  Reanalysis of Einstein IPC data and new observations from the GINGA
  LAC indicate the presence of extended X-ray emission (10-50 kpc) around the
starburst galaxy M82. Here we model this emission by calculating numerical
hydrodynamic simulations of the starburst event to much later times and larger
scales than previously considered. For our models, we adopt a supernova rate of
0.1 ${\rm yr}^{-1}$, and an extended low-density static halo that is bound to
the galaxy. There are three stages to the evolution of the wind-blown bubble
and the propagation of the shock front: the bubble expands in an almost uniform
density disk gas, with a deceleration of the shock front ($t \alt $ 3.6 Myr);
breakout from the disk and the upward acceleration of the shock front (3.6
  Myr $\alt t \alt$ 18 Myr); propagation into the halo, leading to a more
spherical system and shock deceleration (18 Myr $\alt t$). For a halo density
of $10^{-3} {\rm cm}^{-3}$, the outflow reaches a distance of 40-50 kpc from
the center of the starburst galaxy in 50 Myr. We calculate the time evolution
of the X-ray luminosity and find that the extended starburst emits $3\times
10^{39}\lcgs$ to $10^{40}\lcgs$ in the
  GINGA LAC band and $\sim 10^{41}\lcgs$ in the Einstein or ROSAT
  HRI band. The degree of the ionization equilibrium in the outflow and its
effect on the iron K$\alpha$ line emission are discussed.
