Relativistic viscous accretion flow model for ULX sources

We present a model formalism to study the properties of a relativistic, viscous, advective accretion flow around a rotating black hole in presence of cooling. We employ this model to constrain the viable ranges of mass (M_{BH}), spin (a_k), and accretion rate ({\dot m}) of the Ultra-luminous X-ray sources (ULXs). While doing this, we adopt an effective potential to describe the spacetime geometry around the rotating black holes. With this, we obtain the shock-induced global accretion solutions in terms of {\dot m} and viscosity parameter (α), and compute the Quasi-periodic Oscillation (QPO) frequency (ν_{QPO}) of the post-shock matter pragmatically, when the shock front exhibits Quasi-periodic variations. We further compute the disc luminosity for these accretion solutions that contain shocks. We observe that the present formalism is capable to account for the observed ν_{APO} and bolometric luminosity (L_{bol}) of IC 342 X-1 ULX source. Based on our findings, we indicate that the central accretor of IC 342 X-1 is rapidly rotating and it accretes at super-Eddington accretion rate provided IC 342 X-1 harbors a massive stellar-mass black hole (M_{BH} < 100 M_⊙).