  Stars close to the Eddington luminosity can have large low-density inflated
envelopes. We show that the rise times of shock breakout signals from
supernovae can be extended significantly if supernova progenitors have an
inflated stellar envelope. If the shock breakout occurs in such inflated
envelopes, the shock breakout signals diffuse in them, and their rise time can
be significantly extended. Then, the rise times of the shock breakout signals
are dominated by the diffusion time in the inflated envelope rather than the
light-crossing time of the progenitors. We show that our inflated Wolf-Rayet
star models whose radii are of the order of the solar radius can have shock
breakout signals which are longer than ~100 sec. The existence of inflated
envelopes in Wolf-Rayet supernova progenitors may be related to the mysterious
long shock breakout signal observed in Type Ib SN 2008D. Extended shock
breakout signals may provide evidence for the existence of inflated stellar
envelopes and can be used to constrain the physical properties of these
enigmatic structures.

High Energy Astrophysical Phenomena;Solar and Stellar Astrophysics