Context. The solar atmosphere is highly dynamic, and observing the small-scale features is valuable for interpretations of the underlying physical processes. The contrasts and magnitude of the observable signatures of small-scale features degrade as angular resolution decreases.

Aims. The estimates of the degradation associated with the observational angular resolution allows a more accurate analysis of the data.

Methods. High-cadence time-series of synthetic observable maps at λ = 1.25 mm were produced from three-dimensional magnetohydrodynamic Bifrost simulations of the solar atmosphere and degraded to the angular resolution corresponding to observational data with the Atacama Large Millimeter/sub-millimeter Array (ALMA). The deep solar ALMA neural network estimator (Deep-SANNE) is an artificial neural network trained to improve the resolution and contrast of solar observations. This is done by recognizing dynamic patterns in both the spatial and temporal domains of small-scale features at an angular resolution corresponding to observational data and correlated them to highly resolved nondegraded data from the magnetohydrodynamic simulations. A second simulation, previously never seen by Deep-SANNE, was used to validate the performance.

Results. Deep-SANNE provides maps of the estimated degradation of the brightness temperature across the field of view, which can be used to filter for locations that most probably show a high accuracy and as correction factors in order to construct refined images that show higher contrast and more accurate brightness temperatures than at the observational resolution. Deep-SANNE reveals more small-scale features in the data and achieves a good performance in estimating the excess temperature of brightening events with an average of 94.0% relative to the highly resolved data, compared to 43.7% at the observational resolution. By using the additional information of the temporal domain, Deep-SANNE can restore high contrasts better than a standard two-dimensional deconvolver technique. In addition, Deep-SANNE is applied on observational solar ALMA data, for which it also reveals eventual artifacts that were introduced during the image reconstruction process, in addition to improving the contrast. It is important to account for eventual artifacts in the analysis.

Conclusions. The Deep-SANNE estimates and refined images are useful for an analysis of small-scale and dynamic features. They can identify locations in the data with high accuracy for an in-depth analysis and allow a more meaningful interpretation of solar observations.

Aims. We used solar observations of a plage-enhanced network with the Atacama Large Millimeter/sub-millimeter Array (ALMA) in Band 3 and Band 6, together with synthetic continuum maps from numerical simulations with Bifrost in the same bands, to carry out a detailed study of bright small-scale magnetic features.

Methods. We made use of an algorithm to automatically identify and trace bright features within the field of view (FoV) of the ALMA observations and the simulation. In particular, the algorithm recovers information of the time evolution of the shape, motion of the centre of gravity, temperature, and size for each feature. These quantities are used to determine the oscillatory properties of each feature utilising wavelets analysis.

Results. We found 193 and 293 features in the Bands 3 and 6 observations, respectively. In the degraded simulation, the total number of features were 24 for Band 3 and 204 for Band 6. In the original simulation, the total number of features were 36 for Band 3 and 392 for Band 6. Based on the simulation, we confirm the magnetic nature of the features. We have obtained average oscillation periods of 30–99 s for the temperature, 37–92 s for size, and 37–78 s for horizontal velocity. There are indications for the possible presence of transverse (kink) waves with average amplitude velocities of 2.1–5.0 km s⁻¹. We find a predominant anti-phase behaviour between temperature and size oscillations suggesting that the variations of the bright features are caused by compressible fast-sausage magnetohydrodynamics (MHD) modes. For the first time to our knowledge, we estimated the flux of energy of the fast-sausage waves at the chromospheric heights sampled by ALMA as 453–1838 W m⁻² for Band 3 and 3640–5485 W m⁻² for Band 6.

Conclusions. We have identified MHD waves, both transverse (kink) and compressible sausage modes, in small-scale (magnetic) structures, independently, in both ALMA Band 3 and Band 6 observations, along with their corresponding synthetic images from simulations. The decrease of wave energy-flux with height (from Band 6 to Band 3) could possibly suggest energy dissipation at chromospheric heights, namely, wave heating, with the assumptions that the identified small-scale waves are typical at each band and they propagate upward through the chromosphere.

Context. The intensity of radiation from the solar atmosphere at millimetre wavelengths is closely related to the plasma temperature, and the formation height of the radiation is wavelength dependent. It follows from this that the slope of the intensity continuum, or the brightness temperature continuum, samples the local gradient of the gas temperature of the sampled layers in the solar atmosphere.

Aims. We aim to show the added information and diagnostics potential of the solar atmosphere that comes with measuring the slope of the brightness temperature continuum.

Methods. We used solar observations from the Atacama Large Millimeter/sub-millimeter Array (ALMA) and estimated and predicted the slope using a numerical three-dimensional radiation-magnetohydrodynamic simulation. The slope was estimated by the differences between observables at wavelengths corresponding to different sub-bands at opposite sides of the ALMA receiver band 3 (2.8–3.2 mm) and band 6 (1.20–1.31 mm).

Results. The sign of the brightness temperature slope indicates temperature changes with increasing height at the sampled layers. A positive sign implies an increase in temperature, while a negative sign implies a temperature decrease. The differences in brightness temperature between the sub-bands across the field of view of the simulation typically span from −0.4 kK to 0.75 kK for band 3 and −0.2 kK to 0.3 kK at band 6. The network patches are dominated by large positive slopes, while the quiet-Sun region shows a mixture of positive and negative slopes. As the slope of the continuum is coupled to the small-scale dynamics, a negative slope is seen typically under quiet-Sun conditions as a result of propagating shock waves and the corresponding post-shock regions. The temporal evolution of the slopes can therefore be used to identify shocks. The observability of the slope of the brightness temperatures is estimated at bands 3 and 6 for different angular resolutions corresponding to ALMA observations. The simulations also show that the intensity of the radiation at bands 3 and 6 can simultaneously originate from several major components at different heights, which is strongly dependent on the small-scale dynamics and is seen in both quiet-Sun and network patches. Our in-depth analysis of selected shock waves that propagating upward in the atmosphere shows that the delay of shock signatures between two wavelengths (e.g., bands 6 and 3) does not necessarily reflect the propagation speed of the shock front, but might be cause by the rate of change in opacity of higher layers at these wavelengths.

Conclusions. The slope of the brightness temperature continuum sampled at different ALMA receiver sub-bands serves as an indicator of the slope of the local plasma temperature at the sampled heights in the atmosphere. This offers new diagnostic possibilities for measuring the underlying physical properties of small-scale dynamic features and thus contributes to the understanding of these features and the related transport of energy and heat in the chromosphere.

The Atacama Large Millimeter/submillimeter Array (ALMA) offers new diagnostic possibilities that complement other commonly used diagnostics for the study of the Sun. In particular, ALMA’s ability to serve as an essentially linear thermometer of the chromospheric gas at unprecedented spatial resolution at millimeter wavelengths and future polarization measurements has great diagnostic potential. Solar ALMA observations are therefore expected to contribute significantly to answering long-standing questions about the structure, dynamics, and energy balance of the outer layers of the solar atmosphere. In this regard, current and future ALMA data are also important for constraining and further developing numerical models of the solar atmosphere, which in turn are often vital for the interpretation of observations. The latter is particularly important given the Sun’s highly intermittent and dynamic nature that involves a plethora of processes occurring over extended ranges in spatial and temporal scales. Realistic forward modeling of the Sun therefore requires time-dependent three-dimensional radiation magnetohydrodynamics that account for non-equilibrium effects and, typically as a separate step, detailed radiative transfer calculations, resulting in synthetic observables that can be compared to observations. Such artificial observations sometimes also account for instrumental and seeing effects, which, in addition to aiding the interpretation of observations, provide instructive tools for designing and optimizing ALMA’s solar observing modes. In the other direction, ALMA data in combination with other simultaneous observations enable the reconstruction of the solar atmospheric structure via data inversion techniques. This article highlights central aspects of the impact of ALMA for numerical modeling of the Sun and their potential and challenges, together with selected examples.