2. The potential of millimeter-wavelength diagnostics

In the solar atmosphere, the opacity at millimeter wavelengths mainly arises from free-free absorption involving electrons with protons, neutral hydrogen, and H $^{-}$ ions (see, e.g., White et al. Reference White, Loukitcheva and Solanki2006; Wedemeyer et al. Reference Wedemeyer, Bastian and Brajša2016, and references therein). The atmospheric height at which the continuum radiation emerges increases with wavelength, enabling the probing of different layers of the solar atmosphere, or more specifically, the chromosphere. The continuum intensity then provides a linear measure of the local electron temperature of the probed layer, offering a straightforward diagnostic of thermal conditions in the solar atmosphere. Measurements of polarisation allow for the determination of the line-of-sight component of the magnetic field strength (Bogod & Gelfreikh Reference Bogod and Gelfreikh1980; Grebinskij et al. Reference Grebinskij, Bogod and Gelfreikh2000). By combining observations at multiple wavelengths, it is, in principle, possible to apply tomographic analyzes to derive the three-dimensional thermal, magnetic, and kinetic structure of the solar chromosphere. However, the layers probed at a given wavelength are highly corrugated and dynamic, complicating their interpretation (see Fig. 1). There are even signs that the continuum radiation may not always originate from a well-defined height range, but that, owing to the complex atmospheric structure, multiple layers may sometimes contribute (Wedemeyer et al. Reference Wedemeyer, Szydlarski and Jafarzadeh2020). At the same time, the rapid temporal evolution of chromospheric features necessitates high-cadence observations to capture the relevant dynamics accurately. Tomographic reconstruction of the 3D time-dependent atmospheric structure would therefore require simultaneous multi-wavelength observations, combined with sophisticated data inversion techniques (da Silva Santos et al. Reference da Silva Santos, de la Cruz Rodríguez and Leenaarts2020a).

Figure 1.

Synthesised brightness temperatures and formation heights derived from a 3D solar atmosphere model calculated with the Bifrost (Gudiksen et al. Reference Gudiksen, Carlsson and Hansteen2011; Carlsson et al. Reference Carlsson, Hansteen, Gudiksen, Leenaarts and De Pontieu2016) and ART (de la Cruz Rodr guez et al. 2021) codes, demonstrating the tomographic capabilities of high-cadence multi-wavelength observations. The surfaces of optical depth unity (middle) and the corresponding brightness temperature (or intensity) maps (right) are shown for various wavelengths.

Figure 1 Long description

The image contains one 3D model, one diagram, and six photos. The 3D model on the left represents the solar atmosphere, generated using the Bifrost model. The diagram in the middle shows the continuum formation height with a color-coded scale indicating different wavelengths ranging from 0.3 millimeters to 8.6 millimeters. The six photos on the right display the continuum brightness temperature at these wavelengths, with each photo labeled with the corresponding wavelength and time. The purpose of combining these images is to demonstrate the tomographic capabilities of high-cadence multi-wavelength observations in the solar atmosphere. Panel A: The 3D model shows the solar atmosphere with various layers and structures. Panel B: The diagram illustrates the continuum formation height with a color-coded scale and height measurements in megameters (Mm). Panel C: The six photos show the continuum brightness temperature at different wavelengths, with each photo labeled with the wavelength in millimeters and time in seconds.

3. The Atacama Large Millimeter/submillimeter Array (ALMA)

The Atacama Large Millimeter/submillimeter Array (ALMA), consisting of 66 antennas located in the Atacama Desert in Chile, has enabled regular interferometric imaging of the Sun since 2016 (Bastian Reference Bastian2002; Karlický et al. Reference Karlický, Bárta, Dbrowski and Heinzel2011; Shimojo et al. Reference Shimojo, Bastian and Hales2017a; White et al. Reference White, Iwai and Phillips2017). ALMA provides measurements of the continuum intensity in frequency Bands 3 to 5 and Band 7, covering the range from 90 to 350 GHz, corresponding to wavelengths between approximately 0.9 and 3.3 mm. These observations can be performed at a cadence of 1 second, allowing high-temporal-resolution studies of solar dynamics. In addition, regular polarisation measurements in Band 3 have been available since 2024, offering diagnostics of the line-of-sight magnetic field component (Shimojo et al. Reference Shimojo, Bastian, Kameno and Hales2024).

Despite its capabilities, ALMA faces certain diagnostic limitations. Snapshot imaging at a cadence of 1 second is challenging due to the limited number of interferometric baselines available at any given time. Furthermore, observations are restricted to a single receiver band at a time, which precludes simultaneous multi-height observations and thus makes tomographic analysis infeasible. The available field of view is also limited, which constrains the spatial extent of the observed solar regions. Nonetheless, ALMA observations, owing to their high cadence and high angular resolution (for this wavelength range), have produced the first promising results (e.g., Shimojo et al. Reference Shimojo, Hudson, White, Bastian and Iwai2017b; Yokoyama et al. Reference Yokoyama, Shimojo, Okamoto and Iijima2018; Brajša et al. Reference Brajša, Sudar and Benz2018; Jafarzadeh et al. Reference Jafarzadeh, Wedemeyer and Szydlarski2019; Rodger et al. Reference Rodger, Labrosse and Wedemeyer2019; Selhorst et al. Reference Selhorst, Simões and Brajša2019; Wedemeyer et al. Reference Wedemeyer, Szydlarski and Jafarzadeh2020; da Silva Santos et al. Reference da Silva Santos, de la Cruz Rodríguez and White2020b; Eklund et al. Reference Eklund, Wedemeyer, Szydlarski, Jafarzadeh and Guevara Gómez2020; Nindos et al. Reference Nindos, Alissandrakis, Patsourakos and Bastian2020; Patsourakos et al. Reference Patsourakos, Alissandrakis, Nindos and Bastian2020; Brajša et al. Reference Brajša, Skokić and Sudar2021; Chintzoglou et al. Reference Chintzoglou, De Pontieu and Martínez-Sykora2021; Guevara Gómez et al. Reference Guevara Gómez, Jafarzadeh and Wedemeyer2021; Jafarzadeh et al. Reference Jafarzadeh, Wedemeyer and Fleck2021; Nindos et al. Reference Nindos, Patsourakos, Alissandrakis and Bastian2021). Science-ready data products are available via the Solar ALMA Science Archive (SALSAFootnote ¹ ), as described by Henriques et al. (Reference Henriques, Jafarzadeh and Guevara Gómez2022). Nevertheless, it is fair to say that ALMA’s scientific potential for studying the Sun is far from being fully exploited, mostly because of the difficulties in acquiring sufficient observing time and the complications in imaging and post-processing for such a dynamic target.

4. Future observatories

While we here focus on the complementarity of AtLAST (Sect. 4.1) and ALMA (Sect. 4.2), there are several other facilities that are worth mentioning, for instance, the Frequency Agile Solar Radiotelescope (FASR Gary et al. Reference Gary, Chen and White2023), recommended in the U.S. solar and space physics decadal survey, and the Solaris project for continuous solar monitoring and space weather applications (Pellizzoni et al. Reference Pellizzoni, Potenza and Cavaliere2024).

5. Solar Science Cases at Millimeter Wavelengths

Observations of the Sun at millimeter wavelengths contribute significantly to our understanding of both, the solar structure and solar activity. One of the key open questions in solar physics is the coronal heating problem: How is the solar corona heated to temperatures exceeding one million Kelvin? This fundamental issue, known for almost a century (Grotrian Reference Grotrian1934; Edlén Reference Edlén1945), remains unresolved and is central to investigations of the solar atmosphere.

Solar activity represents another major science case. Energetic events, such as solar flares, are triggered by magnetic reconnection and can release vast amounts of energy. Coronal mass ejections (CMEs) involve the ejection of plasma clouds into interplanetary space and are key drivers of space weather phenomena. Other aspects of solar activity include the solar wind and the operation of the solar dynamo, which governs the generation and temporal evolution of the Sun’s magnetic field over the solar activity cycle. These processes have direct implications for Earth, where space weather can impact technological systems and necessitate accurate forecasting (Pomoell & Poedts Reference Pomoell and Poedts2018).

The high-cadence observations of the full solar disk planned for AtLAST would enable continuous monitoring of solar activity. During an observing run, all flares above the instrument’s sensitivity threshold will be detected, ensuring a comprehensive record of eruptive events.

6. Stellar Science Cases – The solar-stellar connection

The Sun serves as the ultimate reference star for stellar astrophysics. Its proximity enables detailed, spatially resolved observations that are not feasible for other stars, offering an in-depth understanding of fundamental processes. By studying the Sun as a star, one can calibrate and interpret unresolved stellar observations, particularly concerning the thermal and magnetic structure of stellar atmospheres. These insights are essential for studying stellar atmospheres and activity across different stellar types. The potential of millimeter observations for investigating the thermal structure of stellar atmospheres has been explored by the EMISSA project, resulting in an initial catalogue of 12 main sequence stars, including the Sun. The employed ALMA observations are complemented by data from other telescopes covering a broad wavelength range. In particular, the presence of a temperature excess at millimeter wavelengths, analogous to what is observed in the solar chromosphere, provides a quantitative means to evaluate atmospheric heating as a function of spectral type. This excess can be quantified in the form of a novel stellar activity indicator ( $\alpha_\mathrm{mm}$ ). For further details, see Mohan et al. (Reference Mohan, Wedemeyer, Pandit, Saberi and Hauschildt2021, Reference Mohan, Wedemeyer, Hauschildt, Pandit and Saberi2022). Future observations from AtLAST and an upgraded ALMA would allow to extend the sample substantially thanks to much increased sensitivity.

Moreover, observations at millimeter wavelengths can contribute to the detection and characterisation of exoplanets, particularly through the analysis of stellar activity that may influence observational signals. Understanding such activity is also crucial for assessing exo-space weather, which can affect the habitability of exoplanets by influencing their atmospheres and potential for hosting life. The combination of solar and stellar flare observations – with AtLAST, an upgraded ALMA, or both – will offer a unique basis for comparative studies and a deeper understanding of magnetic energy release in stellar atmospheres. The resulting flare models would have important implications for evaluating the evolution of exoplanet atmospheres and their habitability (Segura et al. Reference Segura, Walkowicz, Meadows, Kasting and Hawley2010; Mamonova et al. Reference Mamonova, Shan, Kowalski, Wedemeyer and Werner2025).