The 2D disk structure with advective transonic inflow-outflow solutions around black holes

TL;DR

This paper analytically models 2D viscous accretion flows around black holes, revealing how outflows form near the black hole and depend on viscosity, pressure, and ADAF size, with implications for jet collimation.

Contribution

It provides an explicit analytical solution for 2D viscous accretion and outflow structures around black holes, highlighting the role of different viscosity components and parameters.

Findings

Outflows form close to black holes and are influenced by viscosity and pressure ratios.

Outflow strength increases with higher viscosity parameter ($\alpha_1$) and mass-loss parameter ($s$).

Angular momentum transport and outflow collimation are affected by the $ au_{ m hetaeta}$ stress tensor component.

Abstract

We solved analytically viscous two-dimensional (2D) fluid equations for accretion and outflows in spherical polar coordinates ($r, \theta, \phi$) and obtained explicitly flow variables in $r-$ and $\theta -$directions around black holes (BHs). We investigated global transonic advection-dominated accretion flow (ADAF) solutions in $r-$direction on an equatorial plane with using Paczy\'nski-Wiita potential. We used radial flow variables of ADAFs with symmetric conditions on the equatorial plane, as initial values for integration in $\theta-$direction. In the study of 2D disk structure, we used two-azimuthal components of viscous stress tensors namely, $\tau_{\rm r\phi}$ and $\tau_{\rm\theta\phi}$. Interestingly, we found that the whole advective disk is not participating in outflow generation and the outflows form close to the BHs. Normally, outflow strength increased with increasing viscosity parameter ($\alpha_1$), mass-loss parameter ($s$) and decreasing gas pressure ratio ($\beta$). Outflow region increased with increasing $s$, $\alpha_1$ for $\tau_{\rm r\phi}$ and decreasing $\alpha_2$ for $\tau_{\rm\theta\phi}$. The $\tau_{\rm\theta\phi}$ is effective in angular momentum transportation at high latitude and outflows collimation along an axis of symmetry since it changes polar velocity ($v_{\rm\theta}$) of the flow. The outflow emission is also affected by the ADAF size and decreased with decreasing it. Transonic surfaces formed for both inflows ($v_{\rm r}<0$, very close to BH) and outflows ($v_{\rm r}>0$). We also explored no outflows, outflows and failed outflows regions, which mainly depend on the viscosity parameters.