11institutetext: Hvar Observatory, Faculty of Geodesy, University of Zagreb,
Kačićeva 26, HR-10000 Zagreb, Croatia
11email<EMAIL_ADDRESS>22institutetext: University of Applied
Sciences and Arts Northwestern Switzerland, Bahnhofstrasse 6, CH-5210
Windisch, Switzerland 33institutetext: Institute for Particle Physics and
Astrophysics, ETH Zürich, CH-8093 Zürich, Switzerland 44institutetext:
Astronomical Institute of the Czech Academy of Sciences, Fričova 298, CZ-25165
Ondřejov, Czech Republic

# Flares detected in ALMA single-dish images of the Sun

I. Skokić 11 A. O. Benz, 2233 R. Brajša 11 D. Sudar 11 F. Matković 11 M. Bárta
44

(Received -; accepted -)

###### Abstract

Context. The millimeter and submillimeter radiation of solar flares is poorly
understood. Without spatial resolution, it cannot be compared easily to flare
emissions in other wavelengths. The Atacama Large Millimeter-submillimeter
Array (ALMA) offers sufficient resolution for the first time. However, used as
an interferometer, its field of view is smaller than an active region and ALMA
cannot observe on demand when a flare occurs.

Aims. We use readily available large scale single-dish ALMA observations of
solar millimeter flares and compare them to well-known features observed in
other wavelengths. The properties of these other flare emissions, correlating
in space and time, may then be used to interpret the millimeter brightenings
and vice versa. The aim is to obtain reliable associations, limited by the
time and space resolution of single-dish observations.

Methods. Ordinary interferometric ALMA observations require single-dish images
of the full Sun for calibration. We collected such observations at 3 mm and 1
mm and searched for millimeter brightenings during times given in a flare
catalog.

Results. All of the flares left a signature in millimeter waves. We found five
events with 9 or more images that can be used for comparison in time and
space. The millimeter brightenings are associated with a variety of flare
features in cool (H$\alpha$, 304 Å), intermediate (171 Å), and hot (94 Å)
lines. In several cases, the millimeter brightening peaked at the footpoint of
a hot flare loop. In other cases the peak of the millimeter brightening
coincided with the top or footpoint of an active H$\alpha$ filament. We found
correlations also with post-flare loops and tops of a hot loop. In some images
the millimeter radiation peaked at locations, where no feature in the selected
lines was found.

Conclusions. The wide field of view provided by the single-dish observations
allowed for completely overviewing the flare activity in millimeter waves for
the first time. The associated phenomena often changed during the flare in
type and location. The variety of phenomena detected in these millimeter
observations may explain the sometimes bewildering behavior of millimeter
flare emissions observed previously without spatial resolution.

###### Key Words.:

Sun: chromosphere – Sun: flares – Sun: filaments – Sun: radio radiation

##  1 Introduction

Brightenings during solar flares have been reported over the full
electromagnetic spectrum from gamma-rays to decameter radio waves (Benz,
2017). They are caused by various drivers and mechanisms, but their
interpretation remains fragmentary. Little is known about the range from 100
GHz to 10 THz (mid infrared). Contrary to the flare emission below 100 GHz
(Bastian et al., 1998), the spectrum above sometimes increases with frequency,
rising the possibility of a ”THz-component” (Kaufmann et al., 2004). The
millimeter and sub-millimeter flare observations have been reviewed by Krucker
et al. (2013). The ¿100 GHz emission correlates best, but not completely with
HXR and gamma-rays, sometimes with chromospheric lines. The correlation is
often different in the pre-flare, impulsive, and even post-impulsive phases of
a flare and in different flares. In one case, where this was reliably
measured, the position of the 210 GHz emission was on one of the flare ribbons
(Lüthi et al., 2004). Krucker et al. (2013) list ten mechanisms that have been
proposed to interpret the THz-component. They remark that there may indeed be
more than one explanation.

Interferometric observations using the Berkeley-Illinois-Maryland Array (BIMA)
at 86 GHz found that the millimeter emission of a solar flare exhibits
impulsive and gradual phases, both often observed in the same flare (Kundu,
1996). High spatial resolution images of solar flares at millimeter
wavelengths obtained by BIMA showed that most of the gradual phase millimeter
flux came from the top of a flaring loop, with some contribution from the
footpoints (Silva et al., 1996a, b, 1997, 1998). The millimeter emission from
the gradual phase was likely due to thermal bremsstrahlung from the soft
X-ray-emitting hot plasma, while gyrosynchrotron radiation was suggested as
the main mechanism for the impulsive phase. Raulin et al. (1999) et al. found
indications of two different electron populations in the impulsive phase, one
responsible for HXR/microwave emission, the other for millimeter emission.
Kundu et al. (2000) analyzed two solar flares simultaneously observed at 17,
34, and 86 GHz and reported evidence of bipolar (looplike) structures.

The major limit of the previous ¿100 GHz observations was spatial resolution,
impeding the combination with observations at other wavelengths. The Atacama
Large Millimeter-submillimeter Array (ALMA) has a great potential to mitigate
this instrumental gap (Wedemeyer et al., 2016; Bastian et al., 2018). Since
ALMA is not a solar dedicated instrument, however, sporadic flares are
difficult to observe.

For this reason, solar ALMA observations in the past have focused on
stationary phenomena such as radius, center-to-limb and center -to-pole
brightnening measurements (Alissandrakis et al., 2017; Selhorst et al., 2019;
Sudar et al., 2019a, b; Menezes et al., 2021, 2022), identification and
analysis of various stationary structures in full disk (Brajša et al., 2018;
Skokić et al., 2020) and interferometric ALMA images (Iwai et al., 2017;
Bastian et al., 2017; Nindos et al., 2018; Jafarzadeh et al., 2019; Rodger et
al., 2019; Loukitcheva et al., 2019; Molnar et al., 2019; Shimojo et al.,
2020; Wedemeyer et al., 2020; Brajša et al., 2020, 2021).

Recent research extends ALMA results to stationary prominences/filaments
(Heinzel et al., 2022; da Silva Santos et al., 2022; Labrosse et al., 2022),
dynamical phenomena such as oscillations in the quiet Sun (Patsourakos et al.,
2020; Jafarzadeh et al., 2021; Chai et al., 2022) and transients (Nindos et
al., 2020; da Silva Santos et al., 2020; Eklund et al., 2020), and even to
submillimeter structures (Alissandrakis et al., 2022).

The only known flare-related ALMA observation to date is by Shimizu et al.
(2021), who observed an active region with ALMA in interferometric mode at 100
GHz. The field of view was 60″and the resolution 5.″0 x 3.″9. They report a
microflare, which correlated in time with Si IV line emission ($\sim 80\,000$
K) and in space with the footpoint of an SXR loop in the outskirts of the
active region.

Here we report on the first solar flares observed by ALMA with complete
spatial coverage. The aim of this paper is to analyze the temporal and spatial
evolution of five flares observed by ALMA in single-dish mode. We compare
images and time profiles with data from other wavelengths to identify
counterparts and to provide clues for the mechanisms responsible for flare
emission at millimeter wavelengths.

##  2 Data and methodology

Table 1: ALMA observation details. In the period column, start times of the first and last ALMA observation of that period are given. Number of observations in the period is given in the column denoted by N. Date | Period UT | Project code | Freq. | N
---|---|---|---|---
|  |  | GHz |
2017-04-23 | 14:06 – 16:30 | 2016.1.01129.S | 230 | 9
2017-04-26 | 14:17 – 16:19 | 2016.1.00070.S | 107 | 11
2018-04-03 | 13:47 – 17:39 | 2017.1.00072.S | 95 | 23
2018-04-19 | 15:26 – 17:47 | 2017.1.01138.S | 95 | 14
2018-12-15 | 13:08 – 15:12 | 2018.1.01879.S | 95 | 10

Observations of the Sun with the ALMA interferometer require total power full-
disk images for absolute calibration (White et al., 2017; Shimojo et al.,
2017). These full-disk solar images are publicly available from the ALMA
Science Archive111https://almascience.eso.org. We limited the data set to ALMA
bands 3 (100 GHz, $\lambda$=3 mm) and 6 (240 GHz, $\lambda$=1.2 mm) because
other bands were either not public at the time of retrieval or only a small
number of images are available. The final data set consisted of 372 images
taken between 2016 Dec 21 and 2019 Apr 13. They amount to a total on-source
observing time of about 40 hours. The images were then converted to a
helioprojective coordinate system and rotated to the Sun’s north pole pointing
upward (Skokić & Brajša, 2019). We improved the alignment in all images by
limb fitting and double-checked on compact structures. Next, the images were
scaled in intensity so that the brightness temperature of the quiet Sun region
nearest to the solar center is equal to 7300 K (5900 K) in band 3 (6), as
suggested by White et al. (2017). Alissandrakis et al. (2020) reported that in
band 6 the value was most probably underestimated by $\sim$440 K, but we did
not include this correction in the present analysis. Finally, the center-to-
limb brightness variation was removed by the procedure described in Sudar et
al. (2019a).

Depending on the band, it takes ALMA between 10 and 16 minutes to obtain one
full-disk image of the Sun. This is the time the antenna needs to scan the Sun
and perform additional calibration scans limiting the maximum cadence. The
actual scanning of the Sun without calibration takes 301.4 s in band 3 and
581.4 s in band 6, thus defining the temporal uncertainty of the images. We
transferred the DATE-OBS time in the FITS headers of the ALMA images referring
to the beginning of the scan to the middle of the scan.

Table 2: Parameters of the observed flare events retrieved from the HEK database. Class column denotes the GOES flare class, and HPC column lists helioprojective coordinates of the flare in arcseconds at peak time. Date | Start | Peak | End | GOES | HPC
---|---|---|---|---|---
|  |  |  | Class | x, y
2017-04-23 | 15:47 | 15:57 | 16:12 | B1.8 | 15, 470
2017-04-26 | 15:28 | 15:38 | 15:50 | B3.4 | 350, 300
2018-04-03 | 14:13 | 14:17 | 14:32 | B1.2 | -275, -50
2018-04-19 | 15:57 | 16:29 | 17:25 | - | 750, -50
2018-12-15 | 13:40 | 13:53 | 14:15 | B1.0 | -640, 215

Figure 1: Intensity profiles for the SOL2017-04-23 flare. Gray shaded areas
represent time intervals during which an ALMA image was obtained. Black curves
show intensities spatially averaged over the flare region, and red curves show
peak intensities within the flare region. The scale of the red curves is given
on the right axis, in the same units as the black curves given on the left
axis

. Vertical blue lines denote instants that are shown in cutout images and
further analyzed. The same representation is used in all subsequent intensity
profiles.

Figure 2: SOL2017-04-23 flare. The ALMA images are difference images between
the designated time frame and the base pre-flare frame. The other images are
regular full-scale. ALMA contours outline five levels equidistantly within the
range of 100 - 500 K. The peak ALMA brightness in the flaring region, is
marked with a white ”x”. The intensity was clipped in each image to better
show structures of interest.

The observation times of the ALMA images were used to search for coinciding
flare events in the Heliophysics Events Knowledgebase
(HEK222https://www.lmsal.com/hek/). The search returned a list of nearly
hundred entries. However, many of them were related to the same flare event
reported by different observatories or detection methods. These multiple
entries were filtered out, along with short duration events that occurred
between two consecutive ALMA observations and events in which ALMA images were
of poor quality due to the presence of scan artifacts or other effects. A
total of four flare events were singled out. Additionally, one event was
manually found that was visually detected as a small brightening in the ALMA
data, but was not present in the HEK flare catalog. Details of ALMA
observations for all five selected events are listed in Table 1. Flare
properties obtained from the HEK catalog are listed in Table 2.

ALMA images were compared with filtergrams in extreme ultraviolet (EUV) from
the Atmospheric Imaging Assembly (AIA, Lemen et al. 2012) and magnetograms
from the Helioseismic and Magnetic Imager (HMI, Scherrer et al. 2012) on the
Solar Dynamics Observatory (SDO, Pesnell et al. 2012). These complementary
data were obtained from the Joint Science Operations Center
(JSOC333http://jsoc.stanford.edu). We limited the analysis to AIA 94 Å
(flaring regions, characteristic temperature of $T=6\times 10^{6}$ K), 171 Å
(quiet corona and upper transition region, $T=6\times 10^{5}$ K) and 304 Å
(chromosphere and transition region, $T=50\,000$ K). These channels were
selected for their characteristic temperature to complement the ALMA data. HMI
data provided photospheric line-of-sight magnetic field measurements. We used
a cadence of 1 minute for AIA images and 45 seconds for HMI data. Both AIA and
HMI data were preprocessed with routines from the Python aiapy software
package, which is analogous to the usual IDL aia_prep procedure.

For time profiles, we selected a circular region of a size large enough to
cover the entire flaring region and at least the ALMA beam size ($\sim$60″ in
band 3 and $\sim$28″ in band 6). The radius of 100″ was used for the first
four flares and 50″ for the SOL2018-12-15 flare. Both the average intensity
over this flaring region and the intensity of the brightest pixel in the
region were measured in all ALMA and SDO/AIA images at all times. The position
of peak intensity changes over time and in different wavelengths. While the
average intensity is useful for the overall comparison of the ALMA and SDO/AIA
intensity profiles and estimation of the total energy released, the peak
intensity refers to spatially separated individual brightenings and better
assesses the maximum increase of the brightness temperature.

The soft X-ray fluxes for all events were observed by the Geostationary
Operational Environmental Satellites (GOES), specifically by the GOES-15 X-Ray
Sensor (XRS), and were obtained from the National Oceanic and Atmospheric
Administration (NOAA).

GONG H$\alpha$ images are from the Cerro Tololo Interamerican Observatory in
Chile taken at the core of the H$\alpha$ line at 6562.8 Å with a spatial
resolution of 1″ per pixel and 1 minute cadence.

We searched for bursts related to the analyzed flares in dynamic spectra
recorded by the solar radio spectrometers e-CALLISTO in the 20 - 300 MHz range
and Radio Solar Telescope Network (RSTN) GHz data, but found no events.

In the following intensity profile figures, gray shaded areas indicate the
duration of each ALMA scan of the Sun, thus representing time uncertainty of
the ALMA measurements. Average intensity of the circular region containing the
flare is represented by a black curve while maximum intensity is depicted as a
red curve. The mean ALMA intensity error was obtained from the variation of an
intensity profile of a quiet Sun region.

The ALMA images relevant to the flare were further analyzed at the times
indicated by vertical blue lines in the intensity profiles. To better isolate
the flaring region, a difference image was made by subtracting a reference
image. The reference image was usually selected as the ALMA image obtained
just before the start of the flare. The effect of solar differential rotation
was taken into account. Then the contours from the ALMA difference image were
overlaid on the HMI magnetogram, the H$\alpha$ image from the Global
Oscillations Network Group (GONG), and the AIA 304, 171, and 94 Å filtergrams.
This was done in order to find counterparts of the ALMA flare emission.

##  3 Results

###  3.1 SOL2017-04-23 flare

The SOL2017-04-23 flare is the only ALMA band 6 event in the analyzed set. The
advantage of band 6 over band 3 is in twice the spatial resolution of the
images, but at the expense of less temporal resolution due to the longer time
required to scan the entire Sun. The beam size is 28.3″, and the pixel size is
3″. ALMA images were produced from PM01 antenna data at 230 GHz (1.3 mm).

The observed ALMA and SDO/AIA intensity profiles are shown in Fig. 1 and
compared with GOES XRS flux. The time of maximum millimeter brightness
temperature coincides with the maxima in the other wavelengths. The average
ALMA profile and the peak ALMA profile are similar except for the last
measurement, where the average rises but the peak values stay constant. The
reason for this is an increase in total radiation distributed over a larger
area (compare the contours at 16:14 UT and 16:34 UT in Fig. 2). The average
EUV profiles are similar to each other and to the GOES X-ray curve as well.

The peak intensity profiles of the various wavelengths differ more from each
other, especially in 171 Å channel, where many multiple post-maximum peaks can
be seen. They indicate strong brightenings originating from individual small
areas (high loops).

ALMA images of the flaring region are shown in Fig. 2 and compared with HMI
LoS magnetograms, GONG H$\alpha$ images, and AIA filtergrams with overlaid
ALMA 100 - 500 K contours. H$\alpha$ and 304 Å images suggest a two-ribbon
flare scenario. The first image shown, (Fig. 2, 15:57), corresponds to the
peak of the flare. The ALMA contours encompass the extent of the flare in
H$\alpha$, 304 and 94 Å images, and coincide with the polarity inversion line
in the HMI magnetogram. The peak ALMA brightness in the flaring region, marked
with a white ”x”, is located near the southern footpoint of a bright 94 Å
loop. The ALMA peak is also located near the top of a small loop visible in
H$\alpha$, 304, and 171 Å.

A second ALMA component, peaking to the north, coincides with a small filament
visible in H$\alpha$ absorption. The footpoint of a thin loop is visible at
the same location in 304 and 171 Å. A third ALMA source with significant
brightness is located northwest (up right) of the main peak. The movies in
H$\alpha$ and 304 Å suggest that the third source is at the location of plasma
downflow originating from a region near the second peak.

Figure 3: Intensity profiles for the SOL2017-04-26 flare. The colors and
markings are the same as in Fig. 1.

The next time shown, (Fig. 2, 16:14), is around the secondary flare peak,
visible in 304 and 171 Å average intensity profiles (Fig. 1). The ALMA peak
brightness is shifted to the north, next to a small H$\alpha$ filament that
became more pronounced in H$\alpha$ absorption. The ALMA peak location is
consistent with the top of the H$\alpha$ filament but not with any feature at
any other wavelength. However, an intensifying plasma flow can be observed in
304 and 171 Å movies from the main ALMA location, with some of the material
falling back to the surface near the location of the second ALMA bright region
(on the right).

Finally, in the last ALMA image (Fig. 2, 16:34), the H$\alpha$ filament has
intensified (darkened), and the ALMA contours now correspond well to its
shape. The maximum ALMA brightness is situated at the southern footpoint of
the filament. The area at the location of plasma inflow (to the right of the
filament) has slightly brightened. The original ALMA peak located above the
flare ribbons has also brightened and matches the shape of the hot flare loop
visible in 94 Å.

Figure 4: SOL2017-04-26 flare. ALMA contours outline five levels equidistantly
in the 50 - 200 K range.

We note in conclusion that the millimeter emission of SOL2017-04-23 is
associated with a bewildering number of features:

\- footpoint of hot (94 Å) loop (main ALMA peak)

\- top of cool loops in H$\alpha$, 304, and 171 Å

\- downflow region in H$\alpha$, 304, and 171 Å

\- top and footpoint of dark H$\alpha$ filament.

###  3.2 SOL2017-04-26 flare

The flare that occurred on 2017 Apr 26 was recorded by ALMA in band 3 in the
spectral window centered at 107 GHz (2.8 mm). The beam size is 60″ and pixel
size is 6″. Artifacts from the antenna scanning pattern can be seen in ALMA
images, especially in the difference images, somewhat affecting the observed
shape of the flaring region.

The region-averaged ALMA time profile looks similar to 304 Å, 94 Å, and GOES,
but the 171 Å emission peaks significantly later (Fig. 3). The pre-flare 171 Å
average intensity level was even higher than during the flare. This brightness
originates from activity within large loops arching over the region. The ALMA
peak intensity behaves similarly to the average ALMA intensity. The only
difference is that peak curve maximum occurs before the average maximum, in
line with the 304 Å channel behavior.

The ALMA peak in the first image at the time of the flare maximum coincides
with the bright spot in 94 Å (Fig. 4, 15:32). The region is also bright in
H$\alpha$ and 304 Å images, but not in the 171 Å image. Most 171 Å emission
originates from high loops having many small brightenings that do not show in
the ALMA image. These brightenings are visible in H$\alpha$ and 304 Å images
and contribute to the high temporal variability at these wavelengths. Whereas
the ALMA maximum brightness falls exactly on the 94 Å peak in the flare rise
phase, the ALMA peak shifts south along the neutral line in the following time
steps. The ALMA contours outline the whole flaring region in the next time
step (Fig. 4, 15:44). The peak brightness is at the location of the peak in
304 Å. A new thin loop can be seen nearby in 171 Å. The ALMA peak remains in
the same place in the next two frames (Figs. 4, 15:56 - 16:08) where small
filamentary structures are forming in 304 Å, while nothing can be seen in 94
Å. However, a secondary ALMA peak at 16:20 UT (Fig. 3) is located on two
decaying 94 Å flare loops in the northwest.

Millimeter emission of the SOL2017-04-26 flare is associated with:

\- footpoint of a hot flare loop (94 Å)

\- small 171 Å brightenings

\- decaying hot loops in 94 Å.

###  3.3 SOL2018-04-03 flare

The SOL2018-04-03 flare was a short-lived two-ribbon event. The flare lasted
less than 20 minutes, but evolution and post-flare aftermath were well
recorded in 23 ALMA images at 95 GHz (3.2 mm). The beam size is 66″ and pixel
size is 6″.

Figure 5: Intensity profiles for the SOL2018-04-03 flare. The colors and
markings are the same as in Fig. 1

The main ALMA peak seems to be delayed in time compared to all other channels.
However, this may be the result of undersampling of the ALMA time profile,
missing the peak in millimeter waves.

The preflare seen in the ALMA time profile (Fig. 5) coincides in space with a
dark H$\alpha$ filament (Fig. 6, 14:00). Yet, the H$\alpha$ preflare
brightening is related to emissions from the two ribbons located some 28″ to
the southeast. Interestingly, there is initially no visible ALMA enhancement
around the prominent filament located southeast of the small one.

At the peak of the ALMA flare (Fig. 6, 14:22), however, the ALMA maximum moves
to the northern footpoint of the larger filament, and now also encompasses the
flare ribbons and loops visible in 304 and 94 Å. The smaller filament remains
enhanced in the ALMA image. The ALMA emission follows in general the neutral
line (Fig. 6, 14:22). At the same time, the H$\alpha$ filament shrinked in
diameter and length.

Figure 6: SOL2018-04-03 flare. ALMA contours outline five levels equidistantly
in the 50 - 200 K range.

Further in time, the ALMA peak remains on the larger filament which is now
more pronounced. The prominent peaks in 171 Å at 15:04 and 17:10 UT are caused
by large loops leaving no traces in millimeter waves. The ALMA brightness
slightly increases at 16:07, when plasma erupts from the active region and
moves south along the major filament, as can be seen in 304 Å movies. Finally,
at 17:41 UT, the ALMA intensity peaks near the southern H$\alpha$ ribbon at a
footpoint of a hot loop visible in 94 Å emission.

The SOL2018-04-03 flare is an example where the ALMA peak emission is best
associated with H$\alpha$ filaments. They are not steadily bright in
millimeter emission, but become visible due to some activity related to the
flare. Millimeter and 94 Å emission are spatially not related except for a
microflare in the late post-flare phase.

###  3.4 SOL2018-04-19 flare

The SOL2018-04-19 flare was spotted while manually browsing ALMA images.
GOES-15 did not detect it in soft X-rays (Fig. 7). Thus there is no entry in
the HEK flare catalog. The flare is short and compact, and located near the
western solar limb where the ALMA antenna scanning pattern smears out sources
diagonally. This is well noticeable in the background of Fig. 8.

Figure 7: Intensity profiles for the SOL2018-04-19 flare. The colors and
markings are the same as in Fig. 1

The main peak in the EUV lines is sharp and precedes the ALMA peak by around
11 minutes, although the rise of ALMA intensity is visible even before. The
ALMA peak coincides in time with a small peak in 304 Å and 171 Å about 11
minutes after their main peak. The subpeak is not visible in 94 Å, indicating
the absence of hot plasma.

Figure 8: SOL2018-04-19 flare. ALMA contours outline five levels equidistantly
in the 50 - 120 K range.

The main ALMA peak is located 25″ southeast of the maxima in the line
emissions (Fig. 8, 16:32). The ALMA images show a secondary peak northwest of
the main peak. There is no corresponding brightening in the line emissions.
This is the case even in the last image, when the secondary ALMA peak exceeded
the primary peak (Fig. 8, 17:16).

The SOL2018-04-19 flare is a case where ALMA millimeter waves correlate with
cool (H$\alpha$ and 304 Å) lines, with the intermediate 171 Å line, the hot 94
Å, and the extremely hot bremsstrahlung emission (GOES) in time, but are
displaced in space.

###  3.5 SOL2018-12-15 flare

Figure 9: Intensity profiles for the SOL2018-12-15 flare. The colors and
markings are the same as in Fig. 1

The weak SOL2018-12-15 flare occurred close to the limb. ALMA was observing at
95 GHz (3.2 mm). The observed intensity profiles are shown in Fig. 9. The ALMA
intensity profile correlates best with 304 Å average intensities, but not with
the GOES X-ray and the 94 Å profile, which are similar to each other. The
flare reached its peak somewhat earlier in 304 Å relative to the millimeter
waves, but much later in 171 Å. The 171 Å emission is dominated by large loops
arching over the active region (Fig.10, 13:58). The averaged profile has a
minimum intensity at the time of the ALMA flare peak (13:58 UT) due to dimming
of some of the loops.

Figure 10: SOL2018-12-15 flare. ALMA contours outline five levels
equidistantly in the 50 - 150 K range.

The brightening in millimeter waves encompasses most of the active region as
seen in the magnetogram, but peaks 25″ farther south where little emission in
H$\alpha$, 304 Å, 171 Å, and 94 Å originates (Fig.10, 13:46 and 14:25). Only
at the peak time (13:58 UT) of the X-ray and 94 Å intensities, the peak
position of all line emissions coincide with the peak in millimeter waves.

The SOL2018-12-15 flare is another example of weak millimeter emission with
little relation to the emissions in H$\alpha$, 304 Å, 171 Å, 94 Å, and X-rays.

##  4 Discussion

Table 3: List of features in other wavelengths coincident with emission in millimeter ALMA images for each flare. Date | Time UT | Peak source |  Coincides with
---|---|---|---
|  | in mm image |
2017-04-23 | 15:57 | primary |  along neutral line in HMI, near the top of a small loop in H$\alpha$, 304 and 171 Å, footpoint of a 94 Å loop
|  | secondary |  top of H$\alpha$ filament, thin loop footpoint at 304 and 171 Å
|  | tertiary |  plasma downflow in H$\alpha$, 304 Å
| 16:14 | primary |  near the top of H$\alpha$ filament, plasma outflow in 304 and 171 Å
| 16:34 | primary |  footpoint of a dark H$\alpha$ filament
2017-04-26 | 15:32 | primary |  footpoint of a flare loop in 94 Å, bright in H$\alpha$ and 304 Å, nothing in 171 Å
| 15:44-15:56 | primary |  along neutral line in HMI, newly forming filament in H$\alpha$, peak in 304 Å, top of loop in 171 Å, nothing in 94 Å
| 16:20 | secondary |  decaying flare loops in 94 Å
2018-04-03 | 14:00 | primary |  H$\alpha$ filament
| 14:22 | primary |  along neutral line in HMI, H$\alpha$ filament footpoint, thin loops in 304 and 171 Å, near the hot loop top in 94 Å
| 14:22-16:07 | primary |  H$\alpha$ filament footpoint
| 17:41 | primary |  H$\alpha$ ribbon, footpoint of a hot loop in 94 Å
2018-04-19 | 16:21-16:32 | primary |  nothing (displaced from the flaring region)
2018-12-15 | 13:46 | primary |  loops in 171 Å, nothing elsewhere
| 13:58 | primary |  top of the loop in H$\alpha$ and 304 Å, footpoint of the flaring loop in 94 Å
Table 4: NOAA number of the flare active region, peak pixel brightness temperature $T_{b}$ at wavelength $\lambda$ and peak pixel brightness temperature difference $\Delta T_{b}$ from the background level. Flare | NOAA | $\lambda$ | Peak $T_{b}$ | Peak $\Delta T_{b}$
---|---|---|---|---
| region | [mm] | [K] | [K]
SOL2017-04-23 | N/A | 1.3 | 7163 | 563
SOL2017-04-26 | 12652 | 2.8 | 8199 | 263
SOL2018-04-03 | 12703 | 3.2 | 8224 | 321
SOL2018-04-19 | N/A | 3.2 | 7757 | 142
SOL2018-12-15 | 12731 | 3.2 | 8086 | 194

Significant millimeter radiation was found in all 4 flares selected from the
HEK catalogue. In the event selected from ALMA data, brightenings in line
emission in H$\alpha$, 304 Å, 171 Å, and 94 Å are associated. This strongly
confirms a general correlation in time between the different radiations
originating from very hot, hot, intermediate and cool plasma. The comparison
of the images, on the other hand, shows a surprising variety of associations
with spatial features. A summary of features cospatial with the millimeter
emission for each flare is given in Table 3.

In both ALMA bands 3 and 6, the ALMA flare emission occurs mainly above the
neutral line observed in HMI magnetograms. Good examples are Fig. 2 at 15:57,
Fig. 4 at 15:44 and Fig. 6 at 14:22. However, this is not always the case and
millimeter emission may correspond to different features such as

\- H$\alpha$ active filaments (Fig. 2 at 16:14 and 16:34, Fig. 6 at 14:00,
14:22, and 16:07)

\- 94 Å (hot) loop tops (Fig. 4 at 15:56) or footpoints (Fig. 2 at 15:57),

\- post-flare loops (Fig. 4 at 16:08)

\- occasionally to no features in other wavelengths at all (Fig. 8 at 17:16,
secondary peak in Fig. 6 at 17:41)

Millimeter emission originating from flaring loop tops and footpoints was
found previously at 86 GHz with the BIMA interferometer (Silva et al., 1996b,
1998). They estimated that the major part (around 80%) of the emission in the
flare gradual phase came from the top of a loop as free-free radiation emitted
by hot plasma. Kundu et al. (2000) reported a clear detection of both
footpoints of a loop at $\lambda$=3 mm.

It is interesting to note that millimeter flare emission sometimes corresponds
very well with filaments, particularly to the activity within them (e.g.
SOL2018-04-03). Rutten (2017) predicted that the appearance of the Sun at ALMA
wavelengths will be similar to the one in H$\alpha$ with good dark-dark
correspondence. Brajša et al. (2021) did find dark filaments at 3 millimeters.
On the other hand, da Silva Santos et al. (2022) found some of the dark
threads visible in the AIA 304 Å and Mg II resonance lines to have dark
counterparts at 1.25 mm, but their visibility varied significantly across the
filament both spatially and temporally. Here we report occasional dark-bright
correspondence.

Two kinds of time profiles were extracted from the images. The average over
the active region, shown with a black solid curve, corresponds to what a low
resolution telescope would measure. In a second time profile, represented by a
red dashed curve, the peak of the brightest pixel in the area is shown. The
second curve indicates small, individual peaks of emission.

In all time profiles, the peak pixel curves have more maxima and shorter
maxima than the spatially averaged curves. It indicates that the millimeter
flare emission originates from different peaks within the active region. The
effect of a multitude of individual peaks is more pronounced in the SDO/AIA
lines, especially at 171 Å.

The peak pixel intensity measured from the intensity profiles and from the
difference ALMA images is given in Table 4. The largest increase is found in
the band 6 flare with a value of $\Delta T_{b}=563$ K above the pre-flare
level, while in band 3 the values vary between 140 and 320 K. This corresponds
to 500 – 1200 K above the quiet Sun level. These values are lower limits since
the maximum intensity is spread by the antenna beam for compact, unresolved
sources.

To investigate statistically the observed similarity of the ALMA and SDO/AIA
EUV intensity curves, we calculated the Pearson correlation coefficient
between ALMA and EUV, average and maximum, time profiles. The results are
listed in Table 5.

The correlation between average ALMA profile and AIA 94 and 304 Å channels is
quite good. In three cases, the 304 Å channel, indicating cool plasma, has the
highest correlation coefficient. This corresponds to earlier reports about
spatial best correlation with the 304 Å line among all EUV AIA lines (White et
al. 2017; Brajša et al. 2018).

The 94 Å line, originating from hot plasma, has a slightly higher correlation
of the remaining two cases (Table 5). However, the 171 Å line, emitted by
plasma of intermittent temperature in coronal loops, has a much lower
correlation coefficient, or even an anti-correlation. A similar trend with low
171 Å, and high 94 and 304 Å correlations is present in peak intensity
profile. However, there are two exceptions where 171 Å peak emission has a
similarly high correlation as 94 and 304 Å channels. The first one is
SOL2017-04-23 flare where peak pixel 171 Å curve follows the shape of the ALMA
peak and average profiles. The second one is SOL2018-04-19 flare where the
high 171 Å to ALMA correlation is due to the secondary peak(s).

The observed similarity between 304 Å, 94 Å and ALMA time profiles suggests
that the millimeter brightness in flares originates mainly from chromospheric
phenomena, but occasionally also from hot and dense flare components. Geometry
could have a role in the observed correlations as well since the last two
flares from Table 5, with generally the lowest correlation from the set, are
also closest to the solar limb.

The accuracy of the contours and the location of maximum intensity is better
than the ALMA beam width. The confidence interval depends on statistical
significance of the peak above background and the number of samplings of the
single-dish beam by the double-circle scanning pattern. This pattern consists
of minor circles with a radius of 600″, whose centers move steadily in a major
circle around the center of the Sun at a distance of 600″. Each new minor
circle is shifted along the major circle by a defined value called the
sampling length (White et al., 2017). In the worst case scenario when minor
circles fall on top of each other, the largest distance of the sampled points
is less than or equal to the sampling length. So, the beam is at least sampled
at 3 times the beam resolution, and in many places like near the disk center
even more, giving a minimum resolution of 10″ in band 6 and 20″ in band 3. The
location of the peak can be determined even more precisely by centroiding.

The flares of this work were not detected in hard X-rays and microwaves. Using
the time derivative as a proxy for the hard X-ray flux, we estimate the
impulsive phase of the flare by the rise phase of the soft X-rays from
beginning to peak. In the four flares with significant soft X-rays, the ALMA
millimeter intensity is consistent with peaking after the impulsive phase.
Flare SOL2017-04-23 (Fig. 1), however, is also consistent with a maximum
during the impulsive phase, and the peak intensity curve (red) of flare
SOL2017-04-26 (Fig. 3) has its maximum clearly during the impulsive phase.
Thus, ¿100 GHz flares appear to be mostly gradual phase phenomena with
occasional impulsive phase emission.

Table 5: Pearson correlation coefficients between intensity measurements from ALMA and different AIA channels. Top: Flare region averaged, bottom: peak pixel of flare region. Intensity | Date | N | 94 Å | 171 Å | 304 Å
---|---|---|---|---|---
profile |  |  |  |  |
Average | 2017-04-23 | 9 | 0.797 | 0.598 | 0.823
2017-04-26 | 11 | 0.777 | 0.582 | 0.746
2018-04-03 | 23 | 0.799 | 0.045 | 0.882
2018-04-19 | 14 | 0.721 | 0.391 | 0.613
2018-12-15 | 10 | 0.330 | -0.175 | 0.757
Peak pixel | 2017-04-23 | 9 | 0.939 | 0.924 | 0.938
2017-04-26 | 11 | 0.927 | 0.665 | 0.776
2018-04-03 | 23 | 0.771 | 0.064 | 0.713
2018-04-19 | 14 | 0.495 | 0.599 | 0.421
2018-12-15 | 10 | 0.373 | 0.367 | 0.168

##  5 Conclusions

Full-disk ALMA imaging has yielded the first spatially complete solar flare
observations in millimeter wavelengths. The field of view includes the whole
disk. We found a field of 250″$\times$250″ necessary for a complete overview
over the activity in millimeter waves taking place in an active region during
a solar flare. It significantly exceeds the field of view of ALMA in
interferometric mode. Single-dish observations thus complement interferometric
observations in an important way.

Most surprising is the fact that several phenomena in both hot and cold plasma
lead to enhanced brightness in millimeter waves. Although there is no evidence
contradicting the assumption that the emission process is thermal free-free
emission, it seems that the previous scenario of a chromospheric hot spot
heated by a precipitating electron beam is too simplistic.

In addition to footpoints of hot loops, millimeter flare emission was found to
be associated with activated H$\alpha$ filaments, impact points of plasma
motions, post-flare loops, and hot loop tops. Surprisingly, we found cases
where no feature in H$\alpha$, 304 Å, 171 Å, and 94 Å was visible at the
position of a millimeter wave emission peak.

In this work, we focused on comparing flare intensity profiles and coincident
spatial sources at different wavelengths. More information about the flares,
such as temperature and density of the emitting plasma, could be inferred from
comparison with simultaneous soft X-ray observations. Its analysis would
exceed the scope of this paper and it is planned for future work. The detected
flares were too small for significant hard X-ray and microwave emissions.

Higher temporal and spatial resolution are needed to gain a better insight
into the properties of flares at millimeter wavelengths. Both problems can be
solved by observing flares using ALMA interferometric mode, however, this is
difficult due to the ALMA scheduling constraints unable to wait for a flare.
The field of view in interferometric mode is small and a lot of luck is needed
to point at the right location and at the right moment. A possible way to
achieve better temporal resolution is to use the recently implemented total
power regional mapping in single-dish mode. There is also a third possibility
in the future to develop more advanced data analysis methods that could go
beyond the ALMA full-disk single-dish images presented here. The same data may
be much better exploited using specific characteristics and redundancies
present in the data.

###### Acknowledgements.

This work has been supported by the Croatian Science Foundation under the
project 7549 ”Millimeter and sub-millimeter observations of the solar
chromosphere with ALMA”. It has also received funding from the Horizon 2020
project SOLARNET (824135, 2019–2022). This paper makes use of the following
ALMA data: ADS/JAO.ALMA#2016.1.01129.S, ADS/JAO.ALMA#2016.1.00070.S,
ADS/JAO.ALMA#2017.1.00072.S, ADS/JAO.ALMA#2017.1.01138.S,
ADS/JAO.ALMA#2018.1.01879.S. 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. SDO/AIA data courtesy of NASA/SDO and the AIA, EVE, and HMI science
teams. This work utilizes GONG data obtained by the NSO Integrated Synoptic
Program, managed by the National Solar Observatory, which is operated by the
Association of Universities for Research in Astronomy (AURA), Inc. under a
cooperative agreement with the National Science Foundation and with
contribution from the National Oceanic and Atmospheric Administration. The
GONG network of instruments is hosted by the Big Bear Solar Observatory, High
Altitude Observatory, Learmonth Solar Observatory, Udaipur Solar Observatory,
Instituto de Astrofísica de Canarias, and Cerro Tololo Interamerican
Observatory. We are grateful to the GOES team for making the data publicly
available. We acknowledge the use of the ALMA Solar Ephemeris Generator
(Skokić & Brajša, 2019). This research used version 3.1.4 (Mumford et al.,
2022) of the SunPy open source software package (The SunPy Community et al.,
2020). This research used version 0.6.4 of the aiapy open source software
package (Barnes et al., 2020). This research made use of Regions, an Astropy
package for region handling (Bradley et al., 2022).

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