Observational Constrains on Direct Electron Heating in Hot Accretion Flows from Sgr A* and M87*

Fu-Guo Xie, Ramesh Narayan, Feng Yuan

Published 2022-10-06Version 1

An important parameter in the theory of hot accretion flows around black holes is $\delta$, which describes the fraction of ``viscously'' dissipated energy in the accretion flow that directly heats the electrons. The radiative efficiency of a hot accretion flow is determined by its value if other parameters, such as the accretion rate, are determined. Unfortunately, the value of $\delta$ is hard to determine from first principles. The recent Event Horizon Telescope Collaboration (EHTC) results on M87* and Sgr A* provide us with a different way of constraining $\delta$. By combining the mass accretion rates in M87* and Sgr A* estimated by the EHTC with the measured bolometric luminosities of the two sources, we derive good constraints on the radiative efficiencies of the respective accretion flows. In parallel, we use a theoretical model of hot magnetically arrested disks (MAD) to calculate the expected radiative efficiency as a function of $\delta$ (and accretion rate). By comparing the EHTC-derived radiative efficiencies with the theoretical MAD model, we find that Sgr A* requires $\delta > 0.3$, with the most likely value being $\delta \sim 0.5$. A similar comparison in the case of M87* gives inconclusive results, because there is still a large uncertainty in the accretion rate in this source.