# Low angular momentum relativistic hot accretion flow around Kerr black holes with variable adiabatic index

## TL;DR

This paper investigates relativistic accretion flows with low angular momentum around Kerr black holes, analyzing shock formation, oscillations, and implications for high-frequency QPOs, highlighting differences between relativistic and ideal gas equations of state.

## Contribution

It introduces a detailed analysis of shock properties and oscillation frequencies in relativistic accretion flows with variable adiabatic index, connecting these to black hole spin and QPO phenomena.

## Key findings

- Existence of an upper bound for critical point location with REoS
- Disagreement in shock parameter spaces between REoS and IEoS
- Empirical relation between shock oscillation frequency and flow parameters

## Abstract

We study the relativistic, time-independent, low angular momentum, inviscid, advective accretion flow around Kerr black hole. Considering the relativistic equation of state (REoS), we examine the transonic properties of the flow and find that there exists an upper bound of the location of the physically accepted critical point ($r^{\rm max}_{\rm out}$). However, no such limit exists when an ideal gas equation of state (IEoS) is assumed to describe the flow. Further, we calculate the global accretion solutions that contain shock waves and separate the domain of parameter space in angular momentum ($\lambda$) and energy (${\cal E}$) plane. We find ample disagreement between the shock parameter spaces obtained for REoS and IEoS, respectively. In general, post-shock flow (equivalently post-shock corona, hereafter PSC) is characterized by shock location ($r_s$) and compression ratio ($R$, measure of density compression across the shock front) which are uniquely determined for flow with given input parameters, namely $({\cal E}, \lambda)$. Using $r_s$ and $R$, we empirically compute the oscillation frequency ($\nu_{QPO}$) of the shock front which is in general quasi-periodic (QP) in nature and retrace the domain of shock parameter space in the $r_s-R$ plane in terms of $\nu_{QPO}$ for REoS around the weakly as well as rapidly rotating black holes. Finally, we indicate the relevance of the present work to explain the plausible origin of high frequency QPO (HFQPO) and its connection with the spin ($a_k$) of the Galactic black hole sources.