Relativistic viscous accretion flow model for ULX sources: a case study for IC 342 X-1

Abstract

ABSTRACT In this paper, we develop a model formalism to study the structure of a relativistic, viscous, optically thin, advective accretion flow around a rotating black hole in presence of radiative coolings. We use this model to examine the physical parameters of the ultra-luminous X-ray sources (ULXs), namely mass (MBH), spin (ak), and accretion rate (${\dot{m}}$), respectively. While doing this, we adopt a recently developed effective potential to mimic the space–time geometry around the rotating black holes. We solve the governing equations to obtain the shock-induced global accretion solutions in terms of ${\dot{m}}$ and viscosity parameter (α). Using shock properties, we compute the quasi-periodic oscillation (QPO) frequency (νQPO) of the post-shock matter (equivalently post-shock corona, hereafter PSC) pragmatically, when the shock front exhibits quasi-periodic variations. We also calculate the luminosity of the entire disc for these shock solutions. Employing our results, we find that the present formalism is potentially promising to account the observed νQPO and bolometric luminosity of a well-studied ULX source IC 342 X-1. Our findings further imply that the central source of IC 342 X-1 seems to be rapidly rotating and accretes matter at super-Eddington accretion rate provided IC 342 X-1 harbours a massive stellar mass black hole ($M_{\rm BH} \lt 100 \, \mathrm{M}_\odot$) as indicated by the previous studies.