The effect of plasma-$β$ on the heating mechanisms during magnetic reconnection in partially ionized low solar atmosphere

We performed numerical simulations of magnetic reconnection with different strength of magnetic fields from the solar photosphere to the upper chromosphere. The main emphasis is to identify dominant mechanisms for heating plasmas in the reconnection region under different plasma-$β$ conditions in the partially ionized low solar atmosphere. The numerical results show that more plasmoids are generated in a lower $β$ reconnection event. The frequent coalescence of these plasmoids leads to a significant enhancement of turbulence and compression heating, which becomes the dominant mechanism for heating plasma in a lower plasma-$β$ reconnection process. The average power density of the compression heating (Q$_{comp}$) decreases with increasing initial plasma-$β$ as a power function: Q$_{comp} \sim β_{0}^{-a}$, where the value $a$ is $1.9$ in the photosphere and decreases to about 1.29 in the upper chromosphere. In the photosphere and lower chromosphere, the joule heating contributed by electron-neutral collisions Q$_{en}=η_{en} J^2$ eventually dominates over the compression heating when the initial plasma-$β$ is larger than the critical value $β_{0-critical} = 8$. In the upper chromosphere, the ambipolar diffusion heating and the viscous heating will become equally important as the compression heating when the initial plasma-$β$ is larger than the critical value $β_{0-critical} = 0.5$. These results indicate that the compression heating caused by turbulent reconnection mediated with plasmoids is likely the major heating mechanism for the small-scale reconnection events with stronger magnetic fields such as active region EBs and UV bursts. However, the heating caused by the partial ionization effects can not be ignored for those reconnection events with weaker magnetic fields such as quiet Sun EBs and cold surges.