Parameter Space Study of Magnetohydrodynamic Flows around Magnetized Compact Objects

In recent years, the study of magnetohydrodynamic (MHD) accretion flow around compact objects has become very important since the magnetic field in ubiquitous in the universe and it should play a part in the black hole accretion, especially close to the inner disk. The pioneering works of Mestel (1967) and Weber & Davis (1967) etc. were further extended by Chakrabarti (1990) for rotating compact stars and obtained a few global solutions for accretion and winds. The study of MHD flow in Kerr geometry is also carried out by Takahashi et al. (1990). They discussed the properties of smooth trans-Alfv́enic flows and focused on the possible ways to extract energies out of the BH. Nitta et al. (1991) presented an analytical solution of general relativistic Grad-Safranov equation around a rotating BH and obtained few solution topologies. So far, a fully self-consistent study of the global solutions around a compact star in terms of flow parameters was not explored. In this paper, we wish to provide a complete study of the trans-magnetosonic accretion flow around compact objects in presence of both the radial and toroidal magnetic fields using Paczyński-Wiita pseudo-Newtonian potential. We discuss how the nature of the solution topologies depend on the parameter space spanned by the energy (E) and the angular momentum (L) of the flow. We identify eighteen types of solution topologies and divide the parameter space accordingly. We also find that the standing magneto-hydrodynamic shock wave forms which could give rise to the high energy particles ( few MeV) through the shock acceleration mechanism of the electrons. These accelerated particles produce power-law synchrotron radiations which could explain some of the spectral properties of BH candidates. Moreover, soft photons are energized by the hot electrons of post-shock flow through inverse Comptonization. In this paper, we provide all possible solutions of MHD flow with or without shocks and classify the parameter space according to the nature of the flow solution.