# Accretion-ejection in rotating black holes: a model for `outliers' track of radio-X-ray correlation in X-ray binaries

## TL;DR

This paper models accretion and jet ejection around rotating black holes using pseudo-Kerr potentials, exploring shock formation, mass outflows, and their relation to radio-X-ray correlations in X-ray binaries, suggesting rapid black hole spins in outliers.

## Contribution

It introduces a comprehensive analysis of shock solutions and jet power in rotating black holes using multiple pseudo potentials, highlighting the effects of spin, viscosity, and flow parameters on outflows and radio-X-ray correlations.

## Key findings

- Shock solutions exist over a wide parameter range.
- Maximum mass outflow rate weakly depends on black hole spin.
- X-ray binaries along the outliers track may host rapidly rotating black holes.

## Abstract

We study the global accretion-ejection solutions around a rotating black hole considering three widely accepted pseudo-Kerr potentials that satisfactorily mimic the space-time geometry of rotating black holes. We find that all the pseudo potentials provide standing shock solutions for large range of flow parameters. We identify the effective region of the shock parameter space spanned by energy ($\mathcal{E}_{\text{in}}$) and angular momentum ($\lambda_{\text{in}}$) measured at the inner critical point ($x_{\text{in}}$) and find that the possibility of shock formation becomes feeble when the viscosity parameter ($\alpha$) is increased. In addition, we find that shock parameter space also depends on the adiabatic index ($\gamma$) of the flow and the shock formation continues to take place for a wide range of $\gamma$ as $1.5 \le \gamma \le 4/3$. For all the pseudo potentials, we calculate the critical viscosity parameter ($\alpha_{\text{shock}}^{\text{cri}}$) beyond which standing shock ceases to exist and compare them as function of black hole spin ($a_k$). We observe that all the pseudo potentials under consideration are qualitatively similar as far as the standing shocks are concerned, however, they differ both qualitatively and quantitatively from each other for rapidly rotating black holes. Further, we compute the mass loss from the disc using all three pseudo potentials and find that the maximum mass outflow rate ($R^{\rm max}_{{\dot m}}$) weakly depends on the black hole spin. To validate our model, we calculate the maximum jet kinetic power using the accretion-ejection formalism and compare it with the radio jet power of low-hard state of the black hole X-ray binaries (hereafter XRBs). The outcome of our results indicate that XRBs along the `outliers' track might be rapidly rotating.