Magnetic Heating Across the Sun and Solar-like Stars: Universal Scaling Laws from Chromospheres to Coronae

Magnetic activity in cool stars governs the thermal structure and high-energy radiative output of their outer atmospheres, thereby influencing stellar evolution, stellar winds, and the atmospheres of orbiting (exo)planets. A long-standing question in stellar astrophysics is whether the mechanisms responsible for atmospheric heating are universal across the Sun and cool stars spanning different ages and activity levels. In this paper, we review recent progress in understanding magnetic heating across the Sun and Sun-like stars through empirical scaling relations between photospheric magnetic flux and radiative output from the chromosphere, transition region, and corona. Analysis of more than a decade of Sun-as-a-star observations reveals that irradiance and magnetic flux follow power-law relationships over a wide temperature range. While coronal emissions exhibit superlinear scaling with magnetic flux, chromospheric and transition-region diagnostics show weaker, sublinear dependencies. Remarkably, observations of G-type stars with ages ranging from 50 Myr to 4.5 Gyr are found to lie on extensions of the solar scaling laws, suggesting that a common magnetic-heating mechanism operates across different levels of stellar activity. We further discuss the application of these scaling relations to reconstructing stellar X-ray and ultraviolet (XUV) spectra from observed magnetic fluxes. The resulting synthetic spectra reproduce actual observations of young, active solar analogs, providing a practical tool to estimate the ionizing radiation whose extreme UV emissions cannot be directly measured.