Iterative Relaxation Method to Obtain Global Transonic Flows around Compact Objects

TL;DR

This paper introduces a flexible iterative relaxation method to compute global transonic flows around compact objects, incorporating viscosity, heating, cooling, and shocks, unifying accretion and wind solutions.

Contribution

The authors develop a generic methodology, IRM-SP and IRM-SHOCK, capable of generating diverse transonic solutions with detailed algorithms, advancing the modeling of flows around compact objects.

Findings

Successfully generates various accretion and wind solutions.

Incorporates viscosity, heating, and cooling effects.

Provides detailed mathematical and computational algorithms.

Abstract

Flows around compact objects are necessarily transonic. Due to their dissipative nature, finding of sonic points is not trivial. Becker and Le in 2003 (BL03) proposed a novel methodology to obtain global transonic solutions, using iterative relaxation technique and exploiting the inner boundary conditions of the central object. In the current work, we propose a generic methodology -- IRM-SP and IRM-SHOCK to obtain any class of global accretion and wind solutions, given a set of constants of motion. We have considered viscosity in the system, which transports angular momentum outwards. In addition, it heats the system. Radiative processes like bremsstrahlung which cools the system is also incorporated. An interplay between heating and cooling process, along with gravity and centrifugal forces gives rise to multiple sonic points and hence shocks. The proposed methodology successfully generates any class of accretion as well as wind solutions, allowing us to unify them. Additionally, we report here rigorously the mathematical as well as the computational algorithm needed, to find sonic point(s) and thus obtain global transonic flows around compact objects.