The Sun at millimeter wavelengths I. Introduction to ALMA Band 3 observations

We present an initial study of one of the first ALMA Band 3 observations of the Sun with the aim to characterise the diagnostic potential of brightness temperatures measured with ALMA on the Sun. The observation covers 48min at a cadence of 2s targeting a Quiet Sun region at disk-centre. Corresponding time series of brightness temperature maps are constructed with the first version of the Solar ALMA Pipeline (SoAP) and compared to simultaneous SDO observations. The angular resolution of the observations is set by the synthesized beam (1.4x2.1as). The ALMA maps exhibit network patches, internetwork regions and also elongated thin features that are connected to large-scale magnetic loops as confirmed by a comparison with SDO maps. The ALMA Band 3 maps correlate best with the SDO/AIA 171, 131 and 304 channels in that they exhibit network features and, although very weak in the ALMA maps, imprints of large-scale loops. A group of compact magnetic loops is very clearly visible in ALMA Band 3. The brightness temperatures in the loop tops reach values of about 8000-9000K and in extreme moments up to 10 000K. ALMA Band 3 interferometric observations from early observing cycles already reveal temperature differences in the solar chromosphere. The weak imprint of magnetic loops and the correlation with the 171, 131, and 304 SDO channels suggests though that the radiation mapped in ALMA Band 3 might have contributions from a larger range of atmospheric heights than previously assumed but the exact formation height of Band 3 needs to be investigated in more detail. The absolute brightness temperature scale as set by Total Power measurements remains less certain and must be improved in the future. Despite these complications and the limited angular resolution, ALMA Band 3 observations have large potential for quantitative studies of the small-scale structure and dynamics of the solar chromosphere.


Introduction
The Atacama Large Millimeter/submillimeter Array (ALMA) provides new diagnostic possibilities to probe the chromosphere of the Sun at high spatial, temporal, and spectral resolution (see Bastian 2002;Wedemeyer 2016;Wedemeyer et al. 2016;Loukitcheva et al. 2017;Bastian et al. 2018, and references therein). In principle, observing at millimeter wavelengths has the advantage that the radiation is formed under conditions of local thermodynamic equilibrium (LTE) and therefore provides a more direct measure of local gas temperatures in the chromosphere than other commonly used diagnostics at shorter wavelengths, such as optical and UV wavelengths, that are not in LTE. The comparatively long millimeter and submillimeter wavelengths have historically had the disadvantage of a correspondingly lower angular resolution, relying largely on single dish observations (e.g., Bastian et al. 1993, Lindsey et al. 1995, and references therein). Interferometric techniques, using an array of antennas, offer the means of observing the Sun with high angular resolution. These were explored in the 1990s (e.g., Kundu et al. 1993) and 2000s (White et al. 2006) using small arrays. ALMA is the largest and most ambitious array ever built to observe celestial phenomena at millimeter and submillimeter wavelengths, including the Sun. ALMA offers the potential of unlocking this new diagnostic tool for high-resolution studies of the solar chromosphere. An overview of potential science cases with ALMA is given by Wedemeyer et al. (2016), whereas Cycle 4 capabilities are described by White et al. (2017) and Shimojo et al. (2017a). While first regular ALMA observations of the Sun were only offered in Cycle 4 with a first solar campaign in December 2016, earlier observations from Commissioning and Science Verification (CSV) campaigns have been made publicly available. Both regular and CSV data are already used in  White et al. (2017) applied, i.e., mean value in central region rescaled). The white solid circle in the middle indicates the primary beam of a TP antenna at 3.0 mm and with it the field-of-view (FOV) of the interferometric observation. The dashed circle has a radius of 240 ′′ and marks the region that is considered for the correction of the absolute brightness temperature scale. The black square marks the central region with 120 ′′ × 120 ′′ . b) Uncorrected radial profiles for all sub-bands in rings of 10 ′′ width. The lines for each sub-band (see color legend at the top) represent the radial average (solid), average plus/minus the standard deviation (dot-dashed), and the 1 st and 99 th percentile (dotted). The shaded areas cover the value ranges between the percentiles for SB1 (red) and SB4 (blue). The bottom row shows histograms for the brightness temperature distribution within the black square (solid histograms) and within the white dashed circle (dotted histograms, scaled by a factor 3) for all sub-bands c) without and d) with correction to the reference value suggested by White et al. (2017)  Interferometric observations of a dynamic source like the Sun and the reliable reconstruction of corresponding image series are challenging tasks. As a next step, in order to further develop and characterise ALMA's diagnostic capabilities, the available observations have to be thoroughly studied and compared to other diagnostics. Here, we present and analyse observations with ALMA Band 3 at wavelengths around 3 mm from December 2016 (Cycle 4), which were among the first regular observations of the Sun with ALMA. The aim of the results presented here is to illustrate the potential, limitations, and challenges of studying the small-scale structure and dynamics of the solar atmosphere with ALMA Band 3. The technical details of the observations are described in Sect. 2 and the results of the data analysis in Sect. 3. Discussion and conclusions are provided in Sects. 4 and 5, respectively.

Solar observation in Band 3
The Band 3 observations discussed in this article were carried out on December 22, 2016 from 14:22UT -15:07UT. ALMA observations of the Sun currently comprise both interferometric observations of a specific target and full disk maps made with ALMA total power (TP) antennas. For the interferometric ob-servations, an array in configuration C40-3 was used, which included a total of 52 antennas from the 12-m Array as well as the 10 fixed 7m antennas of the Atacama Compact Array. The resulting array has baselines ranging from 9.1 m to 492.0 m resulting in a nominal angular resolution of 1.56 ′′ and a Maximum Recoverable Scale (MRS) of 68 ′′ . In addition to the interferometric observations, ALMA has up to 4 specially designed Total Power (TP) antennas that can perform rapid scans of the whole disk of the Sun . For the observations analysed here, three TP antennas were available for fast-scan mapping. The column of precipitable water vapour (PWV) in Earth's atmosphere during the observation was 1.60 mm.
Because of an operational glitch, the interferometric array did not point at and track the intended target region but instead re-centred on [x,y] = [0",0"] in helioprojective coordinates repeatedly during the observation. As a result, the observed diskcentre Quiet Sun region is slowly drifting through the ALMA field-of-view (FOV) because the telescope pointing did not track solar rotation (see Sect. 2.2). The Band 3 observing sequence consists of 4 scans with a duration of ∼10 min each. These scans are separated by calibration breaks of ∼2.4 min. The observations were carried out with a cadence of 2 s -the highest possible in Cycle 4.
In Cycle 4, ALMA Band 3 was set up for solar observations in 4 spectral windows (hereafter referred to as sub-bands) around a central frequency of 100 GHz. These sub-bands, which we refer to as sub-bands 1 -4 (abbreviated SB1 -SB4) with increasing frequency, are centered on 93 GHz (SB1), 95 GHz (SB2), 105 GHz (SB3), and 107 GHz (SB4), corresponding to wavelengths of 3.224 mm, 3.156 mm, 2.855 mm, and 2.802 mm. Each sub-band has a total bandwidth of 2 GHz (with the central Article number, page 2 of 14 1.875 GHz being retained), which results in two pairs of neighbouring sub-bands (SB1-SB2 and SB3-SB4) with a central gap.
The three available TP maps were completed at 14:23UT, 14:36UT, and 14:49UT. A complete scan in Band 3 took between 12.6 min and 12.9 min, which includes calibration. The net time for scanning the solar disk in a double-circle pattern is 5 min. The TP maps thus cover most of the interferometric observation and can be used for combining the interferometric and TP data, which results in absolute brightness temperatures. The TP map for SB4 for the first scan (from 14:11UT to 14:23UT) is shown in Fig. 1a. Please refer to Sect. A.4 for background information regarding the TP observations.

Interferometric data processing
Approach for the Band 3 data set. The calibrated ALMA data were downloaded from the ALMA Archive and further processed with the Solar ALMA Pipeline (SoAP, Szydlarski et al. in prep. 1 ) based on the Common Astronomy Software Applications (CASA 2 ) package. Please note that solar observing is currently still a non-standard mode. Solar data are therefore not processed with the official ALMA pipeline. Instead, SoAP is used for this publication. Please refer to Sect. A.1 in the appendix for more information on interferometric image reconstruction.
Unique to data from December 2016 are the complications arising from the erroneous pointing and tracking, which resulted in the instrument phase tracking center repeatedly being re-pointed to the apparent center of the solar disk, resulting in a slow drift of the FOV with intermediate jumps. It was therefore necessary to correct for the effect of the Sun's rotation during the course of the observation. To do so, a time series of Band 3 images at 2s cadence was constructed. The image processing required for each snapshot image includes several important steps: first, the ALMA PSF (the "dirty beam") is deconvolved from the image data (the "dirty map") through application of the multi-scale (multi-frequency) CLEAN algorithm (Rau & Cornwell 2011) as implemented in CASA. Here, all interferometric information from the four sub-bands is used to produce one continuum image (referred to as "full-band map") for each time step (see also Sect. A.1). Second, the image data are corrected for the effect of the primary beam (see Sect. 2.3). Third, the interferometric data are combined (also called "feathered") with the TP map in order to add an (DC brightness) offset and thus the absolute brightness temperature scale corresponding to zero-spacing information to the reconstruction (Sect 2.5). Finally, the ALMA Band 3 maps are co-aligned with observational data from other observatories (Sect. 2.6). The apparent drift of snapshot images in time due to solar rotation was then corrected by cross-correlating consecutive 2 s images with a reference image, where the first frame in the times series was taken as the reference. The resulting time sequence represents true snapshot imaging at 2 s cadence with no temporal averaging. We would like to emphasise that self-calibration for a short time window is the recommended approach but that self-calibration resulted in too aggressive corrections and loss of information on small spatial scales for December 2016 data suffering from pointing errors. A detailed description of the data processing with SoAP will be provided in a forthcoming publication (Szydlarski et al. in prep.).

Interferometric field-of-view
For the Band 3 data discussed here, the FWHM beam width varies from 67.5 ′′ for SB1 to 60.0 ′′ for SB4 with 63.8 ′′ for the band centre frequency. Please refer to Sect. A.2 in the appendix for general background information. Since, as a result of the primary beam taper the source brightness decreases with distance from the beam axis while the noise stays constant, the signal-tonoise ratio declines as function of distance from the beam axis. To correct for the primary beam taper, the image data are divided by the relevant Gaussian (unit maximum) out to some userspecified threshold level where the SNR remains significant. The resulting FOV for interferometric ALMA images is therefore set by the wavelength (or frequency) and the chosen threshold for the primary beam. A threshold of 0.3 is a reasonable but generous choice and results in diameters of the FOV from 89 ′′ (SB1) to 79 ′′ (SB4). In the particular case of the data from December 2016, problems with the pointing and resulting coordinate jumps led to a reduction of the final FOV once the data had been corrected for solar rotation. The resulting FOV of these maps was set to a diameter of 65.6 ′′ , which corresponds to effective Gaussian thresholds of 0.52 for SB1 and 0.44 for SB4, respectively.

Synthesized beam
We define the beam representative for the observations considered here (which determines the angular resolution) as the timeaverages of the major axis, minor axis, and position angle. The resulting representative beam corresponds to the band-average frequency of 100 GHz and has a major axis of 2.10 ′′ (full-widthhalf-maximum, FWHM ), a minor axis of 1.37 ′′ (FWHM ) and a position angle of 68.0 deg (see Fig. A.1). The beam for the time step at 2016-12-22 14:42:04UT comes closest to the representative beam in terms of size. During the 48 min covered during the observation with the Sun moving on the sky, the major axis shrank by ∼7 % (see Fig. A.1c), whereas the minor axis stayed almost constant and the position angle increased by less than 2 degrees (see Fig. A.1d). The changes of the beam must be taken into account for a meaningful interpretation of the resulting data. Please refer to Sect. A.3 for more details. White et al. (2017) suggest that, until systematic errors in the dual-load calibration scheme are fully understood and resolved, ALMA Band 3 TP maps should be scaled to a prescribed value of 7300 K. The TP maps for the data presented here were produced for each sub-band and calibrated using the dual-load approach described by White et al. (2017) as implemented in CASA 3 . Please note that, for Band 3, White et al. (2017) recommend to use the average over the inner square region with a size 120 ′′ × 120 ′′ (black square in Fig. 1a), whereas the CASA script provided with the TP data uses the average over the central region of the solar disk with a radius of 240 ′′ (40 pixels, see dashed white circle in Fig. 1a). The histograms in Fig. 1c show the absolute brightness temperatures for the two different regions for the different sub-bands. The average brightness temperatures for the inner 120 ′′ × 120 ′′ in the TP map used here ( The values for the inner 120 ′′ × 120 ′′ region are thus 75-77 K higher than the larger circular region. It should be noted that the 120 ′′ × 120 ′′ region is relatively small considering the width of the primary beam (∼ 60 ′′ ), resulting in poor statistics and susceptibility to untypical brightness temperatures. As a consequence, the histograms for the central square 120 ′′ × 120 ′′ in Fig. 1c-d are much narrower as compared to the histograms of the inner region with a radius of 240 ′′ . It should also be noted that the common procedure is to use only one TP sub-band (typically SB2) for determining the offset and combination with the interferometric data, which thus ignores data from the other three sub-bands.

Absolute temperatures based on Total Power maps
The aforementioned mean values, and also the distribution peak temperatures, are highest for SB1 and lowest for SB4, consistent with the expectation that SB1 is formed higher in the solar atmosphere and that the average gas temperature in the mapped layers is monotonically increasing, as, e.g., reflected by the classic semi-empirical models of Vernazza et al. (1981). On the other hand, the differences between the peak temperatures do not scale according to the sub-band frequencies and are not grouped accordingly into two pairs, suggesting offsets in the brightness temperatures of possibly on the order of 100 K. The radial brightness temperature averages in Fig. 1b show the same differences between the sub-bands and thus the same order. The standard deviation is for all sub-bands between 100 K and 150 K for radii between 150 ′′ and 900 ′′ , which is in line with the sta-tistical uncertainty found by White et al. (2017). Following the re-scaling procedure recommended by White et al. (2017) for all interferometric sub-bands separately would then shift the distributions of all sub-bands to roughly the same peak value (see Fig. 1d). While correcting offsets between the sub-bands, this procedure would also remove brightness temperature differences between the sub-bands that are connected to slightly different formations heights and the average temperature increase in the chromosphere. The resulting corrected sub-band differences are misleading in the sense that they do not reflect the true temperature gradients in the solar atmosphere.
We note that, for the observation presented here, there is a bright feature in the inner region (dashed circle in Fig. 1a, see also Fig. 2) that becomes a strong plage or enhanced network region of opposite polarity in the days following the observation. Excluding the bright feature would change the average value for the inner region with radius 240 ′′ for SB2 from originally 7454 K to 7438 K. This feature alone thus produces a 16 K shift in the absolute brightness temperature scale. Further improvements to the calibration removing such effects are desirable.
For the data presented here, we strictly follow the procedure implemented in the officially provided CASA script and rescale the average over the (unaltered) central region with a radius of 40 pixels (corresponding to 240 ′′ ) in the TP SB2 map to the recommended reference value of 7300 K. The average value in the original SB2 map is 7454 K and thus only 154 K higher than the recommended value, resulting in an applied scaling factor of 0.979 for the whole map. For the moment, significant uncertainties of the TP maps and thus the absolute brightness tempera-  Fig. 5. b) Brightness temperature distributions in the inner regions of the FOV (radius r ≤ 22 ′′ ) over the whole observing time period. All pixels (black) compared to internetwork (blue) and network pixels (red) for the full band maps.
tures remain but will be reduced by future improvements of the calibration procedure.

Final data product and co-observations with SDO
Post-processing with SoAP produced one time series of 1200 full-band (continuum) ALMA maps with a cadence of 2 s divided into 4 scans of ∼ 10 min duration (300 maps each) and intermediate ∼ 2.4 min breaks. As mentioned in Sect. 2.3, the FOV of these maps was limited to a diameter of 65.6 ′′ to ensure that each pixel in the FOV has data for all time steps. The full-disk TP maps for each of the three TP scans are also available for the analysis. Cotemporaneous observations with the Solar Dynamics Observatory (SDO; Pesnell et al. 2012) recorded with the Atmospheric Imaging Assembly (AIA Lemen et al. 2012) and the Helioseismic and Magnetic Imager (HMI; Scherrer et al. 2012) instrument are used here. The ALMA and SDO images have been co-aligned for the whole duration of the observation covering ∼47.6 min including ALMA intermediate calibration breaks. A representative timestep is presented in Fig. 3a. Movies for the whole time series are provided as online material: (i) The ALMA FOV alone and (ii) in comparison to SDO channels. For the movies, additional boxcar averaging with a window of 20 sec is applied (cf. Shine et al. 1994).

Data mask
The FOV (see Fig. 3a, see also Fig. 2) contains a Quiet Sun region with a mixture of magnetic network and internetwork patches. In order to distinguish between Quiet Sun internetwork and network pixels, a data mask is constructed based on a combination of time-averaged maps in SDO/AIA 1700 and SDO/AIA 1600 and saturated SDO/HMI magnetograms and the band-averaged ALMA maps. The time-averages include the whole observing period. The final mask is shown in Fig. 4a.

Atmospheric structure observed with ALMA and SDO
An example of full-band maps for ALMA Band 3 is put into context with co-aligned images from SDO in Fig. 3. The statistics for the brightness temperature values for the whole time series are provided in Table 1. The observed Quiet Sun region contains a few magnetic network elements that are mostly located in the left and top of the FOV. The network elements appear brighter and thus hotter than their surrounding in the ALMA map (see also the HMI magnetogram in Fig. 3c). A corresponding network mask (which excludes the outermost part of the FOV) is marked in Fig. 4a. Most of the remaining FOV is characterised by a dynamic mesh-like pattern resembling the pattern seen in other chromospheric diagnostics (e.g. Wöger et al. 2006). The pattern contains dark regions although their temperature differences with respect to the immediate surrounding varies a lot. Occasionally, elongated features become discernible temporarily and remind of parts of fibrils or dark compact arches but the visibility of these features varies in time 4 . A comparison of the ALMA maps with the SDO maps suggests that at least some of these features might be connected to extended magnetic loops as most notably seen in the 17.1 nm map ( Fig. 3e and Fig. 2a). These features might therefore be caused by weak opacity contributions from coronal loops in the line of sight that then result in weak imprints in the ALMA maps. If and how significant this effect is should be investigated in the future. The correlation between the ALMA and SDO maps is discussed in Sect. 3.4. The small region marked with a red circle in Fig. 3 is discussed in detail in Sect. 3.5.

Brightness temperature distribution
Taking into account the whole observation sequence with all 1200 time steps, results in brightness temperatures ranging from ∼4440 K to ∼10700 K for all pixels and ∼5810 K to ∼9690 K in the inner region (r ≤ 22 ′′ ). The corresponding average and standard deviation is (7500 ± 514) K for the whole FOV and (7400 ± 453) K for the inner region. The brightness temperature distribution for the whole observing period for the inner region has a maximum at 7325 K (see Fig. 4b). In addition, distributions are shown separately for internetwork and network pixels in Fig. 4b, respectively (see Fig. 4a for the pixel mask). The distribution for network pixels has a peak at a higher temperature compared to the internetwork distribution and deviates clearly from a Gaussian distribution, exhibiting a stretched tail at higher temperatures. The values for the maxima and widths of the distributions are provided in Table 1. The difference of the distribution maxima for the network pixels and the internetwork pixels is 160 K, whereas the average temperature differs by 360 K. The distributions for the network is about 11 % broader than for the internetwork except with a FWHM values of 782 K and 702 K, respectively. These results are compared to other ALMA observations in Sect. 4.1.

Temporal variation
One position in the internetwork and one in the network are selected and marked in Fig. 4a and labelled A and B, respectively. The temporal evolution of the brightness temperature at these locations is shown in Fig. 5a-b. There seems to be an oscillation with a period on the order of 3 min as it is expected for chromospheric internetwork regions although such variations are more pronounced for other locations in the internetwork. A more detailed study of the oscillatory behaviour will be published in a forthcoming paper (Jafarzadeh et al. in prep.). The network position does not show an equally clear oscillation but variations on different time scales. Brightness temperature profiles along the x-axis for the two selected position are shown in Fig. 5c and d, respectively. The major and minor axes (FWHM ) of the synthetic beams (see the top of the panels) limit the smallest scales over which variations can be recovered.

Correlation of ALMA and SDO maps
A comparison of the ALMA maps with the SDO maps reveals that the extended magnetic loops as most notably seen in the 17.1 nm map (Fig. 3e) also leave weak imprints in the ALMA maps. In order to quantify such similarities, the crosscorrelations of the ALMA maps with the corresponding SDO maps are calculated for the considered SDO channels. For each time step, the SDO maps are first convolved with the representative ALMA Band 3 beam before calculating the crosscorrelation for the whole inner FOV region (r < 22 ′′ ) but excluding the circular region with the compact loops (red circles in Fig. 3). The resulting time-averaged values C t are highest for ALMA Band 3 -SDO/AIA 30.4 nm and ALMA Band 3 -SDO/AIA 13.1 nm, both reaching a moderate correlation of C t = 0.38, followed by SDO/AIA 17.1 nm with C t = 0.33. The cross-correlation values for only network pixels in the inner region are C t = 0.35, 0.34, and 0.33 for SDO AIA 17.1 nm, SDO/AIA 30.4 nm, and SDO/AIA 13.1 nm, respectively. In general, the correlation is much weaker for internetwork pixels with values staying below 0.28 (SDO/AIA 30.4 nm) and 0.19 (SDO/AIA 13.1 nm). The cross-correlation with selected SDO channels is visualized in Fig. 6 for all pixels and also for network and internetwork pixels separately. The plots for SDO/AIA 17.1 nm and SDO/AIA 13.1 nm (panels e-f) reveal the tendency of increasing brightness temperature with increasing SDO count value, implying that statistically a higher value in these channels is connected to a higher brightness temperature along the same line of sight. Please refer to Sect. 4.3 for a discussion of potential implications for the formation height ranges of ALMA Band 3.

Compact loops
In the top right of the interferometric FOV, a group of short magnetic loops is visible in most SDO channels (see encircled region in Fig. 3 and Fig. 7b for a close-up). The loops connect patches of opposite polarity as visible in the HMI magnetogram. Given the appearance in the SDO maps, we suggest that the features in the ALMA maps (see Fig. 7a) are unresolved loop strands. The projected lengths of the loops are on the order of 10 ′′ , which agrees with the distance between the magnetic foot points seen in the HMI map (Fig. 3b). The ALMA map shows higher brightness temperatures at roughly the same location as the hotter SDO channels (panels d-f), implying that ALMA maps the hot loop tops at brightness temperatures between 8500 K and a maximum of 9650 K. Several elongated features with enhanced temperature are discernible. Their widths are with 2-3 ′′ close to the resolution limit, whereas the distance of 4-6 ′′ between the elongated features is resolved. Between these features, the brightness temperature can be as low as 7500 K and thus close to the average value for the whole FOV. The brightness temperature at the loop tops varies strongly in time between around 8000 K and peak values of close to or in excess of 9000 K. The temperature difference between the loop tops and the surrounding is thus often on the order of 1000 K or more although it varies, resulting in varying contrast of the loops. The brightness temperature variations are compared to the corresponding variations in SDO AIA171 for three selected positions (D, E, F) in Fig. 7c-e. At the beginning of the observing period, some loop tops exhibit several consecutive peaks with about 4-5 min in-between, which may imply oscillatory behaviour. Positions D and E show are located on the loops whereas position F marks a cooler region in-between the loops for the shown time step in Fig. 7a. It is quite clear that Correlation of ALMA Band 3 (full-band) with selected SDO channels: a) HMI continuum, b) HMI magnetogram, c) AIA 1700, d) AIA 304, e) AIA 171, and f) AIA 131. All pixels in the inner region of the FOV (excluding the region with the compact loops) for the whole observing period are considered. All SDO maps are convolved with the representative ALMA Band 3 beam. The two-dimensional histograms in each panel are presented with green shades for all pixels and also with contour levels for all pixels (black), internetwork (blue) and network (red). Thick contours mark levels of 0.5 and thin contours level of 0.01 with respect to the maximum histogram value. The coloured dots show the corresponding maxima. The straight black lines represent the median value for ALMA Band 3 (all pixels) and for the selected SDO channel. Please note that the SDO data used here are integration-time-corrected level 1 data numbers (DN) on a linear scale. loops are not properly resolved and also sway in time, thus affecting the signal at a given fixed spatial position. The loop position D shows a strong temperature rise from 8000 K at t = 20 s to 9200 K at t = 170 s, i.e. 1200 K over 150 s with a corresponding rate of ∼8 K s −1 , here referred to as event 1. This event is followed by another temperature rise (event 2) with a rate of ∼6 K s −1 . For event 2, the SDO AIA171 signal also steeply increases at the same time whereas there is only a moderate increase for event 1. The changes in SDO AIA171 is not always tightly coupled to the changes in ALMA brightness temperature as is most obvious for event 3 at position F. For that event, a steep temperature rise of 1100 K over 120 s is observed (rate: ∼9 K s −1 ) whereas the SDO AIA171 signal slowly decreases.
Analysis of the SDO data for the interferometric FOV and the surroundings (see Fig. 2) before and after the ALMA observation, suggests that the compact loop system is the result of a flux emergence event. The first loop top appears in HMI magnetograms around UT9:11, i.e. about five hours prior to the ALMA observation. Subsequently, two footpoints with opposite magnetic polarity move away from each other and reach their final separation within one hour. In that process, further footpoints emerge next to the initial ones and finally form the group of compact loops. The loops become visible in AIA 171 maps during that emergence phase. After the ALMA observation, the two polarities move towards each other until they mix around UT17:40, followed by the disintegration of the loops. The AIA 304 and AIA 171 data show that the group finally vanishes from about 20UT.
Such emerging magnetic loops are expected to be optically thin at millimeter wavelengths and may reveal the atmosphere underneath, which could provide the thermal properties of the inner part of emerged regions (Nóbrega-Siverio, priv.comm.). Quite opposite to this expectation, the ALMA observation presented here clearly feature bright magnetic loops, suggesting that they are optically thick and thus block the view at the possibly existing cool plasma below. A possible explanation is that the observed loop tops stay at rather low altitude, at least during the 45 min covered by ALMA. The extended coronal loops that traverse the ALMA FOV (see Fig. 3) seem to be located higher in the atmosphere and might prevent the compact loops from rising higher. The consequence would be that the latter remain in the chromosphere with loops containing plasma with higher density and correspondingly larger opacity.

Brightness temperature distribution
The average brightness temperatures in the ALMA Band 3 fullband maps discussed here are on the order of 7400 K for all pixels in the inner parts of the FOV and on the order of ∼ 7590 K and ∼ 7230 K when separating network and internetwork pixels (see Table 1). Accordingly, the difference between the average full-band network and internetwork brightness temperatures is ∼360 K. As expected, these values are close to the reference value of 7300 K suggested by ) because the absolute brightness temperature scale was corrected accordingly. It should be noted, however, that the applied correction was a minor one (see Sect. 2.4). In the following, we compare the brightness temperature distributions of the data presented here to the ALMA Band 3 observations from Cycle 4 by Loukitcheva et al. (2019) and Nindos et al. (2018). Loukitcheva et al. (2019) analyse data obtained on April 27, 2017, for a Quiet Sun region at 200 ′′ distance from solar diskcentre that contains magnetic network and internetwork patches. They state a width of 1.6 ′′ for both axes of their synthesized beam, which is slightly smaller than the representative beam used for the data presented here. The brightness temperatures range from 5630 K to 9140 K in their time-averaged map and from 4370 K to 11170 K in the corresponding time sequence at 2 s cadence. The lowest temperatures are found in a 20 ′′ wide region, which is significantly cooler than the surrounding atmosphere but which is not visible at other wavelengths as observed with SDO. From their Fig. 2, we determine the peaks and FWHM values of the brightness temperature distributions for the selected network and internetwork patches. The network patch has a maximum at 7340 K and a FWHM of 1240 K, whereas the internetwork regions have maxima at 7200 K and 7090 K and   (1-3). For comparison, the average over all pixels contained in the close-up region are shown as orange lines for ALMA and purple lines for SDO 171. The calibration breaks with no science data are marked as grey shaded areas. Please note that the SDO data used here are integration-time-corrected level 1 data numbers (DN) on a linear scale. FWHM s of 530 K and 430 K and corresponding standard deviations of 225 K and 183 K, respectively. In contrast, their cool region has a maximum at 6330 K and a FWHM of 1470 K. The distribution peak temperatures for the internetwork regions are only slightly lower than found in this study (see Table 1 and Sect. 3.2) but it might be argued that they nonetheless agree within the expected uncertainties of possibly a few 100 K. The FWHM of the internetwork temperature distribution found by Loukitcheva et al. (2019) is significantly smaller than for the data set analysed here (702 K, see Table 1). Their distribution for network pixels, on the other hand, has a maximum at 75 K lower than the value found here see Table 1) but it still agrees within the error limits. The corresponding FWHM, however, is much larger than found in this study. As we will demonstrate in Sect. 4.2, the FWHM of the brightness temperature distribution depends on the effective angular resolution of the observation and thus on a number of factors ranging from seeing conditions to details of the image reconstruction procedure. Nindos et al. (2018) observed the Sun with ALMA in Band 3 on March 16, 2017 for several positions from the limb to diskcenter. For the latter, they found an average brightness temperatures of 7530 K for network pixels, 6940 K for internetwork (cell) pixels, and 7220 K as average over the FOV. We find that the average brightness temperatures for network pixels agree quite well with values for the observations presented here whereas the value for internetwork pixels found by Nindos et al.
Article number, page 9 of 14 is almost 300 K lower than the value found here. Accordingly, they state an average difference between network and internetwork of 590 K, whereas it is only 360 K in the data presented here (see Table 1). Furthermore, Nindos et al. (2018) determined the standard deviation over the FOV as 390 K as compared to ∼ 450 K for all pixels in the inner region of the data presented here. The values found by Nindos et al. is similar to the value found here for internetwork pixels (∼340-400 K) and lower than the corresponding network value (∼500 K). Nindos et al. state that the synthetic beam of their disk-center observation has a major axis of 8.1 ′′ and a minor axis of 2.3 ′′ , which is significantly larger than the synthetic beams for the data presented here. Please note that Nindos et al. achieved smaller beams for earlier observations closer to the solar limb. The differences in brightness temperatures between those found by Nindos et al. at solar disk-centre and those reported here might therefore be partially due to the differences in angular resolution in addition to differences arising from the applied post-processing method. We also note that the data run used by Nindos et al. was obtained under worse seeing conditions with a higher amount of precipitable water vapour (PWV) in Earth's atmosphere.
For comparison, we considered the BIMA observation by White et al. (2006) at 85 GHz with a beam (and thus an angular resolution) of 10 ′′ . White et al. find rms variations of ∼120 K for both network and interwork locations. This value is about a factor 3-4 less than for the ALMA results discussed above.

Dependence on angular resolution.
As already demonstrated by Wedemeyer-Böhm et al. (2007), not resolving small-scale chromospheric features due to limited angular resolution results in a reduction of the corresponding stan-  White et al. (2006).   White et al. (2006) (BIMA, black dot-dashed). The distribution for observed Band 3 temperatures is plotted as red line and red shaded area (all pixels, see Fig. 4b).
Article number, page 10 of 14 dard deviation in the obtained brightness temperature maps. The better the angular resolution, the higher the standard deviation in the observations. In the following, we test the influence of reduced angular resolution on the resulting brightness temperature distribution by convolving synthetic brightness temperature maps with different synthetic beams. Brightness temperature maps for ALMA Band 3 frequencies are calculated with the Advanced Radiative Transfer (ART) code (de la Cruz Rodriguez et al., in prep.) for a time series of snapshots from a 3D radiation magnetohydrodynamic simulation with Bifrost (Carlsson et al. 2016;Gudiksen et al. 2011). The series used here has a duration of 20 min and a cadence of 1 s and features an enhanced network region in the middle with surrounding Quiet Sun. For each time step, the maps for the different frequencies are averaged, resulting in band-average maps. See Fig. 8a for an example for a selected time step. Applying the representative beam for the data presented here (see Sect. 2.4), produces a brightness temperature map at an angular resolution equivalent to the analysed ALMA observations (see Fig. 8b). This procedure is repeated for all maps in the time series and also for the ALMA beams used by Nindos et al. (2018) and Loukitcheva et al. (2019), and the BIMA beam by White et al. (2006). The resulting brightness temperature distributions for the original maps and the degraded maps for all four beams are compared to the observational results in Fig. 8c. All time steps are taken into account. For the elliptic beams such as in the observations presented here and for Nindos et al., additional degraded maps are calculated with the beam rotated by 90 deg. This extra step reduces possible artificial effects due to the coincidental alignment of elongated features in the original map with a beam axis. The resulting averages and standard deviations of the brightness temperature maps are summarised in Table 2.
The original maps have an average of 7015 K and a standard deviation of 1549 K. The network pixels in the middle of the map (see dashed rectangle in Fig. 8a-b) have an almost 1000 K higher average and a larger standard deviation whereas both are reduced for the internetwork pixels (outer region of the map in Fig. 8a-b).) Reducing the angular resolution by convolution with a synthetic beam (i.e. a PSF) does not affect the brightness temperature average but results in a narrower distribution (see Fig. 8c) and a correspondingly reduced standard deviation (Table 2). Using the representative beam from the ALMA observations presented here results in a standard deviation of 1033 K, which is very similar to the results obtained with the symmetric 1.6 ′′ wide beam reported by Loukitcheva et al. (2019). The larger and more elliptical beam by Nindos et al. (2018) results in even lower standard deviation of 744 K. For comparison, we also apply the 10 ′′ BIMA beam by White et al. (2006), which returns a standard deviation of 536 K for the whole map and 317 K for internetwork pixels although a substantial mixing of network and internetwork within the beam is expected.
The average brightness temperatures for the whole maps ("all" in Table 2) are only 300 K lower than those derived from the observations presented in this work. The simulated standard deviation, however, is roughly a factor two higher than the corresponding observational value. It is important to note that the original simulated maps represent the best possible maps that can be obtained with a given beam, whereas additional factors can lead to a further reduction of the standard deviation in the observed maps. First of all, interferometric snapshot observations with a finite number of antennas can by nature never provide a truly complete coverage of the spatial Fourier space and resulting degradation must be expected. Furthermore, seeing conditions, noise contributions and technical details of the imaging process itself are possible causes for further reduction. On the other hand, these first results are already very promising.
We conclude that our results agree with the study by Loukitcheva et al. (2019) at least on a qualitative level and also in some aspects with Nindos et al. (2018) but more systematic statistical comparisons should be attempted in the future. There are many factors that influence the brightness temperature distribution ranging from the properties of the observed target regions and accuracy of the applied network mask to different seeing condition and details of the imaging procedure. The small size of the FOV and thus the peculiarities of the observed regions will produce variations in the statistical properties derived from different observations. Such results should be compared to a corresponding analysis of mosaicking data that cover larger FOVs (see, e.g., Bastian et al. 2017;Jafarzadeh et al. 2019). Furthermore, the test for different angular resolutions implies that more extended array configurations of ALMA, which might be offered in future observing cycles, are likely to lead to higher rms variations and thus more contrast in the reconstructed images.

Formation height
White et al. (2017, see also references therein) point out that contributions from the corona to brightness temperatures measured with ALMA should be expected and that the contributions could amount to a few 100 K in Band 3 from the densest parts of the corona. As mentioned in Sect. 3.1 and quantified in terms of cross-correlations in Sect. 3.4, coronal loops that extend across the ALMA field of view and are clearly visible in coronal SDO channels can leave very weak imprints in some ALMA Band 3 maps but are best seen in movies. Internetwork and network regions are clearly seen in the ALMA maps presented here but appear to be more horizontally expanded than SDO/AIA 170 nm maps, which, together with the rather weak to moderate cross-correlation between this SDO channel and ALMA Band 3, may imply that Band 3 is formed above the layer from where the continuum radiation at 170 nm emerges. At the same time, one should be cautious with concluding on the formation height range based on these arguments, especially regarding the cross-correlations, even with these findings supporting the claim by White et al. (2017). Rather, it is essential to study the mapped height ranges and contribution functions along the line of sight in ALMA data in detail. The scientific potential of the measured brightness temperatures can only be truly unfolded once the temperatures can be assigned to precise height ranges and thus being translated into measurements of the chromospheric temperature stratification.

Conclusion and Outlook
Although the solar observing mode of ALMA is still in its early development phase, the ALMA Band 3 data presented here and in previous publications already demonstrate ALMA's potential for scientific studies of the solar chromosphere. The spatial resolution currently achieved in Band 3 certainly limits the study of the chromospheric small-scale structure and dynamics but, at the same time, and this cannot be emphasized enough, it is an enormous leap forward for the observation of the Sun at millimeter wavelengths.
With this tool at hand, the brightness temperature distribution for a Quiet Sun region at disk-centre is quantitatively analysed, also separated in network and internetwork patches, and can thus serve as important test for numerical simulations of the solar atmosphere.
Article number, page 11 of 14 A&A proofs: manuscript no. p19alma1_acc While many aspects such as the exact formation height ranges, possible weak coronal contributions, and details of the imaging procedure need to be investigated in more detail, the presented data already allows for a large range of scientific studies. For instance, we are able to measure the brightness temperatures in a group of compact loops as function of time.
The FOV of the interferometric observations is set by the primary beam, which is due to the aperture of a single antenna. The effect of the primary beam response is to multiply the field of view by an approximately Gaussian function, referred to as the primary beam taper. The size of the Gaussian primary beam is typically specified in terms of its full-width-at-half-maximum 5 The spatial Fourier space is also referred to as " uv space". A component in the uv space is determined by the separation of the two involved antennas (i.e. the baseline length), the observing frequency, and the angles under which the source is observed on the sky.   (FWHM), which depends on the observed wavelength (or frequency, see, e.g., Wedemeyer et al. 2016).