# Solar Observing with the Atacama Large Millimeter-Submillimeter
Array111Accepted for publication in Frontiers in Astronomy and Space Science

T. S. Bastian  National Radio Astronomy Observatory, 520 Edgemont Road,
Charlottesville, VA 22903 USA  M. Shimojo  National Astronomical Observatory
of Japan, 2-21-1, Osawa, Mitaka, Tokyo 181-8588, Japan  M. Bárta  Astronomical
Institute, Academy of Sciences, Fričova 298, 251 65 Ondřejov, Czech Republic
S. M. White  pace Vehicles Directorate, Air Force Research Laboratory, 3550
Aberdeen Avenue SE, Kirtland AFB, NM 87117-5776, USA  K. Iwai  Institute for
Space-Earth Environmental Research, Nagoya University, Furo, Chikusa, Nagoya,
464-8601, Japan

###### Abstract

The Atacama Large Millimeter-submillimeter Array (ALMA), sited on the high
desert plains of Chajnantor in Chile, has opened a new window onto solar
physics in 2016 by providing continuum observations at millimeter and sub-
millimeter wavelengths with an angular resolution comparable to that available
at optical (O), ultraviolet (UV), extreme ultraviolet (EUV), and X-ray
wavelengths, and with superior time resolution. In the intervening years,
progress has been made testing and commissioning new observing modes and
capabilities, in developing data calibration strategies, and in data imaging
and restoration techniques. Here we review ALMA current solar observing
capabilities, the process by which a user may propose to use the instrument,
and summarize the observing process and work flow. We then discuss some of the
challenges users may encounter in imaging and analyzing their data. We
conclude with a discussion of additional solar observing capabilities and
modes under consideration that are intended to further exploit the unique
spectral coverage provided by ALMA.

ALMA, Instrumentation, Millimeter-submillimeter, Solar observing, Calibration,
Data analysis

##  1 Introduction

The Atacama Large Millimeter-submillimeter Array (ALMA) is a high-performance,
general-purpose telescope that has opened a new frontier of astrophysics,
offering fundamentally new observations at mm-$\lambda$ and submm-$\lambda$.
ALMA first became available to the wider scientific community more than a
decade ago, at the end of 2011 (ALMA observing Cycle 0) but it was not until
five years later in late 2016 that solar observations first became available
with ALMA (observing Cycle 4), Since then, the solar physics community has
embarked on a number of ambitious solar observing programs, providing new
insights into outstanding problems in solar physics. Results from several of
these programs are presented in the Frontiers collection of articles and
reviews entitled “The Sun Seen with the Atacama Large mm and sub-mm Array
(ALMA) - First Results ”.

Solar observing with ALMA is not without challenges. First, a number of
technical barriers needed to be overcome to enable solar observing – and
continue to be addressed as new observing modes and capabilities are
considered. Second, as an interferometer the imaging and data reduction
techniques employed by ALMA are not necessarily familiar to the wider solar
community and a learning curve must be surmounted. In fact, solar imaging and
reduction techniques remain under development in some cases. Hence, the ALMA
solar user community is small, but growing. Finally, as a new window onto the
Sun, the observations themselves pose interesting challenges to our
understanding of physical processes on the Sun!

In the remainder of this section we introduce the key attributes of ALMA and
summarize the basic elements of the technical and operational approach to
observing the Sun. Readers may wish to consult additional resources: a general
overview of the instrument may be found in Wootten & Thompson (2009) while
details regarding solar observing and data calibration are presented by
Shimojo et al. (2017) and White et al. (2017). In §2 we summarize ALMA’s
current observing capabilities, with an emphasis on new capabilities that have
been commissioned since Cycle 4. In §3 we discuss the process by which an
interested scientist may propose to observe with ALMA. We then describe, for
successful observing programs, the observing process and the subsequent work
flow leading to data delivery to the observer. In §4 we discuss some of the
lessons learned from experience with ALMA imaging and data analysis. In §5 we
discuss future observing modes and capabilities that will enhance solar
science with ALMA. We conclude in §6.

###  1.1 Organization of the Observatory

Before describing the instrument itself we briefly describe the organization
of the observatory. The observatory is fundamentally international in nature,
a partnership between the United States National Science Foundation, the
European Organization for Astronomical research in the Southern Hemisphere,
and the National Institutes of Natural Sciences of Japan, in cooperation with
the Republic of Chile. Management of the of the observatory is consolidated
under the Joint ALMA Observatory (JAO222See https://www.almaobservatory.org).
The JAO is based in Santiago, Chile, and is responsible for operating,
maintaining, enhancing, and optimizing ALMA on behalf of the wider scientific
community. The JAO organizes and oversees calls for proposals and their
review, executes approved observing programs, and archives the data. The
telescope itself is sited approximately 1500 km north of Santiago at the Array
Operations Site (AOS). Telescope operations are supported and maintained from
the Operations Support Facility (OSF) at a distance of about 30 km from the
AOS. The OSF also supports assembly, integration, and verification of
technology before it is moved to the AOS.

The ALMA scientific community is supported by ALMA Regional Centers (ARCs)
affiliated with each ALMA partner333The roles and responsibilities of the ARCs
can be found at https://almaobservatory.org/en/about-alma/global-
collaboration. These are operated by the National Radio Astronomy Observatory
(NRAO) on behalf of North America, the European Southern Observatory (ESO) on
behalf of its member states, and the National Astronomical Observatory of
Japan (NAOJ) on behalf of East Asia. The North American and East Asia ARCs are
co-located with their national observatories whereas the European ARC follows
a distributed model of seven ARC nodes coordinated from ESO headquarters in
Garching. The ARC node with responsibilities for the European solar community
is based in Ondrejov, Czech Republic. The ARCs are each advised by scientific
advisory committees to ensure that user concerns and priorities are known and
addressed. The overall observatory is advised by the ALMA Scientific Advisory
Committee.

The role of the ARCs or ARC nodes in the workflow of a given project is
discussed in greater detail in §3. It is important to note that the ARCs also
play an important role in education and outreach. For example, the ARCs are
used to organize ALMA Community Workshops prior to each call for proposal. The
goal of those meetings is to help the local community with proposal
preparation.

###  1.2 Overview of the Instrument

ALMA is located on the Chajnantor plateau of the Chilean Andes at a latitude
of $-23^{\circ}$, a longitude of $-67.8^{\circ}$, and an elevation of over
5000 m. It is a general-purpose telescope designed to operate at mm-$\lambda$
and submm-$\lambda$ in order to address an extremely broad program of
astrophysics – from cosmology, to star and planet formation, to
astrochemistry. ALMA is an interferometer comprising an array of antennas that
sample the Fourier transform of the brightness distribution within the field
of view. A given pair of antennas measures a single Fourier component, an
amplitude and a phase referred to as a complex visibility, corresponding to a
spatial frequency defined by the antenna spacing and orientation. A given
antenna spacing is referred to as an antenna baseline. Long antenna baselines
measure small angular scales and short baselines measure large angular scales
in the brightness distribution. The Fourier domain in which the measurements
are made is referred to as the aperture plane or the uv plane, where u and v
refer to the coordinates of antenna baselines, typically measured in
wavelength units. An array of $N$ antennas has $N(N-1)/2$ independent
baselines. The instantaneous uv sampling provided by an array is sometimes
referred to as the “snapshot” uv coverage. For sources that are static in
time, one can exploit the fact that the array geometry, as viewed from the
source, changes due to Earth’s rotation, allowing the uv plane sampling to be
filled in with time. This technique is referred to as Earth rotation aperture
synthesis.

Figure 1: ALMA is an array composed of 50 x 12 m movable antennas (left
background,), $12\times 7$ m fixed antennas (right foreground), and $4\times
12$ m total power antennas.

ALMA has a total of 66 high performance antennas. The 12-m array is composed
of $50\times 12$ m antennas and is reconfigurable. That is, the antennas may
be moved to change the distribution of baselines and, hence, sampling in the
uv plane in order to change the angular resolution and surface brightness
sensitivity of the instrument. Baseline lengths can be as small as 15 m and as
large as 16 km although for solar observing, array configurations are
currently restricted to the four most compact configurations of the ten array
configurations in general use (see Table 2). With all 50 antennas operative in
the 12-m array, a total of 1225 independent baselines are available. The field
of view (FOV) of the 12-m array is determined by the response of a single
antenna which, to first order may be described by a modified Airy function
with a main lobe and sidelobes. The main lobe is well described by a Gaussian.
ALMA antennas are of Cassegrain design; accounting for the taper of the
antenna illumination pattern and blockage by the subreflector and the
quadrupod support structure, the HPBW of the Gaussian main beam – also
referred to as the primary beam – is given by
$\theta_{FOV}=1.13\lambda/D=19.42”\lambda_{mm}$. The Atacama Compact Array
(ACA) comprises $12\times 7$ m antennas and four 12 m total power antennas.
The 7 m antennas are fixed and provide lower-resolution imaging to complement
that provided by the 12-m array, or it can be used in a standalone mode. In
the case of solar observations, the array of 7 m antennas is used to
supplement the angular coverage provided by the 12-m array as discussed
further in §2. The FOV of a 7 m antenna is $\theta_{FOV}=33.3”\lambda_{mm}$.
The four 12 m antennas are available for making total power measurements.
These play an important role in solar observing by effectively filling in the
smallest spatial frequencies that are not otherwise measured by the 12-m array
and the 7 m array of antennas as we discuss further in §2.5 and §4.4.

Interferometric (INT) observations made by with the 12-m array use the
Baseline Correlator (BLC) to produce visibility data. The ACA correlator may
be used to correlate antennas in the 7-m array. Alternatively, as is the case
for solar observations (see §1.2.3 below), correlations between antennas in
the ACA and the 12-m array may be processed together through the BLC.
Continuum observations are performed using the ALMA Time Domain Mode (TDM). A
given target is observed in two frequency ranges above and below the local
oscillator (LO) frequency – the upper and lower sidebands. Each side band is
subdivided into two spectral windows, each of 2 GHz bandwidth. Hence, a total
of four spectral windows is observed with a combined bandwidth of 8 GHz.
Available observing bands and spectral windows are summarized in Table 1. Each
spectral window is currently fixed in frequency as a result of the gain
reduction approach adopted (see §1.3.1). The TDM mode coarsely channelizes
each spectral window into 128 frequency channels. During calibration and data
reduction these are corrected for the instrument response across the spectral
window (bandpass correction), edited to remove radio frequency interference or
unwanted atmospheric lines, and then averaged to form pseudo-continuum
frequency bands.

ALMA antennas measure two orthogonal senses of linear polarization
simultaneously, $X$ and $Y$. All solar observations are currently made in
dual-polarization mode. That is, the BLC produces correlations between
antennas $i$ and $j$ as $X_{i}X_{j}$ and $Y_{i}Y_{j}$ visibilities. The two
linearly polarized correlations are generally summed to produce visibilities
in total intensity (the Stokes I parameter). The two may be differenced as a
means of estimating the thermal noise (Shimojo et al., 2017).The
implementation of full polarimetry for solar observations is currently under
study (§5.1).

###  1.3 Challenges Posed by the Sun

The Sun poses a number of challenges for a general purpose instrument not
specifically designed and optimized for solar observing. These challenges are
over and above the already considerable challenges of observing in the
mm/submm-$\lambda$ range. Among them are:

  * •

The Sun is an intense emitter, so much so that it causes ALMA receivers to go
into compression and for electronic elements along the signal path to saturate
unless provisions are made.

  * •

The Sun is a moving target, not only because of its apparent motion across the
sky, but also because of its (differential) rotation.

  * •

The Sun is much larger than the FOV of a single ALMA antenna, which is $<20”$
at a wavelength of 1 mm, for example.

  * •

Emission from the Sun is highly variable as a result of a variety of
phenomena, ranging from chromospheric oscillations to flares.

We now briefly summarize how each of these challenges have been addressed.

####  1.3.1 Antenna Gain Reduction

The ALMA antennas were carefully designed to allow them to safely point at the
Sun. However, to avoid compression of the receivers and saturation along the
electronic signal path, two steps are taken:

  1. 1.

The gain of the SIS mixers in ALMA receivers is reduced by changing the
voltage bias and/or the local oscillator (LO) current – the so-called “mixer
detuned” or “mixer debiased” (MD) mode. The decrease in receiver gain provides
greater headroom for the receivers to operate without going into compression.
However, to ensure correct calibration transfer, both the Sun and calibrator
sources must be observed in MD mode.

  2. 2.

There is still an enormous differential in the power entering the system when
observing the Sun and observing calibrator sources, which are typically
compact quasars or planets. Stepped attenuators along the signal path are used
to set signal powers to optimum levels during an instrumental setup scan on
the solar target. For all subsequent calibrator scans, the attenuators
settings are reduced by a known and fixed amount on each antenna. In this way,
robust phase transfer is ensured.

As shown by Shimojo et al. (2017) these modifications allow observations of
quiet Sun and active region phenomena. Observations of solar flares are
another matter, one that we discuss in §5.4. A consequence of using the MD
mode is an increase in system temperature which lowers the system sensitivity
when observing calibrator sources, as least for bands 3, 5, and 6. For gain
calibrators, it is highly desirable to observe a bright quasar ($>1$ Jy)
relatively close to the Sun ($<15$ deg). Between late June and early July,
there are no such bright quasars near the Sun, a period of time that should
therefore be avoided for solar observing. In practice, it is rare that
suitable array configurations are available for solar observing at this time
because the larger configurations are favored during Chilean winter.

####  1.3.2 Apparent Source Motion

The Sun and other solar system objects – planets, comets, asteroids – all
display apparent motion. Their apparent position on the celestial sphere is
described by an ephemeris. In the case of the Sun, the ALMA Solar Ephemeris
Generator444The ALMA Solar Ephemeris Generator was developed by Ivica Skokić
and is available at http:celestialscenes.com/alma/coords/CoordTool.html is a
convenient tool for preparing the solar ephemeris needed for observations on
any specified date. The Ephemeris Generator takes into account solar rotation
via a standard or user-specified solar rotation model, as well as target
offsets relative to the center of the solar disk. ALMA scheduling blocks link
the user-specified solar ephemeris to the online system, allowing it to point
and track the solar target of interest as discussed further in §3.

####  1.3.3 Mapping a Large Field of View

The FOV of a single 12 m ALMA antenna is small compared to the angular
diameter of the Sun, or even compared with the typical scale of an active
region (few arcmin). There are two issues:

  * •

In order to increase the size of the angular domain mapped by ALMA, mosaicking
techniques must be used (Cornwell & Fomalont, 1989; Sault et al., 1996)).
Mosaicking entails sequentially sampling a user-specified grid of array
pointings to increase the effective FOV. The spacing between discrete
pointings is set to ensure Nyquist sampling or better. Mosaic pointing
patterns are referenced to the user-specified solar ephemeris.

  * •

A related issue is that, as an interferometer, ALMA acts as a high-pass
filter. While the maximum antenna baselines set the angular resolution of the
array, the minimum antenna baselines determine the largest angular scales
measured by the array. As seen in Table 3, the maximum recoverable scale
measured by a given configuration of the 12 m array are all significantly less
than the FOV! Two measures were implemented to mitigate this state of affairs:

    * i)

Solar observations use both the antennas in the 12-m array and those in the
ACA as a combined array to perform interferometric (INT) observations. That
is, all antenna baselines – 7 m x 7 m, 7 m x 12 m, and 12 m x 12 m are
correlated in the BLC. In doing so, measurements on shorter baselines and
larger angular scales are available and may be helpful in some circumstances
(see §4.1).

    * ii)

Solar observers are provided with contemporaneous fast-scan total power (TP)
maps of the full disk of the Sun (Phillips et al., 2015; White et al., 2017)).
These maps can be used to “fill in” the largest angular scales that are
otherwise not measured by the interferometric array.

We return to some of the subtleties associated with these mitigation
strategies in §4.4.

####  1.3.4 Time Resolution

Solar emission at mm-$\lambda$ and submm-$\lambda$ varies over a wide range of
time scale, from $<1$ s to minutes, hours, and days. Depending on a given
user’s science objectives, it may be necessary to resolve this time
variability on the relevant time scale. If it is acceptable to average over
time variability, one can exploit Earth rotation synthesis to improve sampling
of the uv plane somewhat with the available distribution of antennas. However,
if the user wishes to resolve variable emission on time scales of minutes or
less, the uv coverage does not change appreciably over the relevant time scale
and the user is effectively constrained to snapshot uv coverage. For many
types of science, this trade-off is acceptable: the quality of the imaging is
compromised but the source variability of interest is resolved.

##  2 ALMA Solar Observing Capabilities

We now summarize ALMA’s solar observing modes and capabilities, current as of
Cycle 9 in 2022-2023. We emphasize that development of additional modes and
capabilities is ongoing, as discussed further in §5. We note that while a
number of software packages may be used to image ALMA data, the most powerful
and well-supported is the Common Astronomical Software
Applications555https://casa.nrao.edu (CASA) package. We make occasional
reference to specific tasks or functions found in CASA.

###  2.1 Frequency Bands

Four frequency bands are currently supported by ALMA for continuum solar
observing (Table 1). Bands 3 and 6 were the first to be commissioned and were
offered to the community in 2016 (Cycle 4). Testing and commissioning of solar
continuum observations in ALMA Band 7 (346.6 GHz, 0.86 mm) were completed in
2018 and were made available to the community in 2019 as part of ALMA Cycle 7.
Solar continuum observations in Band 5 (198 GHz, 1.51 mm) were commissioned in
2019 and were to be made available in 2020 for ALMA Cycle 8. Owing to the
pandemic, however, Cycle 7 observations ended prematurely with the shutdown of
the telescope in March 2020 and Cycle 8 was effectively canceled. The
telescope was restarted in 2021 and the observing cycle number was reset to
Cycle 8. Science observations recommenced in October 2021.

Two MD modes were initially commissioned for Bands 3, 5, and 6. MD1 was
initially designed for observations of the quiet Sun and MD2 for observations
of active regions. In practice, however, it is found that MD2 results in more
linear receiver performance although it comes at the cost of higher system
temperature Tsys ($\sim\\!800$, 700, and 800 K, respectively). In the case of
Band 7, no stable voltage de-bias settings were found. Hence, nominal receiver
settings are used for band 7 observations although the stepped attenuators are
optimized for solar observing. On one hand, Tsys remains low ($\sim\\!200$ K);
on the other, the system is in mild compression ($\sim 15\%$).

Table 1: ALMA Solar Observing Bands Freq. Band |  $\nu_{LO}$ (GHz) |  $\lambda_{LO}$ (mm) | spw 0 (GHz) | spw 1 (GHz) | spw 2 (GHz) | spw 3 (GHz)
---|---|---|---|---|---|---
3 | 100 | 3 | 92-94 | 94-96 | 104-106 | 106-108
5 | 198 | 1.51 | 190-192 | 192-194 | 202-204 | 204-206
6 | 239 | 1.25 | 229-231 | 231-233 | 245-247 | 247-249
7 | 346.6 | 0.86 | 338.6-340.6 | 340.6-342.6 | 350.6-352.6 | 352.6-345.6

###  2.2 Array Configurations

Four of the ten possible 12-m array configurations are available for solar
observing as shown in Table 2. Check marks indicate that the configuration is
available for solar observations. There are two reasons for this restriction:
first, at mm-$\lambda$ and submm-$\lambda$ precipitable water vapor in the sky
introduces phase variations to the wavefront incident on each antenna that can
propagate into the visibilities as image motion and/or a loss of coherence
unless corrected. ALMA uses water vapor radiometers (WVRs) on each antenna to
measure brightness temperature variations of the sky, a proxy for the phase
variations (Nikolic et al., 2013) that may be used to make antenna-based phase
corrections. Unfortunately, the WVRs saturate when pointing at the Sun and
such corrections are therefore not available for solar observations. Instead,
self-calibration techniques must be used to correct phase variations (§5).
However, for self-calibration to be effective, the loss of coherence due to
phase fluctuations, which increases with baseline length, must not be so
extreme as to render the technique ineffective because it relies on a
plausible initial model of the source. Hence, the maximum array configurations
in each available frequency band is chosen to ensure that self-calibration
techniques can be used in most cases to correct for phase fluctuations
introduced by the sky.

Table 2: ALMA Array Configurations for Solar Observing | Band | 3 | 5 | 6 | 7
---|---|---|---|---|---
Configuration |  $\nu$ (GHz)/$\lambda$ (mm) | 100/3 | 198/1.51 | 239/1.25 | 346.6/0.86
ACA | bmin (m): 8.7 | ✓ | ✓ | ✓ | ✓
| bmax (m): 45.0 |  |  |  |
C-1 | bmin (m): 14.6 | ✓ | ✓ | ✓ | ✓
| bmax (m): 160.7 |  |  |  |
C-2 | bmin (m): 14.6 | ✓ | ✓ | ✓ | ✓
| bmax (m): 313.7 |  |  |  |
C-3 | bmin (m): 14.6 | ✓ | ✓ | ✓ |
| bmax (m): 500.2 |  |  |  |
C-4 | bmin (m): 14.6 | ✓ |  |  |
| bmax (m): 783.5 |  |  |  |

A second issue is that as the array configuration increases in size with a
fixed number of antennas, sampling in the uv plane becomes increasingly
sparse. Since uv coordinates are measured in wavelength units, it is also the
case that the sampling becomes increasingly diluted with increasing frequency.
This is readily seen in Table 3 which shows the array resolution and the
maximum recoverable scale666The maximum recoverable scale is
$\theta_{MRS}\approx 203\lambda_{mm}/L_{5}$ arcsec, where $L_{5}$ is the
radius in meters within which 5% of the baselines in a given configuration
reside. $L_{5}$ is 9.1, 21.4, 27.0, 36.6, and 54.1 for the ACA, C-1, C-2, C-3,
and C-4 configurations, respectively. $\theta_{MRS}$ for each frequency band
and configuration. While the angular resolution improves for a given
configuration as one moves to higher frequencies, or as one increases the size
of the array configuration at a fixed frequency, the price paid is poorer
sampling of the Fourier domain. This is an important consideration when
imaging a target like the Sun, which emits on angular scales ranging from the
available resolution to scales much larger than the FOV of a given antenna.
The configurations offered for solar use therefore represent a compromise
between angular resolution and the density of uv sampling.

Table 3: ALMA Angular Resolution and Maximum Recoverable Scale | Band | 3 | 5 | 6 | 7
---|---|---|---|---|---
Configuration |  $\nu$ (GHz)/$\lambda$ (mm) | 100/3 | 198/1.51 | 239/1.25 | 346.6/0.86
ACA |  $\theta_{res}$(arcsec) | 11.6 | 6.77 | 5.45 | 3.63
|  $\theta_{MRS}$ (arcsec) | 66.0 | 36.1 | 29.0 | 19.3
C-1 |  $\theta_{res}$(arcsec) | 3.38 | 1.83 | 1.47 | 0.98
|  $\theta_{MRS}$ (arcsec) | 28.5 | 15.4 | 12.4 | 8.25
C-2 |  $\theta_{res}$(arcsec) | 2.30 | 1.24 | 1.00 | 0.67
|  $\theta_{MRS}$ (arcsec) | 22.6 | 12.2 | 9.81 | 6.54
C-3 |  $\theta_{res}$(arcsec) | 1.42 | 0.77 | 0.62 |
|  $\theta_{MRS}$ (arcsec) | 16.2 | 8.73 | 7.02 |
C-4 |  $\theta_{res}$(arcsec) | 0.92 |  |  |
|  $\theta_{MRS}$ (arcsec) | 11.2 |  |  |

It is important to note, however, that any of the four 12-m array
configurations available to solar observers may be used in combination with
the ACA 7-m array. That is, solar observations make use of a single
heterogeneous array that includes available 12-m array antennas and ACA 7 m
antennas. The reason for doing so is readily apparent from Table 3:
$\theta_{MRS}$ for any band and any configuration is less than the FOV.
Inclusion of the ACA 7 m antennas provides sampling up to angular scales
comparable with the nominal FOV; and as previously noted, full-disk total
power maps are also available to fill in emission on the largest angular
scales. We return to issues related to the use of the heterogenous array in
§4.1.

###  2.3 Time Resolution

The time resolution initially offered to the solar community for Cycle 4 was 2
s. This was reduced to 1 s beginning with Cycle 7. ALMA provides a much higher
snapshot imaging cadence than is typically available at UV/EUV wavelengths
from space missions such as the Solar Dynamics Observatory(SDO; 12 s) and the
Interface Region Imaging Spectrograph (IRIS; 20 s). A study led funded by the
European Southern Observatory is exploring opportunities for even higher time
resolution imaging, as well as the use of larger antenna configurations to
enable higher angular resolution imaging (§5).

###  2.4 Mosaicking

The mosaicking technique was introduced in §1.2.3. The upper limit to the
number of pointings in a given mosaic is currently limited to 150 for both
solar and non-solar observations. An example of a large format mosaic is shown
in Fig. 2. The minimum time per pointing for solar observations is 7.6 s,
including overhead for moving the antennas from one point to another.
Therefore, including calibration, more than 20 min is required for a single
large format mosaic. More limited mosaics can, of course, be executed but
users must weigh the tradeoffs between the desired FOV, the time required to
execute a given mosaic, and the time scale on which the source may change. An
example of a ten-pointing mosaic is shown in §4.1.

Figure 2: Examples of large-format mosaics from ALMA science verification
data. Left panel: a 149-pt mosaic in Band 3 (3 mm) of a sunspot-containing
active region. Right panel: a 149-pt mosaic in Band 6 (1.25 mm) of the same
sunspot two days later. The equivalent field of view of the Band 6 image is
shown on the Band 3 as a dashed-line box. Note the difference in brightness
temperature scale. See also Shimojo et al. (2017).

###  2.5 Fast-scan Total Power Mapping

Full-disk TP maps supplement interferometric (INT) observations. These provide
broader context images for the INT data and provide the means of “filling in”
short uv spacings, critical if absolute brightness temperatures are needed.
The most straightforward technique for combining TP and INT data is
“feathering” (Cotton, 2015). See §4.4 for further discussion about combining
TP and INT data.

As described by White et al. (2017) a double-circle pattern is employed to
scan a region centered on the Sun that is 2400” in diameter (see Fig. 3 for an
example). The resolution of the map is determined by the resolution of the 12
m total power antenna: 58.3”, 29.3”, 24.3”, and 16.7” at Bands 3, 5, 6, and 7,
respectively. The time required to produce a full disk map depends on the
frequency band: e.g., 13 min for Band 3 and 17 min for Band 6. Calibration of
the full disk maps is challenging. Non-repeatability between specific
instances led White et al. (2017) to suggest best-values for the quiet Sun
brightness temperature at the center of the solar disk based on an aggregation
of many test observations. Recently, Alissandrakis et al. (2022) performed an
analysis of the center-to limb brightening of ALMA full-disk TP maps in Bands
3, 6, and 7 and showed that Bands 6 and 7 could be cross-calibrated against
Band 3 in a self-consistent manner. Table 4 shows the quiet Sun brightness
temperature originally recommended by White et al. (2017) and those resulting
from the analysis of Alissandrakis et al. (2022). Ultimately, quiet Sun
brightness measurements should be referenced to an independent standard such
as the Moon.

Table 4: Total Power Map Scaling Band | White et al. (2017) | Alissandrakis (2020)
---|---|---
3 | 7300 K | 7347 K
5 |  | 6532 K
6 | 5900 K | 6347 K
7 |  | 6085 K

The time required to produce full-Sun maps (10-20 min) is typically longer
than the time scale of many dynamic phenomena of interest. There is also a
significant mismatch between the time resolution available for INT data (1 s)
and the TP mapping time. It is not possible to drive the TP antennas at higher
rates to produce higher-cadence maps and so the field of view must be reduced
to decrease the mapping time. In Cycle 9, therefore, a second fast-scanning TP
mapping mode has been made available to solar observers: Fast Regional Mapping
(FRM). The intent of the FRM mode is the same as that of the full-Sun maps: to
obtain short-spacing data that is complementary to the INT data, but on a time
scale that is more closely commensurate with changes in the source. Therefore,
the coordinates of the field center are the same as the target coordinates of
the interferometric observation. Moreover, the scan pattern of the FRM
released in ALMA-Cycle 9 is the double-circle pattern, which is the same as
for the full-Sun map, and the shape of the field of view is a circle. The
observer only needs to specify the need for FRM observations in support of a
particular science goal, and specify the diameter of the mapping domain.
Additional scan patterns are under development: the use of a Lissajous scan
patterns allows rectangular mapping domains.

Figure 3: Simulated FRM data. Left panel: Full disk TP image obtained with
Band 6 on 18 December 2015. The circle indicates the field of view of FRM with
300” diameter. Right panels: Simulated FRM image and UV/EUV images. Upper
Left: Simulated FRM image with 300” diameter FoV. Upper Right: UV continuum
(1700Å band). Lower Left: He II 304Å Band, Lower Right: Fe XII 193 Å Band.
Green contours show the FRM image.Examples of a total power full disk map
(left) and FRM map (middle, top). The Band 6 total power map was acquired
during commissioning in December 2015. The FRM map was made using the TP map
in simulation

The size of the field of view and the mapping cadence is a trade-off that
depends on the science objectives. Test observations in Band 6 found that map
durations are 11 s, 21 s, 32 s, and 63 s for map diameters of
$100",200",300"$, and $600"$, respectively, consistent with detailed
simulations. FRM maps can therefore be obtained on a cadence comparable to SDO
or IRIS imaging observations, for example. FRM observations are available
simultaneously with INT observations but, similar to INT observations, FRM
observations must be periodically interrupted for calibration. In addition, at
beginning and end of an FRM observation, full-Sun maps are obtained for flux
calibration. Therefore, an FRM observation always includes numerous regional
maps and two full-disk maps. The FRM maps are calibrated against the full-disk
maps in two steps: the full disk brightness is scaled to the recommended
quiet-Sun value near the center of the the disk and the FRM maps are then
scaled from the full-disk maps at the appropriate offset. Since it is assumed
that the brightness of the reference point does not change significantly
during the observations, the diameter of the FRM mapping domain should be
chosen to include quiet Sun as the reference point. Hence, a mapping region
$\geq 200"$ is recommended, in general.

###  2.6 System Issues

Unfortunately, a number of system issues have affected solar data at various
times to varying degrees. All issues have related to pointing or tracking.
Once identified, most issues have been addressed and subsequent observations
have been unaffected. From a scientific perspective, it has usually been
possible to recover from the errors introduced by these issues but it is
important for users, especially users of archival data, to be aware of them.
The first affects Cycle 4 data observed in December 2016. Instead of tracking
the user-specified ephemeris the system simply tracked the center of the solar
disk; i.e., it did not take any user-specified target offsets into account or
track with solar rotation. At this time, the Sun was in solar minimum and most
programs were to observe the quiet solar chromosphere. Some observers were
able to correct their data for the lack of rotational tracking and address
their science objectives but for others their science objectives were
compromised. The problem was corrected and additional operational checks were
put into place to verify that targeting is indeed as requested by the PI.

Figure 4: The radial position error of the target as a function of target
offset from the solar barycenter.

A second issue is related to the reference coordinates assigned to a given
observations. As an ephemeris object, the geocentric coordinates of the source
change continuously in time. Hence, a reference coordinate corresponding to
the appropriate reference time is assigned. For observations in Cycles 4 and
5, the coordinates were determined using the CASA task fixplanets using the
antenna POINTING table in measurement set. These were found to be inaccurate
by as much as 30”. Since Cycle 6 the ephemeris table is used directly using
the CASA phasecenter function of the msmetadata tool (msmd.phasecenter().
Archival data should be processed using up-to-date scripts.

In Cycle 7, residual pointing effects were traced to general relativistic (GR)
corrections for light bending near the Sun777See the knowledgebase article at
https://help.almascience.org/kb/articles/what-is-a-cycle-7-solar-data-issue-i-
should-be-aware-of for details.. The most important of these occurred as the
result of the misapplication of GR delay corrections for target offsets within
920” of the solar barycenter. The error results in a radial pointing offset
that is a function of the desired target offset. Fig. 4 shows that the radial
pointing offset increasing linearly with target offset from 0” to
$\approx\\!55"$ and then decreases with increasing target offset, dropping
below 5” for radial offsets $>5^{\prime}$. The error is not present for
targets on the solar limb. This problem persisted until March 2020 but has now
been corrected. Users should use source names beginning with “Sun” (case
insensitive) to ensure that GR corrections are disabled for solar
observations. In many cases, the offset introduced by this issue does not
seriously compromise science objectives because the pointing error is $<10"$
in many cases. However, if ALMA images are being compared with data from other
missions and observatories they must obviously be corrected in order to
properly co-align the data. For mosaics, it appears that while the reference
pointing established by the ephemeris is affected, offset pointings relative
to the reference were not.

A related error originates in the 30 s cadence at which GR delay corrections
were made. For an ephemeris object like the Sun there is a drift of the target
relative to the pointing offset that is “reset” with every GR delay event,
resulting in a pointing ramp every 30 s. The magnitude of the effect is of
order $1"$ and can be corrected through self-calibration or cross-correlation.
Fig. 5 shows an example. Not only were interferometric data affected by the GR
delay corrections, antenna pointing was, too. The maximum antenna pointing
error occurs at the limb and is 1.85”. It has no impact on source positions
and is small compared to the primary beam in Band 3 but can affect the primary
beam correction for Bands 6 and 7.

Figure 5: Example of the pointing ramping that results from the application of
the GR delay tracking correction every 30 s. The top panel shows the change in
pointing for the duration of an SB. The bottom panel shows a detail in which
the ramping is vividly illustrated.

Finally, full disk TP maps have been subject to small timing errors that
manifest as low-level artifacts at the solar limb as pointed out by
Alissandrakis et al. (2017). This will soon be corrected with the use of
higher-performance 12 m antennas for TP mapping and updates to the relevant
software.

##  3 ALMA Solar Program Workflow

The life-cycle of any ALMA project, from an initial idea up to publication of
the results, is schematically drawn in Fig. 3. Here, we discuss elements of
proposal preparation, proposal review, solar observing, data calibration, and
quality assurance (QA). Issues related to data imaging and analysis are
discussed in §4.

Figure 6: Schematic representation of the workflow of a project from proposal
development and submission to data reduction and analysis.

The life-cycle of a given science program formally begins by with the
submission of a proposal for observing time in response to an ALMA call for
proposals. Calls are issued on an annual basis in March and the proposal
deadline is in April. Proposal preparation and submission is referred to as
Phase I. Investigators are notified of the disposition of their proposal in
August. Should the proposal be successful in the subsequent evaluation (see
§3.3 below), so called Scheduling Blocks (SBs) are generated from technical
details specified in the proposal. This procedure works mostly automatically,
with a small adjustments made by the Contact Scientist (CS) and the
observatory staff in cooperation with the project Principal Investigator (PI).
This is called Phase II. An SB is later converted to a Python script loaded by
ALMA during observations. An observing cycle lasts one year, beginning on
October 1. Solar observations are only possible with a limited number of array
configurations (Table 3) and so users should be aware of the array
configuration schedule888ALMA antenna configuration schedules can be found at
https://almascience.eso.org/observing/observing-configuration-schedule. during
the course of the year.

The primary interface between ALMA and the user is an ARC. Depending on
nationality, users will be affiliated with a given ARC. From the user point of
view there are three important components of the ARC support: the Helpdesk
system, the Contact Scientist (CS), and Data Analysts (DAs). While the
Helpdesk is open to user queries anytime it also contains a rich knowledgebase
that can be consulted. The CS is an ARC astronomer assigned to a given project
when it is accepted, i.e. before the Phase II starts. The communication
between the PI and CS starts by opening a project-dedicated Helpdesk ticket –
the ARC will do so on PI’s behalf. Following the successful execution of an
observation, the relevant ARC is responsible for calibrating the data and
performing quality assurance. DAs perform these functions as we discuss
further below.

Solar observations with ALMA often coordinate with other ground-based or
space-based telescopes and observatories. Hence, careful coordination between
the PI and JAO science operations is necessary (§3.4) After the observations
are executed by JAO science operations the raw data are transferred to the
ARCs for processing. This includes calibration, reference imaging, and quality
assurance (QA) assessment. This process typically lasts several weeks
following an observations. Should the data pass the QA, they are delivered to
the PI. The PI receives (1) raw data, (2) calibration and imaging scripts
(Python) together with the master scriptForPI.py, and the products – FITS
files with the images, one per each Execution Block, both for interferometric
(INT) and total power (TP) observations. Additional post-processing (e.g. INT
+ TP data combination, time-domain imaging with self-calibration loop, etc.)
is the PI’s responsibility; however, the ARCs can provide assistance and in
some cases and the advice of ARC astronomers can be solicited at any time via
the ALMA Helpdesk system.

###  3.1 Proposal Preparation and Submission

An ALMA proposal is prepared and submitted using the ALMA Observing Tool
(OT)999The ALMA OT, as well as the user manual and online tutorials, is
available at https://almascience.nrao.edu/proposing/observing-tool or at
https://almascience.eso.org/proposing/observing-tool. It is a Java-based GUI
application. In brief, it contains a set of query pages where the PI describes
the project setup:

  * •

Basic information about the project: PI, co-investigators, title, scientific
category. There are five science categories:

    1. 1.

Cosmology and the high redshift universe

    2. 2.

Galaxies and galactic nuclei

    3. 3.

ISM, star formation and astrochemistry

    4. 4.

Circumstellar disks, exoplanets and the solar system

    5. 5.

Stellar evolution and the Sun

  * •

Science goals (SGs): one per target and observing band (e.g. “Prominence in
Band 3”). For each SG one must provide:

    * –

Spectral setup

    * –

Field setup

    * –

Control and performance

    * –

Technical justification.

  * •

Scientific justification

Proposers are encouraged to consult the ALMA Proposer’s Guide101010The ALMA
Proposer’s Guide is updated each observing cycle and is available at
https://almascience.eso.org/documents-and-tools. As noted in §2.6, users
should prefix each source name with “Sun” to ensure that the system handles
relativistic corrections correctly. We briefly summarize key elements of an
SG.

The Spectral setup currently allows only the “single continuum” frequency
bands specified in Table 1. The spectral windows within a given frequency band
are fixed; i.e., one cannot change the LO frequency to place them elsewhere in
the frequency band. Observations of the same target may be performed in more
than a single band – for each, a separate SG must be defined. ALMA cannot
observe multiple frequency bands simultaneously (see §5). The best that can be
done at present is to perform back-to-back observation of the same field
consecutively in different frequency bands.

The Field setup for each SG can be more complicated: one can chose between
single pointing (SP) and a mosaic. An SP has a FOV approximately defined by
the size of the primary beam of a 12-m antenna. Should a larger FOV be
required to meet science objectives, a mosaic must be requested (§§1.2.3, 2.4)
and the user must specify the angular size of the domain to be imaged. The OT
automatically calculates the number of discrete antenna pointings required in
the mosaic. Nyquist sampling is the default spacing between pointings. Any
unique combination of spectral and field setup requires a separate SG.
Beginning in Cycle 9 (2022) the fast regional mapping (FRM; §2.5) capability
became available. The OT allows users to define the circular area to be
scanned with relatively high cadence encompassing the interferometric image.
To avoid the Fourier aliasing, it is recommended that users select a region
that is twice the size of the interferometric FOV. For the purposes of
proposal preparation, a representative solar ephemeris must be uploaded for
each SG in the field setup. As described below, the ephemeris actually used by
a given solar observing program must be provided one or two days before a
given program is executed. All target pointings – SP, mosaic, and FRM – are
referenced to the user-provided ephemeris.

Control and performance parameters in the OT are used by the user to specify
the desired angular resolution or an acceptable range of angular resolutions
for the project. Coupled with the desired spectral setup, the appropriate
array configuration(s) will be determined. Sensitivity parameters for an SG
can often be ignored since there is no lack of signal on solar targets, in
general. Exceptions do occur, however; for example, solar prominences at high
frequencies, as they can be quite optically thin. The default integration time
of 2 s is sufficient in most cases. The maximum time of a single realization
of the observation of the given SG (the so-called Execution Block – EB; see
below) is 2 hours. Note, that this period means $\sim\\!1.5$ hour on the
science target, the rest is spent on instrument setup and calibration.

The Technical justification is used to justify each SG setup and to
demonstrate its feasibility. It is highly recommended that proposers specify
and justify any requests that may have an operational impact: for example,
that back-to-back execution of particular SBs is required, or that
coordination with another telescope will be needed. An excellent resource for
technical aspects of ALMA is the Technical Handbook111111The ALMA Technical
Handbook is available at https://almascience.eso.org/documents-and-tools,
which is updated each observing cycle.

The key component of an ALMA proposal is the scientific justification. It is
of critical importance as it makes the scientific case for an allocation of
telescope time to address the stated science goals. Solar proposers should be
aware that not all reviewers are necessarily solar experts. The proposal
should provide enough context and background for a non-expert to understand
the science goals. The scientific justification is the largest determinant in
whether a given proposal receives a time allocation!

Before a proposal can be submitted it must be “validated”. That is, it is
checked by the OT for completeness and feasibility within the constraints
imposed on solar observing programs. For example, the validator does not allow
you to observe the Sun in Band 9 or to use C-7 array configuration (as implied
from selecting an angular resolution that requires an array configuration that
is not allowed). Upon validation, a proposal may be submitted.

###  3.2 Proposal Review

Before 2021 a large number of ALMA Review Panels (ARPs) was allocated to the
five different science categories based on proposal pressure within each
category. Typically a minimum of 2 ARPs and a maximum of 6 was allocated to
each category to review and rank each proposal within that category. The ALMA
Program Review Committee (APRC), comprising APR Chairs, then convened to
perform a final review of proposal rankings and to determine which large
proposals would be accepted. Large proposals are those requiring allocations
of more than 50 hrs of time on the 12-m array.

Beginning with Cycle 8 (2021) the JAO adopted a Distributed Peer Review (DPR)
system. The process is “double blind”: reviewers do not know the identities of
the proposing team and proposers do not know the identities of proposal
reviewers. All proposals are evaluated and ranked using the DPR process with
the exception of large proposals, which continue to be evaluated by the APRC.
All PIs, or a designated co-investigator, must review ten proposals for each
proposal they submit121212Additional details regarding DPR process and
policies may be found at https://almascience.nrao.edu/documents-and-
tools/cycle9/principles-review-process. Since a given solar proposal is being
evaluated by peers who also submitted proposals, not all of whom are solar
experts, it is important to ensure that a proposal is understandable to non-
experts.

Most proposers are affiliated with one of the four ALMA partners. Those who
are not may still propose for observing time under “open skies”. A total of 5%
of the available observing time is available to unaffiliated
observers131313See https://almascience.nrao.edu/documents-and-
tools/cycle9/alma-user-policies for additional details regarding user
policies. ALMA typically receives 1700-1800 proposals for each observing
cycle. Of these, only a few dozen proposals are typically submitted by the
solar community. The instrument is highly over-subscribed with only 15-20% of
submitted proposals approved for a time allocation and so the number of solar
programs observed to date is not large.

###  3.3 Solar Observing Process

Solar observing in practice has evolved since first becoming available in
late-2016. Initially, solar programs were executed in a “campaign mode”. While
this was a convenient and flexible way to maximize the number of programs
scheduled within the campaign period, they relied on the presence of solar
scientists at the ALMA OSF. A reliance on external solar scientists,
especially if several array configurations were required, was deemed
unsustainable. In more recent years, the execution of solar programs is
coordinated through the PI, the CS, and the Astronomer on Duty (AoD).

Several days before a given observation can potentially be executed, the PI
opens a “Target of Opportunity” (ToO) ticket using the Helpdesk, in which the
PI briefly describes the details of observation, including the target
coordinates, whether to track solar rotation, and any constraints that might
impact operations – e.g., whether possible loss of complementary TP maps
compromises the science goal or is tolerable, whether back-to-back
observations of some blocks are absolutely essential or not, etc. The ToO
ticket should be updated before each potential execution of an SB. The AoD is
currently responsible for generating the solar ephemeris based on information
provided by the PI in the ToO ticket, and for any changes to the orientation
of a mosaic, if one or more is requested. Before the actual observation takes
place, its execution is simulated, the results of which are reviewed and
approved by the PI and CS. If a given SG is being supported by an external
observatory or mission, the PI is responsible for coordinating such support.

As described above, each SG defined in the OT proposal (Phase I) is
automatically transformed into an SB during the Phase II. The SBs represent a
complete observation setup but critical information must still be provided. As
noted, an ephemeris must be generated shortly before an SB is executed. In
addition, it is usually the case that calibrator sources are left unspecified
until the observing window is approximately known. The CS is responsible for
ensuring that appropriate calibrator sources are specified in the SB. Each
execution of an SB (which may be executed more than once) is called an
Execution Block (EB). The SB (or its EB realization) consists of smaller
elements – scans and subscans. The SB for an INT observation typically
contains scans for pointing, flux, and band-pass calibration at the beginning
of each EB followed by multiple science-target scans interleaved with gain
calibration and atmospheric calibration scans (see Shimojo et al. (2017), Fig.
4), for a schematic figure of the EB structure. In the case of mosaic
observations, scans are further broken down into subscans, one for each
instance of a distinct pointing. In parallel to INT observations, fast scan TP
mapping is performed with one or more total power antennas to provide full
disk maps and/or FRM maps.

###  3.4 Solar Data Calibration and Quality Assurance

Once successfully executed, data from an observing program are entered into
the ALMA data archive. A copy of the ALMA data archive is available at each
ARC. The data of a given PI are calibrated and assessed by DAs at the relevant
ARC. Many non-solar observations are sufficiently standard that they can be
automatically processed (pipeline processing). Solar observations are non-
standard and are manually calibrated using specialized scripts and utilities.

Briefly, data calibration entails solving for the instrumental (complex) gain
of each antenna and applying it to source data in order to infer the “true”
amplitudes and phases of the complex visibilities. This is typically done by
observing a gain calibrator, usually a point-like source or a source of known
structure, with a precisely known location and flux density. Taking a point-
like source as an example, the source amplitude of each baseline should be
that of the source itself and the phase should be zero (Fourier transform of a
$\delta$-function). For a given frequency, time, and polarization only N
complex gain solutions are needed whereas N(N-1)/2 observations are available.
The system is highly over-determined for a large-N array like ALMA and the
gains are determined using a non-linear least-squares approach. In general,
the flux density of the gain calibrator is not known a priori and it must be
referenced to an observation of a flux calibrator that has a well-established
and stable flux density. This is not possible for the Sun. For non-solar
observations the source is too weak to contribute to system noise and the
system temperature, $T_{sys}$, is dominated by receiver noise, spillover, etc.
However, when observing the Sun the source itself contributes the bulk of the
system noise, referred to as the antenna temperature, $T_{ant}$. In order to
calibrate the flux scale of solar visibility data it is necessary to measure
$T_{ant}$. Therefore, while observations of a gain calibrator provide phase
solutions, the amplitude scale must be established using the ALMA Calibration
Device at periodic intervals throughout a solar observations. Further details
are available in Shimojo et al. (2017).

Additional calibrations are necessary: at the beginning of an observation an
antenna pointing calibration is performed, delay calibration, and the relative
sideband gains. In addition, as noted in §1, ALMA observes in four spectral
windows, each 2 GHz in bandwidth and channelized into 128 frequency channels.
A bandpass calibrator is therefore also observed at the beginning of an EB to
deduce the relative variation of amplitude and phase across each spectral
window so that it can be removed before averaging frequencies to form pseudo-
continuum datasets. Additional calibrations, e.g., baseline calibration, are
performed by science operations as needed.

After data calibration data analysts image each spectral window and
polarization of each EB to: (i) Ensure that the data are of sufficient quality
to meet the science requirements defined in the proposal (Quality Assurance
level 2 – QA2), and (ii) Serve as a starting point for more advanced data
analysis; e.g., time-domain imaging, self-calibration, feathering, etc. The
QA2 process involves – in addition to data selection (flagging), calibration,
basic imaging and image inspection – final consistency checks of the entire
dataset. QA2 has sometimes revealed issues with the approach to data reduction
or have fed back into telescope operations. For example, as described in §2.6
it was determined that the procedure used to set reference coordinates was
inaccurate for data acquired in Cycle 4 and Cycle 5. The reduction script used
by the DAs was therefore revised and updated to correct the issue. More
recently, it was determined that, for single pointing data the reference
images used standard gridding as the default which resulted in the use of the
7 m primary beam rather than the appropriately weighted primary beam response
of the heterogeneous array. In any case, caution should be exercised when
using the reference images for scientific analysis.

##  4 ALMA Solar Imaging and Data Analysis

Current ALMA solar observing capabilities provide a great deal of flexibility
in terms of frequency band selection, angular resolution, time resolution, and
image size. As described in the previous section, data calibration is handled
by the ARCs and is generally robust. Observers must then confront myriad
issues related to solar imaging and data analysis. The Sun is arguably the
most difficult imaging problem possible for ALMA because while interferometers
are at their best with compact discrete sources, the Sun fills any field of
view with relatively-low-contrast structure on all spatial scales.
Furthermore, it is dynamic on a range of time scales and solar observers
generally cannot take advantage of Earth rotation aperture synthesis to help
fill in spatial scales missing from any snapshot observation as those of
sidereal sources can. A major challenge is to produce high quality images that
recover the critical angular scales needed to address the science objectives
of interest. In this section we summarize some of the challenges and
subtleties associated with imaging and analyzing ALMA solar observations. They
include the use of the heterogeneous array, data weights, self-calibration,
and combining single dish total power data with interferometric data.

###  4.1 Heterogeneous Array

As summarized in Section 4, solar observations with ALMA are performed by the
12-m array in combination with the ACA; that is, as a heterogeneous array
comprising both 12 m and 7 m antennas. The intent is to maximize the range of
spatial scales to which the observations are sensitive. On the other hand, the
use of different antenna sizes, with different fields of view and weighting
(§4.3), introduces subtleties that are not yet fully understood. The effective
use of the heterogeneous array is still an area of active investigation.

Figure 7: Example of a small mosaic formed from ten discrete pointings in 80
s. Left panel: The image produced by joint deconvolution of the ten pointings
in CASA. Right panel: The image produced by imaging each pointing separately
and combining them linearly.

For a single pointing, the use of the heterogeneous array is straightforward
but there are subtleties. The use of the appropriate gridding function
(“mosaic” or “mosaicft”) is necessary in order to handle visibility gridding
for the the different antenna sizes correctly. For sources on the solar disk,
emission fills the primary beam (and beyond) for all telescopes. The issue of
primary beam correction becomes somewhat complicated because the 7 m and 12 m
telescopes have primary beams of different sizes, and therefore do not “see”
the same region of the Sun. In the case of a single-pointing observation, the
standard procedure is to produce a map from the visibilities, deconvolve the
result, then apply a primary beam correction to the deconvolved image, but
neither the 7 m nor the 12 m primary beam, nor any hybrid, truly represents
the appropriate correction. The correct imaging path for this case may be to
have a model of the sky that is then convolved with the spatial response of
each pair of telescopes, using the primary beams appropriate to each
telescope, to form visibilities, and the model is then iteratively corrected
to make the modeled visibilities, or the corresponding map, match the
telescope data. Such a process is not currently available in CASA, but may be
needed to optimally exploit ALMA solar data.

Mosaicking works well in many cases but there appear to be failure modes that
are not fully understood. The problem has been recently explored by da Silva
Santos et al. (2022). Fig. 7 shows a deconvolution of a small mosaic produced
by CASA, using CASA’s “mosaic” gridding option, with an alternate approach in
which the individual pointings are each mapped separately and then combined in
the image plane using a linear mosaic technique and an appropriate primary
beam. For this dataset most CASA images of an 80-second loop of 10-pointing
mosaics have either bright or dark features that corrupt the map, and thus one
cannot reliably produce time-resolved mosaics; the alternate technique,
however, works reliably. The reason for the failure of CASA imaging may be due
to the fact that the mosaic gridding technique limits the field of view to
within a certain distance of the pointing center, but, e.g., the field of view
of the 7 m antennas is larger than the field of view of the 12m antennas, and
thus there is emission outside the 12 m gridded area that is sampled by the
data, and is aliased into the gridded region, but this needs to be
investigated further.

Some users may find that their goals are adequately addressed by using the
12-m array alone, which greatly simplifies the data reduction and avoids some
of the pitfalls described above, which are not fully understood. Others may
wish to use the heterogeneous array as two homogeneous arrays: the 12-m array
together with the ACA. It is straightforward to feather images made with the
12-m array, the ACA, and a TP map, again avoiding some of the issues raised by
using mixed antenna pairs.

###  4.2 Self-calibration

Self-calibration is a technique (e.g., Cornwell & Fomalont (1989)) where the
source itself is used to determine corrections to antenna-based gains. Gain
errors are most often due to atmospheric “seeing” and, as such, are dominated
by phase errors. As discussed in section 2.2, ALMA makes use of WVR
measurements as a proxy for phase fluctuations at each antenna for non-solar
observations. This capability is not available for solar observations because
the WVRs saturate when pointing at the Sun. An active topic of research is to
develop an alternative proxy for phase fluctuations, such as observations of
the Sun in the wing of the 183 GHz water absorption line in Band 5 (see
Section 5.5). Solar observations must therefore rely on self-calibration
techniques in the interim.

Experience to date suggests that a hierarchical approach to self-calibration
is effective, where the average image of a scan is used as the initial source
model to deduce average phase corrections. The corrected data are imaged and
deconvolved to produce a new source model. This is used to determine phase
corrections on a shorter time scale. This can proceed iteratively until
corrections on time scales as short as the integration time are deduced.

The self-calibration of mosaic data is somewhat less straightforward but the
same hierarchical approach can work well. The difference is that it is often
useful to perform the first iteration of self-calibration by determining
average corrections for an entire mosaic before determining solutions for each
pointing separately, using the mosaic as the model.

###  4.3 Data Weights

Data weights enter into the imaging problem in two ways: i) the weight
assigned to each visibility in forming an image through Fourier inversion, and
ii) the weight assigned to each antenna beam in a mosaic. The weight assigned
to a visibility measured by antenna $i$ and $j$ is $1/\sigma_{ij}^{2}$, where
$\sigma_{ij}^{2}$ is the statistical variance of the measurement. For solar
observations, the system noise is dominated by the source (the Sun) and the
variance is of order
$\sigma_{ij}\sim({T_{ant,i}T_{ant,j}/A_{i}A_{j}})({k_{B}}/{\Delta\nu\Delta
t})$ where $T_{ant,i}$ is the antenna temperature of antenna $i$ and $A_{i}$
is its effective area. All other things being equal, visibilities in a
homogeneous array are given approximately the same weight (e.g., the 12-m
array). However, for a heterogeneous array, we have visibility measurement
with 7 m x 7m antennas, 7 m x 12 m antennas, and 12 m x 12 m antennas. The
weights for each of these pairings therefore scale as
$(7/12)^{4}:(7/12)^{2}:1$, or roughly 1/9:1/3:1. For a heterogeneous array of,
say, 10 ACA antennas and 45 antennas from the 12-m array, the total number of
baselines would be 1485. Of these, only 45 would be 7 m x 7 m pairs ($3\%$)
and 450 would be 7 m x 12 m pairs ($30\%$). Coupled with the visibility
weights, 7 m x 7 m correlations have very little impact on imaging and even
the (weighted) 7 m x 12 m correlations come in at the $\sim 10\%$ level.

In the case of mosaic imaging, user should be aware of a second subtlety,
namely, the so-called primary beam correction. The primary beam correction is
formed from the grid of pointings on the sky as
$\Sigma_{k}B(\theta-\theta_{k})/\sigma_{k}^{2}$, where $B$ is the primary beam
response. Consider a mosaic formed with a homogeneous array. The weight
assigned to the antenna primary beam for each pointing $k$ is approximately
the same for all antennas. Since the variance depends on $T_{ant}$, and
$T_{ant}$ may change significantly with $k$, the weight assigned to each
pointing may also vary. An extreme example is given by a Band 7 mosaic on the
solar limb. As noted in Section 1.1, Band 7 uses nominal receiver settings and
$T_{sys}$ is consequently small ( 200 K). When pointing on the solar disk the
system noise is therefore dominated by $T_{ant}$, the variance is high, and
the weight assigned to that pointing is low. When the pointing is such that
the limb only partially fills the beam, or the pointing is above the limb and
the Sun contributes little emission to the system, the variance is low and the
corresponding weight is high. This can lead to a distorted mosaic beam where
the emission of interest is down-weighted relative to pointings above the
limb! Users may therefore wish to correct their mosaic with a uniform weight
applied to each pointing or even use weights proportional to the fractional
filling factor of the Sun, although the latter idea has not been tested.

A minor issue is that if a heterogeneous array is used, the effective primary
beam (FOV) differs from that of a single antenna in a homogeneous array. The
response of a single baseline with identical antennas is the same as that of a
single antenna, while the response of a 7 m x 12 m baseline is geometric mean
of the two antenna power patterns. The effective FOV is the weighted sum of
the relevant FOV for each baseline. The net effect is to slightly broaden the
12-m array FOV ($<10\%$).

###  4.4 Combining Interferometric and Single Dish Data

An interferometer cannot measure angular scales greater than that measured by
the minimum antenna baseline. In the absence of total power information, also
known as the “zero-spacing flux”, ALMA measures the distribution of brightness
relative to the mean. The mean brightness of the background Sun is of order
6000-8000 K, far in excess of the low-contrast variation against the mean. The
restoration of total power information to ALMA images is critical if absolute
brightness temperatures are important to the science objectives.

To zeroeth order, simply adding a constant brightness offset to an image,
corresponding to the mean brightness, largely corrects for the absence of
short spatial frequencies and this approach may indeed be sufficient for
single-pointing imaging on the solar disk. For mosaic images, however, this is
not necessarily sufficient. Solar observations with ALMA provide low-
resolution full-disk maps of the Sun that are observed contemporaneously with
interferometric observations using one or more of the 4 TP antennas.
Calibrated TP maps contain the correct flux on all scales ranging from the 12
m primary beam size to the scale of the Sun in any given frequency band.
Hence, by combining TP observations with interferometric data, one can recover
the largest angular scales.

While it is possible, in principle, to first perform data combination in the
uv domain followed by image deconvolution, it is perhaps more straightforward
to reverse the order and to use a technique called “feathering” (e.g., Cotton
2015). Briefly, feathering begins with TP and interferometric maps, MTP and
MINT, that embody low angular frequencies and high angular frequencies,
respectively. The TP map must be coaligned with the interferometric map. It is
convenient to cutout an imaging domain of the TP map that is perhaps twice the
size of the INT map. The two are then Fourier transformed, $FT(MTP)$ and
$FT(MINT)$, as is the 12 m primary beam FT(B), taken to be Gaussian. A mask is
then formed from FT(B) as $m=1-FT(B)$ and the sum $FT(MTP)+mFT(MINT)$ is
formed. The use of the mask is to smoothly weight down angular scales measured
by the interferometer that overlap with those measured by the single dish TP
map. The sum is then inverse-Fourier transformed $FT^{-1}(FT(MTP)+mFT(MINT))$,
yielding the combined image.

This approach works well in many cases; e.g., mosaics on the solar disk.
However, it has shortcomings when imaging the solar limb. Two factors come
into play: first, fast-scan total power maps sometimes have artefacts at the
limb due to residual scan timing errors. It is undesirable to propagate these
into the combined image. Second, as seen from Table 3, the minimum angular
scales measured by the 12-m array decrease with frequency band and array size.
While the heterogeneous array mitigates this to some extent, the degree of
overlap between the TP data and interferometric data in the uv domain, and the
density of interferometric sampling in the region of overlap, both decrease
with increasing frequency and array size. As a result, angular scales between
the 12-m array MRS and the 12 m FOV are increasingly poorly sampled.

##  5 Future Capabilities and Observing Modes

ALMA capabilities currently support a wide range of solar science but
additional capabilities will no doubt further enrich the scientific
possibilities. We briefly summarize several new instrumental capabilities that
are under active consideration and then briefly touch on possible observing
modes that do not depend on the development technical or data reduction
capabilities but, rather, depend on observatory policy and science operations.

###  5.1 Polarimetry

ALMA currently supports full polarimetry for non-solar observing. A
longstanding goal has been to implement support of polarimetry for solar
observations. Efforts are currently underway to enable polarimetry in Band 3.
Polarimetry involves measuring cross-hand as well as parallel-hand
correlations on each antenna baseline $ij$: i.e., $X_{i}X_{j}$ , $Y_{i}Y_{j}$
, $X_{i}Y_{j}$ , and $Y_{i}X_{j}$ . Formation of the Stokes polarization
parameters requires measuring the phase difference between the $X$ and $Y$
polarization channels and measuring instrumental polarization embodied by
“polarization leakage” terms for each antenna. The challenge has been to
demonstrate that the necessary quantities can be measured using the MD mode
with sufficient accuracy to ensure that the polarization signals are robust.

The Stokes V parameter is of primary interest. It offers a diagnostic of the
chromospheric magnetic field in active regions and flares. Modeling suggests
(Loukitcheva et al., 2017; Loukitcheva, 2020) that 3 mm may be the most
promising wavelength to focus such efforts, at least initially, as it produces
the highest degree of polarization of available frequency bands. Hence,
initial efforts have gone into testing polarization observation in Band 3 with
the intent of making Band 3 solar polarimetry a supported mode. However,
testing is ongoing at the time of this writing and it is not yet known when
the mode will become available.

Figure 8: Model brightness temperature distributions for a bipolar regions in
Band 3 and Band 6 (top) and the corresponding degree of circular polarization
(bottom). After Loukitcheva et al. (2017).

###  5.2 Spectral Line Observing

Spectral line detections would significantly widen the diagnostic value of
ALMA observations for studying the chromosphere, since they would permit line-
of-sight velocity information that is missing from continuum observations. As
reviewed by Wedemeyer et al. (2016), while such lines have been observed at
high millimeter frequencies, there are significant potential issues.

The two best candidates for line detection are hydrogen recombination lines
(e.g., H26$\alpha$ at 353.6 GHz) and CO rotational transitions (e.g., CO 3-2
at 345 GHz). The difficulty in detecting such lines is the fact that they are
strongly pressure-broadened in the chromosphere, which reduces their contrast
with the continuum. Thus, recombination lines were detected in emission by
Clark et al. (2000a, b) in single-dish observations at 662.4 (H21$\alpha$) and
888.0 (H19$\alpha$) GHz, but only at and above the solar limb where pressure
is lower, not against the solar disk. An additional complication in
interpreting the spectra at these frequencies is the presence of numerous
terrestrial atmospheric absorption lines. ALMA interferometer data should
improve on these results since the relatively large beam of the single-dish
maps ($\sim\\!19"$) requires averaging over a large area of extended limb,
resulting in a line peak 10% above continuum level, whereas ALMA can achieve
sub-arcsecond resolution (assuming successful treatment of the sharp solar
limb, as discussed above). Clark et al. (2000b) argued that the line width of
the core of the recombination lines from above the limb seemed to scale
roughly with frequency, from about 550 MHz at H21$\alpha$ to 700 MHz at
H19$\alpha$. If this scaling continued down to ALMA Band 7, we might expect a
width of order 300 MHz for H26$\alpha$, but we note that the
H21$\alpha$/H19$\alpha$ values were a factor of about 3 narrower than expected
from theory (Hoang-Binh et al., 1987). As discussed earlier, ALMA can center a
single baseband 2 GHz wide on a spectral line, with a frequency resolution of
16 MHz in standard solar observing mode, which would be adequate to measure a
line 300 MHz wide, but perhaps not a line that is several times wider with
reduced contrast to the continuum.

Figure 9: Lines present in the ALMA Band 6 frequency range. The blue line
indicates the atmospheric transmission and the black brackets indicate the
current locations of the upper and lower sidebands for solar observing. The
legend indicates the frequencies of the H$\alpha$, H$\beta$, and H$\gamma$
radio recombination lines as well as CO. Note that the lower sideband was
selected to include H30$\alpha$ recombination line and the CO J=2-1 line.

There are, to this point, no confirmed detections of CO lines on the Sun at
mm/submm$-\lambda$. The detections have been made so far mostly in the
infrared (e.g., Ayres et al. (2006)) where a dense concentration of easily-
observable CO rovibrational absorption lines occurs. Conventionally CO
molecule formation requires temperatures of at most 3500 K, so one might
expect CO to be preferentially detected in cool regions such as sunspot
umbrae, but in fact CO can regularly be detected off-limb at heights where
temperatures are expected to be much higher. An interpretation of this result
is that CO forms in cool pockets such as the rarefaction phases of large-
amplitude acoustic waves propagating through the chromosphere, or in the wake
of chromospheric shocks. These interpretations carry the implication that CO
formation is highly dynamic. ALMA observations can help to test these models,
but this will require time-resolved spectral-line mapping in order to track
the dynamics of CO features. CO lines are also expected to be pressure-
broadened, and may form lower in the chromosphere than the recombination
lines, where pressure is higher. However, the higher mass of the CO molecule
should reduce the broadening, as found in simulations reported by Wedemeyer et
al (2016). CO lines may be detected in absorption or emission, depending on
the temperature profile in the region where they are found.

###  5.3 Additional Frequency Bands

Solar observing with ALMA is currently limited to four frequency bands. The
use of additional frequency bands is highly desirable but requires significant
testing and commissioning time. Two bands of interest are Band 1 (35-50 GHz; 7
mm) and Band 4 (125-163 GHz; 2.1 mm). Band 1 (Huang et al., 2016) is an
entirely new capability, not just for the solar community but for the
astronomical community at large. First light with Band 1 receivers was
achieved in August 2021. The goal is to make Band 1 available to the wider
community in Cycle 10 (October 2023) but use by the solar community must await
solar testing and commissioning. While Band 4 is part of the original suite of
ALMA receivers, it has not been available for solar use. It would fill the gap
between Band 3 and Band 5. Extending coverage to Band 8 (385-500 GHz; 0.7 mm)
is also under consideration.

Bands 9 (602-720 GHz), and 10 (787-950 GHz) are also of considerable interest.
They are the most promising frequency bands for spectral line work. However,
their use is problematic for solar INT observing. First, exceptional weather
conditions are required for high-frequency observing under any circumstances.
Daytime observing in Bands 9 and 10 is currently prohibited. Second, Bands 9
and 10 are double-sideband receivers and so the observing strategy may be more
complicated than the MD mode used currently. On the other hand, the system
temperatures for these bands is higher than for the lower frequency receivers
(ranging from a few $\times\\!100$ K for Band 8 to $>1000$ K for Bands 9 and
10) which may simplify their use. Both policy and technical challenges would
need to be overcome to exploit them for interferometric solar observations. We
note, however, that full disk TP mapping in Band 9 was demonstrated (see
(Bastian et al., 2018), Fig. 3) during commissioning and science verification
in 2015 through a sky opacity $\tau\sim 1$!

###  5.4 Flare Mode Observations

Observations of flares at mm-$\lambda$ and submm-$\lambda$ offers the
potential of fundamentally new insights into energy release, particle
acceleration, and emission mechanism on the Sun (see Fleishman et al, this
Frontier collection). Implementation of flare mode observing confronts us with
additional challenges, however. While the MD mode has successfully enabled
observations of quiescent solar phenomena, it is not designed to handle the
much higher flux densities produced by solar flares. Alternatives must be
explored.

It is likely that solar filters installed on the ALMA Calibration Device on
each antenna will be at least part of the approach. The solar filters were the
initial solution adopted by ALMA to manage solar signals. However, as detailed
by Shimojo et al. (2017) the filters have a number of undesirable properties
that led to the development of MD mode observing instead. The solar filter is
placed in front of a given receiver in order to attenuate the incident signal.
The nominal amount of attenuation is 4+2$\lambda_{mm}$ dB, amounting to signal
reductions by factors of 10, 5, 3.5, and 3 for bands 3, 5, 6, and 7,
respectively141414A preliminary assessment of the solar filters for Band 7
showed that the attenuation introduced by the filters did not necessarily
conform to expectations. In addition, single-dish TP maps made through the
solar filters show poorer contrast than maps made without the filter. A
painstaking assessment of the filters lies ahead..

The antenna temperature is $T_{ant}=SA_{e}/2k_{B}\approx 124S_{SFU}$ K where
$S_{SFU}$ is the flux density in solar flux units ($10^{-19}$ ergs s-1 cm-2
Hz-1), $A_{e}=\eta A$ is the effective area of the antenna, and $k_{B}$ is
Boltzmann’s constant. For the non-flaring Sun, $T_{ant}\sim T_{B}\sim
6000-8000$ K. With the signal attenuation factors as given, ALMA could
accommodate flares of order 600, 250, 160, and 120 SFU within the antenna beam
for bands 3, 5, 6, and 7, respectively. This may be sufficient to observe many
flares but may be problematic for some: the so-called “sub-THz” component of
certain flares displays an inverted spectrum (Krucker et al., 2013). That is,
the flux density increases with frequency and the system may saturate in the
higher frequency bands. Preliminary tests of the filters in Band 7 indicate
that the degree of attenuation is less than nominal, possibly exacerbating the
problem. Alternative, or additional, strategies may be necessary to observe
flares. Possibilities include the use of MD mode in tandem with solar filters
and/or off-pointing the antennas so that a given flare occurs in a sidelobe of
the antenna response. The first sidelobe of the 12-m antennas is a factor of
100 less sensitive than the center of the main response lobe. It is expected
that testing and commissioning efforts for solar mode flare observations will
begin in the coming year.

###  5.5 High Angular Resolution

Solar observations are currently restricted to the four most compact array
configurations for reasons given in §2.2. This limits the available angular
resolution to $\approx 0.6"-0.9"$. On the other hand, the high brightness of
solar emission can also yield opportunities that are impossible for “standard”
interferometry of relatively weak targets for which the implicit assumption is
that we need rather long observing (total signal integration) times to reach a
sufficiently high signal to noise ratio (SNR). Since the image integration in
“standard” interferometry is typically performed over periods greatly
exceeding the time-scale of the phase variations, the resulting image is
blurred and the resolution (long-duration coherence) is lost unless provisions
are made – the use of the WVRs and self-calibration. Phase variations occur on
time scales of seconds to tens of second. Depending on the details of seeing
conditions and the array configuration, these may largely manifest as low
order distortions of the snapshot solar images: e.g., image wander and
warping. These distortions can be, to a large extent, distinguished and
separated from the true dynamics of the Sun: the large-scale solar structures
change at much longer timescale (minutes) than the integration time or the
time scale of phase variations over the array. The Sun allows a good SNR to be
achieved even on the shortest integration times (currently 1 s, but as short
as 0.16 s in principle), which enable time series of relatively sharp, but
distorted images, to be obtained instead of a single blurry image by, in
effect, freezing the phase variations. Self-calibration techniques are a well-
established and tested means of mitigating phase variations in solar data,
even in the absence of WVR corrections. It is anticipated that higher angular
resolution imaging with ALMA is possible by extending observations to larger
array configurations. Higher angular resolution imaging is the subject an ESO
ALMA Development Study that started in July 2022.

###  5.6 Standalone Total Power Mapping

ALMA science operations currently provides TP full-disk and/or FRM maps as a
complement to the interferometric observations. The full disk TP maps have
been exploited scientifically in their own right (Brajša et al., 2018; Sudar
et al., 2019; Selhorst et al., 2019; Alissandrakis et al., 2017, 2020, 2022).
There is interest in the solar community of using TP antennas in a mode that
is independent of the 12-m array or ACA. A particularly attractive possibility
is to perform multi-band TP or FRM mapping in standalone mode, possibly even
in bands not currently supported for INT observing. As noted above, full disk
TP mapping in Band 9 has been successfully demonstrated. Support of such a
mode would require a policy change by the JAO as well as changes to the OT and
operations.

###  5.7 Science Sub-arrays

It is currently not possible to observe the Sun in more than one frequency
band simultaneously. One might suppose that time sharing between two or mode
frequency bands might be a promising strategy but the time overheads in
switching frequency bands is prohibitive and significant changes would be
needed to SBs. A more feasible approach may be the use of antenna subarrays,
where the antennas of the 12-m array are distributed among two or more groups
of antennas that operate as independent arrays. A user could allocate half of
the antennas to one subarray and half to another; or divide them into three
arrays with comparable number of antennas. However, since the number of
antenna baselines and, therefore, uv samples is $\sim\\!N^{2}/2$ the uv
coverage provided by a given subarray quickly degrades with the number of
subarrays and so users would need to consider carefully the advantages and
disadvantages of the approach.

##  6 Concluding Remarks

ALMA is a remarkable instrument that has opened a new wavelength regime for
exploration. Solar observations with ALMA have been possible since late-2016
but the number of programs that have been successfully executed has been
relatively modest. There are several reasons for this: i) as a general purpose
instrument used by the entire astronomy and astrophysics community,
competition for observing time is fierce – only a few solar observing programs
are observed per cycle; ii) as an interferometer, ALMA is not necessarily
familiar to segments of the solar community – a learning curve must be
surmounted through education and outreach; iii) the data can be challenging to
reduce and analyze – progress on establishing and sharing “best practices” is
ongoing.

Nevertheless, as the solar community becomes increasingly knowledgable about
solar observing at mm/submm-$\lambda$ and as new observing modes and
capabilities continue to be developed, the scientific impact of ALMA will
continue to increase. This is particularly true in light of next-generation
instruments coming online at other wavelengths; e.g., the Daniel K. Inouye
Solar Telescope (DKIST), operating at O/IR wavelengths. Powerful synergies are
available that will only increase the impact of ALMA.

## Conflict of Interest Statement

The authors declare that the research was conducted in the absence of any
commercial or financial relationships that could be construed as a potential
conflict of interest.

## Author Contributions

TB authored the bulk of the manuscript. MB wrote §3, contributed to §2.6. MS
contributed §2.5 and §5.1 as well as numerous comments and corrections. SW
contributed to §2.6, and wrote §4.1 and §5.2. All authors discussed and
revised the manuscript and contributed numerous comments and corrections.

## Funding

MB acknowledges support by projects 20-09922J and 21-16808J by the GACR, and
project LM2015067 by the Ministry of education of the Czech Republic. SW
acknowledges support from AFOSR grant 20-RV-COR-026.

## Acknowledgments

We wish to thank our friend and colleague, Prof. Richard Hills, now deceased,
for both his important contributions to, and his unstinting encouragement for,
making solar observations with ALMA a reality.

We thank the reviewers for their careful reading of the manuscript and for
their constructive comments. ALMA is a partnership of ESO (representing its
member states), NSF (USA) and NINS (Japan), together with NRC (Canada), MOST
and ASIAA (Taiwan), and KASI (Republic of Korea), in cooperation with the
Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO and
NAOJ. The National Radio Astronomy Observatory is a facility of the National
Science Foundation operated under cooperative agreement by Associated
Universities, Inc. This article made use of the following ALMA data:
ADS/JAO.ALMA#2011.0.00020.SV.

## References

  * Alissandrakis et al. (2022) Alissandrakis, C. E., Bastian, T. S., & Nindos, A. 2022, A&A, 661, L4, doi: 10.1051/0004-6361/202243774
  * Alissandrakis et al. (2020) Alissandrakis, C. E., Nindos, A., Bastian, T. S., & Patsourakos, S. 2020, Astronomy & Astrophysics, 640, A57, doi: 10.1051/0004-6361/202038461
  * Alissandrakis et al. (2017) Alissandrakis, C. E., Patsourakos, S., Nindos, A., & Bastian, T. S. 2017, A&A, 605, A78, doi: 10.1051/0004-6361/201730953
  * Ayres et al. (2006) Ayres, T. R., Plymate, C., & Keller, C. U. 2006, ApJS, 165, 618, doi: 10.1086/504847
  * Bastian et al. (2018) Bastian, T. S., Bárta, M., Brajša, R., et al. 2018, The Messenger, 171, 25.  https://ui.adsabs.harvard.edu/abs/2018Msngr.171...25B
  * Brajša et al. (2018) Brajša, R., Sudar, D., Benz, A. O., et al. 2018, A&A, 613, A17, doi: 10.1051/0004-6361/201730656
  * Clark et al. (2000a) Clark, T. A., Naylor, D. A., & Davis, G. R. 2000a, A&A, 357, 757\.  https://ui.adsabs.harvard.edu/abs/2000A&A...357..757C
  * Clark et al. (2000b) —. 2000b, A&A, 361, L60.  https://ui.adsabs.harvard.edu/abs/2000A&A...361L..60C
  * Cornwell & Fomalont (1989) Cornwell, T., & Fomalont, E. B. 1989, in Astronomical Society of the Pacific Conference Series, Vol. 6, Synthesis Imaging in Radio Astronomy, ed. R. A. Perley, F. R. Schwab, & A. H. Bridle, 185.  https://ui.adsabs.harvard.edu/abs/1989ASPC....6..185C
  * Cotton (2015) Cotton, W. 2015, Obit Memo 41: Image Combination by Feathering, Tech. rep., National Radio Astronomy Observatory
  * da Silva Santos et al. (2022) da Silva Santos, J. M., White, S. M., Reardon, K., et al. 2022, Frontiers in Astronomy and Space Sciences, 9, 898115, doi: 10.3389/fspas.2022.898115
  * Hoang-Binh et al. (1987) Hoang-Binh, D., Brault, P., Picart, J., Tran-Minh, N., & Vallee, O. 1987, A&A, 181, 134.  https://ui.adsabs.harvard.edu/abs/1987A&A...181..134H
  * Huang et al. (2016) Huang, Y. D. T., Morata, O., Koch, P. M., et al. 2016, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 9911, Modeling, Systems Engineering, and Project Management for Astronomy VI, ed. G. Z. Angeli & P. Dierickx, 99111V, doi: 10.1117/12.2232193
  * Krucker et al. (2013) Krucker, S., Giménez de Castro, C. G., Hudson, H. S., et al. 2013, A&A Rev., 21, 58, doi: 10.1007/s00159-013-0058-3
  * Loukitcheva (2020) Loukitcheva, M. 2020, Frontiers in Astronomy and Space Sciences, 7, 45, doi: 10.3389/fspas.2020.00045
  * Loukitcheva et al. (2017) Loukitcheva, M., White, S. M., Solanki, S. K., Fleishman, G. D., & Carlsson, M. 2017, A&A, 601, A43, doi: 10.1051/0004-6361/201629099
  * Nikolic et al. (2013) Nikolic, B., Bolton, R. C., Graves, S. F., Hills, R. E., & Richer, J. S. 2013, Astronomy & Astrophysics, 552, A104, doi: 10.1051/0004-6361/201220987
  * Phillips et al. (2015) Phillips, N., Hills, R., Bastian, T., et al. 2015, in Astronomical Society of the Pacific Conference Series, Vol. 499, Revolution in Astronomy with ALMA: The Third Year, ed. D. Iono, K. Tatematsu, A. Wootten, & L. Testi, 347\.  https://arxiv.org/abs/1502.06122
  * Sault et al. (1996) Sault, R. J., Stavley-Smith, L., & Brouw, W. N. 1996, Astronomy and Astrophysics Supplement Series, 120, 375
  * Selhorst et al. (2019) Selhorst, C. L., Simões, P. J. A., Brajša, R., et al. 2019, ApJ, 871, 45, doi: 10.3847/1538-4357/aaf4f2
  * Shimojo et al. (2017) Shimojo, M., Bastian, T. S., Hales, A. S., et al. 2017, Sol. Phys., 292, 87, doi: 10.1007/s11207-017-1095-2
  * Sudar et al. (2019) Sudar, D., Brajša, R., Skokić, I., & Benz, A. O. 2019, Sol. Phys., 294, 163, doi: 10.1007/s11207-019-1556-x
  * Wedemeyer et al. (2016) Wedemeyer, S., Bastian, T., Brajša, R., et al. 2016, Space Sci. Rev., 200, 1, doi: 10.1007/s11214-015-0229-9
  * White et al. (2017) White, S. M., Iwai, K., Phillips, N. M., et al. 2017, Sol. Phys., 292, 88, doi: 10.1007/s11207-017-1123-2
  * Wootten & Thompson (2009) Wootten, A., & Thompson, A. R. 2009, IEEE Proceedings, 97, 1463, doi: 10.1109/JPROC.2009.2020572