Estimation of mass outflow rates from dissipative accretion disc around rotating black holes

Abstract

We study the properties of the dissipative accretion flow around rotating black holes in presence of mass loss. We obtain the complete set of global inflow-outflow solutions in the steady state by solving the underlying conservation equations self-consistently. We observe that global inflow-outflow solutions are not the isolated solution, instead such solutions are possible for wide range of inflow parameters. Accordingly, we identify the boundary of the parameter space for outflows, spanned by the angular momentum ($\lambda_{\rm in}$) and the energy (${\cal E}_{\rm in}$) at the inner sonic point ($x_{\rm in}$), as function of the dissipation parameters and find that parameter space gradually shrinks with the increase of dissipation rates. Further, we examine the properties of the outflow rate $R_{\dot m}$ (defined as the ratio of outflow to inflow mass flux) and ascertain that dissipative processes play the decisive role in determining the outflow rates. We calculate the limits on the maximum outflow rate ($R_{\dot{m}}^{\rm max}$) in terms of viscosity parameter ($\alpha$) as well as black hole spin ($a_k$) and obtain the limiting range as $3\% \le R_{\dot{m}}^{\rm max} \le 19\%$. Moreover, we calculate the viable range of $\alpha$ that admits the coupled inflow-outflow solutions and find that $\alpha \lesssim 0.25$ for $R_{\dot m} \ne 0$. Finally, we discuss the observational implication of our formalism to infer the spin of the black holes. Towards this, considering the highest observed QPO frequency of black hole source GRO J1655-40 ($\sim 450$ Hz), we constrain the spin value of the source as $a_k \ge 0.57$.