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Abstract Waves and oscillations are important solar phenomena, not only because they can propagate and dissipate energy in the chromosphere, but also because they carry information about the structure of the atmosphere in which they propagate. The nature of the 3 minute oscillations observed in the umbral region of sunspots is considered to be an effect of propagation of magnetohydrodynamic waves upward from below the photosphere. We present a study of sunspot oscillations and wave propagation in NOAA Active Region 12470 using an approximately 1 hr long data set acquired on 2015 December 17 by the Atacama Large Millimeter/submillimeter Array (ALMA), the Goode Solar Telescope (GST) operating at the Big Bear Solar Observatory, the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory, and the Interface Region Imaging Spectrograph. The ALMA data are unique in providing a time series of direct temperature measurements in the sunspot chromosphere. The 2 s cadence of ALMA images allows us to well resolve the 3 minute periods typical of sunspot oscillations in the chromosphere. Fourier analysis is applied to ALMA Band 3 (∼100 GHz, ∼3 mm) and GST H α data sets to obtain power spectra as well as oscillation phase information. We analyzed properties of the wave propagation by combining multiple wavelengths that probe physical parameters of solar atmosphere at different heights. We find that the ALMA temperature fluctuations are consistent with that expected for a propagating acoustic wave, with a slight asymmetry indicating nonlinear steepening. 

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. 

This white paper is on the HMCS Firefly mission concept study. Firefly focuses on the global structure and dynamics of the Sun's interior, the generation of solar magnetic fields, the deciphering of the solar cycle, the conditions leading to the explosive activity, and the structure and dynamics of the corona as it drives the heliosphere.