Self-Similar Dynamics of a Magnetized Polytropic Gas

Abstract

In broad astrophysical contexts of large-scale gravitational collapses and outflows and as a basis for various further astrophysical applications, we formulate and investigate a theoretical problem of self-similar MHD for a non-rotating polytropic gas of quasi-spherical symmetry permeated by a completely random magnetic field. We derive two coupled nonlinear MHD ordinary differential equations (ODEs), examine properties of the magnetosonic critical curve, obtain various asymptotic and global semi-complete similarity MHD solutions, and qualify the applicability of our results. Unique to a magnetized gas cloud, a novel asymptotic MHD solution for a collapsing core is established. Physically, the similarity MHD inflow towards the central dense core proceeds in characteristic manners before the gas material eventually encounters a strong radiating MHD shock upon impact onto the central compact object. Sufficiently far away from the central core region enshrouded by such an MHD shock, we derive regular asymptotic behaviours. We study asymptotic solution behaviours in the vicinity of the magnetosonic critical curve. Numerically, we construct global semi-complete similarity MHD solutions that cross the magnetosonic critical curve zero, one, and two times. For comparison, counterpart solutions in the case of an isothermal unmagnetized and magnetized gas flows are demonstrated in the present MHD framework at nearly isothermal and weakly magnetized conditions. For a polytropic index $\gamma =1.25$ or a strong magnetic field, different solution behaviours emerge. In these cases, there exist semi-complete similarity solutions crossing the magnetosonic critical curve only once, and the MHD counterpart of expansion-wave collapse solution disappears.

37 pages, 36 figures, accepted by Astrophysics and Space Science

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Cited by in corpus (13)

• Magnetized massive stars as magnetar progenitors
• Dynamic Evolution of a Quasi-Spherical General Polytropic Magnetofluid with Self-Gravity
• Self-Similar Dynamics of a Relativistically Hot Gas
• Starless Cloud Core L1517B in Envelope Expansion with Core Collapse
• Perturbation Analysis of a General Polytropic Homologously Collapsing Stellar Core
• Forming Protostars in Molecular Clouds with Shocked Envelope Expansion and Core Collapse
• Three-dimensional Hydrodynamic Instabilities in Stellar Core Collapses
• Dynamic Evolution Model of Isothermal Voids and Shocks
• Collisional interaction limits between dark matters and baryons in `cooling flow' clusters
• Intermediate-Mass Black Holes in Globular Clusters
• Self-Similar Shocks and Winds in Galaxy Clusters
• Supermassive Black Holes in Galactic Bulges
• Mass and Mean Velocity Dispersion Relations for Supermassive Black Holes in Galactic Bulges