  We investigate self-similar magnetohydrodynamic (MHD) processes in an
isothermal self-gravitating fluid with a quasi-spherical symmetry and extend
the envelope expansion with core collapse (EECC) solutions of Lou & Shen by
incorporating a random magnetic field. Stagnation surfaces of EECC solutions
that seperate core collapse and envelope expansion propagate at constant speeds
either sub-magnetosonically or super-magnetosonically. Crossing the
magnetosonic line twice analytically, there exists an infinite number of
discrete magnetized EECC and ECCC solutions. In addition to the EECC shock
solution which could change the central accretion rate, the magnetic field can
also affect the core accretion rate. As the magnetic parameter $\lambda$
increases, the core accretion rate appropriate for the MHD EWCS becomes larger.
Under the frozen-in approximation, magnetic fields in the envelope expansion
portion would scale as $B\propto r^{-1}$, while in the core collapse portion
they would scale as $B\propto r^{-1/2}$. We discuss several astrophysical
applications of EECC similarity solutions to the formation process of
proto-planetary nebulae connecting the AGB phase and the planetary nebula, to
supernova remnants, collapse of magnetized molecular cloud, to $\textrm{H}\
{\textrm{\small{II}}}$ clouds surrounding massive OB stars and to a certain
evolution phase of galaxy clusters.

Astrophysics