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

Abstract

We solved analytically viscous two-dimensional (2D) fluid equations for accretion and outflows in spherical polar coordinates ($r,\theta ,\varphi$) 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 Paczyński-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, ${\tau }_{\mathrm{r}\varphi }$ and ${\tau }_{\theta \varphi }$. 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 ${\tau }_{\mathrm{r}\varphi }$ and decreasing ${\alpha }_2$ for ${\tau }_{\theta \varphi }$. The ${\tau }_{\theta \varphi }$ is effective in angular momentum transportation at high latitude and outflows collimation along an axis of symmetry since it changes polar velocity ($v_{\theta }$) of the flow. The outflow emission is also affected by the ADAF size and decreased with decreasing it. Transonic surfaces formed for both inflows ($v_{\mathrm{r}}<0$, very close to BH) and outflows ($v_{\mathrm{r}}>0$). We also explored no outflows, outflows and failed outflows regions, which mainly depend on the viscosity parameters.

22 pages, 9 figures, Accepted for publication in ApJ

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