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Observational Constraints on Direct Electron Heating in the Hot Accretion Flows in Sgr A* and M87*

An important parameter in the theory of hot accretion flows around black holes is $δ$, which describes the fraction of ``viscously'' dissipated energy in the accretion flow that goes directly into heating electrons. For a given mass accretion rate, the radiative efficiency of a hot accretion flow is determined by $δ$. Unfortunately, the value of $δ$ 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 $δ$. 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 $δ$ (and accretion rate). By comparing the EHTC-derived radiative efficiencies with the theoretical results from MAD models, we find that Sgr A* requires $δ\ga 0.3$. %with the most likely value being $δ\sim 0.5$. A similar comparison in the case of M87* gives inconclusive results as there is still a large uncertainty in the accretion rate in this source.