General Polytropic Magnetofluid under Self-Gravity: Voids and Shocks
  We study the self-similar magnetohydrodynamics (MHD) of a quasi-spherical
expanding void (viz. cavity or bubble) in the centre of a self-gravitating gas
sphere with a general polytropic equation of state. We show various analytic
asymptotic solutions near the void boundary in different parameter regimes and
obtain the corresponding void solutions by extensive numerical explorations. We
find novel void solutions of zero density on the void boundary. These new void
solutions exist only in a general polytropic gas and feature shell-type density
profiles. These void solutions, if not encountering the magnetosonic critical
curve (MCC), generally approach the asymptotic expansion solution far from the
central void with a velocity proportional to radial distance. We identify and
examine free-expansion solutions, Einstein-de Sitter expansion solutions, and
thermal-expansion solutions in three different parameter regimes. Under certain
conditions, void solutions may cross the MCC either smoothly or by MHD shocks,
and then merge into asymptotic solutions with finite velocity and density far
from the centre. Our general polytropic MHD void solutions provide physical
insight for void evolution, and may have astrophysical applications such as
massive star collapses and explosions, shell-type supernova remnants and hot
bubbles in the interstellar and intergalactic media, and planetary nebulae.
