Nanoflare Heating of the Solar Corona Observed in X-rays

Abstract: The existence of the million-degree corona above the cooler photosphere is an unsolved problem in astrophysics. Detailed study of quiescent corona that exists regardless of the phase of the solar cycle may provide fruitful hints towards resolving this conundrum. However, the properties of heating mechanisms can be obtained only statistically in these regions due to their unresolved nature. Here, we develop a two-step inversion scheme based on the machine learning scheme of Upendran & Tripathi (2021a) for the empirical impulsive heating model of Pauluhn & Solanki (2007), and apply it to disk integrated flux measurements of the quiet corona as measured by the X-ray solar monitor (XSM) onboard Chandrayaan - 2. We use data in three energy passbands, viz., 1 - 1.3 keV, 1.3 - 2.3 keV, and 1 - 2.3 keV, and estimate the typical impulsive event frequencies, timescales, amplitudes, and the distribution of amplitudes. We find that the impulsive events occur at a frequency of $\approx$25 events per minute with a typical lifetime of $\approx10$ minutes. They are characterized by a power law distribution with a slope $\alpha\leq2.0$. The typical amplitudes of these events lie in an energy range of $10<sup>{21}$ - $10<sup>{24}$ ergs, with a typical radiative loss of about $\approx10<sup>3$ erg cm$<sup>{-2}$ s$<sup>{-1}$ in the energy range of 1 - 2.3 keV. These results provide further constraints on the properties of sub-pixel impulsive events in maintaining the quiet solar corona.