Superbubble evolution in disk galaxies, I. Study of blow-out by
  analytical models
  Galactic winds are a common phenomenon in starburst galaxies in the local
universe as well as at higher redshifts. Their sources are superbubbles driven
by sequential supernova explosions in star forming regions, which carve out
large holes in the interstellar medium and eject hot, metal enriched gas into
the halo and to the galactic neighborhood. We investigate the evolution of
superbubbles in exponentially stratified disks. We present advanced analytical
models for the expansion of such bubbles and calculate their evolution in space
and time. With these models one can derive the energy input that is needed for
blow-out of superbubbles into the halo and derive the break-up of the shell,
since Rayleigh-Taylor instabilities develop soon after a bubble starts to
accelerate into the halo. The approximation of Kompaneets is modified in order
to calculate velocity and acceleration of a bubble analytically. Our new model
differs from earlier ones, because it presents for the first time an analytical
calculation for the expansion of superbubbles in an exponential density
distribution driven by a time-dependent energy input rate. The time-sequence of
supernova explosions of OB-stars is modeled using their main sequence lifetime
and an initial mass function. We calculate the morphology and kinematics of
superbubbles powered by three different kinds of energy input and we derive the
energy input required for blow-out as a function of the density and the scale
height of the ambient interstellar medium. The Rayleigh-Taylor instability
timescale in the shell is calculated in order to estimate when the shell starts
to fragment and finally breaks up. Analytical models are a very efficient tool
for comparison to observations, like e.g. the Local Bubble and the W4 bubble
discussed in this paper, and also give insight into the dynamics of superbubble
evolution.
