We study the conditions for disk galaxies to produce superbubbles that can break out of the disk and produce a galactic wind .
We argue that the threshold surface density of supernovae rate for seeding a wind depends on the ability of superbubble energetics to compensate for radiative cooling .
We first adapt Kompaneets formalism for expanding bubbles in a stratified medium to the case of continuous energy injection and include the effects of radiative cooling in the shell .
With the help of hydrodynamic simulations , we then study the evolution of superbubbles evolving in stratified disks with typical disk parameters .
We identify two crucial energy injection rates that differ in their effects , the corresponding breakout ranging from being gentle to a vigorous one .
( a ) Superbubbles that break out of the disk with a Mach number of order 2 \hbox { - - } 3 correspond to an energy injection rate of order 10 ^ { -4 } erg cm ^ { -2 } s ^ { -1 } , which is relevant for disk galaxies with synchrotron emitting gas in the extra-planar regions .
( b ) A larger energy injection threshold , of order 10 ^ { -3 } erg cm ^ { -2 } s ^ { -1 } , or equivalently , a star formation surface density of \sim 0.1 M _ { \odot } yr ^ { -1 } kpc ^ { -2 } , corresponds to superbubbles with a Mach number \sim 5 \hbox { - - } 10 .
While the milder superbubbles can be produced by large OB associations , the latter kind requires super-starclusters .
These derived conditions compare well with observations of disk galaxies with winds and the existence of multiphase halo gas .
Furthermore , we find that contrary to the general belief that superbubbles fragment through Rayleigh-Taylor ( RT ) instability when they reach a vertical height of order the scale height , the superbubbles are first affected by thermal instability for typical disk parameters and that RT instability takes over when the shells reach a distance of approximately twice the scale height .