Chromospheric UV emissions: frequency spectra in network and internetwork regions
Draft 9 by Noah S. Heller and E.J. Zita, The Evergreen State College
20 March 2003
Abstract
The anomalous heating of the chromosphere is almost certainly due in part to
magnetic dynamics. We analyze UV oscillations in the chromosphere to investigate their
dependence on frequency and position, and distinguish effects in network and
internetwork regions. We assume that UV-bright regions trace locally strong magnetic
network regions (Lites et al. 1993). We find that oscillations excited by photospheric pmodes lose power as they rise into the chromosphere. We find indirect evidence that
transformations to magnetohydrodynamic (MHD) waves may carry energy to higher
altitudes in low-frequency oscillations. We find evidence that high-frequency
oscillations may be locally suppressed, deflected, or transformed in the network regions.
Complementary numerical simulations shed light on our analyses of observed data
(Johnson et al. 2002, Bogdan et al. 2002). These combined efforts support a developing
understanding about the role of mode mixing and interactions in chromospheric heating.
A more complete model of the role of MHD waves in energy transport in the solar
atmosphere requires more information about chromospheric magnetic structures in 3D.
Introduction
The chromosphere, the hot thin atmosphere above the visible solar surface, is only
partially understood. Its magnetic topology is complex and changing, and its high
temperature remains unexplained. Visual observations during solar eclipses reveal that
the chromosphere glows pink. This is due to the hydrogen Balmer line (n=3 to n=2
transition), the predominant emission in the chromosphere. Spectroscopic observations
of the radiation reveal higher than expected temperatures in the chromosphere. In fact,
more energetic photons are observed at higher altitudes, indicating that temperature
increases with altitude. For example, light of wavelength 91 nm comes from an altitude
of about 1.8 Mm above the photosphere, where T > 6500 K, while 170 nm light comes
from an altitude of about 0.4 Mm, at the "temperature minimum" where T ~ 4000 K
(Judge et al. 2002). This paper analyzes UV radiation in this range as one step toward
investigating the role of magnetic fields in chromospheric heating.
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Chromospheric UV emissions: frequency spectra in network and internetwork regions
Draft 9 by Noah S. Heller and E.J. Zita, The Evergreen State College
20 March 2003
Observations also reveal that nonlinear dynamics such as mode transformations
and shock waves can evolve from photospheric p-modes. Acoustic waves (pressure
modes) driven by turbulence from the underlying convection zone have a characteristic
speed cs   P

. As these p-modes rise into the less dense chromosphere, energy
conservation can yield acceleration into shock waves (Gibson, 1963). Shock heating can
account for only part of the temperature rise to 105 K in the high chromosphere and 106 K
in the corona. The observed increase in chromospheric temperature with altitude
probably requires a combination of energy transport by magnetic waves and energy
release by mode conversion and magnetic reconnection mechanisms (Dwivedi and
Phillips, 2001; Bogdan et al., 2002).
Mode conversions (or transformations) can change the form of energy transported
by waves. Energy can be transported through the chromosphere mechanically, as heat, or
as magnetohydrodynamic (MHD) waves. Mechanical energy includes large-scale flow
of plasma, such as convection. Heat energy includes microscopic particle motions and
increases with plasma entropy. Magnetic energy includes tension in bent field lines and
pressure in compressed field lines. Magnetic energy can be stored and released by
bending and straightening of field lines. Changes in magnetic tension can propagate in
2
the form of Alfvén waves, with characteristic speed v A  B 4 . Magnetic energy can
also be stored and released when field lines compress and expand. Changes in magnetic
pressure can propagate via magnetosonic waves, with speeds that depend on cs, vA, and
the angle of the wave with respect to the magnetic fields. MHD waves such as Alfvén
waves and magnetosonic waves can carry energy higher into the chromosphere than pmodes can.
Chromospheric magnetic fields can mediate mode transformations. Pressure
modes can become MHD waves and vice versa. Waves can drive new waves, interact
with each other, and dissipate their energy in the form of heat. Magnetic mode
transformations depend on the local gas pressure, magnetic pressure, and magnetic
topology.
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Chromospheric UV emissions: frequency spectra in network and internetwork regions
Draft 9 by Noah S. Heller and E.J. Zita, The Evergreen State College
20 March 2003
Gas pressure decreases exponentially with height in the chromosphere, and
magnetic pressure increases with the local magnetic field strength. This depends on
details of the local magnetic structure. It is convenient to define the plasma "beta" as the
ratio of gas pressure to magnetic pressure:  
Pgas
Pmag
. In highly conducting plasmas
such as the Sun, the ionized gas is “frozen” to the field lines. Therefore, wherever
magnetic pressure exceeds gas pressure ( <1), the fluid moves with the magnetic
perturbations. This happens, for example, in the strong magnetic field or “network”
regions.
Where the gas pressure dominates, (>1), the magnetic field lines move or
bend in response to the fluid motion. This happens, for example, in the low field strength
or "internetwork" regions. Where magnetic pressure is comparable to gas pressure (
1), the sound speed is comparable to the Alfvén speed (cs  vA,).
In the interesting and complex "1" regions, rich "mode mixing" is possible.
Pressure modes traveling at the sound speed can resonate with Alfvénic modes, bending
magnetic field lines and exciting Alfvén waves. Gas compressions can compress field
lines and excite magneosonic waves (and vice versa). Energy can flow from one form of
wave to another, so waves in these regions are in general hybrids rather than purely sonic,
Alfvenic, or magnetosonic. Observationally, this can appear as a loss of p-mode energy
and generation of MHD waves (or vice versa).
We present indirect evidence for such mode transformations in the satellite data
analyzed below. Fluctuations in UV brightness can give clues about the source of
chromospheric heating and the role of magnetic fields. Complementary 2D MHD
simulations also indicate mode transformations as acoustic waves travel to higher
altitudes and in and out of magnetic regions of the chromosphere (Johnson et al., 2002).
We analyze the brightness and oscillations of chromospheric UV emissions to see
how chromospheric dynamics depend on the local magnetic field. We are concerned
primarily with the effects of acoustic waves traveling up from the photosphere.
Millihertz p-modes are excited by turbulent convection beneath the photosphere. As they
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Chromospheric UV emissions: frequency spectra in network and internetwork regions
Draft 9 by Noah S. Heller and E.J. Zita, The Evergreen State College
20 March 2003
compress and expand the plasma locally, they alternately heat and cool chromospheric
gas, which then glows brighter and dimmer in UV light.
By analyzing the resultant UV oscillations, we find three main results. First, UV
oscillation power in the p-mode frequency band decreases with height in the
chromosphere. This suggests that p-modes indeed are a primary driver of chromospheric
oscillations and that they lose power as they rise, either to heating or to mode
transformations. Second, UV oscillation power is stronger in highly magnetic regions at
low frequencies. This suggests that the low-frequency p-modes may be channeled along
magnetic structures. Third, UV oscillation power is stronger in less magnetic regions at
higher frequencies. This suggests that high-frequency p-modes may be excluded from
magnetic regions and propagate more freely in low-field regions.
Methods: Data Acquisition
We analyzed UV emissions from the solar chromosphere over a range of
wavelengths, corresponding to a range of temperatures and altitudes. We isolated
timeseries in regions of stronger and weaker solar magnetic field. We Fourier
transformed the timeseries and studied trends and differences in three frequency ranges
around the dominant p-mode signals of 3-5 mHz.
Our data came from SUMER, a UV spectrograph aboard the SOHO spacecraft.
Between March 1996 and May 1999, SUMER took time series data of the UV continuum
in the quiet Sun. SUMER works by reflecting sunlight through a narrow slit onto a
diffraction grating where light of specified wavelength can be directed at two CCD
detectors. These detectors count the number of photons that hit each pixel during one
exposure, and then average over all the pixels to record the intensity of light of a given
wavelength at each position and time. The variables that the observer can control in the
instrumentation include slit size, cadence and wavelength (Judge et al., 2001; SUMER
website).
SUMER is most sensitive to wavelengths in the UV continuum, which sample the
chromosphere. Continuum emission comes from free to bound transitions and from free
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Chromospheric UV emissions: frequency spectra in network and internetwork regions
Draft 9 by Noah S. Heller and E.J. Zita, The Evergreen State College
20 March 2003
to free transitions. Continua respond more simply to the passage of waves because
continuum opacities are essentially constant with wavelength (Gibson).
Our time series are sets of exposures that followed an area of the Sun as it
rotated. The data was transmitted to Earth in binary and stored in 2 dimensional arrays,
intensity as a function of space and time, for each wavelength. The resultant gray scale
plots of intensity in time and space show variations of intensity in both domains (Fig.1).
Methods: Data Analysis
We ran SUMER Software (SUMER website) in IDL to look at plots of UV
intensity, with position along the slit on the x-axis and time on the y-axis (Fig.1). These
gray scale plots show clear bands of relatively strong and weak emission from one spatial
region to the next. Lites et al. (1993) demonstrated a statistical correlation between
average intensity and magnetic field strength in the chromosphere. For example, the
areas of high magnetic flux (“network” regions) are relatively UV-bright compared to
weak-field “internetwork” regions. We follow the method of Judge et al. (2001), whose
software automatically averages signals along the slit over time to identify the brightest
30% as network regions and the dimmest 40% as internetwork regions. The rough
assignation of network regions with bright UV regions can be checked against data from
MDI, which measures line of sight field strength directly (Fig.2).
Variations of UV intensity in time give indirect evidence of temperature
oscillations in the chromosphere. Intensity plots such as Fig.1 show intensity oscillations
in time as well as in space. We Fourier transformed timeseries data to obtain the power
versus frequency for a given position along the slit. We generated these power spectra
for each wavelength of interest. After identifying a network region from a given UVbright region, we integrated the power spectra at each point. We repeated this for each
wavelength, in both network and internetwork regions.
We used the power spectra to determine noise levels and analyze frequency
dependence on magnetic field. Noise is evident when the power levels off and appears to
oscillate around some equilibrium with increasing frequency, e.g. at the 4 x 10-6 level in
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Chromospheric UV emissions: frequency spectra in network and internetwork regions
Draft 9 by Noah S. Heller and E.J. Zita, The Evergreen State College
20 March 2003
Fig.3. We were able to pick out noise levels by viewing the power distribution. This
allowed us to calculate signal to noise ratios and get rid of poor data. As most of our
power spectra plateau above 10 mHz, we ignored all higher frequency signals as noise.
We integrated the total power over specified frequency bands and subtracted the
integral of the noise to get a sense of the dominant dynamics. We quantify relative
fluctuations as the square of the variance (standard deviation), which is equal to the
integral of power over all frequencies, by Parseval’s Theorem (Press, p.384). For all our
data sets we integrated power from 0-2, 3-5, and 5-10 mHz. We then plotted integrated
power vs. wavelength, spanning our entire collection of data. Finally, we calculated
ratios of the integrated power in network vs. internetwork regions for each data set
(Fig.4).
Results
Fourier transformation of the UV oscillation timeseries shows global peaks in the
power spectrum at 0-2 mHz, close to granulation periods. Local peaks in the 2-5 mHz
range correspond to photospheric p-mode periods around 3-5 minutes. Oscillation
amplitudes are lower in the highest frequency range we study, 5-10 mHz. We neglect as
noise oscillations higher then 10 mHz.
We discern several trends from power spectra of different wavelengths. (1)
Power in the 2-5 mHz band appears increases wavelength (or decreases with height) in
the solar atmosphere. (2) In the 0-2 frequency range, there is consistently more power in
the network (magnetic) regions than in internetwork regions (Fig.5). (3) In the 5-10
frequency range, there tends to be more power in the internetwork regions (Fig.6).
Discussion
Convective turbulence perturbs the photosphere with a checkerboard pattern of pmodes. These disturbances propagate through the chromosphere as a broad spectrum of
mHz oscillations, with highest amplitudes in the 5-minute oscillations. Pressure waves
cause oscillations in the UV continuum because as chromospheric gas contracts and
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Chromospheric UV emissions: frequency spectra in network and internetwork regions
Draft 9 by Noah S. Heller and E.J. Zita, The Evergreen State College
20 March 2003
expands, it heats and cools. The intensity of UV emission also increases with
temperature. Our analysis shows that p-mode power decreases with altitude from the
photosphere. This suggests that the mechanical energy of photospheric modes dissipates
or transforms, as disturbances originating as p-modes propagate up through the
chromosphere.
Our analysis also shows that the frequency of UV oscillations depends on the
local magnetic field. Low-frequency oscillations (0-2 mHz) are stronger in network
regions, and high-frequency oscillations (5-10 mHz) are stronger in internetwork regions.
Oscillations in the dominant p-mode frequencies (2-5 mHz) show no such distinction.
This may indicate mode transformations to MHD waves, or selective channeling or
exclusion of acoustic waves, depending on local magnetic field strength and structure.
Preliminary comparisons of SUMER data with magnetic field data from MDI (Fig.2)
suggest a correlation between magnetic field structure and suppressed high-frequency pmodes. More detailed tests of Judge's hypothesis (2001) that the network’s magnetic
canopy "shadows" p-mode oscillations will require 3D extrapolation of magnetic fields
from MDI data.
We conclude that chromospheric UV spectra depend on local magnetic field
strength and topology, that p-modes lose power as the rise into the chromosphere, and
that network regions tend to support lower-frequency oscillations. Analyzing UV
oscillations in network and internetwork regions can reveal effects of local magnetic
fields on chromospheric waves excited by photospheric p-modes.
Acknowledgments:
This work was supported by NASA's Sun-Earth Connection Guest Investigator Program,
NRA 00-OSS-01 SEC.
We thank many HAO staff, not all of whom are named, for facilitating this research. Phil
Judge gave us the data and analysis programs, taught us to use them, and answered many
questions in depth; his generous guidance was invaluable. Tom Bogdan, Michael
Knoelker, and Anna Pietorilla contributed helpful conversations, impromptu tutorials,
feedback, and guidance; Eric McDonald, Vic Tisone, and Bunny Pfau provided expert
computer and data analysis support; Cindy Worster and many others provided general
support. A. Bertsch (TESC) participated in preliminary data analysis.
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Chromospheric UV emissions: frequency spectra in network and internetwork regions
Draft 9 by Noah S. Heller and E.J. Zita, The Evergreen State College
20 March 2003
Bibliography and References
Bogdan, … 2001
Bogdan, … 2002
Dwivedi, B.N., and Phillips, K.J.H. 2001 (June), Scientific American p.40-47
Gibson, E.G. 1973. The Quiet Sun. 1st ed. NASA Scientific Publications.
Durrant, C.J. 1988. The Atmosphere of the Sun. Bristol: Adam Hilger.
The Analysis and Restoration of Astronomical Data via the Fast Fourier Transform.
Astron. & Astrophys. 13: 169-189.
Judge, P.G., T.D. Tarbell, and K. Wilhelm. 2001. A Study of Chromosheric Oscillations
using the SOHO and TRACE spacecraft. Astrophysical Journal 554: 424-444.
The Solar Magnetic Field. AUTHOR? Encyclopedia of Astronomy and Astrophysics.
The Sun: Basic Properties. AUTHOR? Encyclopedia of Astronomy and Astrophysics.
SUMER website: http://www.linmpi.mpg.de/english/projekte/sumer/
Parker, E.N. 2000. The Physics of the Sun and the Gateway to the Stars. Physics Today,
June 2000, p.26-31.
Press, W.H., et al.1986 Numerical Recipes, Cambridge University Press
Johnson, M.C., S. Petty-Powell, and E.J. Zita. 2002. Energy Transport by MHD Waves
above the Photosphere: Numerical Simulations.
http://academic.evergreen.edu/z/zita/research/____
The Chromosphere: Emerging Flux Regions. Encyclopedia of Astronomy and
Astrophysics. AUTHORS?
The Sun as a Star. Encyclopedia of Astronomy and Astrophysics.
DeBula, and F.G. Fiamingo. 1998. Introduction to Unix. Columbus: University
Technology Services.
Kaulfmann and Freedman, Universe.
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Chromospheric UV emissions: frequency spectra in network and internetwork regions
Draft 9 by Noah S. Heller and E.J. Zita, The Evergreen State College
20 March 2003
Fig.1: UV oscillations vary in time and space. SUMER intensity timeseries data
(acquired 1996 Oct. 2) shows variation in UV intensity in space (horizontal axis) and
time (vertical axis). The bright locations correspond roughly to network regions and the
dark locations to internetwork regions. At a given spatial location (e.g. x=90 arcsec),
oscillations in time from light to dark correspond to stronger and weaker emissions.
Fig.2: Strong field regions correlate with UV-bright regions. MDI measurements of
photospheric magnetic field show strong field spots near positions 20 and 90 along the
SUMER slit. These "network" regions are also evident in Fig.1 as UV-bright regions.
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Chromospheric UV emissions: frequency spectra in network and internetwork regions
Draft 9 by Noah S. Heller and E.J. Zita, The Evergreen State College
20 March 2003
Fig.3: Power spectrum (power versus frequency) from Fourier transform of UV light at a
given wavelength (91 nm), averaged over network positions (around x=20 and x=90 in
Figs. 1 and 2).
Fig.4: UV oscillation power increases with wavelength, or decreases with altitude. We
plot power (integrated over the dominant p-mode frequencies of 2-5 mHz) versus
wavelength in both network (◊) and internetwork (+) regions.
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Chromospheric UV emissions: frequency spectra in network and internetwork regions
Draft 9 by Noah S. Heller and E.J. Zita, The Evergreen State College
20 March 2003
Fig.5: Lower-frequency oscillations are stronger in network than in internetwork regions.
We integrate the UV oscillation power from 0-2 mHz for signals in UV-bright and UVdim regions. The ration of (network power)/(internetwork power) vs wavelength shows
that at all heights, there is more power in this frequency range in the network regions.
network/internetwork power ratios in 0-2 mHz range
3.50
3.00
power ratio
2.50
2.00
1.50
1.00
0.50
0.00
80
90
100
110
120
130
140
wavelength (nm)
Fig.6: Higher-frequency oscillations are stronger in internetwork than in network
regions. We integrate the UV oscillation power from 5-10 mHz for signals in UV-bright
and UV-dim regions. The ration of (network power)/(internetwork power) vs wavelength
shows that at most heights (below the 91 nm level), there is more power in this frequency
range in the internetwork regions.
network/internetwork power ratios in 5-10 mHz range
1.00
0.90
0.80
power ratio
0.70
0.60
0.50
0.40
0.30
0.20
0.10
0.00
80
90
100
110
120
wavelength (nm)
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130
140