A GRMHD-Calibrated Semi-Analytical Model for Hot Sub-Keplerian Accretion Flows in Kerr Spacetime

Abstract

We develop a simple, semi-analytical, kinematic model for hot, thick accretion flows, constructed by interpolating between Keplerian and free-fall geodesic solutions in the Kerr metric. Unlike self-consistent general relativistic magnetohydrodynamics (GRMHD) frameworks, our model contains no explicit magnetic fields or stress terms; instead, it uses a smooth, radially varying transition function T(r) to connect the velocity components from near-Keplerian rotation at large distances to a free-fall state near the event horizon. While the coefficients $\alpha$ and $\beta$ remain constant, the transition function is a true function of radius, allowing the flow properties to vary smoothly with radius. We calibrate and validate this model against time- and azimuthally averaged profiles from long-duration magnetically arrested disk (MAD) simulations spanning a wide range of black hole spins ($a=-0.9$ to $+0.9$). The model successfully captures the properties of accretion flow parameters across both prograde and retrograde configurations. Quantitatively, the predicted radial velocity, angular velocity, and density profiles match the simulation data to within an average factor of approximately 1.8, 1.6, and 1.6, respectively, while the specific angular momentum exhibits the closest agreement, remaining within a factor of approximately 1.2. This fast semi-analytical prescription gives significantly lower errors than previous constant-coefficient models and it is a computationally affordable tool for various applications such as ray tracing, accretion parameter exploration, and spectral modelling.