas components is thus approximately 3.6 × 1055 erg.
This feature may be interpreted in the following way. The H I observations imply
the presence of an expanding shell about 4000 above the midplane, which may not
be closed at the highest z. Within that shell, Hα emitting gas is present, with
a large linewidth that may also indicate expansion. Starting at the H I shell and
reaching upwards is a filament of ionized gas, which may extend radially outward as
it stretches well up into the halo. As height increases, the azimuthal velocity of the
filament decreases until it reaches approximately the systemic velocity.
95
Chapter 2. DIG Halo Kinematics in NGC 5775
2.6.3
F3
The Hα moment-0 map shows a prominent pair of filaments reaching high above the
disk. These filaments are very clearly visible in Fig. 2.3a, as well as in Fig. 1b of
Collins et al. (2000). Unlike the appearance of the ionized structures near F1 and
F2, these filaments are very much perpendicular to the major axis, though in the
smoothed Hα image displayed in Fig. 8 of Collins et al. (2000) there is a hint that the
ionized structure is closed at the top. The H I shell shows an open-topped structure,
and Lee et al. (2001) note that the ionized gas lies along the inner rim of the neutral
structure. Unlike F1 and F2, the Hα emission is not seen to fill the H I loop.
Figure 2.23 shows that the ionized gas in this region reaches up nearly as far as
that associated with F2, yet its mean velocity does not change significantly above
z ≈ 3000 . At heights z . 3000 , the ionized gas follows the H I emission, which, as noted
by Lee et al. (2001), shows a velocity gradient consistent with a drop in azimuthal
velocity with height (unless the position of the filament is not azimuthally constant).
Because of the open topped double filamentary structure apparent in the moment-0
map, a double-peaked Hα velocity profile might be expected, but instead, as in the
H I emission, we only see a single peak (except in Fig. 2.23c, where the H I shows a
second velocity component, and there is a hint of a similar splitting in the Hα profile
but at low statistical significance). Once again, the Hα profiles are broader than the
H I profiles, but although this is morphologically the most classic-looking example of
a shell in this galaxy, there are no obvious signs of expansion such as clearly split line
profiles or large line widths. In fact, the FWHM of the Hα profiles at z = +4000 in this
region are roughly: 95 km s−1 in Fig. 2.23a; 75 km s−1 in Fig. 2.23b; 100 km s−1 in
Fig. 2.23c. These values are considerably lower than the FWHM measured in F1 and
F2, and are more similar to the FWHM measured in non-filamentary regions of the
halo. We nevertheless estimate the energy requirement under the assumption that
the velocity widths are due to expansion. Using the same technique as for the other
96
2.6. H I Loops
Figure 2.23 Overlays of H I (white contours) and Hα (black contours) column density PV diagrams for the region containing F3, at offset distances parallel to the
major axis relative to the coordinates in Table 2.3: (a) 1100 southeast; (b) 000 ; (c)
800 northwest. The H I contour values and noise level are the same as in Fig. 2.21.
The Hα contour levels are the same as in Fig. 2.22, except that here L0 is (a) 1700
pc, (b) 2700 pc, and (c) p
2200 pc. The noise level in the Hα data corresponds to
19
(f /0.1)(L/L0 ) cm−2 (Hα channel)−1 in (a), (b), and (c),
1.06, 1.33, and 1.20 × 10
respectively. All velocities are relative to Vsys . The H I and Hα channel widths are
41.67 km s−1 and 11.428 km s−1 respectively.
two regions, a total mass in ionized gas of Mtot = 1.54 × 106
p
(f /0.1)(L/Lav ) M
is estimated, where in this case Lav = 2700 pc. We thus estimate a kinetic energy
p
2
KE ' Mtot vFWHM
/2 = 3.06 × 1053 (f /0.1)(L/Lav ) erg. Under the assumption
that . 10% of the initial total energy was converted to kinetic energy, this estimate
implies that an initial total energy of at least 3.1 × 1054 erg was required to provide
the observed expansion. This is an order of magnitude lower than the one-time
energy injection estimates made by Lee et al. (2001) for the neutral gas in this
region, 3.0 × 1055 erg. The total energy required to power the expansion of both
components is thus roughly the same as the H I estimate, 3.3 × 1055 erg. Lee et al.
(2001) estimate its energy requirements to be higher than the others, but when the
97
Chapter 2. DIG Halo Kinematics in NGC 5775
ionized components are included, the energy requirements of all three features are
comparable.
2.7
Conclusions
We have obtained Fabry-Perot spectra of the Hα emission line in the nearly edge-on
spiral galaxy NGC 5775. Major axis radial density profiles and rotation curves were
obtained for the ionized and molecular components of this galaxy. The observations
have also allowed us to examine the azimuthal velocity variation as a function of
height in the halo. We have found that a vertical gradient in the azimuthal velocity
with a magnitude 1 km s−1 arcsec−1 , or about 8 km s−1 kpc−1 , is able to reproduce
the gross features of PV diagrams constructed parallel to the major axis (but a
larger gradient may be appropriate in localized regions of the halo). Such a gradient
is primarily indicated for the approaching side of the galaxy, though mean velocities
from slit 2 of Rand (2000) suggest the presence of a gradient on the receding side
as well (at least at the highest z, but recall that the radial density profile was not
taken into account in that analysis). The magnitude of the gradient should be
considered approximate because of uncertainties in the radial density profile and
rotation curve adopted (especially for the halo gas) in this study. One should also be
aware that the interaction with NGC 5774 may lead to significant deviations from
axisymmetry in the halo, as has been assumed in the modeling here. Nevertheless, it
is apparent that a non-zero gradient is present in this galaxy. Comparisons between
PV diagrams constructed from the data and from galaxy models suggest either a
radial redistribution of gas in the halo or a shallower rise in the rotation curve
than is observed along the major axis. Further evidence for the former possibility
is provided by total intensity profiles constructed at various heights parallel to the
major axis.
98
2.7. Conclusions
The ballistic model of CBR has been analyzed in more detail. We have found that
while azimuthal velocities decrease gently with increasing z, the corresponding mean
velocities decrease more steeply (particularly at lower radius). This steep gradient
in mean velocity is due to radial outflow of gas in the ballistic model. This result
emphasizes the importance of using caution when interpreting mean velocities in
edge-on or nearly edge-on galaxies. If the radial density profile of radiating gas is
not well understood, the use of mean velocities as indicators of rotation speed can
be highly misleading.
The decrease in azimuthal velocity with height in the ballistic model is, in fact,
shallower than that which has been inferred from the data, suggesting that additional
mechanisms are important. We note here some effects which may be at work in
the halo of NGC 5775. In a picture of a fluid disk in hydrostatic equilibrium, as
described by, e.g., Benjamin (2000), the steeper gradient inferred from the data may
imply pressure declining with radius in the halo, which is not unreasonable to expect.
By considering the baroclinic solutions to stationary hydrodynamics, Barnabè et al.
(2005) were successful in generating a model in agreement with the vertical gradient
in the rotation curve of NGC 891 (Fraternali et al. 2005); it would be interesting to
test whether this method is able to reproduce the gradient measured in this work as
well. A completely different physical picture which must also be considered is that
of gas accretion. Kaufmann et al. (2005) were also able to reproduce the lag in the
halo of NGC 891 with SPH simulations of infalling multiphase gas. Although we
have considered the halo in this actively star forming galaxy to be star formation
driven, the fact that NGC 5775 is interacting with its companion may suggest that
such considerations are relevant here.
We have also compared the structure of Hα and H I emission in PV diagrams
constructed within H I loops previously identified by Irwin (1994). The large Hα
linewidths observed in F1 and F2 suggest that these features are expanding. The
99
Chapter 2. DIG Halo Kinematics in NGC 5775
kinetic energies of the ionized components of F1 and F2 are comparable, but that
of F3 is significantly smaller due to its narrower Hα linewidth. When the energy
requirements estimated from the H I and Hα data are considered together, all three
features have similar energy requirements, equivalent to on the order of 104 supernova
explosions in each case. In F2, the data indicate the presence of an ionized filament,
rooted in the underlying H I loop, and extending to at least z = 10000 = 12 kpc. A
gradient in mean velocity with height is observed in this filament, indicating that
either the azimuthal speed of the gas, or the projection of the azimuthal velocity
vector along the line of sight, is decreasing with height.
100
Chapter 3
DIG Halo Kinematics in NGC 891
3.1
Chapter Overview
We present high and moderate spectral resolution spectroscopy of diffuse ionized gas
(DIG) emission in the halo of NGC 891. The data were obtained with the SparsePak
integral field unit at the WIYN1 Observatory. The wavelength coverage includes
the [N II]λλ 6548, 6583, Hα, and [S II]λλ 6716, 6731 emission lines. Position-velocity
(PV) diagrams, constructed using spectra extracted from four SparsePak pointings
in the halo, are used to examine the kinematics of the DIG. Using two independent
methods, a vertical gradient in azimuthal velocity is found to be present in the
northeast quadrant of the halo, with magnitude approximately 15 − 18 km s−1 kpc−1 ,
in agreement with results from H I observations. The kinematics of the DIG suggest
that this gradient begins at approximately 1 kpc above the midplane. In another
part of the halo, the southeast quadrant, the kinematics are markedly different, and
suggest rotation at about 175 km s−1 , much slower than the disk but with no vertical
1 The
WIYN Observatory is a joint facility of the University of Wisconsin-Madison,
Indiana University, Yale University, and the National Optical Astronomy Observatory.
101
Chapter 3. DIG Halo Kinematics in NGC 891
gradient. We utilize an entirely ballistic model of disk-halo flow in an attempt to
reproduce the kinematics observed in the northeast quadrant. Analysis shows that
the velocity gradient predicted by the ballistic model is far too shallow. Based on
intensity cuts made parallel to the major axis in the ballistic model and an Hα
image of NGC 891 from the literature, we conclude that the DIG halo is much more
centrally concentrated than the model, suggesting that hydrodynamics dominate
over ballistic motion in shaping the density structure of the halo. Velocity dispersion
measurements along the minor axis of NGC 891 seem to indicate a lack of radial
motions in the halo, but the uncertainties do not allow us to set firm limits.
This chapter, with slight modifications, has been accepted for publication in the
Astrophysical Journal.
3.2
Introduction
In recent years, deep observations of external spiral galaxies have led to the realization
that the multiphase nature of the ISM in disks is found in halos as well. Gaseous halos
are found to contain neutral hydrogen (H I; e.g., Irwin 1994; Swaters et al. 1997),
diffuse ionized gas (DIG; e.g., Rand et al. 1990; Dettmar 1990; Rossa & Dettmar
2003a), hot X-ray gas (e.g., Bregman & Pildis 1994; Tüllmann et al. 2006), and dust
(e.g., Howk & Savage 1999; Irwin & Madden 2006). The origin of the multiphase
gaseous halos remains unclear, but the gas is generally considered to be participating
in a star formation-driven disk-halo flow, such as that described by the fountain or
chimney model (Shapiro & Field 1976; Bregman 1980; Norman & Ikeuchi 1989),
being accreted from companions (e.g., van der Hulst & Sancisi 2005), or originating
in a continuous infall (Toft et al. 2002; Kaufmann et al. 2005). Determining which
of these pictures is dominant in halos, and thus gaining a better understanding of
how disks and halos share their resources, will have a significant impact on how we
102
3.2. Introduction
view the evolution of galaxies.
Observations of extraplanar DIG (EDIG) in edge-on systems provide strong lines
of evidence supporting the idea that star formation in the disk is responsible for
the large quantities of gas observed in halos. Filamentary structures, often rooted
in H II regions in the disk, are seen in many halos (e.g., Rand 1996). Additionally,
the total amount of EDIG emission correlates with a measure of the star formation
2
rate per unit area, the surface density of far infrared luminosity (LFIR /D25
, where
D25 is the optical isophotal diameter at the 25th magnitude) (Rand 1996; Miller
& Veilleux 2003a; Rossa & Dettmar 2003a). H I observations have revealed the
presence of vertical motions in some face-on disks (e.g., Kamphuis & Sancisi 1993);
these vertical motions are thought to be indicative of injection of matter into the
halo.
Accretion, on the other hand, is an attractive alternative for the origins of the cold
halo gas, particularly in systems displaying morphological or kinematic lopsidedness,
or obvious signs of interactions (see, e.g., van der Hulst & Sancisi 2005). Increasingly
deep H I observations reveal clear connections between disks and companions, and
suggest important connections between disks and external sources of matter (see
also Sancisi 1999). Continuous infall of halo gas over a galaxy’s lifetime has been
invoked to explain the star formation histories of galaxies and the “G-dwarf problem”
(e.g., Pagel 1997). It is possible that a good understanding of the kinematics of such
extraplanar gas, perhaps by considering the different gas phases in parallel, may help
reveal the importance of all of these processes.
To begin to understand the dynamics of gaseous halos in external spirals, edge-on
galaxies are good targets because confusion between emission from the disk and from
the halo is minimized. A prime target for such studies has been NGC 891, a nearby
edge-on spiral. Early observations by Sancisi & Allen (1979) revealed the presence
of a thick vertical H I distribution. Detailed three-dimensional modeling of deep
103
Chapter 3. DIG Halo Kinematics in NGC 891
Westerbork Synthesis Radio Telescope (WSRT) H I data by Swaters et al. (1997)
indicated that the halo gas lags the disk by about 25 to 100 km s−1 . Even deeper
WSRT observations and more detailed modeling of the kinematics have recently been
performed (Fraternali et al. 2005), showing that a gradient in azimuthal velocity with
height above the midplane (z) exists, with magnitude 15 km s−1 kpc−1 .
For the DIG component of halos, progress has been made only recently in robustly
measuring rotational properties. Early work focused on mean velocities determined
from slit spectra (e.g., Rand 2000; Tüllmann et al. 2000), but because the distribution
of emitting gas along the line of sight contributes to the shape of the line profile (this
is especially important in edge-ons), mean velocities are not indicative of the rotation
speeds. To properly explore the kinematics of DIG halos, high spectral resolution
emission line data in two spatial dimensions are required, and can be obtained with
Fabry-Perot etalons or Integral Field Units (IFUs). This method has been used by
Heald et al. (2006b, hereafter Paper I), who measured a vertical gradient in azimuthal
velocity in the halo of NGC 5775, with magnitude ≈ 8 km s−1 kpc−1 .
The ultimate goal of these kinematic studies is to gain insight into the physics of
the disk-halo interaction and the origin of halo gas. To that end, a handful of simple
but tractable models, representing distinct physical pictures, have been developed
in an attempt to match the observations. Collins et al. (2002) constructed a purely
ballistic model of a galactic fountain. Although the model naturally predicts a vertical gradient in rotational velocity, it is too shallow to match the observations of
NGC 5775 (Paper I). Recently, Fraternali & Binney (2006) also considered a ballistic
model; the velocity gradient produced by their model is too shallow when compared
to the H I kinematic data of NGC 891 presented by Fraternali et al. (2005). Both
of these models treat the material participating in the disk-halo flow as a collection
of non-interacting particles. Physically, this picture is appropriate if the density
contrast between the orbiting clouds and the ambient medium is sufficiently high
104
3.2. Introduction
that the presence of the latter may be neglected. At the other extreme, two distinct
models which treat the halo gas hydrostatically or hydrodynamically have been considered. A hydrostatic model of a rotating gaseous halo (Barnabè et al. 2006) has
been shown to reproduce the H I results of Fraternali et al. (2005). Such a model
corresponds to a quiescent halo with no disk-halo interaction of the type considered
in the ballistic models. The other model is a smoothed particle hydrodynamic simulation but one in which the halo gas has a completely different origin: accretion
during galaxy formation (Kaufmann et al. 2005). This model, too, has been able
to reproduce accurately the observed H I kinematics of the halo of NGC 891. The
models described here cover an extremely broad range of physical possibilities. When
the results are considered together with the observations of gaseous halos described
above, no individual physical model is completely satisfactory. Further observational
and theoretical work will be necessary to help resolve this issue.
Here we present high and moderate resolution IFU observations of EDIG emission
in the halo of NGC 891. Classified as Sb in the Third Reference Catalogue of Bright
Galaxies (RC3; de Vaucouleurs et al. 1991), NGC 891 has a systemic velocity of
528 km s−1 (RC3), and we take the distance to be 9.5 Mpc after van der Kruit &
Searle (1981). At that distance, 1 kpc subtends about 2200 . The surface density of far
2
infrared luminosity (LFIR /D25
) is 3.19 × 1040 erg s−1 kpc−2 (Rossa & Dettmar 2003a),
which is indicative of moderate ongoing star formation via the prescription given by
Kennicutt (1998) for LFIR . The EDIG component has been paid great observational
attention due to NGC 891’s proximity, similarity to our own Milky Way, and edge-on
orientation. The first studies (Rand et al. 1990; Dettmar 1990) made use of narrowband imaging to reveal an extremely prominent DIG halo, extending up to at least
4 kpc above the plane, consisting of vertical filamentary structures superimposed on
a smooth but asymmetric background. Previous ground-based imaging (e.g., Howk
& Savage 2000), high spatial resolution HST imaging (Rossa et al. 2004), and deep
long-slit spectroscopy (e.g., Rand 1997; Otte et al. 2002), have greatly enhanced our
105
Chapter 3. DIG Halo Kinematics in NGC 891
understanding of the distribution and physical conditions of the gas. For a brief
discussion on the current status of how these lines of evidence fold into the larger
picture of gaseous halos, see Dettmar (2005).
A critical parameter for accurate determination of velocities later in the paper
is the inclination angle of NGC 891. Estimates of the inclination include i > 87.5◦
(Sancisi & Allen 1979); i ≥ 88.6◦ (Rupen et al. 1987); and, most recently, i =
89.8 ± 0.5◦ (Kregel & van der Kruit 2005). The last result is based on modeling of
stellar kinematics and dust extinction. The inclination angle is extremely close to
i = 90◦ , and we adopt that value in this paper. Slight deviations from this value will
not significantly alter our results.
This paper is arranged as follows. We describe the observations and the data
reduction steps in §3.3. The halo kinematics are examined in §3.4, and the ballistic
model is compared to these results in §3.5. We conclude the paper in §3.6.
3.3
Observations and Data Reduction
Data were obtained during the nights of 2004 December 10–12 at the WIYN 3.5-m
telescope. The SparsePak IFU (Bershady et al. 2004, 2005) was used in conjunction
with the Bench Spectrograph in two different configurations. For the first two nights,
the echelle (316 lines mm−1 ) grating was used at order 8, which provided a dispersion
0.205 Å pixel−1 and a resolution σinst = 0.38 Å (17 km s−1 at Hα); on the third night
the 816 lines mm−1 grating was used at order 2, yielding a dispersion 0.456 Å pixel−1
and a resolution σinst = 0.81 Å (37 km s−1 at Hα). The grating angles for the two
setups were 62.974◦ and 51.114◦ , respectively. In both setups, the wavelength coverage included the [N II]λλ 6548, 6583, Hα, and [S II]λλ 6716, 6731 emission lines. The
individual pointings of the fiber array are overlaid on an Hα image of NGC 891
(from Rand et al. 1990) in Figure 3.1. An observing log is presented in Table 3.1,
106
3.3. Observations and Data Reduction
Figure 3.1 The SparsePak pointings presented in this paper, overlaid on the Hα image
of Rand et al. (1990). The spectrograph was set up in echelle mode for pointing H
(black circles) and in a lower spectral resolution mode for pointings L1, L2, and L3
(gray circles). “Sky” fibers lying along the major axis are colored white for clarity.
The rotational center of NGC 891 is marked with a white cross. The spatial scale
(assuming D = 9.5 Mpc) is shown in the lower left. Ranges of fibers used to construct
PV diagrams (see text) are marked z1 (2500 < z < 4500 ), z2 (4500 < z < 6500 ),
and z3 (6500 < z < 10500 ). These heights correspond to 1.2 kpc < z < 2.1 kpc,
2.1 kpc < z < 3.0 kpc, and 3.0 kpc < z < 4.8 kpc, respectively.
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Chapter 3. DIG Halo Kinematics in NGC 891
Table 3.1. NGC 891 SparsePak Observing Log
Pointing ID
RAa
Decl.a
Array PA
R0 b
zb
Exp. Timec
rms Noised
(see Fig. 1)
(J2000.0)
(J2000.0)
(◦ )
(00 )
(00 )
(hr)
(erg s−1 cm−2 Å−1 )
H
02 22 42.84
42 22 24.10
−68
−155 to −85
30 to 98 (E)
9.2
8.69(8.06) × 10−18
L1
02 22 38.39
42 20 31.44
−68
−32 to 38
27 to 95 (E)
1.5
6.28(6.15) × 10−18
L2
02 22 27.71
42 21 19.24
+112
−32 to 38
33 to 101 (W)
1.5
6.37(6.12) × 10−18
L3
02 22 33.94
42 18 38.78
−68
91 to 161
23 to 91 (E)
2.5
5.05(4.80) × 10−18
a
R.A. and Decl. of fiber 52 (the central non-“sky” fiber in the SparsePak array) for each pointing.
b
Ranges of R0 and z covered by each pointing of the fiber array. “Sky” fibers are not included in these ranges. R0 is positive
on the south (receding) side. Letters E and W indicate that the pointing is on the east and west side of the disk, respectively. At
D = 9.5 Mpc, 2200 = 1 kpc.
c
Total exposure time, which is the sum of individual exposures of about 30 minutes each.
d
The rms noise was measured in the continuum near the Hα line for each of the 82 fibers in every pointing. The tabulated values
are the mean (median).
and includes the ranges of radii (R0 ) and heights (z) covered by each pointing2 .
The pointings shown in Figure 3.1 were selected based upon the following considerations. First, regions with prominent DIG emission are expected to be physically
interesting since these areas host more active disk-halo flows. Moreover, bright EDIG
is clearly preferable so that high signal-to-noise spectra may be obtained far from the
plane. Because we are interested in the shapes of the velocity profiles, we need higher
signal-to-noise than would be necessary to calculate velocity centroids. The analysis
presented in § 3.4.2 requires spectra at large R0 , where the rotation curve is flat (not
rising), for the reasons described in that section. On the other hand, interesting kinematics may be observed along the minor axis (see § 3.5.3). Ideally, spectra would be
obtained at the highest possible spectral resolution everywhere in the halo, but the
necessary integration times make this prohibitive. Instead, we chose to observe at
high spectral resolution where the DIG is brightest (the northeast quadrant), and at
moderate spectral resolution in other regions of interest. The pointings were placed
2 To
avoid confusion, we use R0 to indicate major axis distance, and R to indicate
galactocentric radius, throughout the paper.
108
3.3. Observations and Data Reduction
close enough to the plane to ensure DIG detection in all fibers, yet far enough to
maximize our leverage on the determination of how rotation speeds vary with height.
It is important to note the details of the EDIG morphology observed at the
locations of the SparsePak pointings (especially H and L3). As noted by both Rand
et al. (1990) and Dettmar (1990), the EDIG emission is fainter in the southern half
of NGC 891, possibly a consequence of a lower star formation rate in the underlying
disk; pointing L3 is located in that region. In the northwest quadrant, Rossa et al.
(2004) detect thin extended filaments and loop structures atop the bright smooth
component. In the northeast quadrant, the EDIG distribution appears to be largely
smooth, with two prominent vertical filaments extending well away from the disk.
We chose to place pointing H at the location of the latter filamentary structure. The
perpendicular slit from Rand (1997) passes through the area covered by pointing H.
With these choices of location for pointings H and L3, we observe regions of differing
EDIG morphology.
Data reduction steps were performed in the usual way using the IRAF3 tasks
CCDPROC and DOHYDRA. Cosmic-ray rejection was accomplished in the raw
spectra with the package L.A.Cosmic (van Dokkum 2001). The wavelength calibration was based on observations of a CuAr comparison lamp which was observed
approximately once every 1.5 hr during the observing run. Spectrophotometric standard stars were observed throughout each night, and were used to perform the flux
calibration. Because the standard stars were only observed with a single fiber, the
flux calibration in other fibers is based on throughput corrections calculated from
flat field exposures. The precision of our spectrophotometry was estimated by inspecting each flux calibrated standard star spectrum, which revealed variations at
the 1% level on the third night, and variations at the 10% level on the first two
3 IRAF
is distributed by the National Optical Astronomy Observatories, which are operated by the Association of Universities for Research in Astronomy, Inc., under cooperative
agreement with the National Science Foundation.
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Chapter 3. DIG Halo Kinematics in NGC 891
nights. These variations result from slight errors in centering the standard stars
on the central fiber, and from atmospheric seeing conditions scattering some of the
starlight into adjacent fibers.
Subtraction of night-sky emission lines proved to be a difficult endeavor. The
large angular size of NGC 891 prevented us from being able to use the dedicated
sky fibers for their intended purpose, so an alternative procedure is needed. Because
the response of the spectrometer to an unresolved emission line changes (slowly)
as a function of fiber (Bershady et al. 2005), the night sky emission line spectrum
cannot be satisfactorily subtracted from the object data by pointing the array at
a patch of blank sky and averaging over all fibers; the changing line shape from
fiber to fiber, intrinsic to the instrument, causes the average to be inappropriate for
subtraction from the individual fibers. As indicated by Bershady et al. (2005), one
might adopt a “beam-switching” observing strategy, but at the cost of doubling the
needed exposure times. A new, effective technique for subtracting sky lines based
solely on the information in the object data has been developed (see §6 of Bershady
et al. 2005), but requires that the object emission be spread over a range of velocities.
Since we observe only the approaching side of NGC 891 with pointing H, for example,
there is not enough variation in the line velocities (as a function of fiber) to use this
method. We were able, however, to use a modified version of this technique for
pointing L3; see below.
We have attempted two alternative methods, not requiring object emission to be
spread over a range of velocities, for removing sky lines which contaminate the line
emission of interest. One method considers the shape of isolated sky lines located
close to (and bracketing) the contaminating line, interpolates the observed line shape,
and multiplies this interpolated sky line template by an appropriate factor (the factor
begins near zero, and increases until negative fluxes result from the subtraction) to
subtract the contaminating sky line. The other fits gaussian profiles to isolated sky
110
3.3. Observations and Data Reduction
lines and interpolates fit parameters to subtract the contaminating sky line (again,
the amplitude, unknown because of blending with the line of interest, is increased
until negative emission results). Both methods worked reasonably well, but left
residuals behind. If we were simply interested in integrated line fluxes, the residuals
would be acceptable. However, we seek information about the shape of the line,
especially in the wings (see §3.4), which may be significantly altered by the sky line.
Therefore, the spectra presented here have been corrected for continuum emission,
but the sky emission lines have in general not been subtracted. We note throughout
the paper where sky lines are present in the spectra. In cases where we present
sky-line subtracted spectra, the sky lines were originally located far enough out on
the wings of the emission line of interest that a gaussian profile could be well fit and
subtracted.
Final spectra were obtained by averaging the individual exposures at each pointing. The rms noise in each fiber was measured at each pointing; the mean and median
of these values over all fibers are included in Table 3.1 (the rms noise in fibers toward
the edges of the CCD is systematically higher than in the center of the chip, where
the system throughput is higher; see Bershady et al. 2005). The final spectra were
used to construct position-velocity (PV) diagrams at the three different heights indicated in Figure 3.1, using the following procedure. The coordinates R0 and z of each
fiber were calculated in the galaxy frame [we take R0 positive on the receding (south)
side]. The corresponding spectrum was then placed into the output PV diagram at
the correct radius. We use radial bins of 4.700 (equal to the fiber diameter) so that
the PV diagrams are largely continuous in R0 . Note that at the largest z (range z3
in Fig. 3.1), more than one fiber occupies each value of R0 ; overlapping spectra were
averaged in this case, increasing the signal-to-noise.
Significant contamination by night sky emission lines has caused us to disregard
the Hα line in pointings H and L3. In the former, the sky line falls on the side
111
Chapter 3. DIG Halo Kinematics in NGC 891
of the profile farthest from the systemic velocity, which is the part of the profile
containing information about the rotation curve (see §3.4.1). In the latter, the sky
line is at the same wavelength as the Hα line. In both cases, we instead consider
the sum of the [N II]λ 6583 and [S II]λ 6716 lines. Note that in pointing L3, an
additional sky line was located on the side of the [N II] profile closest to systemic;
this does not affect our ability to extract rotational information but should be kept
in mind. To remove that line, we utilized the method developed by Bershady et al.
(2005). Because much of the object emission is at roughly the same wavelength, some
oversubtraction occurred. However, we were able to utilize the farthest fiber from
the disk, which received no object flux, to correct for this oversubtraction (which was
the same in all fibers). Careful examination of the resulting subtracted spectra and
the shapes of the subtracted sky lines confirmed that this approach works well for
these observations. Any errors which may have crept into the final spectra will be
mainly present on the side of the line profiles opposite from the critically important
envelope side.
Our use of the forbidden lines [N II] and [S II] in this context deserves some
comment, since the ratios [N II]/Hα and [S II]/Hα are well known in some DIG halos
including NGC 891 to vary beyond what is expected based solely on photoionization.
Wood & Mathis (2004), for example, are able to reproduce most line ratios with
photoionization alone, but additional heating sources (such as shocks) may still be
required. Despite this possibility, the method used in § 3.4.2 in particular should
be largely insensitive to such effects. The assumptions are that we can reproduce
the density structure of the gas reasonably well, and that the kinematics of the gas
are dominated by rotation. If these assumptions are reasonable, it is unlikely that
localized energetic phenomena will significantly affect our results.
112
3.4. Halo Kinematics
3.4
Halo Kinematics
In this section, we seek to extract information about the kinematics of the DIG in
NGC 891 from the final spectra. The nearly edge-on viewing angle imposes the
need to carefully consider the shape of the line profiles, which depend on both gas
density and rotational velocity along the entire line of sight (LOS). We utilize two
independent methods of extracting rotational information: in §3.4.1, we apply the
envelope tracing method (e.g., Sofue & Rubin 2001; Sancisi & Allen 1979) to the
observed line profiles; in §3.4.2, we develop a three-dimensional model of the galaxy
for comparison with the data. Data from pointings H and L3 are considered in
this section, because the radii included are large enough that the rotation curve is
approximately flat. Pointings L1 and L2, which lie along the minor axis, contain
emission from gas at radii where the rotation curve is still rising. As pointed out
by Fraternali et al. (2005), at these small radii changes in the rotation curve and
the density profile cannot be distinguished. Therefore, we cannot robustly extract
rotational information from those spectra. We come back to those pointings later in
the paper.
3.4.1
Envelope Tracing Method
The envelope tracing method works under the assumption of circular rotation. A
LOS crossing through such a disk will intercept gas at many different galactocentric
radii, but at the line of nodes (the line in the plane of the sky where R = R0 ), the
projection of the velocity vector on the LOS is maximized. Thus, the highest velocity
(relative to the systemic velocity, and after a correction for velocity dispersion has
been made) in a velocity profile at R0 is taken to be the value of the rotation curve
at galactocentric radius R = R0 . By following this procedure for every R0 in a
PV diagram, a rotation curve Vrot (R) is built up. The details of our algorithm for
113
Chapter 3. DIG Halo Kinematics in NGC 891
implementing this method are described in Paper I and are not repeated here. We
note, however, the values used for the envelope tracing parameters (refer to eqns.
1 and 2 in Paper I): η = 0.2, Ilc = 3σ (where σ refers to the rms noise), and
2
2
(σinst
+ σgas
)1/2 = 20 km s−1 . The latter quantity, determined empirically during the
modeling process described in § 3.4.2, adds a constant offset to all of the derived
rotation speeds; as long as σgas is approximately constant with z, our determination
of the change in rotation curve with height is insensitive to the adopted value. In
any case, the instrumental broadening dominates for these observations.
The envelope tracing method was applied to the PV diagrams extracted from
pointing H, at each of the three z-heights. The results are shown in Figure 3.2a.
It seems clear from visual inspection that a vertical gradient in rotational velocity
is present. To derive the value of this gradient, two methods were used. First, at
each height, the mean rotational velocity was determined (see Figure 3.2b). A linear
fit to those points revealed a gradient with value dv/dz = 17.5 ± 5.9 km s−1 kpc−1
(throughout this paper, to be consistent with previous studies, we use the symbol
dv/dz to mean the magnitude of the gradient as in eq. 3.1; it actually represents
a negative quantity because the halo is rotating slower than the disk). The best-fit
line is shown in Figure 3.2b. We also calculated a linear fit to the velocities (as a
function of height) at each R, and took the average of the gradients determined at
each radius; that value was dv/dz = 17.6 ± 5.3 km s−1 kpc−1 . The large error bar
reflects the fact that the gradient appears to be somewhat steeper at lower R.
In principle, we could use the linear fits described above, in conjunction with
information about the major axis rotation curve, to constrain the starting height
of the gradient, zcyl . However, our choices of the envelope tracing parameters (in
particular, Ilc ) are somewhat arbitrary, and lead to an uncertainty in the zero-point
scaling of the velocities derived from the method. This issue does not affect our
ability to determine the value of dv/dz, but an error in the zero-point offset would
114
3.4. Halo Kinematics
translate directly to an error in zcyl . In § 3.4.2, we utilize a more powerful method of
examining the halo kinematics, which also leads to more robust constraints on the
value of zcyl than can be provided by the envelope tracing method.
3.4.2
PV Diagram Modeling
In the envelope tracing method, the rotation speed determined within each velocity
profile of a PV diagram lies between the intensity peak of the profile, and the part
of the profile at 3σ (see Sofue & Rubin 2001). One could imagine using the envelope
tracing method on the same velocity profiles but with increased noise values. As
the noise value increases relative to the peak of the profile, the part of the profile
at 3σ moves closer to the profile peak, and the location of the rotation speed will
thus move away from the true rotational velocity and toward the systemic velocity.
Therefore, since the signal-to-noise ratio decreases with increasing z, what we take to
be a rotation velocity gradient in Figure 3.2 could be an artifact of how the envelope
tracing method determines rotation velocities. To check that our result is robust,
we have generated galaxy models in order to analyze the halo kinematics with a
method which takes the noise into account. We begin by generating models intended
to match the data from pointing H only, and later attempt to model the data from
pointing L3 separately.
The galaxy models described in this section are generated with a modified version
of the Groningen Image Processing System (GIPSY; van der Hulst et al. 1992) task
GALMOD. The modifications include the addition of a vertical gradient in rotation
velocity, resulting in rotation speeds of the form

 V (R, z = 0)
for z ≤ zcyl
rot
Vrot (R, z) =
 Vrot (R, z = 0) − dv [z − zcyl ] for z > zcyl
dz
(3.1)
where Vrot (R, z = 0) is the major axis rotation curve, dv/dz is the magnitude of
115
Chapter 3. DIG Halo Kinematics in NGC 891
the vertical gradient in rotation velocity, and zcyl is the height at which the gradient
begins (below that height, the halo rotates cylindrically). To keep the number of free
parameters to a minimum, given our limited information, we assume that dv/dz is
constant with z. This assumption appears to be justified based on the results of the
envelope tracing method (see Figure 3.2b).
The model inputs include the distance, inclination, and systemic velocity of NGC
891 (these are set to the values discussed in § 3.2), as well as the velocity dispersion,
radial density profile, and major axis rotation curve. The best value of the velocity
dispersion was found to be 20 km s−1 (note that this value includes the instrumental
broadening as well as the gas dispersion, and is strictly appropriate only for pointing
H); this determination of the velocity dispersion motivated our use of the same
value in the envelope tracing method (see § 3.4.1). To estimate the radial density
profile, cuts were made through the Hα image of Rand et al. (1990), along slices
parallel to the major axis and at heights corresponding to the heights of the PV
diagrams constructed from the SparsePak data. The GIPSY task RADIAL was used
to produce radial density profiles that would result in these intensity cuts. The
amplitude of the model radial density profiles is set so that the model signal-to-noise
ratio (the artificial observations created by GALMOD include noise) is matched as
well as possible to that in the data. A flat rotation curve was used initially, and the
radial density profile was adjusted until the appearance of the PV diagrams was well
matched. A flat rotation curve was sufficient to obtain an excellent match to the
data, and was therefore used for the remaining modeling (we select Vrot (z = 0) =
230 km s−1 , but this value cannot be uniquely constrained for this method with our
data; see below). The best fit radial density profiles are shown in Figure 3.3. By
specifying a different radial density profile for each height, we hope to match the
true gas distribution at each location with greater success than by assuming that the
shape of the radial density profile is constant with z.
116
3.4. Halo Kinematics
Figure 3.2 Results of applying the envelope tracing method to PV diagrams constructed from the spectra obtained in pointing H (northeast quadrant). (a) Rotational velocities are shown for 1.2 kpc < z < 2.1 kpc (solid circles), 2.1 kpc < z <
3.0 kpc (empty squares), and 3.0 kpc < z < 4.8 kpc (crosses). A major axis rotation
curve determined from H I observations is included for reference (dashed line). (b)
The average rotational velocity at each height is shown for the DIG (empty circles)
and for the H I (for radii included in pointing H; solid squares). Horizontal errors
for the DIG data indicate the range of z covered by the fibers used to construct
the individual PV diagrams; those for the H I data reflect the angular resolution
(3000 = 1.4 kpc). The best-fit solution for the DIG (dv/dz = 17.5 ± 5.9 km s−1 kpc−1 ),
described in the text, is plotted for reference (solid line). The H I data were kindly
provided by F. Fraternali.
117
Chapter 3. DIG Halo Kinematics in NGC 891
The output models take the form of RA-Decl.-vhel data cubes. We have written
a GIPSY script which performs artificial SparsePak observations of the output data
cubes. Specifically, it extracts spectra along sight lines, arranged in the pattern of
the SparsePak fibers on the sky, through the data cube. Thereafter, PV diagrams
are created from the actual SparsePak data and the modeled SparsePak data in the
same way. We proceed by generating a grid of models, constructing difference PV
diagrams, and selecting the models that minimize the absolute mean difference and
rms difference. Using this method, we are able to specify a best-fit value of dv/dz, but
without a direct measurement of the major axis rotation curve, we cannot uniquely
specify zcyl . Instead, we obtain a relationship between the rotation speed at z = 0
and the starting height of the gradient.
Using the procedure described above, an initial exploration of parameter space
suggested dv/dz = 14.9 km s−1 kpc−1 . To constrain the value of zcyl , we consider
the range of major axis rotation speeds allowed by the H I observations (Fraternali
et al. 2005), roughly 220 to 235 km s−1 . Those values correspond to zcyl = 1.6 and
0.6 kpc, respectively. For our adopted value Vrot (z = 0) = 230 km s−1 , we obtain
zcyl = 0.9 kpc. To ensure consistency, another grid of models, differing only in the
value of dv/dz, was generated using the adopted values of Vrot (z = 0) and zcyl ; the
best values of dv/dz were 15.2 km s−1 kpc−1 and 15.4 km s−1 kpc−1 for 2.1 kpc < z <
3.0 kpc and 3.0 kpc < z < 4.8 kpc, respectively.
The models described above are completely azimuthally symmetric. In reality,
NGC 891 is certainly not azimuthally symmetric, due to the presence of spiral arms,
filamentary halo structures, H II regions, and so on. To check that our results are not
biased by a poor specification of the radial density profile, we have also constructed
a grid of models with a completely flat radial density profile (see the lower four
rows of Figure 3.4.2). Although this choice of density profile poorly reproduces the
shape of the data PV diagrams, the best match occurs once again for the model with
118
3.4. Halo Kinematics
dv/dz ≈ 15 km s−1 kpc−1 . This suggests that errors in our best-fit radial density
profiles will not significantly alter the results that we have derived for the halo
kinematics. Put another way, the changes in the PV diagrams as a function of z are
dominated by the decrease in rotational velocity with height.
Although we have presented strong evidence for a vertical gradient in azimuthal
velocity with a magnitude very close to 15 km s−1 kpc−1 , this result is only valid
for the region of the halo of NGC 891 covered by pointing H (in the northeast
quadrant – incidentally, this falls within the same region examined by Fraternali
et al. 2005). Can this result be extended to describe the kinematics elsewhere in
the halo? Unfortunately, we have not obtained high spectral resolution SparsePak
data covering the entire halo of this galaxy, but a lower spectral resolution pointing
(L3) has been obtained in the southeast quadrant. We now attempt to model that
quadrant of NGC 891 to test whether the kinematics are consistent with the results
from pointing H.
A galaxy model appropriate for the region covered by pointing L3 was produced
in the manner described above. Initially, the best-fit model parameters obtained
for pointing H were considered, with the exception that the dispersion velocity was
corrected for the instrumental broadening, and set to 40 km s−1 . In Figure 3.5, we
display a comparison between the data and a model with a constant gradient dv/dz =
15 km s−1 kpc−1 (top panels). Such a model is clearly inadequate to match the data.
Inspection of the PV diagrams shows that the rotation speeds at each height are
not consistent with halo kinematics of the form in equation 3.1. Rather, the data
indicate a halo with a negligible velocity gradient, but with a constant rotation
velocity (∼ 170 − 180 km s−1 ) much slower than that of the underlying disk. In the
bottom panels of Figure 3.5, we compare the data to a model with a constant rotation
speed Vrot (R, z) = 175 km s−1 , and no gradient at all. This second model clearly gives
much better agreement. We conclude that the kinematics in the southeast quadrant
119
Chapter 3. DIG Halo Kinematics in NGC 891
Figure 3.3 Profiles of gas density as a function of galactocentric radius which are
used to generate the models described in the text. Profiles are shown for 1.2 kpc <
z < 2.1 kpc (solid line), 2.1 kpc < z < 3.0 kpc (long-dashed line), and 3.0 kpc <
z < 4.8 kpc (dotted line). Because we seek to match the signal-to-noise ratio in the
model to that in the data, the actual density values are of little importance. Each
profile has been normalized to its peak for presentation.
120
3.5. The Ballistic Model
of NGC 891 are markedly different than those in the northeast quadrant, and are
well described by a constant velocity of approximately 175 km s−1 .
3.5
The Ballistic Model
The physical cause for the vertical gradient in rotation velocity measured in NGC 891
is not well understood. To be sure, two independent models have been shown by other
researchers to predict such a gradient and reproduce its magnitude: a hydrostatic
model (Barnabè et al. 2006) and a hydrodynamic model of gas accretion during
disk formation (Kaufmann et al. 2005). Yet neither model allows for the apparent
connection between star formation activity in the disk and the prominence of gaseous
halos (e.g., Miller & Veilleux 2003a; Rossa & Dettmar 2003a). The evidence seems
to favor a physical situation similar to that described by the fountain model (Shapiro
& Field 1976; Bregman 1980). As a first step toward realizing such a model, we have
developed the “ballistic model” (Paper I; Collins et al. 2002). We note that Fraternali
& Binney (2006) have developed a similar model to ours, and have recovered similar
results.
The ballistic model is described elsewhere; only a brief description will be given
here. The model numerically integrates the orbits of clouds in the galactic potential
of Wolfire et al. (1995). The clouds are initially located in an exponential disk with
a scale length R0 set to match the observations, and are launched into the halo with
an initial vertical velocity randomly selected to be between zero and a maximum
“kick velocity” Vk , which effectively sets the vertical scale height of the halo density
distribution, and can thus be constrained by observations. As the clouds move
upward out of the disk, they feel a weaker gravitational potential and migrate radially
outward; in order to conserve angular momentum, the rotational velocity of the
clouds decreases. The ballistic model therefore naturally produces a vertical gradient
121
Chapter 3. DIG Halo Kinematics in NGC 891
Figure 3.4 Comparison between PV diagrams constructed from the SparsePak data and
from the galaxy models described in §3.4.2. In the left panels (a, c, and e) of each pair of
columns, the data are shown with white contours, and the models are displayed with black
contours. In the right panels (b, d, and f), the difference between data and model is shown.
The leftmost columns (a and b) are for heights 2500 < z < 4500 ; the central columns (c
and d) for 4500 < z < 6500 ; and the rightmost columns (e and f) for 6500 < z < 10500 .
The top four rows include models constructed using the best-fit radial density profiles
shown in Figure 3.3; the bottom four rows include models constructed using flat radial
density profiles. The azimuthal velocity gradient used in the models in each row is listed
on the right edge. From left to right, the contour levels in each column are (a) 10σ to
40σ in increments of 5σ; (b) 3, 5, and 7σ (positive for solid contours, negative for dashed
contours); (c) 5σ to 20σ in increments of 3σ; (d) the same as in (b); (e) 3σ to 12σ in
increments of 1.5σ; and (f) 2, 4, and 6σ (positive for solid contours, negative for dashed
contours). The systemic velocity is 528 km s−1 . |R0 | increases to the north. The angular
size corresponding to 1 kpc is shown in the bottom left panel.
122
3.5. The Ballistic Model
Figure 3.5 Comparison between PV diagrams constructed from pointing L3 (white
contours), and two models: one including a gradient 15 km s−1 kpc−1 as described
in the text (black contours, top panels), and the other including a constant rotation
speed with height Vrot (R, z) = 175 km s−1 (black contours, bottom panels). Contour
levels are (a,d) 10σ to 30σ in increments of 5σ for 2500 < z < 4500 ; (b,e) 5σ to 20σ
in increments of 5σ for 4500 < z < 6500 ; and (c,f) 3σ to 9σ in increments of 3σ for
6500 < z < 10500 . Pointing L3 is on the receding side of the galaxy; the systemic
velocity is 528 km s−1 . R0 increases to the south. The angular size corresponding to
1 kpc is shown in the bottom left panel.
in azimuthal velocity. The specific parameters that form the ballistic “base model”
for NGC 891 (as determined by Collins et al. 2002) are R0 = 7 kpc, Vk = 100 km s−1 ,
and the circular velocity Vc = 230 km s−1 .
3.5.1
Rotation velocity gradient
The individual orbits of clouds in the ballistic model can be directly examined to
explore the predicted variation in rotational velocity with height. We have directly
extracted the average rotation curve at three heights, corresponding to the ranges
of z considered in § 3.4: 1.2 kpc < z < 2.1 kpc; 2.1 kpc < z < 3.0 kpc; and
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Chapter 3. DIG Halo Kinematics in NGC 891
3.0 kpc < z < 4.8 kpc. These rotation curves are shown in Figure 3.6a. Note that
the lack of measured rotational velocities at inner radii is because no clouds at these
radii reach these heights in the model. The evacuated region in the model is roughly
cone-shaped; therefore the range of radii with no measured velocities increases with
height. We come back to the issue of radial redistribution of clouds in § 3.5.2.
Figure 3.6a demonstrates that a vertical gradient in azimuthal velocity is indeed
present in the ballistic model, but the magnitude of the gradient is extremely shallow.
The gradient, averaged over all radii where data are present at all three heights,
is 1.1 ± 0.1 km s−1 kpc−1 . In comparison to the gradient measured in pointing H
(15 − 18 km s−1 kpc−1 ), the ballistic model prediction is too shallow by over an order
of magnitude.
We also consider the effect of counting only clouds which are moving upwards in
the ballistic model, and only clouds which are moving downwards. Physically, these
cases would correspond to a fountain flow in which only the gas leaving (returning
to) the plane is ionized. In the latter case (see Figure 3.6c), the average gradient
is even shallower: 1.0 ± 0.5 km s−1 kpc−1 . Even in the upward-moving case, the
gradient is only 1.7 ± 0.6 km s−1 kpc−1 . Clearly, the ballistic model in its present
form is inadequate to explain the observed kinematics in the halo of NGC 891 at
pointing H. There is little or no gradient above z = 1.2 kpc at pointing L3, but the
large decrease in azimuthal velocity that we conclude occurs between z = 0 and
z = 1.2 kpc is definitely inconsistent with the ballistic model.
3.5.2
Emission profiles
The ballistic model also makes strong predictions regarding the steady-state spatial
distribution of clouds in the halo. In the simulation, a cloud with a fixed initial
vertical velocity will reach higher z when initially placed at larger R, where the
124
3.5. The Ballistic Model
gravitational potential is weaker (see, for example, Fig. 14 in Paper I). Because
clouds in the outer disk orbit higher than clouds in the inner disk, the halo is more
vertically extended at larger R. Note that this behavior manifests itself regardless of
the level of radial migration which may be predicted by the model. When viewed from
an edge-on perspective, a halo with such a density structure would show distinctive
emission profiles parallel to the major axis. Are such profiles actually observed?
Because we are only interested in total Hα intensity as a function of radius, and
to increase the area over which we can make a comparison, we consider radial cuts
through the Hα image from Rand et al. (1990). These intensity cuts are compared
to similar cuts made through a total intensity map generated from the output of the
ballistic model, and are shown in Figure 3.7. We note that we are only interested
in the shape of the intensity cuts, so the absolute values are unimportant. We also
note that in the model, each cloud is assumed to provide equal intensity; therefore,
the expected total intensity scales linearly with the column density of clouds.
Inspection of Figure 3.7 shows a lack of agreement between the data and the
model. Cuts through the ballistic model show a strong central depression which
grows with height. For example, the emission at z = ± 1 kpc peaks in the radial
range R0 . 5 kpc, but at z = ± 3 kpc, the peaks are located at R0 ≈ 15 kpc. In
contrast, the Hα profiles show a general decline in intensity with increasing radius
at all heights. An exception is perhaps seen on the east side of the disk, though the
central depression is not nearly as pronounced as in the model. The data do not seem
to indicate a significant change in the shape of the radial density profile with height.
The behavior of the ballistic model is caused by the weakening of the gravitational
potential with increasing radius; it is therefore unlikely that any realistic mass model
would lead to different results. This large discrepancy indicates a further failure of
the ballistic model. The relatively small variation of the profiles in Figure 3.7 with
z suggests a hydrodynamic effect which regulates the vertical flow.
125
Chapter 3. DIG Halo Kinematics in NGC 891
Figure 3.6 Azimuthal velocities extracted from the ballistic base model, for (a) all
clouds, (b) clouds moving upward (away from the disk), and (c) clouds moving
downward (toward the disk). The rotation curves are averages computed within
1.2 kpc < z < 2.1 kpc (squares), 2.1 kpc < z < 3.0 kpc (plusses), and 3.0 kpc <
z < 4.8 kpc (triangles).
126
3.5. The Ballistic Model
3.5.3
Minor-axis velocity dispersion
Along the minor axis, the rotational velocity vectors should be perpendicular to the
LOS (assuming circular rotation). On the other hand, any radial motions would be
parallel to the LOS, and would thus contribute to the width of the velocity profiles.
We therefore examine the velocity dispersions in pointings L1 and L2 to search for
evidence of radial motions along the LOS. First, we make artificial observations of the
best-fit model from § 3.4.2 (generated with velocity dispersion 40 km s−1 to account
for the lower spectral resolution of these pointings). Velocity widths were calculated
in the same way for the Hα line in these pointings and from artificial observations
of the model. Note that in making this comparison, we assume the axisymmetry of
the best-fit model. The results are shown in Figure 3.8.
It appears that the observed velocity dispersions in the data are roughly consistent with the velocity dispersion in the model. It should be stressed that we have
determined the value of the gas dispersion from pointing H, and have only adjusted
the model inputs to account for a different value of instrumental broadening. At the
lowest heights (2500 < z < 4500 ), the modeled velocity dispersions are slightly higher
than those in the data; it seems unlikely that there are any significant radial motions
at these locations in the halo. Elsewhere, the large uncertainties in the data could
allow for additional radial motions at the level of vrad ≤ 30 km s−1 .
What level of radial motion is predicted by the ballistic model? In Figure 3.9, we
display the average radial motions of individual clouds as a function of radius in the
three height ranges considered here. In the model, radial velocities are higher farther
from the disk, and range from approximately 5 km s−1 to 20 km s−1 at the largest
heights. The data presented in Figure 3.8 may just be consistent with radial motions
of this magnitude. The large uncertainties in the velocity dispersions measured from
the data do not allow us to place stronger constraints on possible radial motions.
127
Chapter 3. DIG Halo Kinematics in NGC 891
Figure 3.7 Intensity profiles along cuts through the ballistic model (black lines) and
the Hα data (white lines). The vertical scale is in units of EM (pc cm−6 ) for the
Hα data and number of clouds (multiplied by a constant for presentation) for the
ballistic model data. The cuts were made parallel to the major axis at heights (a)
z = 3 kpc (to the east of the disk); (b) z = 2 kpc (east); (c) z = 1 kpc (east); (d)
z = 0 kpc; (e) z = 1 kpc (west); (f) z = 2 kpc (west); and (g) z = 3 kpc (west). The
sky coordinate R0 increases to the south.
128
3.5. The Ballistic Model
Observations of the same region with higher spectral resolution (as in pointing H)
would allow us to better understand how radial motions contribute to the minor axis
velocity dispersions.
Note that even hydrostatic models, like those of Barnabè et al. (2006), in general
will require an increasing velocity dispersion as a function of height to preserve
hydromagnetic stability. Hydrostatic models of Boulares & Cox (1990), for example,
predict a velocity dispersion increasing from 30 km s−1 at 1 kpc to 60 km s−1 at 4 kpc.
Our data also provide constraints on this class of models.
3.5.4
Halo potential
In previous papers, it was shown that the exact form of the dark matter halo potential
is of little importance in shaping the orbits of the clouds in the ballistic model.
Here, as an aside, we examine the relative importance of contributions to the total
galactic potential from the disk, bulge, and halo. The vertical and radial components
of the gravitational acceleration are calculated numerically on a grid of R and z,
using gR,i (R, z) = −∂φi (R, z)/∂R and gz,i(R, z) = −∂φi (R, z)/∂z, where the index
i indicates that the disk, halo, and bulge contributions are considered separately.
Finally, the total barycentric gravitational acceleration is calculated: gi(R, z) =
2
2 1/2
(gR,i
+ gz,i
) .
Figure 3.10 shows the regions where the disk, bulge, and halo potentials provide
the maximum contribution to the radial, vertical, and total gravitational acceleration.
Clearly, the halo potential is crucial in driving the dynamics at large radii (which is
why the halo potential is incorporated in the first place) and large heights, but the
disk and/or bulge potentials remain dominant within the R and z through which most
clouds travel (for orbits with initial radii R = 4, 8, 12, and 16 kpc, the maximum
heights reached are approximately z ≈ 1.2, 2.5, 4.5, and 6.5 kpc respectively; see
129
Chapter 3. DIG Halo Kinematics in NGC 891
Figure 3.8 Hα velocity dispersions (open circles) from pointings L1 (a–c) and L2
(d–f), and velocity dispersions measured from the best fit model described in § 3.4.2
(solid lines), which was modified to correct for the instrumental broadening (making
the dispersion in the model 40 km s−1 ). Widths were calculated using PV diagrams
constructed at heights (a,d) 1.2 kpc < z < 2.1 kpc; (b,e) 2.1 kpc < z < 3.0 kpc;
and (c,f) 3.0 kpc < z < 4.8 kpc. Errors on the model line widths are typically about
0.5 − 1 km s−1 . For R0 > +0.9 kpc, the Hα widths should be considered lower limits
due to confusion with a sky line. The exceptionally high data points in (d) are due
to confusion with another, fainter sky line, and should be disregarded.
130
3.6. Conclusions
Figure 3.9 Average radial velocities, as a function of galactocentric radius, predicted
by the ballistic base model. Radial velocities were computed within height ranges
1.2 kpc < z < 2.1 kpc (squares); 2.1 kpc < z < 3.0 kpc (plusses); and 3.0 kpc <
z < 4.8 kpc (triangles). Missing data points at low radius correspond to a lack of
clouds at those locations.
Figure 3 of Collins et al. 2002). At the largest radii and heights, the halo begins to
become the dominant factor, but in general the disk and bulge potentials are most
important. Thus the rotational velocities which we extract from the ballistic model
are rather insensitive to the shape (spherical or flattened) of the dark matter halo.
We note that the same insensitivity to halo shape is also observed in the model of
Fraternali & Binney (2006), who use a different formulation of the galactic potential.
3.6
Conclusions
We have presented SparsePak observations of the gaseous halo of the edge-on NGC
891. Spectra from the individual fibers that make up the SparsePak array were
131
Chapter 3. DIG Halo Kinematics in NGC 891
arranged into PV diagrams, which were then analyzed in two separate ways to investigate the rotation field of the halo gas. First, rotational speeds were directly
extracted from the PV diagrams using the envelope tracing method, revealing a vertical gradient in azimuthal velocity with magnitude 15 km s−1 kpc−1 in the northeast
quadrant. In a completely independent method, a detailed model of the density and
velocity structure in that part of the halo was generated. PV diagrams constructed
from the data and the model were compared (both visually and by consideration of
residual statistics); the results of this method confirmed the presence of a velocity
gradient, with the same magnitude determined via the envelope tracing technique.
The results of this study are of interest with respect to recent observations
of the neutral gas in the halo of NGC 891 (Fraternali et al. 2005).
We have
concluded that a vertical gradient in azimuthal velocity is present, of magnitude
≈ 15 − 18 km s−1 kpc−1 , in the same area studied by that group. This value of the
gradient is the same as has been determined for the H I component (for the northeast
quadrant alone) despite the very different radial distributions of the two components.
Although extinction in the plane prohibits a determination of the major axis
rotation curve from optical emission lines, evidence presented here suggests that
the velocity gradient begins at approximately z = 0.6 − 1.6 kpc. Fraternali et al.
(2005) were unable to distinguish a corotating layer up to z = 1.3 kpc from the
effects of beam smearing. We suggest that a thin corotating layer is the more likely
interpretation.
In the southeast quadrant of the halo, the situation is quite different. Instead of a
linear decline in rotation velocity with height, we find evidence for a constant rotation
velocity (∼ 175 km s−1 ), significantly slower than the disk. Whether this, like the
different EDIG morphology, is a consequence of the lower level of star formation
activity in the southern disk is not yet clear, but the explanation for the discrepancy
may have a significant impact on our understanding of the disk-halo interaction.
132
3.6. Conclusions
The ballistic model of Collins et al. (2002) was unsuccessful in reproducing the
halo kinematics of this galaxy. The velocity gradient in the model, driven mainly
by the radially outward motion of clouds during their orbit through the halo, was
found to be too shallow by more than an order of magnitude. To summarize, the
envelope tracing method indicates dv/dz = 17 − 18 km s−1 kpc−1 for pointing H;
the PV diagram modeling method indicates dv/dz = 15 km s−1 kpc−1 for pointing
H, while in pointing L3 the data suggest a rapid decline in rotation speed with z,
followed by a constant rotation velocity ∼ 175 km s−1 ; in comparison, the ballistic
model predicts a gradient of only about dv/dz = 1 − 2 km s−1 kpc−1 .
Cuts through total intensity maps of the ballistic model and the Hα image of Rand
et al. (1990) were also compared. Because the ballistic model predicts larger vertical
excursions where the galactic potential is weaker, the vertical extent of the halo grows
with increasing radius. This characteristic density structure is not observed in the
data. The velocity widths measured along the minor axis of NGC 891 do not show
evidence for radial motion in the halo, but this result is uncertain.
Taken together, these results emphasize that the ballistic model, in its current
form, is not sufficient to explain the dynamics of gaseous halos. Future models will
need to provide a steeper vertical gradient in rotation velocity, while suppressing the
tendency to produce halos of the “flared” appearance seen in the ballistic model. The
hydrostatic and hydrodynamic models of Barnabè et al. (2006) and Kaufmann et al.
(2005), respectively, have proven successful in reproducing the gradient in NGC 891.
We suggest that the next logical step may be to consider hybrid models consisting
of quasi-ballistic particles orbiting within a (hydrodynamic or hydrostatic) gaseous
halo, interacting with it via a drag force, for example.
The discrepancy between the data and the ballistic model is in the same sense
as the results presented in Paper I for NGC 5775. We note, however, that the
magnitude of the discrepancy is more pronounced in NGC 891 than in NGC 5775
133
Chapter 3. DIG Halo Kinematics in NGC 891
(the ballistic model gradient was too low by only a factor of two in that case; see
Paper I). The morphology of the EDIG in NGC 5775 is more filamentary than in
NGC 891. Although Rossa et al. (2004) observe vertical filamentary structures in the
halo of NGC 891 using high-spatial resolution HST images, and although pointing
H covers two large, well-defined filaments, those features are far less pronounced
relative to the underlying smooth EDIG component than is the case in NGC 5775.
The differences in EDIG morphologies in NGC 5775 and NGC 891 may suggest that
the disk-halo interaction in the former galaxy is closer to a pure galactic fountain,
and thus the dynamics are more closely reproduced with ballistic motion. At present,
we can only speculate on this possible relationship between the appearance of the
halo gas and its dynamical evolution. It is also essential to recognize that NGC
5775 is experiencing an interaction with its companion NGC 5774, while NGC 891
appears to be far more isolated. Therefore, the differences in halo kinematics might
alternatively be attributed to different levels of gas accretion. More observations of
edge-ons are required to understand the relative importance of these effects. In a
forthcoming paper, we present SparsePak observations of NGC 4302, completing a
study of halo kinematics in a small sample of edge-ons with morphologically distinct
EDIG emission. NGC 4302, which has the smoothest EDIG of the three galaxies,
should have kinematics most different from the predictions of the ballistic model,
if the appropriate class of disk-halo model is suggested by the appearance of the
extraplanar gas. We note that NGC 4302 has a companion, NGC 4298; its possible
interactions with that galaxy may also be an important factor.
134
3.6. Conclusions
Figure 3.10 Depictions of the regions in the ballistic model within which the disk,
bulge, and halo potentials contribute the most to the (a) radial component of the
gravitational acceleration; (b) the vertical component of the gravitational acceleration; and (c) the total gravitational acceleration.
135
Chapter 3. DIG Halo Kinematics in NGC 891
136
Chapter 4
DIG Halo Kinematics in NGC
4302
4.1
Chapter Overview
We present moderate resolution spectroscopy of extraplanar diffuse ionized gas (EDIG)
emission in the edge-on spiral galaxy NGC 4302. The spectra were obtained with
the SparsePak integral field unit (IFU) at the WIYN1 Observatory. The wavelength
coverage of the observations covers the [N II] λ 6548, 6583, Hα, and [S II] λ 6716, 6731
emission lines. The spatial coverage of the IFU covers the entirety of the EDIG
emission noted in previous imaging studies of this galaxy. The spectra are used
to construct position-velocity (PV) diagrams at several ranges of heights above the
midplane. Azimuthal velocities are directly extracted from the PV diagrams using
the envelope tracing method, and indicate an extremely steep dropoff in rotational
velocity with increasing height (with magnitude ≈ 30 km s−1 kpc−1 ). We have also
1 The
WIYN Observatory is a joint facility of the University of Wisconsin-Madison,
Indiana University, Yale University, and the National Optical Astronomy Observatory.
137
Chapter 4. DIG Halo Kinematics in NGC 4302
performed artificial observations of galaxy models in an attempt to match the PV
diagrams. The results of a statistical analysis favor a gradient of ≈ 30 km s−1 kpc−1 ,
but a visual inspection indicates that a lower gradient of ≈ 15 km s−1 kpc−1 is also
plausible. Our conclusion is that the bulk of the evidence points to a gradient of
≈ 30 km s−1 kpc−1 , but that a somewhat lower value is possible.
We compare these results with an entirely ballistic model of disk-halo flow, and
find a strong dichotomy between the observed kinematics and those predicted by the
model. The disagreement is worse than has been found for other galaxies in previous
studies; we speculate that this may be due to the relatively low rate of current star
formation in the disk. Finally, we compare intensity cuts parallel to the major axis,
extracted from both the ballistic model output and an Hα image of NGC 4302. The
radial intensity profiles from the data are steeper in the halo than in the disk, but
the opposite is true in the ballistic model. The effect observed in the Hα image could
be due to extinction, but it would appear that the signature of the large-scale radial
outflow predicted by the ballistic model is not observed in the data.
The conclusions of this paper are compared to results from two other galaxies,
NGC 5775 and NGC 891, and possible trends are discussed. First, the magnitude
of the discrepancy between the measured gradients in rotation speed, and the predictions of the ballistic model, may be related to the morphology of the extraplanar
gas. Second, the measured gradient may itself be related to the degree of filamentary
structure and scale height of the EDIG, as well as the level of star formation in the
underlying disk. Further observations will be required to validate these trends.
4.2
Introduction
Gaseous halos are potentially excellent laboratories for the study of important aspects
of spiral galaxy evolution. External, and some internal, processes have a significant
138
4.2. Introduction
extraplanar nature. Interactions between the galaxy and its surrounding intracluster medium (e.g., Vollmer et al. 2001), intergalactic medium (such as primordial
accretion; e.g., Oort 1970), and/or neighboring galaxies (e.g., Moore et al. 1998),
can obviously have effects outside of the disk. Internal processes, too, can have an
impact on the environment beyond the star forming disk, such as galactic winds
(e.g., Martin 2003; Veilleux et al. 2005), and somewhat milder events such as those
described by fountain (Shapiro & Field 1976; Bregman 1980) or chimney (Norman &
Ikeuchi 1989) models. High velocity clouds (HVCs; Wakker & van Woerden 1997),
whether they are internal or external in origin, may have a direct impact on the star
formation history of the galaxy, in addition to potentially redistributing material in
the disk and halo. An understanding of all these processes and their effects on galaxy
evolution requires an understanding of the properties of the material surrounding the
disk.
Gas has been found in the halos of many spiral galaxies in the form of neutral hydrogen (e.g., Swaters et al. 1997; Matthews & Wood 2003; Fraternali et al. 2005), hot
X-ray gas (e.g., Bregman & Pildis 1994; Strickland et al. 2004; Tüllmann et al. 2006),
and diffuse ionized gas (DIG) (e.g., Rand et al. 1990; Dettmar 1990; Rand 1996; Rossa
& Dettmar 2003a; Miller & Veilleux 2003a). Together with extraplanar dust (e.g.,
Howk & Savage 1999; Irwin & Madden 2006) and star formation (Tüllmann et al.
2003), these observations paint a picture of a multiphase ISM extending well above
the star forming disk. The origin and evolution of this extraplanar ISM are not
yet clear, but two alternatives are generally considered. First, the gas could have
been accreted from the IGM (e.g., Oort 1970), or from companion galaxies (e.g., van
der Hulst & Sancisi 2005). Alternatively, the gas could be participating in a star
formation-driven disk-halo flow, such as the one described by the fountain model.
Lines of evidence which link the morphological and energetic properties of the extraplanar DIG (EDIG) to the level of star formation activity in the underlying disk
(see, for example, Rand 1996; Hoopes et al. 1999; Rossa & Dettmar 2003a) would
139
Chapter 4. DIG Halo Kinematics in NGC 4302
seem to support the latter idea, but clear examples of the former (see the examples
in van der Hulst & Sancisi 2005) are observed. It is not yet clear how important the
accretion process may be in more normal systems. To shed light on this question,
additional evidence may be gained by studying the motion of the halo gas.
The kinematics of extraplanar gas have been investigated by several groups in
recent years. The H I halos of several galaxies have been found to rotate more
slowly than the underlying disk: NGC 5775 (Lee et al. 2001), NGC 2403 (Fraternali
et al. 2001), NGC 891 (Swaters et al. 1997; Fraternali et al. 2005), and possibly the
low surface brightness galaxy UGC 7321 (Matthews & Wood 2003). Early studies of extraplanar rotation in the optical (e.g., Rand 2000; Tüllmann et al. 2000;
Miller & Veilleux 2003b) were limited by the long-slit spectra, in the sense that the
one-dimensional observations did not allow for disentanglement of the density and
velocity information encoded in the line profiles. Recent work (Heald et al. 2006b,a,
hereafter Papers I and II respectively) has benefited greatly from the ready availability of integral field units (IFUs), which allow spectra to be obtained simultaneously
over a two-dimensional portion of the sky. With these observations, the effects of
density and velocity can be decoupled. In Paper I, TAURUS-II Fabry-Perot observations were used to establish that the EDIG in NGC 5775 has a gradient in rotational
velocity with height above the midplane (z) of ≈ 8 km s−1 kpc−1 ; in Paper II, analysis
of SparsePak observations of NGC 891 showed a gradient of ≈ 15 km s−1 kpc−1 in
the NE quadrant of the halo. The latter result agrees with H I results reported by
Fraternali et al. (2005).
To begin to assess whether the extraplanar gas has an internal origin, the kinematics of the EDIG in both NGC 5775 and NGC 891 have been compared to the
results of a ballistic model (developed by Collins et al. 2002) of disk-halo flow. Both
galaxies are observed to have a steeper rotational velocity gradient than predicted
by the ballistic model (note, too, that the discrepancy described by Fraternali &
140
4.2. Introduction
Binney 2006, for the neutral halo of NGC 891 is in the same sense). The difference
between observations and model is greater for NGC 891, which has a less filamentary
EDIG morphology than NGC 5775. Any statements about whether these pieces of
evidence are causally related are obviously still speculative, but it seems plausible to
guess that halos with a more filamentary appearance are better described by models
of ballistic motion. In this paper, we address the EDIG kinematics of a third edge-on
spiral galaxy with well-studied extraplanar gas, NGC 4302.
NGC 4302 is classified as Sc in the Third Reference Catalogue of Bright Galaxies
(RC3; de Vaucouleurs et al. 1991), but this classification is somewhat uncertain
because the galaxy is very nearly edge-on. A bar is likely to be present; see, for
example, Lütticke et al. (2000). NGC 4302 is a member of the Virgo Cluster, and
has a nearby companion, NGC 4298, with some signs of an interaction (see, e.g.,
Koopmann & Kenney 2004, and discussion in § 4.4). In this paper we assume
a distance to NGC 4302 of D = 16.8 Mpc, after Tully (1988). To estimate the
inclination angle, we closely examined the Two Micron All Sky Survey (2MASS;
Skrutskie et al. 2006) J, H, and Ks images of NGC 4302, all of which show a
clearly defined dust lane. Based on the apparent offset of the dust lane from the
major axis, we estimate an inclination angle i ≈ 89◦ , and adopt that value for the
remainder of the paper. Small deviations from this value will not significantly alter
the results of our paper. The dust lane is very pronounced in the optical bands, and
individual features are observed far from the midplane (up to ≈ 1.5 kpc; see Howk &
Savage 1999). The possible effects of dust extinction are discussed where appropriate
throughout the paper.
The EDIG morphology of NGC 4302 is smoother than that of both NGC 5775
and NGC 891. It has been observed as a part of several EDIG imaging surveys
(e.g., Pildis et al. 1994; Rand 1996; Rossa & Dettmar 2000). Taken together, the
survey images demonstrate an extremely faint, smooth EDIG layer reaching up to
141
Chapter 4. DIG Halo Kinematics in NGC 4302
z ≈ 2 kpc, and with an apparently sharp radial cutoff at R0 ≈ 4 kpc2 . A single faint
plume, extending to z ≈ −0.73 kpc (we take z < 0 on the east side of the disk),
near the nucleus of the galaxy was first reported by Pildis et al. (1994), and later
confirmed by Rossa & Dettmar (2000). We are not aware of any other distinct EDIG
features (in contrast to the extraplanar dust extinction, which has a quite intricate
filamentary appearance). We note that although the extended dust distribution can
significantly alter the appearance of the Hα emission, as Howk & Savage (2000) point
out in their investigation of NGC 891, we consider it unlikely that the dust extinction
in NGC 4302 has significantly altered the appearance of the EDIG.
This paper is arranged as follows. We describe the observations and the data
reduction steps in §4.3. The halo kinematics are examined in §4.4, and the ballistic
model is compared to the results in §4.5. We conclude the paper in §4.6.
4.3
Observations and Data Reduction
We used the SparsePak fiber array (Bershady et al. 2004, 2005) to observe NGC 4302
during the nights of 2004 March 16-17 at the WIYN 3.5-m telescope. SparsePak’s
82 fibers fed the Bench Spectrograph, which was set up with the 860 lines mm−1
grating at order 2. This setup yielded a dispersion of 0.462 Å pixel−1 and a spectral
resolution σinst = 0.84 Å (39 km s−1 at Hα). The wavelength range covered the [N II]
λλ6548, 6583, Hα, and [S II] λλ6716, 6731 emission lines. In Figure 4.1, the two
pointings are shown overlaid on the Hα image of NGC 4302 from Rand (1996). An
observing log is presented in Table 4.1.
The pointings were chosen to cover the brightest EDIG emission in the galaxy.
The layer reported by Rand (1996), defined by |z| ≤ 2 kpc and |R0 | ≤ 4 kpc was
2 To
avoid confusion, we use R to represent galactocentric radii, and R0 for major axis
distance, throughout the paper.
142
4.3. Observations and Data Reduction
Table 4.1. NGC 4302 SparsePak Observing Log
(see Fig. 1)
(J2000.0)
(J2000.0)
(◦ )
(00 )
(00 )
(hr)
rms Noised
(erg s−1 cm−2 Å−1 )
N
12 21 43.10
14 36 29.64
89
−72 to − 3
−43 to + 24
6.3
3.37 (3.26) × 10−18
S
12 21 43.10
14 35 15.96
89
+2 to + 71
−42 to + 26
6.8
3.22 (3.05) × 10−18
Pointing ID
RAa
Decl.a
Array PA
R0b
z 0b
Exp. Timec
a
R.A. and Decl. of fiber 52 (the central non-“sky” fiber in the SparsePak array) for each pointing.
b
Ranges of R0 and z 0 covered by each pointing of the fiber array. “Sky” fibers are not included in these ranges. R0 is positive on
the south (receding) side, and z 0 is positive to the west. At D = 16.8 Mpc, 1200 = 1 kpc.
c
Total exposure time, which is the sum of individual exposures of about 30 minutes each.
d
The rms noise was measured in the continuum near the Hα line for each of the 82 fibers in every pointing. The tabulated values
are the mean (median).
143
Chapter 4. DIG Halo Kinematics in NGC 4302
within the coverage obtained with our two pointings (see Table 4.1). The spectrograph setup described above allowed us to detect the EDIG, which is quite faint. A
higher resolution setup (as was used by Heald et al. 2006a, to observe the brighter
EDIG in NGC 891) would have yielded significantly improved velocity resolution,
but would also have greatly lengthened the exposure times necessary to obtain useful signal-to-noise ratios in the velocity profiles at the same heights that we consider
here.
The initial data reduction steps were performed in the normal way using the
IRAF3 tasks CCDPROC (for bias corrections) and DOHYDRA. This second task
performs the flat field correction, and calibrates the wavelength scale using observations of a CuAr lamp, which were obtained approximately once per hour during the
observing run. DOHYDRA also does a rough fiber throughput correction using flat
field observations, and finally extracts the spectra. At this point, the relative aperture throughput has been corrected, but the absolute correction remains unknown.
Before determining the flux calibration using observations of a spectrophotometric
standard star, light which fell outside the central fiber because of atmospheric blurring of the point spread function or imperfect centering of the star on the fiber must
be accounted for. To correct for these effects, Bershady et al. (2005) have empirically determined the appropriate gain corrections (see their Appendix C4) based on
measurements of the amount of starlight in the central fiber and the six surrounding
fibers (which sample the wings of the standard star’s point spread function). We
have measured the amount of spillover for each of our spectrophotometric standard
observations (obtained approximately once per hour throughout the run), applied
the appropriate gain correction, and completed the flux calibration using the IRAF
task CALIBRATE.
3 IRAF
is distributed by the National Optical Astronomy Observatories, which are operated by the Association of Universities for Research in Astronomy, Inc., under cooperative
agreement with the National Science Foundation.
144
4.3. Observations and Data Reduction
Once the spectra were fully reduced, the continuum and skyline emission were
subtracted in the following way. First, short segments of the spectra, containing
object emission lines, were clipped out. These segments were chosen to be short
enough that the continuum is well defined and can be removed with a linear fit.
Next, sky lines were subtracted using our implementation of the “iterative clipping”
method described by Bershady et al. (2005, their Appendix D). This method is
intended for observations wherein the object emission is Doppler-shifted to widely
varying wavelengths in the different fibers. In that way, sky lines (which vary little
from fiber to fiber) may be readily distinguished from object emission and subtracted
out. Because of the locations of our pointings (one on the receding side and the
other on the approaching side), the object emission in our data is not distributed
widely in wavelength space. Thus, application of this sky subtraction method leads
to some oversubtraction of object emission. In the region including Hα and [N II]
emission, the oversubtraction was minimal; in the region including the [S II] lines,
the oversubtraction was more severe. We have corrected for this oversubtraction by
subsequently subtracting the average of the spectra from fibers farthest from the
midplane of NGC 4302 (fibers 6, 17, 19, 36, 38, 39, and 57), which did not receive
any object flux. This has the effect of adding the oversubtracted galaxy emission line
flux back into the spectra. The technique seems to work well for these observations.
We tested for the possibility that line shapes were significantly affected by the skyline
subtraction by comparing Hα, [N II], and [S II] profile shapes in each fiber (because
sky lines fall on different parts of the object emission line profiles, the line shapes
should be affected in different ways for each emission line). This analysis did not
reveal any systematic line shape errors. Following the sky subtraction, any residual
continuum emission was subtracted from the spectra.
In § 4.4, we will analyze position-velocity (PV) diagrams constructed from the
spectra. The PV diagrams were constructed by calculating the position, in the galaxy
frame, of each fiber, and sorting the spectra into the appropriate ranges of R0 and
145
Chapter 4. DIG Halo Kinematics in NGC 4302
z. Each PV diagram contains spectra from a different range of z. We choose the
separation of pixels in the R0 axis to match the fiber diameter, thus maximizing
the continuity of the diagrams. Note that when multiple spectra occupy the same
location in a PV diagram, the average is used.
Because the EDIG in NGC 4302 is faint, with a small scaleheight (≈ 550−700 pc;
Collins & Rand 2001), the number of independent PV diagrams that can be generated
is small. We were able to detect EDIG in PV diagrams created for each of the
following ranges of z: −2000 < z < −500 (−1.6 kpc < z < −0.4 kpc at D =
16.8 Mpc); the major axis −500 < z < 500 (−0.4 kpc < z < 0.4 kpc); 500 < z < 2000
(0.4 kpc < z < 1.6 kpc); 2000 < z < 3000 (1.6 kpc < z < 2.4 kpc). We constructed
PV diagrams separately for the Hα line and the sum of the [N II]λ6583 and [S II]λ6716
lines (the sum is used to increase signal-to-noise in the spectra). Note that if there
were any line shape errors induced by the sky subtraction algorithm, they should
appear as systematic differences between the results from each type of PV diagram.
No such differences are observed.
4.4
Halo Kinematics
In this section, we analyze the PV diagrams constructed from the SparsePak spectra
in an attempt to characterize the kinematics of the EDIG in NGC 4302. First, the
envelope tracing method (Sancisi & Allen 1979; Sofue & Rubin 2001) is used to
directly extract rotation curves from the PV diagrams. We also present comparisons
between the data PV diagrams and artificial model galaxy observations.
146
4.4. Halo Kinematics
4.4.1
Envelope Tracing Method
For an edge-on galaxy such as NGC 4302, care must be taken when deriving rotation
speeds, for the reasons described by, e.g., Kregel & van der Kruit (2004). Briefly,
a line of sight (LOS) through an edge-on disk crosses many orbits. Each orbit
has a different velocity projection onto the LOS, and thus contributes differently
to the total emission line profile. In the case of circular orbits, only one of those
projections is maximal: the orbit that is intercepted by the LOS at the line of nodes
(i.e., the line along which R = R0 ). Therefore, only that contribution to the line
profile directly provides information about the rotation speed. The envelope tracing
method uses PV diagrams to extract that information and build up rotation curves,
under the assumption of circular orbits. To be more specific, the rotation velocity
Vrot (R) is found by determining the observed radial velocity furthest from systemic
in the velocity profile at each R0 (after corrections for the velocity dispersion of the
material, and the velocity resolution of the instrument). We consider the results of
the envelope tracing method to be valid only at radii where the rotation curve is
approximately flat. At inner radii, where the derived rotation curve is still rising, a
rising rotation curve cannot be distinguished from a changing radial density profile
(see also Fraternali et al. 2005).
The details of the envelope tracing algorithm are described elsewhere, and are
not repeated here. For the interested reader, we use the following values of the
parameters described in Paper I (see eqns. 1 and 2 in that paper): η = 0.2, Ilc = 3σ
q
−1
2 + σ2
(where σ refers to the rms noise), and σgas
instr = 40 km s , where σgas is the
velocity dispersion of the DIG. With the last value, we assume that σinstr = 39 km s−1
dominates over the dispersion in the DIG. If this assumption is incorrect, all of the
derived rotation speeds will be incorrect by an additive constant, but the derived
gradient will be unchanged. The value used here was determined during the method
described in § 4.4.2, where it is better constrained.
147
Chapter 4. DIG Halo Kinematics in NGC 4302
Because dust extinction in the disk may prevent the velocity profiles from including information from the line of nodes, we have also calculated a major axis
rotation curve from H I observations of NGC 4302 (Chung et al. 2005). The H I
observations were obtained with the VLA in C configuration; the beam size is
1700 × 1600 (1.4 kpc × 1.3 kpc) at a position angle −59◦ , and the velocity resolu-
tion is σinstr = 10.4 km s−1 . A major axis cut was extracted from the data cube and
kindly provided to us by J. Kenney; we used the resulting PV diagram to obtain an
H I rotation curve using the envelope method. Note that the H I rotation curve was
also used to verify the systemic velocity, under the assumption that the receding and
approaching sides have the same rotation speed (≈ 175 km s−1 ). The best value of
the systemic velocity was confirmed to be 1150 km s−1 .
In Figure 4.2, we compare the rotation curve derived from the H I data to the
one derived from the optical emission lines. Note that the radial extent of the H I
disk is much greater than the SparsePak coverage. The optical rotation curve shows
a great deal more scatter, as can be expected since the H I beam is much larger than
the angular size of a SparsePak fiber. Still, the magnitude of the rotation curves
appears to be approximately the same. Extinction may explain some of the scatter
in the optical rotation curve, and the apparently slower rotation speeds derived from
the optical lines at R & 5 kpc on the approaching (north) side of the disk. There
are no other obvious signs that extinction may be systematically altering the optical
rotation curves.
Having verified the value of the systemic velocity, and having found no evidence
for significant extinction errors in the derivation of the rotation speeds, we next
utilize PV diagrams constructed on the east and west sides of the disk to search for
a change in rotation speed with height above the midplane. This quantity will be
estimated in two ways: (1) by calculating the change in average rotation speed with
height (dVaz /dz); and (2) by considering the average change in rotation speed with
148
4.4. Halo Kinematics
height, as determined at each radius individually (dVaz /dz). In order to maintain
consistency with previous papers, and to agree with Equation 4.1 in its written form,
we adopt the convention that dV /dz > 0 for rotation speed decreasing with increasing
height.
For the west side of the galaxy, azimuthal velocity curves were derived for PV
diagrams constructed from spectra at 500 < z < 2000 and 2000 < z < 3000 , and are
shown in Figure 4.3. A decrease in rotation speed with increasing height is apparent
in the figure, though there is a large amount of scatter owing to the faint EDIG
emission (recall that the scale height, 0.55 − 0.7 kpc, is considerably less than the
positions of the highest fibers, 1.6 kpc < z < 2.4 kpc), and perhaps some localized
extinction. We nevertheless attempt to quantify the decrease in rotation speed with
height, for the approximately flat part of the rotation curves. By determining the
mean azimuthal velocity at each height for R ≥ 25 − 3000 ≈ 2 kpc (see Figure 4.3),
and fitting a linear relation to a plot of Vaz -vs.-z, we have obtained values of dVaz /dz,
which are listed in Table 4.2. We have also tabulated the gradients implied by the
change in mean rotation speed from the midplane to the range 0.4 kpc < z <
1.6 kpc, and from 0.4 kpc < z < 1.6 kpc to 1.6 kpc < z < 2.4 kpc. The values of
dVaz /dz (described above) are also listed.
We note that if extinction is preventing us from observing emission from the
line of nodes, and therefore not truly measuring the azimuthal velocities, then our
measured gradients will be lower limits. The effects of extinction should diminish
with increasing height, meaning that the line of sight probes farther into the disk as
distance from the midplane increases. In a cylindrically rotating halo, such an effect
would lead to an apparent rise in rotation speed with height. Regardless, comparison
with the H I rotation curve indicated that extinction is not significantly affecting the
derived rotation speeds.
On the east side of the disk, we are unable to trace the EDIG as far from the
149
Chapter 4. DIG Halo Kinematics in NGC 4302
Table 4.2. Summary of dV /dz Values for the West Side, using Envelope Tracing
Method
PV Diagram
[dVaz /dz]fit
[dVaz /dz]0,1
[dVaz /dz]1,2
[dVaz /dz]0,1
[dVaz /dz]1,2
(1)
(2)
(3)
(4)
(5)
(6)
App., Hα
27
45
13
31
20
App., [N II]λ 6583 + [S II]λ 6716
35
32
39
51
27
Rec., Hα
34
34
33
31
38
Rec., [N II]λ 6583 + [S II]λ 6716
39
28
60
31
50
Note. — (1) PV diagrams were constructed from fibers on the approaching (App.) or receding (Rec.) side, using
either the Hα line or the sum [N II]λ 6583 + [S II]λ 6716.
(2) Gradient determined from a linear fit to the average azimuthal velocity at all three heights (−0.4 kpc < z <
0.4 kpc, 0.4 kpc < z < 1.6 kpc, 1.6 kpc < z < 2.4 kpc).
(3) Gradient determined from only the average azimuthal velocities at −0.4 kpc < z < 0.4 kpc and 0.4 kpc < z <
1.6 kpc.
(4) Gradient determined from only the average azimuthal velocities at 0.4 kpc < z < 1.6 kpc and 1.6 kpc < z <
2.4 kpc.
(5) Gradient determined by averaging the variations in azimuthal velocity from −0.4 kpc < z < 0.4 kpc to 0.4 kpc <
z < 1.6 kpc at each radius.
(6) Gradient determined by averaging the variations in azimuthal velocity from 0.4 kpc < z < 1.6 kpc to 1.6 kpc <
z < 2.4 kpc at each radius.
plane as on the west side. We are able to recover azimuthal velocities in the range
−2000 < z < −500 (−1.6 kpc < z < −0.4 kpc), but no higher. Because of the
possibility that a gradient, if present, does not begin at z = 0, we hesitate to draw
conclusions from the absolute difference between azimuthal velocities in the midplane
and in the range −2000 < z < −500 . Instead, we compare the azimuthal velocities to
the east of the disk to those on the west side, to check whether the rotation appears
to be consistent on both sides.
In Figure 4.4, we compare the azimuthal velocity curves. Average azimuthal
velocities for the approximately flat part of the rotation curves have also been calculated. The plot demonstrates very little difference between the rotation of EDIG on
150
4.4. Halo Kinematics
the east and west sides of the halo at the same absolute distance from the midplane,
indicating that the west side (the side facing its companion, NGC 4298) does not
have significantly different kinematics than the opposite side. This does not rule out
a connection to a possible tidal interaction, but there is no evidence that the halo
on one side of the disk is reacting differently than the other.
4.4.2
PV Diagram Modeling
The envelope tracing method is sensitive to the signal-to-noise ratio of the line profiles
under consideration, and therefore the apparent gradient found above could be in
part due to the falling signal-to-noise ratio with increasing height. In order to test for
this possibility, and to ensure that the density profile of the gas is properly accounted
for, we utilize another, independent method to derive the kinematics of the EDIG in
NGC 4302. This method is based on constructing model galaxies with signal-to-noise
ratios matched to the data at each z, performing artificial SparsePak observations of
the models, and comparing modeled PV diagrams to the data.
To generate the galaxy models, we use a modified version of the Groningen Image
Processing SYstem (GIPSY; van der Hulst et al. 1992) task GALMOD. GALMOD
builds galaxies from a series of concentric rings. The properties of the rings are
specified by: the radial density profile of emitting material; the major axis rotation
curve; the velocity dispersion of the emitting material; the exponential scale height;
and the viewing angle of the galaxy. Each parameter is allowed to vary from ring to
ring, but with the exception of the radial density profile we force all parameters to be
constant with radius. Note especially that by allowing the viewing angle to vary with
radius, a warp can be built into the disk. The signature of a warp could be confused
with a changing rotation speed with height (see, e.g., Swaters et al. 1997), but we
assume that the star forming disk is not warped. Discretization noise is included in
151
Chapter 4. DIG Halo Kinematics in NGC 4302
the model.
Our modification of the task allows for a linear variation in the rotation speed
with increasing height, of the form


Vrot (R, z = 0)
Vrot (R, z) =

Vrot (R, z = 0) −
for z ≤ zcyl
dV
dz
(4.1)
[z − zcyl ] for z > zcyl
where Vrot (R, z = 0) is the major axis rotation curve, dV /dz is the magnitude of
the linear gradient (note that dV /dz is positive for a declining rotation speed with
increasing height), and zcyl is the height at which the gradient begins. In general, we
allow zcyl to take nonzero values, but the present observations do not allow us to set
any constraints on the value of this parameter, and we choose to leave it set to zero
for the remainder of the modeling. The vertical scale height of the EDIG in NGC
4302 has been measured by Collins & Rand (2001) to be 0.55−0.7 kpc; for the models
described here, the value 0.65 kpc was found to work well. The signal-to-noise ratio
was matched to the data by adjusting the magnitude of the density distribution at
the midplane.
The output of GALMOD is an artificial data cube. The noise is measured from
the difference of two models constructed by varying only the random number seed.
We have written a script which performs artificial SparsePak observations of the
output data cubes, by extracting spectra in the pattern that the SparsePak fibers
project onto the sky. Once the artificial observations have been made, the spectra
are handled exactly like the data. The size of pixels along the velocity axis in the
model is, by construction, the same as in the data, and the velocity resolution is set
to be the same as in the data. In both the data and the model, PV diagrams are
constructed separately for the approaching and receding sides of the disk and then
joined together, except where noted.
To search for the best model for NGC 4302, we first attempted to estimate the
152
4.4. Halo Kinematics
radial density profile using the same technique employed in Papers I and II. In those
investigations, the GIPSY task RADIAL was used to generate radial density profiles
by considering intensity cuts in Hα images parallel to the major axis. Using the Hα
image of NGC 4302 from Rand (1996), we followed this procedure, but the radial
density profiles returned by the task were characterized by alternating empty and
bright rings, which we took to be unphysical. Indeed, models created using these
radial density profiles did not match the data very well.
On the other hand, models created using pure exponential disks (scale length
7 kpc), while unable to match some of the localized, small-scale features, were overall quite successful in matching the data. In retrospect, this result is expected because the EDIG distribution is extremely smooth and featureless (see, e.g., Rossa
& Dettmar 2000). We therefore use the pure exponential radial density profile to
generate our best-fit model. We also use a flat rotation curve (175 km s−1 based on
the rotation curves derived from the H I data; see Figure 4.2), and a total velocity
dispersion of 40 km s−1 (as in the envelope tracing method).
Next, a sequence of models which vary only in their value of dV /dz was generated. PV diagrams were constructed from the models as described above, for the
same ranges of z used to make the data PV diagrams. Difference PV diagrams are
inspected, and the value of dV /dz that minimizes the reduced chi-square (χ2ν ), and
the value that minimizes the mean difference between data and model, are chosen to
define the best model for that particular data PV diagram. The results are presented
in the first six rows of Table 4.3. Note that for the z-range 0.4 kpc < z < 1.6 kpc
(both in Hα and [N II]λ 6583 + [S II]λ 6716), clumpy structures in the data could not
be fit well by an axisymmetric model. We therefore mask the three radii containing
the largest deviations from axisymmetry in the PV diagrams.
The results of this analysis cluster around a gradient of approximately 30 km s−1
kpc−1 , as did the envelope tracing analysis. There is a hint that the gradient is
153
Chapter 4. DIG Halo Kinematics in NGC 4302
a bit higher than 30 km s−1 kpc−1 . To demonstrate the quality of the PV diagram
matching, we present overlays in Figures 4.5 and 4.7, for the west and east sides,
respectively. An example of the variation in χ2ν with the parameter dv/dz is demonstrated in Figure 4.6, for the range 1.6 kpc < z < 2.4 kpc, and using the sum
[N II]λ 6583 + [S II]λ 6716.
Visual inspection of the overlay plots confirms that a vertical gradient in azimuthal velocity of magnitude 30 km s−1 kpc−1 provides the best match to the data,
but in some cases the model with dV /dz = 15 km s−1 kpc−1 is also a good match.
The conclusion from this analysis supports the result of the envelope tracing method,
but there is some uncertainty in the exact value.
Because this technique relies on the model density profile being reasonably accurate to match the data, we test for the possibility that our adopted exponential disk
model is biasing the results. To do this, we repeat the procedure described above,
but using a flat radial density profile. This density profile does not match the data
as well as the exponential disk, but we were able to analyze the statistics in the same
way as before. The results are shown in the lower rows of Table 4.3. Despite a large
scatter due presumably to the poor match between data and model, and an apparent
tendency for the best fit gradient to be somewhat lower than in the exponential disk
models, these results are still consistent with dV /dz = 30 km s−1 kpc−1 .
4.5
The Ballistic Model
The physical explanation for the vertical decrease in azimuthal velocity observed in
NGC 4302, and other galaxies recently studied, is not yet understood. One possible
scenario is described by the fountain model, which postulates that hot gas is lifted up
into the halo by star formation activity in the disk. This hot gas would then cool and
condense into clouds which move through the halo, and eventually rain back down
154
4.5. The Ballistic Model
onto the disk. As a first step toward understanding the dynamics implied by such a
picture, a fully ballistic model of disk-halo cycling has been developed independently
by two groups (Collins et al. 2002; Fraternali & Binney 2006). Models such as these,
which consider the motion of non-interacting point masses in a gravitational potential, will be appropriate in cases where the density of the cycling clouds is sufficiently
greater than that of the surrounding medium, so that their motion is essentially unperturbed by hydrodynamics. Whether the relative importance of hydrodynamics
is indicated by an observable parameter, such as the morphology of the EDIG, is
unknown, but it seems plausible that filamentary halo structures may imply a more
ballistic disk-halo flow than smooth diffuse extraplanar gas layers. We return to this
possibility in § 4.6.
We have utilized the ballistic model of Collins et al. (2002) in an attempt to
model as closely as possible the kinematics of NGC 4302. The model numerically
integrates the orbits of ballistic gas clouds in the galactic potential described by
Wolfire et al. (1995). The clouds are initially placed in an exponential disk, and are
launched vertically with an initial velocity randomly chosen to be between zero and
a maximum “kick velocity,” Vk . As the clouds move upward and experience a weaker
gravitational acceleration, they move radially outward. In order to conserve angular
momentum, their azimuthal velocity drops as they move outward. Thus, a gradient
in rotation speed is naturally included in the model. Together with the circular speed
of the disk (Vc , which effectively sets the strength of the galactic potential), the kick
velocity is the most critical parameter in setting the bulk kinematics of the clouds,
as well as the scale height of the resulting steady-state halo of clouds (this latter
observable sets a strong constraint on the chosen value of Vk ; see below). The clouds
are assumed to have constant temperature, density, and size (and therefore equal Hα
intensities); hence emission intensity is proportional to cloud column density along
any line of sight. The interested reader should refer to Collins et al. (2002) for a
more complete description of the model.
155
Chapter 4. DIG Halo Kinematics in NGC 4302
We set the scale length of the exponential disk to half the measured radius of the
Hα disk (≈ 14000 from the Hα image in Figure 4.1): Rsc = 7 kpc. The circular speed
is directly measured from the H I rotation curve in Figure 4.2: Vc = 175 km s−1 .
The kick velocity is chosen so that the scale height of the model output is close
to the measured scale height of the actual galaxy (550 − 700 pc; Collins & Rand
2001): Vk = 60 km s−1 . The model is run until the system reaches steady state (after
≈ 1 Gyr). The model outputs are the position and velocity of each cloud; these
positions and velocities can then be used to generate an artificial data cube.
The azimuthal velocities of the individual gas clouds can be directly extracted
from the outputs of the ballistic model, and used to generate rotation curves. To
compare the predictions of the ballistic model to the kinematics of the EDIG in NGC
4302, we have extracted rotation curves, using cloud velocities in the same height
ranges considered in our analysis of the SparsePak data: z < 0.4 kpc, 0.4 kpc < z <
1.6 kpc, and 1.6 kpc < z < 2.4 kpc. The results are shown in Figure 4.8. Note that
we have extracted rotation curves for upward-moving and downward-moving (relative
to the disk) clouds separately, in addition to considering all clouds together. The
first condition would be appropriate if the clouds leave the disk as warm, ionized
gas, but then cool and return as neutral gas. The second condition corresponds to
a picture where the clouds leave the disk as hot gas, and return to the disk as warm
ionized gas. Which of these options is more physical is not yet known.
Inspection of Figure 4.8 reveals immediately that the decrease in rotation velocity with height in the ballistic model is extremely shallow. The gradient, calculated in the radial range considered during the data analysis described in § 4.4.1,
is approximately 1.1 km s−1 kpc−1 for upward-moving clouds, 1.2 km s−1 kpc−1 for
downward-moving clouds, and 1.0 km s−1 kpc−1 for all clouds considered together.
These gradients were calculated using only clouds in the vertical ranges z < 0.4 kpc
and 0.4 kpc < z < 1.6 kpc, because radial redistribution in the ballistic model leads
156
4.5. The Ballistic Model
Figure 4.1 The two pointings of SparsePak, overlaid on the Hα image of NGC 4302
from Rand (1996). The labels N and S indicate the IDs used for each pointing. The
horizontal bar in the bottom left corner indicates the spatial scale at the adopted
distance D = 16.8 Mpc.
157
Chapter 4. DIG Halo Kinematics in NGC 4302
Figure 4.2 Comparison of major axis rotation curves derived from the H I (solid line:
approaching side; dashed line: receding side), Hα (filled squares: approaching side;
open squares: receding side), and [N II]λ 6583 + [S II]λ 6716 (filled circles: approaching side; open circles: receding side) major axis PV diagrams.
158
4.5. The Ballistic Model
Figure 4.3 Plots of azimuthal velocity curves, determined at each height, on the west
side of the disk. The PV diagrams used to obtain these velocities were constructed
from fibers at −0.4 kpc < z < 0.4 kpc (filled squares), 0.4 kpc < z < 1.6 kpc (open
circles), and 1.6 kpc < z < 2.4 kpc (crosses). The open, dashed, and dotted lines
respectively indicate the average azimuthal speed determined for each height, as described in the text. Azimuthal velocities were derived separately for the approaching
side of the disk (left panels) and the receding side of the disk (right panels), using the
Hα line alone (top panels) and the sum [N II]λ 6583 + [S II]λ 6716 (bottom panels).
159
Chapter 4. DIG Halo Kinematics in NGC 4302
Figure 4.4 Comparison of azimuthal velocities, as derived from PV diagrams constructed using spectra from the ranges −1.6 kpc < z < −0.4 kpc (east; filled
squares), and 0.4 kpc < z < 1.6 kpc (west; open circles). Average azimuthal velocities for R & 2 kpc are plotted as solid and dashed lines for the east and west z-ranges,
respectively. Azimuthal velocities were derived separately for the approaching side
of the disk (left panels) and the receding side of the disk (right panels), using the
Hα line alone (top panels) and the sum [N II]λ 6583 + [S II]λ 6716 (bottom panels).
160
4.5. The Ballistic Model
Table 4.3. Summary of Determinations of dV /dz using PV Diagram Modeling
Method
PV Diagram
Emission line(s)
Disk model
[dVaz /dz]χ2
[dVaz /dz]mean
(1)
(2)
(3)
(4)
(5)
−1.6 kpc < z < −0.4 kpc
Hαa
Exp
36
31
−1.6 kpc < z < −0.4 kpc
NSa
Exp
37
36
0.4 kpc < z < 1.6 kpc
Hα
Exp
28
36
0.4 kpc < z < 1.6 kpc
NS
Exp
31
31
1.6 kpc < z < 2.4 kpc
Hα
Exp
27
22
1.6 kpc < z < 2.4 kpc
NS
Exp
33
34
−1.6 kpc < z < −0.4 kpc
Hαa
Flat
23
34
−1.6 kpc < z < −0.4 kpc
NSa
Flat
23
15
0.4 kpc < z < 1.6 kpc
Hα
Flat
22
38
0.4 kpc < z < 1.6 kpc
NS
Flat
18
18
1.6 kpc < z < 2.4 kpc
Hα
Flat
12
10
1.6 kpc < z < 2.4 kpc
NS
Flat
26
26
ν
Note. — (1) PV diagrams were constructed from fibers on both the approaching and receding side unless otherwise
noted, in the listed ranges of z.
(2) The data PV diagrams were constructed using either the Hα line or the sum [N II]λ 6583 + [S II]λ 6716 (marked
‘NS’ here).
(3) The model PV diagrams were constructed using either an exponential or flat disk, as described in the text.
(4) Gradient determined by minimizing the χ2ν between data and model PV diagrams.
(5) Gradient determined by minimizing the mean difference between data and model PV diagrams.
a In
the range −1.6 kpc < z < −0.4 kpc, the spectra on the southern (receding) side were not able to be recreated
with a realistic density profile, and are therefore not used for this analysis.
161
Chapter 4. DIG Halo Kinematics in NGC 4302
Figure 4.5 Comparisons between PV diagrams constructed from the data (white
contours) and the galaxy models described in the text (black contours). The data
PV diagrams were constructed from the Hα line (first and third rows) and the sum
[N II]λ 6583 + [S II]λ 6716 (second and fourth rows), at the height ranges 500 < z <
2000 (top pair of rows) and 2000 < z < 3000 (bottom pair of rows). The models were
constructed using the base parameters described in the text, but different values
of the gradient: dV /dz = 15 km s−1 kpc−1 (first column), dV /dz = 30 km s−1 kpc−1
(middle column), and dV /dz = 45 km s−1 kpc−1 (third column). Contour levels for
both data and model are 10σ to 80σ in increments of 17.5σ (first row), 10σ to 90σ
in increments of 20σ (second row), 2σ to 8σ in increments of 2σ (third row), and 3σ
to 12σ in increments of 3σ (fourth row), where σ refers to the rms noise. Positive R0
is to the south. The systemic velocity is 1150 km s−1 .
162
4.5. The Ballistic Model
Figure 4.6 Variation in the χ2ν statistic with the parameter dv/dz, for the PV diagram
constructed from [N II]λ 6583 + [S II]λ 6716 at 1.6 kpc < z < 2.4 kpc. The minimum
χ2ν occurred for dV /dz = 33 km s−1 kpc−1 , as shown in Table 4.3.
163
Chapter 4. DIG Halo Kinematics in NGC 4302
Figure 4.7 Comparison between PV diagrams constructed from the data (white contours) and the galaxy models described in the text (black contours). The data PV
diagrams were constructed from the sum [N II]λ 6583 + [S II]λ 6716, at the height
range −2000 < z < −500 . The models were constructed using the base parameters
described in the text, but different values of the gradient: dV /dz = 15 km s−1 kpc−1
(left), dV /dz = 30 km s−1 kpc−1 (middle), and dV /dz = 45 km s−1 kpc−1 (right).
Contour levels for both data and model are 5σ to 35σ in increments of 6σ, where σ
refers to the rms noise. North is to the left. The systemic velocity is 1150 km s−1 .
164
4.5. The Ballistic Model
to a lack of clouds in the range 1.6 kpc < z < 2.4 kpc for R . 10 kpc, which is a
larger radial range than is covered by the SparsePak data. We return to the issue of
radial redistribution later.
The gradient in the ballistic model is far less than the value gleaned from the
data, ≈ 30 km s−1 kpc−1 . Recall that the value of the gradient in the ballistic model is
driven mainly by the value of the ratio of parameters Vk /Vc ; in the case of NGC 4302,
our best model (selected by matching the resulting exponential scale height to the
data) is characterized by Vk /Vc = 60/175 = 0.34. In order to attain a gradient with a
higher magnitude, we might consider raising the value of the maximum kick velocity.
However, a model with a kick velocity of 150 km s−1 (Vk /Vc = 150/175 = 0.86),
while producing a gradient of up to ≈ 8 km s−1 kpc−1 , also generates a galaxy with
a vertical scale height of ≈ 31 kpc. Clearly, increasing the kick velocity will never
allow the ballistic model to match both the vertical gradient in azimuthal velocity
measured in the data, while simultaneously matching the scale height of the EDIG
layer.
We also note that there is a great deal of flexibility in choosing the shape of
the halo potential, without drastically affecting the kinematics of the clouds in this
model. The reason for this, as illustrated in Paper II, is that the region in which the
halo potential dominates the gravitational acceleration experienced by the clouds
is outside of the area typically populated by the orbiting clouds. Hence, realistic
changes to the halo potential will not dramatically change the orbital speeds of the
ballistic particles.
The plots in Figure 4.8 are missing some data points in the range 1.6 kpc < z <
2.4 kpc because of a large amount of radial redistribution predicted by the ballistic
model. But is the amount of radial redistribution predicted by the model borne out
by the data? In Figure 4.9, we present intensity cuts through the Hα image, as well
as a moment-0 map generated from the ballistic model output. The cuts are along
165
Chapter 4. DIG Halo Kinematics in NGC 4302
the major axis and at two heights parallel to the major axis.
Comparison of the intensity cuts shows that while the distribution of clouds in the
model at heights 0.4 kpc < z < 1.6 kpc is relatively flat, the intensity distribution
in the data is much steeper. In the Hα disk, the scale length of the intensity cut is
approximately 7 − 8 kpc; in the range 0.4 kpc < z < 1.6 kpc, the scale length has
dropped to about 2 − 5 kpc, depending on location. Meanwhile, the scale length of
the ballistic model intensity cuts are ≈ 5 kpc in the disk, and about 10 − 20 kpc for
0.4 kpc < z < 1.6 kpc. This shows that the outward radial migration in the ballistic
model is excessive. The scale length of the radial intensity cuts could artificially
appear to decrease with height in the data if extinction obscures emission from the
central regions preferentially at lower z, but we consider this explanation unlikely.
4.6
Conclusions
We have presented SparsePak observations of the EDIG emission in NGC 4302.
By creating PV diagrams from the spectra, using both the Hα line and the sum
[N II]λ 6583 + [S II]λ 6716 individually, we extracted rotation curves at and above the
midplane with the envelope tracing method, and used those azimuthal velocities to
quantify the decrease in rotation speed with increasing height. The magnitude of the
gradient appears to be approximately 30 km s−1 kpc−1 , though there is a good deal
of scatter (approximately 10 km s−1 kpc−1 ).
As an alternative method for determining the variation in rotation speed with
height above the disk, we have generated galaxy models constructed using different
vertical gradients in azimuthal velocity, with signal-to-noise ratios match to the data
at each range of z considered. Artificial observations of these models were used to
construct PV diagrams, which were then compared to the data. Overall, the data
tended to favor a gradient consistent with the envelope tracing results, dV /dz ≈
166
4.6. Conclusions
Figure 4.8 Plots of azimuthal velocities extracted from the ballistic model. Rotation
curves were created for clouds in the range z < 0.4 kpc (filled squares), 0.4 kpc <
z < 1.6 kpc (open circles), and 1.6 kpc < z < 2.4 kpc (crosses). Separate rotation
curves were extracted for (a) upward-moving clouds, (b) downward-moving clouds,
and (c) all clouds.
167
Chapter 4. DIG Halo Kinematics in NGC 4302
Table 4.4. Summary of Galaxy Parameters
Galaxy
[dV /dz]obs
[dV /dz]BM
EDIG Scale
( km s−1 kpc−1 )
( km s−1 kpc−1 )
Height (kpc)a
8c
4c
NGC 5775
2
LFIR /D25
EDIG
(1040 erg s−1 kpc−2 )b
Morphologyb
2.1 − 2.2
8.1
Many bright filaments
NGC 891
15
1 − 2d
1
2.2
Bright diffuse + filaments
NGC 4302
30e
1e
0.55 − 0.7
< 2.3f
d
a
From Collins & Rand (2001).
b
From Rand (1996).
Faint diffuse
c From Paper I.
d
e
From Paper II.
This work.
f NGC 4302 and its companion, NGC 4298, are not well resolved from each other in the IRAS survey, from which the values of L
FIR
are derived.
30 km s−1 kpc−1 , but somewhat lower values are also possible.
The ballistic model of Collins et al. (2002) was used to test the idea that the EDIG
in NGC 4302 is taking part in a star formation-driven disk-halo flow. In the ballistic
model, a radial outflow of clouds leads naturally to a decline in rotation speed with
height. We extracted rotation curves directly from the output of the model, and
comparison with the data revealed that the predicted gradient is far too shallow. It
is possible to obtain higher values of the gradient by increasing the kick velocity, but
this leads to extremely an large vertical scale height in the cloud distribution which
is not observed in the data.
The ballistic model has an additional problem in reproducing the observations.
Because the clouds migrate radially outward, the cloud distribution rapidly flattens
with increasing height, when viewed from an edge-on perspective. There is no evidence in the Hα image of Rand (1996) to suggest that this radial redistribution is
taking place.
Now that the ballistic model has been applied to a small sample of spirals with
168
4.6. Conclusions
known, differing gradients in rotation speed, it may be appropriate to begin to look
for patterns in order to guide future observations. We have summarized some important parameters of the galaxies in Table 4.4. It is clearly too early to make any
strong inferences from this collection of data, but a few trends, if they hold up to
future observational results, are intriguing. The tendency for the observed velocity
gradient to diverge from the ballistic model predictions as the EDIG morphology
becomes smoother and less filamentary may be an indication that smoother halos
are intrinsically less governed by ballistic motion. It may also be suggestive that the
velocity gradient is seen to decrease as the filamentary appearance of the halo, the
EDIG scale height, and the level of star formation activity in the disk each increase.
A larger sample of galaxies with varying EDIG morphologies, star formation rates,
and observed rotation velocity gradients may be able to refine this picture.
169
Chapter 4. DIG Halo Kinematics in NGC 4302
Figure 4.9 Plots of intensity cuts parallel to the major axis in the the Hα image
(white lines) and the ballistic model (black lines). Profiles are plotted for ranges (a)
−1.6 kpc < z < −0.4 kpc, (b) −0.4 kpc < z < 0.4 kpc, and (c) 0.4 kpc < z <
1.6 kpc.
170
Chapter 5
Future Work
The results presented in this thesis suggest several avenues for future research. Here,
I describe three projects motivated by this thesis.
5.1
Exploring the Cause of the Velocity Gradient
Taken together, the results from Chapters 2 – 4 suggest two individual trends that
relate the kinematics of the gaseous halos to other observables (see the discussion in
§ 4.6). First, the discrepancy between the observed vertical gradients in rotational
velocity and the corresponding predictions of the ballistic model thus far demonstrate
a relationship to the morphology of the EDIG. As the EDIG becomes less filamentary
in appearance and becomes more smoothly distributed, the ballistic model tends to
more closely match the observed kinematics.
The other trend is demonstrated in Table 4.4. The observed vertical gradient
in rotational velocity appears to be related to other properties of the EDIG, in the
following way. As the velocity gradient increases, the scale height is observed to
be smaller, and the EDIG morphology gets less filamentary and more smooth in
171
Chapter 5. Future Work
appearance. The star formation rate, traced by the surface density of far infrared
luminosity, also seems to decrease as the velocity gradient increases.
These trends can be explained in terms of a picture where both star formation
driven disk-halo flows and accretion take place in normal galaxies. In this picture,
disks with a higher star formation rate produce stronger fountain flows, and thus
larger EDIG scale heights and more filamentary halo appearance. The kinematics of
such halos might be expected to be closer to ballistic motion. On the other hand,
galaxies with lower star formation rate have less prominent, smoother halos. The
kinematics of these gaseous halos are less dominated by fountain-type flows, and
more dominated by the process of accretion of low angular-momentum material. If
this low angular momentum gas quickly spins up as it nears the disk, it would yield
a steeper velocity gradient.
The picture just described has very little observational support. In order to determine whether these trends are real, the kinematics of gaseous halos in galaxies
with widely varying star formation rates and EDIG morphologies must be determined. Either conclusion would have interesting consequences: if the trends hold
true, then the kinematics of halos are related to the disk star formation rate; if not,
the kinematics of halos are unrelated to the disk star formation rate. Additional
work is needed to answer this question.
It should be noted that additional theoretical modeling of the disk-halo interface
will be required to determine the physics necessary for matching the variation in
velocity gradient described in this thesis. For example, the effect of hydrodynamics
on this evolving picture is still unclear, but is expected to be important.
172
5.2. Putting Extraplanar DIG in a Cosmological Perspective
5.2
Putting Extraplanar DIG in a Cosmological
Perspective
Another interesting question is how the correlation between the disk star formation
rate and the scale height of EDIG emission (e.g., Rossa & Dettmar 2003a) evolves
with redshift. The average star formation rate appears to have decreased by about
an order of magnitude since z ∼ 1 (e.g., Madau et al. 1998). The importance of
star formation driven disk-halo flows in shaping gaseous halos may be illuminated
by testing whether the scale height of EDIG in galaxies beyond the local Universe
changes to maintain the current correlation.
Spectra of QSOs reveal absorption lines (primarily Mg II and C IV) which are
associated with galaxies intercepted along the line of sight (e.g., Steidel et al. 1994).
Although the census of absorbing galaxies is far from complete, a relationship has
emerged between the luminosity of the absorbing galaxy and the maximum impact
parameter for which absorbing gas is detected, indicating that intermediate redshift
galaxies are embedded in extended gaseous envelopes. Detecting extraplanar gas in
emission, and relating its properties to those of the underlying galaxy and the gas
detected in absorption, may help to clarify the nature of these gaseous envelopes by
providing an observational bridge between the galaxy and the absorbing gas.
To investigate this issue, the redshifted [O II] λ3727 emission line, which is relatively bright in nearby EDIG layers, should be observed in galaxies associated with
Mg II absorption lines in QSO spectra. At intermediate redshifts (0.2 < z < 1), the
[O II] line will be redshifted to ≈ 4500 − 7500Å, making it accessible to optical spectrometers. For example, FLAMES/GIRAFFE at the VLT is an excellent choice for
performing deep spectroscopic observations of a sample of QSO absorption-selected
galaxies. The [O II] emission line has already been observed in the disk components
of some intermediate redshift galaxies (e.g., Steidel et al. 2002); following detection of
173
Chapter 5. Future Work
halo emission, the vertical extent of this gas can be studied as in the nearby galaxies.
Observations of emitting halo gas at moderate spectral resolution will provide
extremely interesting information regarding the kinematics of the gaseous envelope.
Kinematics of the absorbing gas have already been inferred from the QSO spectra,
and have been compared with rotation curves of the associated (edge-on spiral)
galaxies (e.g., Steidel et al. 2002; Ellison et al. 2003). These observations indicate that
the kinematics of the gaseous envelopes are dominated by rotation, and suggest the
presence of extremely thick rotating layers, and/or a variation in rotation velocities
with height above the disk, as is observed in nearby galaxies (e.g., Heald et al. 2006b).
With information about the rotation of the emitting halo gas, the observational gap
between the kinematics of the disk and those inferred from the QSO absorption lines
will be narrowed. The additional data provided by such a project would allow more
detailed modeling of the galaxy-halo system, placing the kinematics of the absorbing
gas in a more complete picture.
5.3
Testing the Galactic Fountain Model
Theoretical models have had moderate success in reproducing observational results of
gaseous halo kinematics. Although hydrostatic models of extraplanar gas (Barnabè
et al. 2006) and models of “quiet” gas accretion (Kaufmann et al. 2005) are able
to correctly reproduce the observed vertical gradient in rotational velocity in one
system (NGC 891), the morphologies of extraplanar gas layers seem to be explained
more naturally with a galactic fountain picture (except in cases where minor merger
activity is apparent). The observed vertical filamentary structures in edge-ons are
reminiscent of the chimney model (Norman & Ikeuchi 1989), while the correlation
between diffuse ionized gas halo prominence and the level of star formation in the disk
(e.g., Rossa & Dettmar 2003a) suggests that the presence of extraplanar gas is closely
174
5.3. Testing the Galactic Fountain Model
related to conditions in the disk. However, as shown in this thesis, while a galactic
fountain can provide the correct qualitative behavior, the modeled vertical gradient
in rotational velocity is too shallow. At present, the situation remains unresolved.
To date, studies of gaseous halos have focused on actively star forming galaxies. In order to determine the importance of disk star formation in creating and
maintaining gaseous halos, galaxies with little ongoing star formation must also be
considered. This approach has already begun with two edge-on “super-thin” low
surface brightness (LSB) galaxies (see Matthews 2005). An H I halo has been discovered in one (UGC 7321; Matthews & Wood 2003); the authors state that formation
of massive stars in the disk provides sufficient energy to support the halo, but that
the possibility of slow accretion cannot not be excluded. To clarify this picture, the
lessons learned through the successful studies of bright galaxies should be applied to
observations of LSB galaxies by choosing a sample of targets viewed with a range of
inclination angles. In this way, additional velocity components of the halo gas may
be sampled (see below).
This strategy should be employed by observing a small sample of LSB galaxies
with the Westerbork Synthesis Radio Telescope (WSRT). In selecting galaxies for
inclusion in the sample, three parameters are of interest. First, the inclination angles
to be included are (1) face-on, to search for vertical (perpendicular to the disk)
motions, which are indicative of star formation driven outflows; (2) intermediate
(i ∼ 60◦ ), to search for radial (parallel to the disk) motions; and (3) edge-on, to
investigate the vertical profile of H I emission, and to test for a decrease in rotational
velocity with height in the halo. Second, the galaxies should be nearby (D . 10
Mpc) in order to resolve localized features (this is particularly important for the
face-on target). Finally, the selected galaxies should have low disk star formation
rates. Based on these selection criteria, a preliminary sample might consist of the
galaxies listed in Table 5.1.
175
Chapter 5. Future Work
Table 5.1. Tentative LSB Sample for WSRT Observations
Galaxy
UGC 7007a
UGC 7874a
UGC 290b
a
Inclination
Distance
SFR
(degrees)
(Mpc)
(M yr−1 )
∼ 25◦
9.4
6 × 10−3
64◦
3.0
83◦
5.3
9 × 10−3
7 × 10−4
UGC 7007 and UGC 7874 were selected from James et al. (2004), based on the
data tabulated here.
b
UGC 290 was selected from Matthews et al. (2005), based on the data tabulated
here.
Observations of vertical motions are of further interest in testing the idea that
at least some of the H I holes observed in face-on galaxies are the equivalents of
chimney-like structures seen in edge-ons, and therefore potential sites of injection of
gas into the halo. In NGC 6946, Boomsma et al. (2005) find a large quantity of H I
with velocities significantly different (> 50 km s−1 ) than local rotation speeds, and
suggest that in the inner star forming disk, these velocities are indicative of vertical
motions. A question that naturally follows is whether vertical motions are present
in the ionized component as well. Such vertical motions would be apparent as either
broad velocity wings and/or distinct high-velocity components of the Hα and [N II]
emission line profiles. It is expected that the locations of H I holes may indicate the
most likely locations to find such features.
To address this question, the locations of H I holes in the disks of face-on spirals
should be observed with optical spectroscopy. Echelle spectra at the locations of six
176
5.3. Testing the Galactic Fountain Model
H I holes in M101 have been obtained using the Kitt Peak 4-m telescope, and will
be used to search for ionized outflows. Additional galaxies, such as M83 (which is a
nearby face-on that has been well-studied in H I, making it an excellent candidate)
can be observed in the optical using, for example, UVES at the VLT. With the high
spectral resolution provided by this spectrograph, high-velocity components (greater
than ∼ 50 km s−1 relative to local rotation speeds, as suggested by H I observations)
of the optical emission lines, if present, should be readily distinguished from the local
disk (H II region) line profiles.
Detection of high-velocity ionized gas at the locations of H I holes would not only
lend support to the picture of H I holes being the signature of chimneys in face-on
disks, but would provide critical constraints to galactic fountain models. At present,
the initial vertical velocity at outflow locations in the models can only be constrained
by matching the modeled and observed vertical scale height of gas emission (e.g.,
Collins et al. 2002). Observations of actual outflow speeds will provide an essential
check against the speeds required to match the models to observation. Moreover,
the integration of the high-velocity emission line components will provide estimates
of the total gas mass being injected into the halo at individual locations.
177
Chapter 5. Future Work
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