We model sunspot brightness temperature in the wavelength range 0.3-10 mm using the Atacama Large Millimeter/submillimeter Array (ALMA) single-dish measurements together with other instruments. Our modeling idea starts from an existing model, the 1D semi-empirical Avrett-Tian-Landi-Curdt-W & uuml;lser (ATLCW) model for sunspots. The original model is then modified in density and temperature with a constant factor over all heights. A least-square fit in both density and temperature to the observed values yields an improved model for sunspot brightness temperature. Observations show that sunspots are darker than QS at wavelengths below 2 mm and brighter beyond, while fitting of the ATLCW sunspot model imply that sunspots should be darker than QS over the entire ALMA range. The best-fitted sunspot brightness temperature profiles resulted in 3.6-4.0 times lower sunspot density compared to the original sunspot ATLCW model, or 1.4-1.8 times higher density compared to QS. The temperature came out around 1.2 times higher than the original ATLCW predictions for sunspots, or 1.2 times lower than QS temperature. Even with improved density and temperature parameters, the remaining discrepancy between the best-fitted models and observations indicated that additional improvements are needed in the ATLCW model and modeling assumptions.

An analysis of the solar differential rotation (DR) during solar cycle No. 24 (SC24) (2009–2019), based on the Kanzelhöhe Observatory for Solar and Environmental Research (KSO) data set, is presented. The white-light images were processed and positions of sunspot groups were extracted using the morphological image processing technique. The sample was constrained to ±58° in central meridian distance (CMD). Two methods were applied to derive the sidereal angular rotation rate (ω) and, in turn, the solar rotation parameters A and B: (a) calculating synodic rotation velocities from daily CMD differences and elapsed time (daily shift method); (b) applying a robust linear least-squares fit to the time series CMD(t) for each sunspot group. To assess the relationship between rotation parameters and solar activity, we analyzed the yearly mean total sunspot number from the Sunspot Index and Long-term Solar Observations (SILSO). This study marks the first complete analysis of SC24 using the KSO sunspot groups’ data. Our goal is to extend the previous analysis of DR from the KSO data to the present, especially because the Solar Optical Observing Network/United States Air Force/National Oceanic and Atmospheric Administration data set (SOON/USAF/NOAA) and Debrecen Photoheliographic Data (DPD) catalogues do not provide data after 2018.

Societal dependence on space-based services demands major advances in predicting the impacts of eruptive solar events. Millimeter-wavelength observations offer uniquely direct access to the time-dependent physical conditions in the atmospheric layers of the Sun where these events originate. A facility capable of full-disk, high-cadence, multi-frequency imaging would provide a transformative view of the Sun and its influence on the heliosphere. AtLAST is ideally suited to deliver this capability, and to establish a European leadership role in advancing the scientific foundations that will enable reliable, operational space-weather forecasting for the first time.

In September 1777 Ruđer Bošković observed and measured the sunspot positions to determine the solar rotation elements. In 1785, among other methods, he described a trigonometric spherical solution for the determination of the position of the axis and rate of the solar rotation using three sunspot positions, but without equations. For the first time, we derive the equations that are applicable to modern computers for calculating the solar rotation elements, as they were described by Bošković. We recalculated Bošković’s original example using his measurements of sunspot positions from 1777 and the equations developed here, confirming his results from 1785. Bošković’s methodology of arithmetic means determines i , Ω , and the sidereal period T' separately, while the planar trigonometric solution determines i and Ω together. His spherical trigonometric solution calculates i , Ω , and the sidereal period T' in a single procedure.

We study solar differential rotation for solar cycle No. 19 (1954 – 1964) by tracing sunspot groups on the sunspot drawings of Kanzelhöhe Observatory for Solar and Environmental Research (KSO). Our aim is to extend previous differential rotation (DR) analysis from the KSO data (1964 – 2016) to the years prior to 1964 to create a catalog of sunspot group positions and photospheric DR parameters from KSO sunspot drawings and white light images. Synodic angular rotation velocities were first determined using the daily shift (DS) and robust linear least-squares fit (rLSQ) methods, then converted to sidereal velocities, and subsequently used to derive solar DR parameters. We compare the DR parameters obtained from different sources and analyse the north–south asymmetry of rotation for solar cycle No. 19. It has been shown that our results for the equatorial rotation velocity (parameter A ) and the gradient of DR (parameter B ) coincide with earlier results from the KSO data (performed with a different method), as well as with results from the Kodaikanal Solar Observatory (KoSO) and the Yunnan Observatories (YNAO). In contrast, the values of parameter A from three different earlier studies based on the Greenwich Photoheliographic Results (GPR) exhibit statistically significant differences when compared to the values of parameter A derived from KSO, KoSO and YNAO. These findings suggest that the GPR data have the largest inconsistency compared to the other three data sources, highlighting the need for further analysis to identify the causes of these discrepancies. The analysis of the north-south asymmetry in the solar rotation profile using two different methods shows that the DR parameters of the hemispheres coincide, indicating a rotational symmetry around the equator. This is consistent with previous results from KSO and YNAO data. However, all sources indicate slightly higher equatorial rotation velocities in the southern hemisphere.

Prominences (PRs) are among the most common solar phenomena, yet their full physical picture, particularly their chromospheric mm emission, remains incomplete. The new Atacama Large Millimeter/submillimeter Array (ALMA) presents an opportunity to study PRs at mm and sub-mm wavelengths through a combination of measurements and theoretical modeling. We utilize ALMA single-dish measurements alongside data from other radio instruments to model the PR brightness temperature through adaptation and modification of the 1D semi-empirical Avrett-Tian-Landi-Curdt-W & uuml;lser (ATLCW) quiet-Sun (QS) model. The calculated and measured PR brightness temperatures were found to be lower than the measured QS value and predictions from the unperturbed ATLCW QS model across the ALMA wavelength range, consistent with PRs appearing in absorption. The PR density was found to be 60-163 times higher and temperature 155-163 times lower than the QS level, aligning with previous measurements. A key finding emerged with the non-hydrostatic equilibrium assumption, yielding a more physically consistent PR brightness temperature. This suggests that PR stability is most likely maintained by its magnetic field obeying magnetostatic conditions rather than by pure hydrostatic equilibrium, supporting recent studies. Additionally, our results confirm that thermal bremsstrahlung is the dominant radiation mechanism for PRs at mm and sub-mm wavelengths.

Observations at (sub-)millimeter wavelengths offer a complementary perspective on our Sun and other stars, offering significant insights into both the thermal and magnetic composition of their chromospheres. Despite the fundamental progress in (sub-)millimeter observations of the Sun, some important aspects require diagnostic capabilities that are not offered by existing observatories. In particular, simultaneous observations of the radiation continuum across an extended frequency range would facilitate the mapping of different layers and thus ultimately the 3D structure of the solar atmosphere. Mapping large regions on the Sun or even the whole solar disk at a very high temporal cadence would be crucial for systematically detecting and following the temporal evolution of flares, while synoptic observations, i.e., daily maps, over periods of years would provide an unprecedented view of the solar activity cycle in this wavelength regime. As our Sun is a fundamental reference for studying the atmospheres of active main sequence stars, observing the Sun and other stars with the same instrument would unlock the enormous diagnostic potential for understanding stellar activity and its impact on exoplanets. The Atacama Large Aperture Submillimeter Telescope (AtLAST), a single-dish telescope with 50 m aperture proposed to be built in the Atacama desert in Chile, would be able to provide these observational capabilities. Equipped with a large number of detector elements for probing the radiation continuum across a wide frequency range, AtLAST would address a wide range of scientific topics including the thermal structure and heating of the solar chromosphere, flares and prominences, and the solar activity cycle. In this white paper, the key science cases and their technical requirements for AtLAST are discussed.

Observations at (sub-)millimeter wavelengths offer a complementary perspective on our Sun and other stars, offering significant insights into both the thermal and magnetic composition of their chromospheres. Despite the fundamental progress in (sub-)millimeter observations of the Sun, some important aspects require diagnostic capabilities that are not offered by existing observatories. In particular, simultaneous observations of the radiation continuum across an extended frequency range would facilitate the mapping of different layers and thus ultimately the 3D structure of the solar atmosphere. Mapping large regions on the Sun or even the whole solar disk at a very high temporal cadence would be crucial for systematically detecting and following the temporal evolution of flares, while synoptic observations, i.e., daily maps, over periods of years would provide an unprecedented view of the solar activity cycle in this wavelength regime. As our Sun is a fundamental reference for studying the atmospheres of active main sequence stars, observing the Sun and other stars with the same instrument would unlock the enormous diagnostic potential for understanding stellar activity and its impact on exoplanets. The Atacama Large Aperture Submillimeter Telescope (AtLAST), a single-dish telescope with 50m aperture proposed to be built in the Atacama desert in Chile, would be able to provide these observational capabilities. Equipped with a large number of detector elements for probing the radiation continuum across a wide frequency range, AtLAST would address a wide range of scientific topics including the thermal structure and heating of the solar chromosphere, flares and prominences, and the solar activity cycle. In this white paper, the key science cases and their technical requirements for AtLAST are discussed.

Observations at (sub-)millimeter wavelengths offer a complementary perspective on our Sun and other stars, offering significant insights into both the thermal and magnetic composition of their chromospheres. Despite the fundamental progress in (sub-)millimeter observations of the Sun, some important aspects require diagnostic capabilities that are not offered by existing observatories. In particular, simultaneously observations of the radiation continuum across an extended frequency range would facilitate the mapping of different layers and thus ultimately the 3D structure of the solar atmosphere. Mapping large regions on the Sun or even the whole solar disk at a very high temporal cadence would be crucial for systematically detecting and following the temporal evolution of flares, while synoptic observations, i.e., daily maps, over periods of years would provide an unprecedented view of the solar activity cycle in this wavelength regime. As our Sun is a fundamental reference for studying the atmospheres of active main sequence stars, observing the Sun and other stars with the same instrument would unlock the enormous diagnostic potential for understanding stellar activity and its impact on exoplanets. The Atacama Large Aperture Submillimeter Telescope (AtLAST), a single-dish telescope with 50m aperture proposed to be built in the Atacama desert in Chile, would be able to provide these observational capabilities. Equipped with a large number of detector elements for probing the radiation continuum across a wide frequency range, AtLAST would address a wide range of scientific topics including the thermal structure and heating of the solar chromosphere, flares and prominences, and the solar activity cycle. In this white paper, the key science cases and their technical requirements for AtLAST are discussed.