Role of thermal conduction in relativistic hot accretion flow around rotating black hole with shock

Abstract: We investigate the properties of low angular momentum, relativistic, viscous, advective accretion flows around rotating black holes that include shock waves in the presence of thermal conduction. We self-consistently solve the governing fluid equations to obtain the global transonic accretion solutions for a set of model parameters, namely energy ($\mathcal{E}$), angular momentum ($\lambda$), viscosity ($\alpha$), conduction parameter ($\Phi_{\rm s}$) and cooling parameter ($f_{\rm c}$). We observe that depending on the model parameters, accretion flow experiences centrifugally supported shock transition and the present study, for the first time, focuses on examining the shock properties, such as shock radius ($r_{\rm s}$), compression ratio ($R$) and shock strength ($\Psi$) regulated by the dissipation parameters ($\Phi_{\rm s},~f_{\rm c}$). We show that shock-induced global accretion solutions persist for wide range of model parameters and identify the boundary of the parameter space in energy-angular momentum plane that admits standing shocks for different dissipation parameters ($\Phi_{\rm s},~f_{\rm c}$). Finally, we compute the critical conduction parameter ($\Phi_{\rm s}^{\rm cri}$), beyond which shock ceases to exist. We find that $\Phi_{\rm s}^{\rm cri}$ directly depends on the black hole spin ($a_{\rm k}$) with $\Phi_{\rm s}^{\rm cri} \sim 0.029$ and $\sim 0.04$ for weakly ($a_{\rm k}\rightarrow 0$) and rapidly ($a_{\rm k}\rightarrow 1$) rotating black hole. Furthermore, we observe that $\Phi_{\rm s}^{\rm cri}$ decreases with increasing viscosity ($\alpha$), and shocked accretion solutions continue to exist for $\alpha \lesssim 0.065$ ($a_{\rm k} \rightarrow 0$) and $\lesssim 0.104$ ($a_{\rm k} \rightarrow 1$), respectively.