Impact of Equation of State on Black Hole Accretion Flows and Radiative Properties

Abstract: Previous literature has documented that black hole shadow images are mainly shaped by spacetime geometry and plasma microphysics governing accretion flows. However, the influence of equations of state (EoS) remains under-explored. In this paper, we quantify how different plasma microphysics prescriptions, specifically the choice of EoS and electron-heating models, affect flow thermodynamics and the corresponding synthetic black-hole images. We perform three-dimensional general-relativistic magnetohydrodynamics (GRMHD) simulations using two constant-$γ$ ideal EoSs with $γ= 4/3$ and 5/3 and a temperature-dependent variable EoS (TM) in both accretion flow states: Standard And Normal Evolution (SANE) and Magnetically Arrested Disk (MAD) regimes. The dynamical models are post-processed with general-relativistic radiative transfer (GRRT) calculations at 86GHz and 230GHz, employing thermal and hybrid $κ$ electron distribution functions for synchrotron radiation. We also compare the two-temperature electron heating prescription based on turbulent heating and magnetic reconnection. The constant-$γ$ EoSs systematically overestimate or underestimate gas and electron temperatures across disk and jet regions, whereas the variable EoS provides a smoother trans-relativistic interpolation between the two limiting regimes. These differences substantively impact the synchrotron emissivity, image morphology, and the amplitude of flux variability. In particular, the variable EoS exhibits systematically larger temporal variability than the constant-$γ$ models. These results demonstrate that adopting a physically self-consistent description of the EoS is essential for realistic modeling of accretion-flow thermodynamics and horizon-scale images like Event Horizon Telescope (EHT) observations.