The Sun and Sun-like stars commonly host the multi-million-K corona and the 10,000-K chromosphere. Because these extremely hot gases generate X-ray and extreme ultraviolet (XUV) emissions that may impact the erosion and chemistry of (exo)planetary atmospheres, influencing the climate and conditions for habitability, it is of crucial importance in solar and stellar physics to understand the responsible heating mechanisms. While, for the Sun, the magnetic field is thought to play a pivotal role in driving and transporting the energy from the surface upwards, it is not clear whether such a magnetically driven heating is commonly at work on other stars. Here we present the analysis of 10 years of multi-wavelength synoptic observations of the Sun and comparison with stellar data, providing the critical clues to the common nature of the heating mechanisms of coronae, transition regions, and chromospheres of the Sun and Sun-like stars. First, by analyzing the sequences of solar images of sunspot transit events, we derive the means to understand the magnetic and thermal environments of starspot magnetic fields that cannot be spatially resolved. Specifically, it is found that the surface magnetic flux can be inferred from the chromospheric light curves and that the thermal structures around the starspots can be inspected from the sub-MK UV light curves. Second, by investigating the power-law relationships between the surface magnetic flux and the luminosity of various emission lines with the formation temperatures from the corona to the chromosphere of the Sun, we discover that, in any temperature ranges, the solar scaling laws can be extended to the Sun-like stars with the ages of 50 Myr to 4.5 Gyr. This suggests that the magnetically-driven heating of the atmospheres is universal among the Sun and Sun-like stars, regardless of age or activity. Furthermore, by deriving the scaling laws between the magnetic flux and XUV spectrum, it is now possible to empirically reproduce the XUV spectra for various solar-type stars given the observationally-obtained magnetic fluxes. It is expected that the reproduced XUV spectra are used for photochemical calculations of (exo)planets of various solar-type stars, including the young Sun, and estimation of atmospheric formation and habitability of surface life.

{"references": ["Toriumi, S. & Airapetian, V. S. (2022), ApJ, 927, 179", "Toriumi, S. et al. (2022), ApJS, 262, 46", "Toriumi, S. & Wang, H. (2019), LRSP, 16, 3"]}