Kinematics of globular clusters in NGC 1407:
constraining the galaxy mass and its dark
matter halo
A.J. Cenarro1 , M.A. Beasley1 , J. Strader2 , J.P. Brodie2 and D.A. Forbes3
1
2
3
Instituto de Astrofı́sica de Canarias, Vı́a Láctea s/n, E-38200, La Laguna, Spain
cenarro@iac.es
Lick Observatory, University of California, CA 95064, USA
Centre for Astrophysics & Supercomputing, Swinburne University, Hawthorn
VIC 3122, Australia
Summary. NGC 1407 is a massive elliptical galaxy (E0) dominating the Eridanus
group of galaxies. Radial velocities for a sample of 20 globular clusters in this galaxy
have been derived from high-quality, Keck/LRIS spectroscopic data, and used to
constrain both the galaxy mass and the dark matter content of the galaxy group halo.
Our results are in excellent agreement with previous work on the galaxy kinematics
within the Eridanus group, and reinforce the idea that the NGC 1407 group has a
very large dark matter content.
1 Introduction
It is well known that the kinematics of globular cluster (GC) systems can
provide information about the mass of their parent galaxy (see e.g. Huchra &
Brodie 1987; Kissler-Patig et al. 1998; Larsen et al. 2002; Beasley et al. 2004,
2006; Romanowsky 2006).
With a total, dynamical mass of ∼ 1.0 × 1012 M¯ (Quintana et al. 1994;
hereafter Q94), NGC 1407 is the dominant elliptical in the Eridanus region
of galaxies (e.g. Willmer et al. 1989; Brough et al. 2006). The high mass-tolight ratio reported for this group of galaxies (e.g. M/LB ∼ 3000M¯ /L¯ h−1 ,
Gould 1993; M/LB ∼ 560M¯ /L¯ , Q94; M/LK ∼ 230M¯ /L¯ , Brough et
al. 2006) has been widely interpreted as an evidence for the existence of large
amounts of dark matter. In particular, values of ∼ 7 × 1013 M¯ h−1 (Gould
1993), ∼ 1 − 7 × 1013 M¯ (Q94) and ∼ 7 × 1013 M¯ (Brough et al. 2006) have
been derived for the virial mass of the dark matter halo.
In this work, we present new measurements of both the mass of NGC 1407
and the dark matter content of the galaxy group halo on the basis of the
kinematics of a sample of GCs in this galaxy.
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A.J. Cenarro et al.
2 Sample selection, observations and data reduction
GC candidates of NGC 1407 were selected on the basis of photometric data
taken in the F435W and F814LP filters using ACS/WFC on the Hubble Space
Telescope (HST; proposal ID = 9427). We refer the reader to the papers by
Harris et al. (2006) and Forbes et al. (2006; hereafter F06) for a thorough
analysis of the above data.
Spectroscopic data for 20 GC candidates of NGC 1407 were taken in October 2003 at the Keck I telescope, using LRIS-B in multi-object mode and
0.8 arcsec width slits. The total exposure time for the GC candidates was 7 h.
A 15 min, long-slit spectrum along the major axis of NGC 1407 (P.A. = 56o ;
Longo et al. 1994) was also obtained. In addition, five Lick/IDS template stars
(Worthey et al. 1994) and spectro-photometric standard stars (Oke 1990) were
observed for calibrations using the same configuration. Optical spectra in the
range ∼ λ3400 − 5800 Å were obtained for the above targets at an overall
spectral resolution (full width at half maximum; FWHM) of 3.7Å.
A standard spectroscopic reduction procedure (bias subtraction, flatfielding, cosmic ray cleaning, C-distortion correction, wavelength calibration, Sdistortion, sky subtraction, extinction correction, and flux calibration) was
4
performed with REDuc
m E (Cardiel 1999). Mean signal-to-noise ratios per
angstrom for the final, GC spectra range from 15 up to 102 Å−1 , with a mean,
typical value for the whole GC sample of ∼ 38 Å−1 .
3 Radial velocity measurements and error estimates
Radial velocities (RVs) for the GC candidates, as well as for the central
spectrum of NGC 1407 within an aperture of Reff /8 (an effective radius of
36.4 arcsec was taken from Diehl & Statler 2006), were computed using the
MOVEL algorithm (González 1993), which is an improvement of the classic
Fourier quotient method to determine RVs and velocity dispersions of galaxy
spectra.
The five calibrating Lick/IDS stars were separately used as reference spectra for this method, thus deriving five independent values of RV for each
object. In each case, random errors in the derived RVs were computed by
MonteCarlo simulations in which Gaussian noise is added to the problem
and reference spectra according to their corresponding error spectra. Final
RVs were computed as error-weighted means of the five individual estimations. To account for systematic errors due to small deviations from a linear
wavelength scale, each single spectrum was also cross-correlated with an appropriate MILES5 (Sánchez-Blázquez et al. 2006) template in ∼ 150 small,
overlapping spectral regions along wavelength. The root-mean-square (rms)
4
5
http://www.ucm.es/info/Astrof/software/reduceme/reduceme.html
Medium resolution INT Library of Empirical Spectra
Kinematics of globular clusters in NGC 1407
3
Fig. 1. Radial velocities of the GCs corrected for the systemic radial velocity
(RVsys = 1769±70 km s−1 ) as a function of the projected distance from the center of
NGC 1407. Different symbols represent GCs with B − I < 1.87 (circles; metal-poor)
and B − I > 1.87 (squares; metal-rich). A distance of 20.9 Mpc (Forbes et al. 2006)
has been assumed for the galaxy.
standard deviation of all the RV solutions obtained from each individual region was considered as a reliable estimation of the absolute uncertainties in
the derived RVs. Such uncertainties range from 17 to 34 km s−1 , with a mean
value of ∼ 24 km s−1 .
4 The globular cluster kinematics
For the Reff /8, central spectrum of NGC 1407, the velocity dispersion and
heliocentric radial velocity derived in this work are 293.5 ± 4.1 km s−1 and
1785.6 ± 5.2 km s−1 respectively. These values are in reasonably good agreement with previous determinations (e.g., 273 km s−1 and 1783 ± 26 km s−1
respectively, from Hyperleda).
On the basis of the 20 GCs, the mean heliocentric radial velocity of our GC
subsystem (RVsys ) is 1769±70 km s−1 , with an overall rms standard deviation
of 313 km s−1 . Figure 1 displays the distribution of the GC RVs as a function
of the projected distance from the center of NGC 1407 (galactocentric radius;
Rgc ). It is clear from this figure that the dispersion of the GC RVs decreases
with the increasing projected distance. In particular, when the rms standard
deviation of the GC RVs is separately computed within three different radial
bins, we obtain 361 km s−1 (Rgc < 10 kpc), 244 km s−1 (5 < Rgc < 15 kpc)
and 149 km s−1 (Rgc > 10 kpc). Interestingly, this trend may have important
implications on the kind of orbits that the GCs follow within the potential
well of the galaxy. In fact, the existence of radial orbits (rather than isotropic
ones) would help to explain the distribution of GC RVs shown in Fig. 1.
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A.J. Cenarro et al.
Fig. 2. Relative radial velocities of the GCs as a function of projected distance to
different axis: major axis (a), minor axis (c) and two intermediate directions (b and
d). No systematic rotation of the GC system around the galaxy is detected. Symbols
as in Fig. 1.
Rotation around the host galaxy is a common signature of GC systems (see
e.g. Zepf et al. 2000; Côté et al. 2001, 2003). Therefore, prior to the galaxy
mass estimates performed in the next section, we have checked whether the
GC sample exhibits a significant rotation around the galaxy. If this were the
case, it would lead to an overestimation of the RV dispersion and, hence, of
the derived galaxy mass. In Figure 4 we illustrate the GC RVs relative to
RVsys as a function of the projected distance to four different directions: the
major and minor axes, and the two intermediate orientations. It is clear from
that figure that there exist no obvious hints for rotation around any direction.
There may still be a weak rotating signature for MP GCs, although the small
number of GCs does not allow us to carry out a reliable statistical analysis.
5 Mass estimates for NGC 1407 and the dark matter
halo of the galaxy group
Making use of the virial mass estimator of Heisler et al. (1985), the so called
virial mass (MVT ) can be estimated as
MVT
PN
3πN i=1 Vi2
,
=
PN
2G i<j 1/ri,j
(1)
where N is the total number of GCs, Vi is the radial velocity of the ith GC
with respect to RVsys and ri,j is the projected distance between the ith and the
jth GCs. Alternatively, the projected mass (MP ; Bahcall & Tremaine 1981) is
given by
N
fp X 2
V ri ),
(2)
(
MP =
GN i=1 i
where fp is a parameter that depends on whether the orbits are isotropic,
radial or tangential (fp = 16/π, 32/π or 32/3π respectively; see Bridges et
Kinematics of globular clusters in NGC 1407
5
al. 1997) and ri the projected distance of the ith GC to the center of the
galaxy. Assuming i) no GC rotation, ii) a distance of 20.9 Mpc to NGC 1407
(F06), and iii) isotropic orbits for the total sample of 20 GCs, we obtain
MVT = (1.40 ± 0.10) × 1012 M¯ and MP = (5.89 ± 0.40) × 1011 M¯ , with
errors being computed by means of a Jacknife procedure. If, as mentioned
above, radial orbits were assumed rather than isotropic ones, the estimated
projected mass would become twice as large and consistent with the virial
mass value.
The “tracer mass estimator” (TME) was introduced by Evans et al. (2003)
as a generalization of the projected mass estimator. It is given by
MTME =
with
C=
N
C X 2
(
V ri ),
GN i=1 i
16(α + γ − 2β) 4 − α − γ 1 − (Rin /Rout )3−γ
.
π(4 − 3β)
3 − γ 1 − (Rin /Rout )4−α−γ
(3)
(4)
In this case, Rin and Rout are the inner and outer three-dimensional radii of
the tracers, α is a parameter that describes the underlying gravity field, β
is the anisotropy parameter by Binney (1981), and γ is the exponent of the
power-law (r−γ ) that describes the number density of the tracer population
within Rin and Rout .
To have an estimation of the mass predicted by the TME, we assume that
our GCs are moving in a large scale mass distribution with a flat rotation
curve (α = 0), γ = 2.57 –as computed in F06, although note that a flatter
power-law could better reproduce the GC number density at the innermost
region of the galaxy–, and that Rin and Rout are well represented by the
projected values rin and rout (∼ 2 and 17 kpc respectively). Similar values of
MTME = (7.72 ± 0.64) × 1011 M¯ and (6.84 ± 0.56) × 1011 M¯ are obtained
assuming either isotropic (β = 0) or purely radial (β = 1) orbits respectively.
In any case, given the typical uncertainties of these methods, it is clear that
all values are consistent with previous estimations of the mass of NGC 1407.
In the recent work by Diemand et al. (2005), cosmological simulations of
the distribution and kinematics of material from early, high-density peaks in
present-day haloes predict that typical outer halo objects –like GCs– preferentially exhibit radial orbits, just becoming isotropic only near the galactic
center. Our observed, projected kinematics are consistent with their simulated
GC systems for a halo virial mass in the range 4.3 − 7.9 × 1013 M¯ (depending
on shape and orientation, e.g. spherical model yields 5.5 × 1013 M¯ ) which
corresponds to a total mass of 0.5 − 1.0 × 1012 M¯ within 17 kpc. It is worth
noting, however, that simulated orbits become preferentially radial at a significant fraction of the virial radius, whilst the projected distances of our GCs
do not extend so far away. A more detailed analysis and explanation of these
results is presented in Diemand et al. (2007, in preparation). Once again, the
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A.J. Cenarro et al.
dark matter content is consistent with previous determinations based on the
galaxy kinematics within the group.
Acknowledgements
The authors are grateful to Juerg Diemand for his work on preliminary cosmological
simulations for our GC set. This work has been supported by NSF grant AST 0507729 and the Spanish research project AYA2003-01840. A.J.C. is a Juan de la
Cierva Fellow of the Spanish Ministry of Education and Science. The authors wish
to recognize and acknowledge the very significant cultural role and reverence that the
summit of Mauna Kea has always had within the indigenous Hawaiian community.
We are most fortunate to have the opportunity to conduct observations from this
mountain.
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