Universal Scaling Laws for Solar and Stellar Atmospheric Heating

The Sun and Sun-like stars commonly host multimillion-kelvin coronae and 10,000 K chromospheres. These extremely hot gases generate X-ray and extreme ultraviolet emissions that may impact the erosion and chemistry of (exo)planetary atmospheres, influencing the climate and conditions for habitability. However, the mechanism of coronal and chromospheric heating is still poorly understood. While the magnetic field most probably plays a key role in driving and transporting energy from the stellar surface upwards, it is not clear whether the atmospheric heating mechanisms of the Sun and active Sun-like stars can be described in a unified manner. To this end, we report on a systematic survey of the responses of solar and stellar atmospheres to surface magnetic flux over a wide range of temperatures. By analyzing 10 years of multiwavelength synoptic observations of the Sun, we reveal that the irradiance and magnetic flux show power-law relations with an exponent decreasing from above unity to below as the temperature decreases from the corona to the chromosphere. Moreover, this trend indicating the efficiency of atmospheric heating can be extended to Sun-like stars. We also discover that the power-law exponent depends on the solar cycle, becoming smallest at maximum activity, probably due to the saturation of atmospheric heating. Our study provides observational evidence that the mechanism of atmospheric heating is universal among the Sun and Sun-like stars, regardless of age or activity.