The Distribution of Time Delays Between Nanoflares in Magnetohydrodynamic Simulations

Abstract

Nanoflares are thought to be an important energy source for heating the solar corona. The exact amount of heating contributed by nanoflares depends, in part, on the frequency of the heating and the time interval between nanoflares. Several numerical models have attempted to constrain the frequency of the heating by fitting to observed emission measures. To date, however, no physically motivated value for the time interval between nanoflares has been obtained. In this paper, we calculate a physically motivated distribution of time intervals between successive “nanoflare” reconnection events in driven magnetohydrodynamic simulations. We show that this distribution follows a power law with a slope near −1, much shallower than previously inferred from observations and determined from loop model comparisons with observations. We show that the energy flux injected into the corona in our model is of order $10^{7}~\text{erg}\,\text{cm}^{-2}\,\text{s}^{-1}$, and that the heating rate due to these reconnection events reaches values of order $1\mbox{--}10~\text{erg}\,\text{cm}^{-3}\,\text{s}^{-1}$. Additionally, we show that this power law slope is dependent only weakly on the amount of magnetic helicity injected into the solar magnetic field by the photospheric motions, but the rate of reconnection is about $45\%$ higher if no magnetic helicity is injected.