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 (ϵ0), angular momentum (ℓ0), viscosity parameter (α), and saturation constant (Φs) regulating the effect of thermal conduction. We find that Φs plays a pivotal role in deciding the transonic properties of the global accretion solutions. In general, when Φs is increased, the critical point (rc) 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 Φs, we compare the global transonic solutions with the self-similar solutions, and observe that the maximum saturation constant ($\Phi ^{\rm max}_{\rm s}$) estimated from the global solutions exceeds the saturated thermal conduction limit (Φsc) derived from the self-similar formalism. Moreover, we calculate the correlation between α and $\Phi ^{\rm max}_{\rm s}$ 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 Φs. Finally, we indicate the relevance of this work in the astrophysical context in explaining the possibility of massloss/outflows from the unbound disc.

Accretion flows around spinning compact objects in the post-Newtonian regime

“…However, we are interested in the outer critical point passing solutions, as the present post-Newtonian regime is valid outside 10 r g (see section 2 for details). Further, we find two real roots for the 'X'-type critical points: dV dr | rc < 0, which corresponds to accretion, and the other dV dr | rc > 0 refers to the wind solutions (see [11,73] and references therein). It is also important to note that the flow possessing MCPs can potentially harbor shock waves [10,14,75], such scenarios are beyond the scope of this paper.…”

“…Hence, we fix Γ = 13/9 throughout to maintain the trans-relativistic nature (see figure 1f in [11]) of the flow unless stated otherwise. Also, for the ideal fluid, the internal energy per unit mass is given by (see for instance [73]),…”

“…In order to determine the global transonic solution for the steady, thin, axisymmetric, low-ℓ accretion flow in the post-Newtonian space-time near a spinning compact object, one must solve a set of coupled differential equations. These include the wind equation, the azimuthal momentum equation, and the temperature gradient equation (as detailed in [9,11,73]). We aim to focus only on the outer critical point (r out c ) passing solutions as the 1PN correction works smoothly outside 10 r g .…”

Low-angular-momentum General Relativistic Magnetohydrodynamic Accretion Flows around Rotating Black Holes with Shocks

“…Accordingly, we obtain two unique values of dv dr ; r c ( )| one of them relates to accretion, and the other one is for wind. When both dv dr r c ( )| values are real and opposite in sign, a saddle-type critical point is formed (Das 2007;Das et al 2022;Mitra et al 2022Mitra et al , 2023. Such points have special significance, as transmagnetosonic solutions can only pass through these points before entering into the BH.…”