The 230 GHz Variability of Numerical Models of Sagittarius A* II. The Physical Origins of the Variability

We continue our previous work, Chan et al. 2024, to investigate how variations in the electron temperature prescription parameter, $R_{\rm Low}$, influence the $3$-hour variability at $230$\,GHz, $M_{\Delta T}$, in magnetic-arrested disk (MAD) models of Sagittarius~A* (Sgr~A*), through analyzing a series of general-relativistic magnetohydrodynamics and raytracing simulations. For models with a black hole spin $a > 0$, we discovered that increasing $R_{\rm Low}$ renders the photon ring more optically thick, obscuring the varying accretion flows that contribute to the variability. However, as $R_{\rm Low}$ increases further, MAD flux eruptions become more pronounced, compensating for the decrease in $M_{\Delta T}$. For models with a spin $a < 0$, although a higher $R_{\rm Low}$ also increases the optical thickness of the fluid, voids within the optically thick gas fail to cover the entire photon ring. Similarly, flux eruptions become more prominent as $R_{\rm Low}$ increases further, contributing to the observed rise in $M_{\Delta T}$ relative to $R_{\rm Low}$. For black holes with a spin $a = 0$, although the effect of increasing optical depth is still present, their $230$\,GHz light curves, and hence $M_{\Delta T}$, are insensitive to changes in $R_{\rm Low}$. Furthermore, we found that the variability of the $230$\,GHz light curves at $R_{\rm Low} = 1$ might correlate with fluctuations in the internal energy of the gas near the black hole, and we listed potential causes and solutions to the over-variability problem. Our findings highlight potential approaches for refining $M_{\Delta T}$ to better align with observations when modeling Sgr~A*.