Iterative Relaxation Method to Obtain Global Transonic Flows around Compact Objects

• Published in: Lobachevskii journal of mathematics Vol. 46; no. 1; pp. 143 - 156
• Main Authors: Sarkar, Shilpa, Kulikov, I. M.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01.01.2025; Springer Nature B.V
• Subjects: Algebra; Algorithms; Analysis; Angular momentum; Boundary conditions; Bremsstrahlung; Centrifugal force; Compacts; Geometry; Mathematical Logic and Foundations; Mathematics; Mathematics and Statistics; Methodology; Probability Theory and Stochastic Processes; Relaxation method (mathematics); Transonic flow; accretion; transonic; shocks; winds; compact objects; 2010 Mathematics Subject Classification: 68-04
• ISSN: 1995-0802; 1818-9962
• DOI: 10.1134/S1995080224608397

Flows around compact objects are necessarily transonic. Due to their dissipative nature, finding of sonic points is not trivial. [ 1 ] 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 compacts objects.