Envelope Expansion with Core Collapse. III. Similarity Isothermal Shocks in a Magnetofluid

We explore magnetohydrodynamic (MHD) solutions for envelope expansions with core collapse (EECC) with isothermal MHD shocks in a quasi-spherical symmetry and outline potential astrophysical applications of such magnetized shock flows. By including a random magnetic field in a gas medium, we further extend the recent isothermal shock results of Bian & Lou who have unified earlier similarity isothermal shock solutions of Tsai & Hsu, of Shu et al. and of Shen & Lou in a more general framework. MHD shock solutions are classified into three classes according to the downstream characteristics near the core. Class I solutions are those characterized by free-fall collapses towards the core downstream of an MHD shock, while Class II solutions are those characterized by Larson-Penston (LP) type near the core downstream of an MHD shock. Class III solutions are novel, sharing both features of Class I and II solutions with the presence of a sufficiently strong magnetic field as a prerequisite. Various MHD processes may occur within the regime of these isothermal MHD shock similarity solutions, such as sub-magnetosonic oscillations, free-fall core collapses, radial contractions and expansions. Both possibilities of perpendicular and oblique MHD shocks are analyzed. Under the current approximation of MHD EECC solutions, only perpendicular shocks are systematically calculated. These similarity MHD shocks propagate at either submagnetosonic or super-magnetosonic constant speeds. We can construct Class I, II and III MHD shocks matching with an isothermal magnetostatic outer envelope or an MHD breeze. We can also construct families of twin MHD shock solutions as well as an ‘isothermal MHD shock’ separating two magnetofluid regions of two different yet constant temperatures. The versatile behaviours of such MHD shock solutions may be utilized to model a wide range of astrophysical problems, including star formation in magnetized molecular clouds, ‘MHD champagne flows’ in HII regions around luminous massive OB stars, MHD link between the asymptotic giant branch phase to the protoplanetary nebula phase with a hot central magnetized white dwarf, relativistic MHD pulsar winds in supernova remnants, radio afterglows of soft gamma-ray repeaters and so forth.