Global Transonic Solution of Hot Accretion Flow with Thermal Conduction

Abstract

We examine the effect of thermal conduction on the low-angular momentum hot accretion flow (HAF) around non-rotating black holes accreting mass at very low rate. While doing so, we adopt the conductive heat flux in the saturated form, and solve the set of dynamical equations corresponding to a steady, axisymmetric, viscous, advective accretion flow using numerical methods. We study the dynamical and thermodynamical properties of accreting matter in terms of the input parameters, namely energy (${\epsilon }_0$), angular momentum (${\ell }_0$), viscosity parameter ($\alpha$), and saturation constant (${\Phi }_{\mathrm{s}}$) regulating the effect of thermal conduction. We find that ${\Phi }_{\mathrm{s}}$ plays a pivotal role in deciding the transonic properties of the global accretion solutions. In general, when ${\Phi }_{\mathrm{s}}$ is increased, the critical point ($r_{\mathrm{c}}$) is receded away from the black hole, and flow variables are altered particularly in the outer part of the disc. To quantify the physically acceptable range of ${\Phi }_{\mathrm{s}}$, we compare the global transonic solutions with the self-similar solutions, and observe that the maximum saturation constant (${\Phi }_{\mathrm{s}}^{\max }$) estimated from the global solutions exceeds the saturated thermal conduction limit (${\Phi }_{\mathrm{sc}}$) derived from the self-similar formalism. Moreover, we calculate the correlation between $\alpha$ and ${\Phi }_{\mathrm{s}}^{\max }$ and find ample disagreement between global solutions and self-similar solutions. Further, using the global flow variables, we compute the Bernoulli parameter ($Be$) which remains positive all throughout the disc, although flow becomes loosely unbound for higher ${\Phi }_{\mathrm{s}}$. Finally, we indicate the relevance of this work in the astrophysical context in explaining the possibility of massloss/outflows from the unbound disc.

12 pages, 8 figures; accepted for publication in MNRAS

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