High Resolution Millimeter Interferometer Observations of the Solar Chromosphere
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Astronomy & Astrophysics manuscript no. bima˙maria January 24, 2006
(DOI: will be inserted by hand later)
High–Resolution Millimeter–Interferometer
Observations of the Solar Chromosphere
S. M. White1 , M. Loukitcheva2,3, and S. K. Solanki3
1 Astronomy Department, University of Maryland, College Park, MD 20742
e-mail: white@astro.umd.edu
2 Astronomical Institute, St. Petersburg University, 198504 St. Petersburg, Russia
3 Max-Planck-Institut für Sonnensystemforschung, D-37191 Katlenburg-Lindau, Germany
Received / Accepted
Abstract.
The use of millimeter–interferometer data for the study of chromospheric structure and dynam-
ics is tested using 85 GHz observations with the 10–element Berkeley–Illinois–Maryland Array
(BIMA). Interferometer data have the advantage over single–dish data that they allow both high
spatial resolution and dense temporal sampling simultaneously. However, snapshot imaging of
the quiet solar atmosphere with a small number of dishes is challenging. We demonstrate that
techniques are available to carry out this task successfully using maximum entropy deconvolution
from a default image constructed from the entire observation: one of our results is that the solar
chromosphere at millimeter wavelengths exhibits features that are long–lasting and the map of
the entire observation is significant provided that atmospheric phase errors do not prevent de-
convolution. We compare observations of quiet Sun, active region and coronal hole targets. The
interferometer is not sensitive to the disk emission and the positivity constraint of the maximum
entropy algorithm used forces the zero level in the images to be at the temperature of the coolest
feature in each field. The brightest features in the images are typically 1000 – 1500 K above
the zero level, with a snapshot noise level of order 100 K. We use extensive tests to determine
whether oscillation power can be recovered from sequences of snapshot images and show that
individual sources can be down to quite weak levels at locations in the image where significant
flux is present; oscillation power located in cool regions of the image is not well recovered due
to the deconvolution method used and may be redistributed to brighter regions of the
millimeter image. We then investigate whether the data do show oscillation power
using uninterrupted 30–minute scans of the target regions. Intensity oscillations with signifi-
cant power in the frequency range 1.5-8.0 mHz are found in the quiet–Sun and active region
targets. For the quiet–Sun region we compare the oscillation properties of network
boundaries and cell interiors (internetwork) in the spatially–resolved time series.
In agreement with investigations at other wavelengths, in the millimeter data the power in the
network tends to be at periods of 5 minutes and longer while power in the internetwork is present
also at shorter (3-minute) periods.
Key words. Sun: chromosphere – Sun: radio radiation1. Introduction Lindsey & Kopp, 1995). The Nobeyama 45 m
telescope has been able to achieve similar reso-
Observations of the quiet Sun at millimeter wave-
lution at λ = 3 mm (Kosugi et al., 1986; Irimajiri
lengths are an important technique for study-
et al., 1995), while the NRAO 12 m telescope
ing the solar chromosphere. At these short wave-
at Kitt Peak can reach a resolution of 4000 at 1
lengths the Sun’s atmosphere becomes optically
mm (Buhl & Tlamicha, 1970; Kundu, 1970, 1971;
thick in the chromosphere and since the wave-
Lantos & Kundu, 1972).
length lies in the Rayleigh–Jeans limit, the mea-
However, by their nature single–dish observa-
sured radio brightness temperature corresponds
tions are not ideal for searching for spatially–
to the electron temperature in the layer be-
resolved time variability in the solar chromo-
ing observed, without the complications of non–
sphere. A single dish only samples the flux from
equilibrium line formation that have to be taken
a given location when it is pointing there, and
into account when analyzing visible and UV line
thus its duty cycle for sampling the time varia-
observations of the chromosphere. Millimeter–
tion at a given point is poor if the telescope is
wavelength observations have played an impor-
carrying out imaging since, by definition, most of
tant role in forming thermal models of the
the time it is pointed at the other locations within
chromosphere (e.g., Vernazza et al., 1976, 1981;
the field being mapped (e.g., the raster scan of a
Fontenla et al., 1990; Gu et al., 1997), and it is
40000 square region by Lindsey & Jefferies, 1991,
natural to ask what they reveal about chromo-
required 45 minutes with a 1 s integration at each
spheric heating (see Solanki, 2005).
of 1600 pointings). Single–dish observations are
There have been many single dish observations
excellent for studying time variability in the to-
of the Sun at millimeter and sub–millimeter wave-
tal flux from a fixed location (i.e., the spatially–
lengths. The limitation of single dish measure-
integrated flux within the telescope beam; e.g.,
ments is always spatial resolution: a typical tele-
Simon & Shimabukuro, 1971; Kundu & Schmahl,
scope with a diameter of 10 m has a spatial res-
1980; Lindsey & Roellig, 1987; Kurths et al.,
olution of λmm 3000 , where λmm is the observing
1988; Kopp et al., 1992), but cannot simultane-
wavelength in mm, and thus, e.g., a 10 m tele-
ously image. Multibeam receivers on single–dish
scope operating at 90 GHz cannot resolve features
telescopes can speed up this process but do not
smaller than about 10000 . This problem has been
change the nature of the data. The attraction of
circumvented in two ways: by observing eclipses,
interferometer observations is that they offer the
when the Moon’s limb acts as a knife edge cross-
opportunity for simultaneously achieving higher
ing the field of view, and the time dependence of
temporal and spatial resolution observations than
the millimeter flux can be converted into (one–
can be achieved with a single dish telescope. Since
dimensional) spatial resolution much finer than
for a single dish telescope the field of view is the
the telescope beam (e.g., Tolbert et al., 1964;
same as the spatial resolution, the telescope must
Hagen et al., 1971; Beckman et al., 1975; Swanson
have a large aperture and be physically driven to
& Hagen, 1975; Shimabukuro et al., 1975; Lindsey
different pointing locations in order to map a re-
et al., 1984; Roellig et al., 1991; Ewell, Jr. et al.,
gion. By contrast, an interferometer with smaller
1993); and by going to submillimeter wavelengths
dishes (sensitivity not being much of an issue for
(smaller λ), which is possible with the James
the Sun) can make an image with many resolu-
Clerk Maxwell Telescope (JCMT) and Caltech
tion elements across the field of view, and achieves
Submillimeter Telescope (CSO) on Mauna Kea,
high time resolution because it forms an image
Hawaii. These telescopes have been able to make
without repointing and thus can stare at the
images of the solar disk at submillimeter wave-
same field of view continuously, providing com-
lengths with a spatial resolution as small as 2000
plete sampling of the light curve in each resolu-
(Horne et al., 1981; Lindsey & Jefferies, 1991;
tion element. On the other hand, an interferome-
Bastian et al., 1993a,b; Lindsey et al., 1995;
ter has two disadvantages: it is insensitive to the
Send offprint requests to: S. White background flux of the Sun, which is resolved outWhite, Loukitcheva & Solanki: Millimeter Observations of the Chromosphere 3
because it comes from a source too large to be to fill in the sampling (the technique of “Earth–
sampled by the interferometer spacings; and an rotation synthesis”), but this can only work if
interferometer is equivalent to a sparsely filled the target observed is steady over the time pe-
aperture, meaning that it does not completely riod used: if not, then samples at different times
sample the spatial structure within the field of refer to different brightness distributions and can-
view at any instant, and this creates difficulties in not be combined. If the chromosphere’s millime-
reconstructing images (discussed further below). ter emission is such that its pattern changes from
Interferometer observations of the (non–flaring) minute to minute, then clearly Earth–rotation
Sun at millimeter wavelengths have been carried synthesis will not work. Single dish observations
out since the 1970s (e.g., Labrum et al., 1978; do not suffer from this problem, since each point
Labrum, 1978; Janssen et al., 1979; Belkora et al., is only observed briefly, but equally single-dish
1992; White & Kundu, 1994), but generally not observations cannot easily be used to investigate
with a sufficient number of telescopes for snap- this issue.
shot imaging to be feasible. Here we discuss inter- In this paper we analyze millimeter–
ferometer images of the Sun made at a wavelength interferometer observations of the solar chro-
of 3.5 mm with the Berkeley–Illinois–Maryland mosphere obtained with BIMA and look for
Array (BIMA), which, with the largest number of spatially–resolved oscillation power in the
dishes of any existing millimeter interferometer, observations. We observe and compare an active
is the telescope best suited for such observations. region, quiet–Sun region and a coronal hole. The
It is not at all clear, a priori, that millimeter in- imaging technique used for the millimeter data is
terferometer observations of the quiet Sun will be discussed in some detail. An important question
successful due to the dynamic nature of the chro- is the sensitivity of the observations to oscillation
mosphere. Evidence from all wavelengths is that power, and we present extensive tests of this
the chromosphere is a turbulent layer, constantly issue. In the companion paper by Loukitcheva
pushed from below by convective motions and et al. (2005) we compare the observed millime-
waves, and being bombarded from above by en- ter intensity variations derived in the present
ergetic particles. Radiative energy loss timescales analysis with the oscillation properties predicted
are quite short, and motions are common: Zirin by the Carlsson & Stein models (Carlsson &
(1996) comments that “In high–resolution movies Stein, 1995, 1997) and discuss the reasons for
the Hα chromosphere is a seething, oscillating differences that we find.
mass of fibrils”. At centimeter wavelengths radio
images of the Sun are usually dominated by very 2. Radio emission from the quiet Sun
bright, relatively compact sources in the corona
above active regions, but at millimeter wave-
at millimeter wavelengths
lengths the image consists of temperature fluctu- Radio emission at millimeter wavelengths be-
ations on the optically thick layer in the chro- comes optically thick in the solar chromosphere
mosphere corresponding to the frequency ob- due to the opacity contributed by thermal
served, and these will fill the field of view with bremsstrahlung. At temperatures below 104 K the
low–contrast features. Such an image requires dominant species (H and He) are mostly neutral,
many components to describe it adequately and, but the total electron and proton densities can
as we discuss below, a single instantaneous obser- remain high because the total density increases
vation, even with BIMA, does not contain enough rapidly with depth and compensates for the de-
information to reconstruct the brightness distri- crease in fractional ionization. Below 5000 K (i.e.,
bution within the field of view. A standard tech- in the temperature minimum) essentially all hy-
nique used by interferometers to overcome the in- drogen is neutral. Free electrons are still present
stantaneously sparse sampling of spatial scales is at these temperatures due to ionization of met-
to integrate over a long period, using the Earth’s als such as sodium, but there are insufficient free
rotation and the changing elevation of the source protons to provide significant free–free opacity.4 White, Loukitcheva & Solanki: Millimeter Observations of the Chromosphere
EIT 195 A
In this situation a mechanism involving free elec- 1000
trons and neutral H dominates the radio opac-
ity: an electron polarizes an H atom and the in-
teraction between the electron and the dipolar
500
atom provides opacity known as “H− opacity”.
However, at the wavelength we investigate here, AR
CH
3.5 mm (85 GHz), we can assume that electron–
arcsec
proton bremsstrahlung still dominates the radio 0 QS
opacity.
The expression for this opacity from the top
of the solar corona down to a height h0 in the
-500
chromosphere is given by
.01
τ =
f2 -1000
Z -1000 -500 0 500 1000
∞ ne (np + 4nHe++ )(17.6 + 1.5 ln T − ln f ) arcsec
dh
h0 T 1.5 Fig. 1. An EIT 195 Å image of the Sun at 19:12 UT
where f is the frequency, ne the electron number on 2003 August 31 (reversed color table, so that dark
density, np the proton number density, nHe++ the features represent bright emission) together with cir-
cles showing the targets observed by BIMA. The cir-
fully–ionized Helium number density and T is the
cles have a diameter of 15000 , just slightly larger than
temperature. Apart from f , all these quantities
the half–power beam width of the BIMA antennas at
depend on height and this expression can only be 85 GHz, and are labelled for the appropriate feature:
evaluated in the context of a model atmosphere “AR” (active region), “QS” (quiet Sun), and “CH”
in which both the density and the ionization frac- (coronal hole).
tion are specified as a function of height. Radio
measurements of T (which is the same as the ra-
dio brightness temperature since the radio mea-
surement is in the Rayleigh–Jeans limit and the
source is optically thick) as a function of f pro-
vide constraints for such models (e.g., Vernazza
et al., 1976, 1981; Fontenla et al., 1990; Ewell, Jr. layers around τ = 1 should lead directly to an in-
et al., 1993; Gu et al., 1997). At millimeter wave- crease in the millimeter brightness temperature
lengths the temperature varies much more slowly since the integrated column above the heated lo-
than electron density as a function of height. As cation will not change greatly. Heating in the op-
a result, the optically thick frequency, i.e. the fre- tically thin layers above the τ = 1 surface, on the
quency at which optical depth unity (τ = 1) is other hand, decreases the optically thin contri-
reached at a given height h0 , depends predomi- bution from the locally heated material but can
nantly on the density gradient: lead to an increase in the column density of ne as
Z ∞
heat propagates downwards to the denser layers
f2 ∝ ne np dh. and causes them to expand, pushing the τ = 1
h0
layer up the temperature gradient. This is likely
With only a weak dependence on the tempera- to occur on a timescale slower than that of the
ture gradient, this result implies that the optically heating, but may well affect the radio brightness
thick surface at a given frequency is determined temperature and thus also result in sensitivity of
by the column density above the surface and is mm–wavelength radiation to heating that is lo-
relatively independent of the temperature on the calized in a layer away from the τ = 1 surface
surface. Thus, heating in the chromosphere in the (Loukitcheva et al., 2004).White, Loukitcheva & Solanki: Millimeter Observations of the Chromosphere 5
3. BIMA observing procedure and been implemented by R. L. Plambeck and D.
data analysis Bock (described in Plambeck, 2000). Each chop-
per wheel on the BIMA antennas carries in one
3.1. BIMA Observations quadrant a partially transparent vane (a “pel-
licle”) with a transmission factor of order 70%
BIMA is a 10-element interferometric array con- (measured in the laboratory prior to installation).
sisting of 6.1 m diameter dishes (Welch et al., The pellicles can be rotated into the beam path
1996). The BIMA observations followed the stan- and the receiver response at 70% of the Sun’s
dard practice of alternating observations of an brightness temperature can then be compared
unresolved strong point source for phase calibra- with the response when the Sun is observed di-
tion with observations of the target regions. In rectly. A suitable modification of the Ulich &
this case, we alternated between the three tar- Haas (1976) formula allows the gain to be com-
gets (active region, quiet Sun and coronal hole) puted, under the assumption that the Sun’s tem-
with scans 31 minutes long (29 minutes of inte- perature at 3 mm wavelength is 7000 K, which
gration) interspersed with scans of the calibration should be appropriate (e.g., see the survey by
source 1058+015. The three target regions are Urpo et al., 1987). This correction is implemented
shown on an EIT 195 Å Fe XII image in Figure by a customized module in the on-line correla-
1. BIMA tracks a fixed point on the solar sur- tor software. The dielectric beamsplitter used for
face by correcting for solar rotation in real time. the vane is polarization-dependent and this in-
The correlator was set to observe two 800 MHz– troduces some uncertainty in the amplitude cali-
wide sidebands at 85 and 88 GHz. BIMA was in bration. We cross–checked the amplitude calibra-
its most compact (“D”) configuration for these tion scheme by comparing BIMA data with three
observations, resulting in a nominal resolution of other sources: Nobeyama Radio Polarimeter data
order 1000 , but minimizing the effects of atmo- for a flare at 80 GHz that BIMA observed at 85
spheric phase distortions on the data. Phase vari- GHz; estimates of thermal free–free emission dur-
ations in the data due to diurnal changes in the ing the decay phase of flares based on GOES soft
lengths of the optical fibers connecting the anten- X–ray data; and total power measurements on
nas to the central building amounted to several BIMA antenna 3, which has an older Schottky
thousand degrees, but these are measured accu- receiver that is more linear than the receivers on
rately by the on–line system and removed during the newer BIMA antennas. From this comparison,
the calibration process. Errors due to atmospheric we presently estimate a conservative uncertainty
phase fluctuations appeared to be relatively small in the absolute interferometer fluxes of 30%.
until the end of the observation when the Sun was
low on the western horizon, and we exclude the
last (fifth) scan of the active region for this rea-
son, leaving four scans of each of the three target
regions. The time resolution was 4 seconds with The total power level on antenna 3 at BIMA is
an integration time of 3 seconds. known to show oscillations associated with
Solar observations with BIMA do not use the the water chiller on the antenna that can
standard amplitude calibration method because propagate into the visibility data. The os-
the Sun fills the antenna beam with a bright- cillation was seen in total power with pe-
ness temperature of order 7000 K, and requires riods ranging from 13 to 16 minutes dur-
the receivers to operate in a regime quite differ- ing this observation but there was no obvi-
ent from normal observations where the system ous sign of such oscillations in the visibil-
temperature is of order 300 K. In order to mea- ity data; in any case, at those long periods
sure the system gain at the Sun’s brightness tem- they should not interfere with the search
perature, a modified version of the conventional for periods from 3 to 5 minutes. None of the
chopper wheel method (Ulich & Haas, 1976) has other antennas show such oscillations.6 White, Loukitcheva & Solanki: Millimeter Observations of the Chromosphere
3.2. Image processing flux, and restored the deconvolved images with
restoring beams of 1000 for the images presented
The advantage of using an interferometer to ob-
here. Since maxen has a positivity constraint, the
serve the chromosphere is that it can achieve bet-
deconvolution process sets the zero level at the
ter spatial resolution than a single dish observa-
flux of the most negative real feature in the image
tion at the same frequency. The disadvantage is
and forces all other features to be brighter than
that the interferometer is insensitive to flux on
this. Therefore the zero level in the images has lit-
spatial scales larger than the angular scale cor-
tle meaning. The total power measurements from
responding to the Fourier fringe spacing of the
the receivers indicated that the active region tar-
shortest antenna spacing, and in particular it is
get showed a total power about 2% larger than
insensitive to the background solar disk level.
the quiet Sun region and about 1% larger than
We know that millimeter images of the solar at-
the coronal hole.
mosphere should consist of features with contrast
of order hundreds to 1–2 thousand K against a The 6.1m BIMA antennas have a half–power
flat background of order 7000 K, and relative to beam width of 13700 at 85 GHz and the first null
that background the images will have patterns of is at a radius of 17000 from the center of the pri-
positive and negative emission. This is seen in, mary beam (Lugten, 1995). We made images 128
e.g., high–resolution interferometer images of the pixels square with a cell size of 300 , and looked for
solar chromosphere at microwave frequencies (4– flux in the inner region of the image, i.e., a circu-
22 GHz: Erskine & Kundu, 1982; Gary et al., lar region of diameter 19200 , which extends
1990; Bastian et al., 1996; Benz et al., 1997). beyond the half–power size. However, gener-
ally flux in the deconvolved images is confined to
Since the images are expected to have emis-
within the half–power region.
sion in many pixels but with relatively low con-
trast, the appropriate deconvolution method is
maximum entropy (“MEM”) rather than the 3.3. Snapshot imaging and BIMA
“CLEAN” process usually used for high–contrast sensitivity
images with small bright features (Cornwell,
1988). We attempted to use the “CLEAN” pro- One of the goals of this investigation is to look
cedure but it failed to produce maps that were for oscillations in the chromospheric emission at
believable, presumably because of the combina- timescales from 3 to 5 minutes, requiring imaging
tion of high sidelobes (up to 50% in snapshot to be carried out on much shorter timescales, i.e.,
maps) and the presence of flux in just about ev- snapshot imaging. We made images at intervals
ery pixel in the image. Even small amounts of flux of 15 seconds throughout the day, with each in-
being redistributed by the point–source response terval including about 4 integrations. Maximum
causes problems in a low–contrast image because entropy deconvolution of these snapshots without
at any location you can get spurious contributions using a priori models did not produce satisfactory
from pixels all across the image, whose decon- images. The reasons for this can be understood
volution by “CLEAN” would require excessively as follows. When all ten antennas were operat-
large numbers of “CLEAN” components and a ing (only true for a period after 21 UT), BIMA
very slow “CLEAN” step. We used the maxen pro- obtained 45 complex numbers in a snapshot (one
gram in the MIRIAD package for MEM decon- for each antenna pairing), so that at best an im-
volution1 , allowing the program to find the total
used by maxen, but also has a positivity con-
1 We compared the results from maxen straint), and UTESS (which has no positivity
with the MEM deconvolution programs constraint). VTESS gave essentially the same re-
in the AIPS package maintained by the sults as maxen, with the total fluxes determined
National Radio Astronomical Observatory, by the two programs agreeing to within 10%,
VTESS (which uses the Cornwell entropy mea- but UTESS failed to converge to a suitable so-
sure rather than the Gull entropy measure lution.White, Loukitcheva & Solanki: Millimeter Observations of the Chromosphere 7
age with about 30 distinct emission components the chromosphere are so close to one another.
in it can be reconstructed (a single point source The snapshot images at the two frequencies were
requires 3 pieces of information: a flux and two made independently using identical methods and
position coordinates). The BIMA field of view, compared. The two images were always consistent
however, contains about 400 resolution elements with one another. The noise level in the snapshot
(14000 field with 1000 beam, requiring 4 samples difference maps was typically of order 0.006 solar
per beam), and we expect flux to be present ev- flux units (sfu) per beam (1 sfu = 104 Jy) or 100
erywhere, unlike the case at longer wavelengths K brightness temperature (for a 1000 beam).
or for flares where a few bright sources dominate. Secondly, we added model point sources of dif-
Therefore a snapshot does not contain enough in- ferent fluxes to snapshot visibilities and mapped
formation to reconstruct the brightness distribu- the resulting data as before. This test indicated
tion completely. that model sources as weak as 0.001 sfu (17 K)
We address this problem by using a priori mod- could be recovered adequately in regions of the
els as default images for each snapshot. The mod- images where the flux is high, but in other regions
els used are the results of deconvolving the data (regions with low flux) sources as strong as .05 sfu
for each target region for the whole day. Earth ro- (800 K) could not be recovered. We present an
tation synthesis then gives us enough information explanation for this behaviour later in discussing
to reconstruct the brightness distribution, pro- tests of the recovery of oscillating sources.
vided that it is reasonably stable over the day.
At a gross level this was found to be the case, 4. Comparison of millimeter images
particularly for the active region target. Using a
model as a default image for deconvolution is the
with other diagnostics
well–discussed process of supplying a priori in- In order to provide a context for understanding
formation (Cornwell & Braun, 1989). The decon- the millimeter observations, we compare them
volution procedure should then only modify the with the following data: (i) a longitudinal mag-
model where the snapshot data require it, i.e., netogram obtained at 19:11 UT by the Michelson
only where the data contain features that are not Doppler Interferometer (MDI) on the Solar and
consistent with the default model to within the Heliospheric Observatory (SOHO); (ii) a 195 Å
noise level. In a sense, we are asking the deconvo- image (dominated by an Fe XII line formed in
lution process to reconstruct changes in a small the corona at 1.5 × 106 K) at 19:13 UT from the
number of pixels where the emission changes by Extreme–ultraviolet Imaging Telescope (EIT) on
amounts that are significantly larger than the SOHO; (iii) a 304 Å EIT image at 19:19 UT dom-
noise level (smaller changes are irrelevant), rather inated by the He I line formed at about 105 K;
than in every pixel in the image that contains (iv) a line–center Hα image obtained by the Big
flux. This approach should minimize the effects of Bear Solar Observatory (BBSO) at 19:02 UT; (v)
the snapshot u, v distribution varying throughout a BBSO Ca II K line image acquired at 16:37
the day, but it complicates the issue of determin- UT; and (vi) a 17 GHz image from the Nobeyama
ing the sensitivity of the method to fluctuating Radio Heliograph (NoRH) made by averaging 60
sources. This approach produced snapshot maps samples 1 minute apart covering the time range
of excellent quality that clearly showed changes 23:00–23:59 UT (after sunrise in Japan) with so-
with time, whereas images constructed without lar rotation removed from the brighter features.
using a priori information were poor (with both Since it is close to the mid–time of the BIMA ob-
CLEAN and maximum entropy deconvolution). servations, we use 19:00 UT as the reference time
The tests carried out to determine the be- and all images were rotated to the common time
lievable level of fluctuations in the images were for comparison. The 85 GHz images used here
twofold. Firstly, images in the two sidebands at have a spatial resolution of 1000 . The 17 GHz im-
85 and 88 GHz should be essentially identical age has a spatial resolution of 1200 , while all the
since the corresponding optically thick layers in optical and EUV images have resolutions of order8 White, Loukitcheva & Solanki: Millimeter Observations of the Chromosphere
2–400 . The line–center Hα and Ca II K emissions clearly indicates a chromospheric component. In
are believed to form in the chromosphere at tem- the 17 GHz image this feature has a peak bright-
peratures of order 6000–8000 K. At 17 GHz the ness temperature contribution of order 15000 K
solar disk has a brightness temperature of 10000 (median of order 10000 K), and if it is optically
K, so this frequency is also a chromospheric di- thin bremsstrahlung from coronal material then
agnostic in principle and is optically thick at a it should contribute a peak of 600 K (median 400
height above the formation levels of Hα and Ca K) to the 85 GHz image. The actual brightness
II K. However, in active regions coronal material temperatures in the 85 GHz image in this region
can also contribute at 17 GHz due to optically are in the range 900 (median) to 1500 K above
thin bremsstrahlung from the hot plasma in coro- the sunspot level, so the optically thin coronal
nal loops. Since optically thin bremsstrahlung has contribution from this feature may be partially
a brightness temperature spectrum ∝ f −2 , where masked by a larger optically thick chromospheric
f is frequency, the brightness temperature contri- contributions along the line of sight at 85 GHz.
bution of coronal material at 85 GHz should be Comparisons of the 85 GHz and magnetic field
just 4% (≈ (85/17)−2 ) of its contribution at 17 data with the Ca II K image of the region are
GHz. Coalignment of target region images at dif- shown in more detail in Figure 3. In this case
ferent wavelengths was based on full–disk images; the 85 GHz data and the magnetic field mea-
fine coalignment was possible using the active re- surements (represented by the ± 40 G contours
gion field in which the sunspot is clearly visible plotted over the Ca II K image) are from times
at many different wavelengths. closer to the acquisition time of the Ca II K image
(16:37 UT). In the left panel we plot a single 85
GHz contour at a brightness temperature of 500
4.1. Active region
K (about 20% of the peak). This contour follows
The small active region NOAA 10448 north of the outer edge of the bright Ca II K emission ex-
the solar equator (Fig. 1) was the target for tremely well, and confirms the success of the 85
these observations. Images of the region at six GHz imaging. Note that there are two “holes” in-
wavelengths are shown in Figure 2. The largest terior to the bright Ca II K emission of different
sunspot in the region is actually at the trailing character: the hole on the left lies over the sunspot
(eastern) end of the region. Clear depressions over and is prominent in the 85 GHz image, while the
this sunspot are seen in all six panels: at 85 GHz, hole to the right of center lies over weak mag-
this is the location of the weakest emission (the netic fields and is simply a low–activity region:
zero level in the maximum entropy maps). The it is not as prominent in the 85 GHz image. The
loop of bright emission encircling this sunspot in high degree of association between strong mag-
the Ca II K image is essentially reproduced in netic fields and bright Ca II K emission is obvious
the 85 GHz image. The Hα image shows a nar- in the right hand panel, with the obvious excep-
row filament in the south of the region that is tion of the sunspots. The visual impression of a
not a prominent feature at any of the other wave- high degree of correlation of the 85 GHz emission
lengths. with the Ca II K emission is confirmed quanti-
The brightest emission in the 17 GHz, 195 Å tatively. Within a radius of 8000 the linear cor-
Ca II K and Hα images consists of a broad upright relation coefficient (Pearson’s) between the two
“V” of emission north of the center of the region. images is 0.60, and the rank correlation coeffi-
This feature is not conspicuously present in the 85 cient (Spearman) is 0.70, while for the magnetic
GHz image, although there is certainly millimeter field strength the correlations with Ca II K are
emission in its vicinity. The nature of this feature 0.44 and 0.70, respectively. We take this excellent
(coronal or chromospheric) is not obvious from correlation as confirmation of the success of the
the images: the 195 Å image suggests that it con- BIMA observations. Also note that these correla-
sists of discrete features low in the atmosphere, tion coefficients cannot take account of temporal
while its presence in the Ca II K and Hα images variations: the 85 GHz images are averages overWhite, Loukitcheva & Solanki: Millimeter Observations of the Chromosphere 9
300 85 GHz 17 GHz 195 A
250
arcsec
200
150
300 Ca II K Magnetogram Hα
250
arcsec
200
150
0 50 100 150 0 50 100 150 0 50 100 150
arcsec arcsec arcsec
Fig. 2. Comparison of the active region (AR) field of view at a number of wavelengths (labelled): the BIMA
image at 85 GHz, the NoRH image at 17 GHz, the EIT 195 Å Fe XII image, the BBSO Ca II K image, the
MDI longitudinal magnetogram and the BBSO Hα image. The 85 GHz image is of the data from the first
two 30–minute scans and has been corrrected for the primary beam response and truncated in a 96 00 radius
field of view, which is also imposed on the 17 GHz, 195 Å and Ca II K image. The magnetogram display
range is ± 500 G, at 17 GHz the display range is 1.0 to 2.5 × 10 4 K, and at 85 GHz the display range is 0
to 2000 K (above the background disk level of order 7000 K).
an 8 hour period, while the images at most of the 1000 K brighter. However, in standard chromo-
other wavelengths are instantaneous snapshots. spheric models such as Vernazza et al. (1981) and
Fontenla et al. (1990, 1991), we expect that the
The total flux recovered in the BIMA image is
3.5 mm emission comes from somewhat higher
about 5 sfu; for comparison, the BIMA primary
in the atmosphere than the 0.85 mm emission,
beam filled with a source at 7000 K should pro-
and thus larger variations in brightness tempera-
duce 77 sfu at 85 GHz. The peak flux is around .09
ture are possible. The higher spatial resolution of
sfu per beam, corresponding to a brightness tem-
our observations are another likely cause of the
perature of order 1600 K (without primary beam
higher brightness temperature contrasts. Lindsey
correction). Recall that this peak brightness tem-
et al. (1990) also observed sunspots at 0.85 mm
perature really reflects the range in temperature
and did not find them to be significantly darker
from the coolest (the sunspot) to the hottest fea-
than the quiet Sun level (although clearly darker
ture in the image. This range is similar to that
than the surrounding plage in active regions), but
seen in probably the highest quality single–dish
Lindsey & Kopp (1995) carried out a more ex-
millimeter image, that of Bastian et al. (1993a)
tensive analysis and concluded that sunspot um-
with a resolution of 2100 at 0.85 mm. They ob-
brae at 0.85 mm can be considerably cooler than
served an active region in which a sunspot ap-
the quiet Sun, as low as 4000 K (at least 2000
peared as a depression with a temperature of 6000
K cooler than the chromosphere at that wave-
K, while the surrounding active region was up to10 White, Loukitcheva & Solanki: Millimeter Observations of the Chromosphere
300 85 GHz/Ca Mag/Ca
250
arcsec
200
150
0 50 100 150 0 50 100 150
arcsec arcsec
Fig. 3. Overlays of contours of the BIMA 85 GHz emission (left) and the MDI longitudinal magnetic field
(right) on the BBSO Ca II K 16:37 UT image (greyscale) for the active region field of view. The millimeter
contour is for the second active region scan at a brightness temperature of 500 K, while the magnetic field
contour is at ± 40 G.
length). The sunspot in Fig. 2 is not large enough The prominent 17 GHz depression is not evi-
for us to treat the penumbra and the umbra sep- dent as a feature at any other wavelength apart
arately here. from 85 GHz, where it is also the coolest loca-
tion in the image, 400 K cooler than the median
level in the image but 2000 K cooler than the
4.2. Quiet Sun brightest feature. The location of the depression
The target for this observation was a region of at 85 GHz is not exactly the same as in the 17
diffuse coronal emission in the EIT 195 Å im- GHz image, but it is a steady feature during the
age that clearly lay neither over an active region observations and since the 17 GHz image corre-
nor in a coronal hole (Fig. 1). Images of the re- sponds to a period at the end of the BIMA obser-
gion at six wavelengths are shown in Figure 4. vation, we are confident that they are the same
This field of view is distinguished by the almost feature. Inspection of MDI data for several days
complete absence of strong magnetic fields in the before and after the day of the BIMA observa-
magnetogram: the largest field strength is 120 G, tion did not show any optical feature at this lo-
but only 5% of the pixels shown in Fig. 4 have cation. The 17 GHz and 85 GHz images have a
field strengths in excess of 20 G. The Hα image linear (Pearson’s) correlation coefficient of 0.23,
is correspondingly devoid of prominent features. and a rank (Spearman) correlation coefficient of
The BIMA image at 85 GHz shows a pattern of 0.19, but due to the absence of strongly mag-
bright and dark features resembling the cell pat- netic features in this field of view, the degrees
tern of the network, while the 17 GHz image is of correlation between the other images at dif-
dominated by a depression on the east side of the ferent wavelengths are generally low. While this
field of view that is 2000 K cooler than the sur- may raise questions about features in the 85 GHz
rounding 10000 K disk. By contrast, the brightest images, we note that the quiet–Sun and coronal
feature at 17 GHz is only 1000 K above the disk hole scans were interleaved with the active re-
level. The total flux in the 85 GHz image is about gion scans during the observation and the data
4 sfu. from all three targets were processed in exactlyWhite, Loukitcheva & Solanki: Millimeter Observations of the Chromosphere 11
85 GHz 17 GHz 195 A
0
-50
arcsec
-100
-150
Ca K Magnetogram Hα
0
-50
arcsec
-100
-150
-350 -300 -250 -200 -350 -300 -250 -200 -350 -300 -250 -200
arcsec arcsec arcsec
Fig. 4. Comparison of the quiet Sun (QS) field of view at a number of wavelengths in the same format as
Figure 2. The magnetogram display range is ± 100 G, at 17 GHz the display range is 9000 to 10900 K, and
at 85 GHz the display range is 0 to 2000 K (with correction for primary beam respose).
the same way: the excellent correlation of the 85 tive polarity. 12% of the pixels in this field have
GHz active–region data with other wavelengths field strengths exceeding 20 G and 5% exceed
(Fig. 3) establishes that the features in the other 50 G, with a maximum field strength of 300 G.
85 GHz target regions should be valid. However, as the 195 Å image shows, the corona
Gary et al. (1990) measured brightness tem- has very low density over the coronal hole. Again
perature contributions of up to 15000 K from the the Hα image shows little structure but Ca K
network at a wavelength of 3 cm. Bastian et al. shows significantly more bright features than did
(1996) used the VLA to observe the quiet Sun at the quiet Sun region, and they are well corre-
wavelengths of 2 and 1.3 cm. They determined the lated with magnetic field strength (linear correla-
absolute level of emission using total power mea- tion coefficient of 64%, rank coefficient 0.35). The
surements from the VLA antennas themselves, brightest features in the 85 and 17 GHz images
accurate to about 20%. They found a tempera- coincide, and lie over a bright Ca K feature in the
ture range of about 2000 K across their field of south-east of the field but still within the coronal
view at 1.3 cm and 3000 K at 2 cm. hole. The correlation coefficients between the Ca
K image and the 85 GHz image are 0.26 (linear)
and 0.31 (ranked), while between Ca K and 17
4.3. Coronal hole GHz they are 0.41 (linear) and 0.42 (ranked): we
The coronal hole target chosen is just to the west do not regard the difference between these corre-
of disk center (Fig. 1). Images at six wavelengths lations as significant.
are shown in Figure 5. In contrast to the quiet Sun Figure 6 shows overlays of contours of the 85
region, this coronal hole field contains a number GHz emission (left) and the longitudinal mag-
of strong magnetic features, almost all of nega- netic field (right) on the Ca K image for the coro-12 White, Loukitcheva & Solanki: Millimeter Observations of the Chromosphere
200
85 GHz 17 GHz 195 A
150
arcsec
100
50
200
Ca K Magnetogram Hα
150
arcsec
100
50
300 350 400 450 300 350 400 450 300 350 400 450
arcsec arcsec arcsec
Fig. 5. Comparison of the coronal hole (CH) field of view at a number of wavelengths in the same format
as Figure 2. The magnetogram display range is ± 300 G, at 17 GHz the display range is 8500 to 12500 K,
and at 85 GHz the display range is 0 to 2000 K (with correction for the primary beam response).
200
85 GHz/Ca Mag/Ca
150
arcsec
100
50
300 350 400 450 300 350 400 450
arcsec arcsec
Fig. 6. Overlays of contours of the BIMA 85 GHz emission (left) and the MDI longitudinal magnetic field
(right) on the BBSO 16:37 UT Ca II K image (greyscale) for the coronal hole field of view. The millimeter
contour is for the second active region scan at a brightness temperature of 600 K, while the magnetic field
contour is at ± 40 G.White, Loukitcheva & Solanki: Millimeter Observations of the Chromosphere 13
0.015
nal hole field. This overlay again emphasizes the
general agreement between the 85 GHz morphol- 0.010
ogy and the Ca K morphology (consistent with
0.005
the fact that the ranked correlation coefficient of
Flux (sfu)
the two images is larger than the linear correla- 0.000
tion coefficient). The boundary of the bright 85 -0.005
GHz emission matches the bright features in the
Ca II K image very well. The ranked correlation -0.010
coefficient between the magnetic field image and -0.015
the Ca II K image is 0.35, very similar to that 0.015
between Ca II K and the 85 GHz image. There 0.010
are no deep depressions in the radio images of
0.005
this field. The total flux in the 85 GHz image is
Flux (sfu)
about 4.9 sfu (not corrected for primary beam 0.000
response), with a peak flux of order 0.10 sfu per
-0.005
beam corresponding to a brightness temperature
range of 1700 K. -0.010
-0.015
5. Sensitivity of millimeter 0 500 1000 1500
Time (s)
interferometer data to oscillations
Fig. 7. Comparison of the recovery of the flux of the
A motivation for observing the solar chromo- test oscillating source in two cases. In each panel the
sphere with a millimeter–wavelength interferom- plus symbols are the fluxes recovered by fitting the
eter is to be able to make images with high spa- difference between the deconvolved image with the
tial resolution at high time resolution and thus to test source and the deconvolved image without it,
look for wave power. Due to the unusual way in while the solid line represents the flux of the oscil-
which the snapshot BIMA images have to be de- lating test source. The upper panel shows the results
rived (i.e., maximum entropy deconvolution with for a 290 s oscillation with an amplitude of 0.012 sfu
a default image based on the average over the located in a region of low flux, while the lower panel
whole time period), in a search for wave power shows the results for a 185 s oscillation of amplitude
it is important to understand the sensitivity of 0.008 in a region of higher flux.
the imaging technique to waves. In section 2 we
briefly described tests of the sensitivity of the im- we made the test somewhat more complex by
ages to changes. In this section we specifically test adding two point sources at a time, one with a pe-
for the ability to recover oscillations. riod of 290 s (five–minute oscillation) and an am-
The tests were carried out as follows. The ac- plitude of 0.012 sfu that was 15% of the maximum
tual sequence of visibility data for a given tar- in the mean image, and the other with a period of
get was modified by the addition of point sources 185 s (three–minute oscillation) and an amplitude
whose amplitude varied sinusoidally in time (us- of 0.008 sfu that was just 10% of the maximum
ing the MIRIAD task uvmod). The data with in the mean image. In the images these point test
and without the test source were then processed sources should appear as 1000 features with bright-
identically, as described above: dirty maps were ness temperature amplitudes of 200 and 135 K,
inverted from the visibilities and deconvolution respectively. Seven different test sequences were
was carried out using maximum entropy with a run, each consisting of 118 integrations 15 s apart
default image. The final maps without the test using the second scan of the quiet–Sun target re-
source (i.e., the original BIMA data) were then gion, with the two sources in different locations
subtracted from the corresponding maps made each time. In each case, Gaussian fits to the dif-
with data including the test source. In practice, ference images were made at the known locations14 White, Loukitcheva & Solanki: Millimeter Observations of the Chromosphere
of the test sources, limiting the size of the fit- We also plot values for two other comparisons:
ted source to be no bigger than about twice the in a given test we can create the above product
restoring beam size. using the “wrong” test source fluxes, i.e., mul-
The nature of the results can be seen in Figure tiplying the measured fluxes at the location of
7, where we compare the resulting light curves the 290 s source with the model fluxes for the
for one of the best recovered oscillations (lower 185 s source, and vice–versa. These two quanti-
panel, 185 s period) and one of the worst (upper ties should be out of phase and thus on average
panel, 290 s period) with the input test source cancel out: the triangle symbols in the right panel
fluxes. Even in the poorer case, the oscillation is represent this quantity and show that this is in-
clearly seen, while in the lower panel the agree- deed the case. Secondly, to investigate whether
ment between the input fluxes and the recovered flux that is not recovered at the location of the
fluxes is extremely good. However, the fits al- test source is spread out over the rest of the map,
ways recovered sources that were spatially more we measured fluxes at the location marked by the
extended than the model point source, indicat- square in the left panel of Fig. 8. This location has
ing that maximum entropy deconvolution did not a mean flux that is 20% of the maximum in the
have enough information in the data to get the average map. The squares in the right panel of
source dimensions correct. The recovered source Fig. 8 show the “fraction of the model flux recov-
dimensions were small in cases where the oscil- ered” at this location, i.e., the sums defined above
lations were well recovered but much broader in where the Si values are measured at this location,
cases of poor recovery. In some cases the decon- for both the 290 s and 185 s test source Ti values.
volved test source did not resemble the model at This quantity is zero in the cases where the test
all: for example, the test source located in the cir- source was well recovered, but can be quite large
cular depression centered at coordinates (-23300 , - and often negative in the cases of poor recovery,
5300 ) produced flux in the deconvolved maps that suggesting that indeed the flux of the oscillating
appeared in the bright ring surrounding the de- source can be redistributed over the image, but
pression rather than in the depression itself, con- often out of phase, when the oscillation is located
sistent with poor flux recovery at low flux values. in a region of low mean flux.
In Figure 8 we present a summary of the overall The pattern in the upper panel of Fig. 7 ac-
test. In the left panel we show the locations of the tually suggests a reason for the poor recovery of
test sources overlaid on the mean image for the test source flux at locations of low flux in the
period being considered. On the right panel we mean map. There is an asymmetry in the recovery
plot the fraction of the oscillation recovered (en- of the positive and negative values of the model
circled plus symbols) as a function of the flux at source: the positive values in general seem to be
the location of the test source in the average map. better recovered. This may be related to the pos-
The fraction of the oscillation recovered here is itivity constraint of the maximum entropy algo-
P P
defined as the quantity ( i Si Ti )/( i Ti2 ), where rithm used here: if the test source location be-
Si are the measured fluxes from the Gaussian comes more negative than the rest of the field,
fits to the difference images and Ti are the in- then in order for it to be recovered while the pos-
put fluxes of the test source at that location; this itivity constraint is satisfied, all other pixels in the
quantity is unity for perfect recovery of the model image need to have their flux values increased. In
fluxes, Si = Ti , but if the Si measurements do this case recovery of the model requires changes in
not correlate with the Ti values the product will many pixels to be correctly tracked by the decon-
be zero. The results are in agreement with the volution within the finite number of iterations of
earlier tests: at locations where the mean flux is maximum entropy deconvolution typically chosen
high the test source is recovered extremely well, to reach a stable result within a reasonable time.
whereas at locations with low mean fluxes recov- By contrast, in the case where the test flux is
ery can be quite poor (although in no case do we positive or the underlying flux is quite large, the
fail to see the test source at all). deconvolved image will only show changes at theWhite, Loukitcheva & Solanki: Millimeter Observations of the Chromosphere 15
50
Oscillating fraction recovered
1.0
0
-50 0.5
arcsec
-100
0.0
-150
-0.5
-350 -300 -250 -200 -150 0 5 10 15 20
arcsec Mean flux
Fig. 8. Tests of the recovery of oscillating test sources in the BIMA observations. The left panel indicates
14 locations (black plus symbols surrounded by white circle) where oscillating sources were placed in seven
separate simulations (two sources per simulation, one with a 290 s period and the other with a 185 s period)
of the second scan of the quiet Sun (average image shown). The right panel shows the fraction of the test
P
source flux recovered for each of the 14 sources (plus symbols surrounded by circles), defined as ( i Si Ti )
P 2
/( i Ti ) where Si are the recovered flux values and Ti are the input test source fluxes, so that a value of
1.0 corresponds to perfect recovery of the input source. For comparison, the triangles are the same quantity
for the 14 locations but swapping the 185 s and the 290 s test fluxes: the S i and Ti values then should be
out of phase with each other and cancel, as is found. The squares represent the same quantity but for the
location marked by a square in the left panel, where no test source was located: in each of the seven tests
we extracted the light curve at this location and constructed the product above for both the 290 s and 185
s oscillations, resulting in the 14 values plotted. In each case the square symbol is plotted underneath the
corresponding test source product.
location of the test source and relatively few pix- but the test sources used here represent only a
els need to be changed, presumably making for a small fraction of the total flux present (in these
simpler deconvolution problem. tests, the two sources total about 0.5% of the 4
From these tests, we conclude that individual sfu of flux in the deconvolved images), so the re-
oscillating sources can indeed be recovered down sults do indicate that quite small levels of oscil-
to quite low amplitudes (certainly less than 10% lation power can be detected with the technique
of the contrast in the image, i.e., of order 100 K) described.
using the mapping technique for BIMA data ap- However, if oscillation power is present every-
plied here, provided that they lie in regions where where in the image simultaneously then the lim-
the mean flux is not too low. It seems plausible ited number of baselines available to make the
that heating power should predominantly lie in snapshot images will limit our ability to recon-
regions where the mean flux is higher since we struct oscillation power in many resolution ele-
expect that regions of strong heating are likely ments simultaneously. We have carried out a test
to be bright in the BIMA images. These tests do in which 8 model point sources are added to the
not, of course, truly represent the likely appear- visibility data for a single snapshot at random lo-
ance of oscillation power in the millimeter images, cations and then the resulting snapshot data are16 White, Loukitcheva & Solanki: Millimeter Observations of the Chromosphere
deconvolved using the same default model as be- parison with models is presented in a com-
fore. As expected based on the arguments given panion paper by Loukitcheva et al. (2005).
above, we find that some of the sources are well
recovered in the deconvolved map, while those lo-
6.1. Analysis Technique
cated in regions of weak flux are not and their flux
appears redistributed, spread as diffuse emission After the procedures of image restoration and
across other brighter locations in the image. On elimination of poorer data we are left with nine
this basis, we argue that oscillation power present uninterrupted 30–minute sequences of snapshot
in the target region does not seem to be lost by images (in units of brightness temperature): 3
the deconvolution approach we adopt here, but successive quiet-Sun scans (QS2, QS3, QS4), 3
it may not appear in the correct location since active region scans (AR2, AR3, AR4) and 3
the tests indicate that power located in regions of coronal hole scans (CH1, CH2, CH4). All im-
low flux may not be accurately recovered. Bright ages were corrected for the primary beam re-
oscillating sources in locations of steady bright sponse and truncated in a 7200 radius field of view.
emission, on the other hand, may be well repre- For the analysis of the radio oscillations we em-
sented in the final maps. This is a limitation of ployed two standard techniques: Fourier power
the technique we employ (the only technique we spectra, and wavelet transforms. Comparison
found which produced satisfactory results, lim- of results from two independent techniques
ited by the small number of antennas in the ar- gives us more confidence in our conclu-
ray and the low–contrast nature of the bright- sions. Power spectra were obtained by applying
ness distribution), and better results will require the Fast Fourier Transform algorithm including
images from an interferometer with many more a 10% cosine apodisation. Before processing, the
elements, such as the Atacama Large Millimeter long term evolution in each pixel was removed
Array (ALMA). We briefly investigate what oscil- by subtracting a third order polynomial fit to the
lation properties the BIMA image sequences dis- brightness temperature time series. No other fil-
play in the following section. tering was carried out in order to preserve the
original oscillatory power. The statistical signif-
icance of the oscillations for individual and spa-
6. Oscillation power in the millimeter tially averaged time series was estimated using
the prescription of Groth (1975), depending on
images
the level of the (white) noise in the power spec-
Based on the analysis given in the pre- tra. (The actual noise characteristics are difficult
ceding section, we expect that if the os- to assess given the complex processing undergone
cillation power is dominated by a small by the data, but for simplicity we will proceed
number of features located in regions of as if white noise is the appropriate assumption.)
bright emission then it should be well rep- Only power above the 99% significance level was
resented by these data, but if significant considered significant.
oscillation power resides in locations that The Nyquist frequency of the image sequences
are faint in the daily average image used is 33 mHz, corresponding to a period of 30 sec-
as a model for the time–dependent analy- onds, and due to the discrete sampling any pe-
sis then it is likely to be redistributed into riod in the signal shorter than 30 seconds will
regions of bright emission and contaminate be aliased. The duration of the significant oscil-
the oscillation spectra there. In this sec- lations as well as the evolution of their periods
tion we investigate the oscillation proper- were studied by means of a wavelet analysis. As a
ties shown by these data using standard mother wavelet we use the complex valued Morlet
analysis approaches, bearing in mind the wavelet that consists of a plane wave modulated
limitations imposed by the deconvolution by a Gaussian. For the wavenumber k, which
method. A more detailed analysis and com- describes the number of oscillations within theYou can also read
