  The first light from a supernova (SN) emerges once the SN shock breaks out of
the stellar surface. The first light, typically a UV or X-ray flash, is
followed by a broken power-law decay of the luminosity generated by radiation
that leaks out of the expanding gas sphere. Motivated by recent detection of
emission from very early stages of several SNe, we revisit the theory of shock
breakout and the following emission. We derive analytic light curves, paying
special attention to the photon-gas coupling and deviations from thermal
equilibrium. We then consider the breakout from several SNe progenitors. We
find that for more compact progenitors, white dwarfs, Wolf-Rayet stars (WRs)
and possibly more energetic blue-supergiant explosions, the observed radiation
is out of thermal equilibrium at the breakout, during the planar phase (i.e.,
before the expanding gas doubles its radius), and during the early spherical
phase. Therefore, during these phases we predict significantly higher
temperatures than previous analysis that assumed equilibrium. When thermal
equilibrium prevails, we find the location of the thermalization depth and its
temporal evolution. Our results are useful for interpretation of early SN light
curves. Some examples are: (i) Red supergiant SNe have an early bright peak in
optical and UV flux, less than an hour after breakout. It is followed by a
minimum at the end of the planar phase (about 10 hr), before it peaks again
once the temperature drops to the observed frequency range. In contrast WRs
show only the latter peak in optical and UV. (ii) Bright X-ray flares are
expected from all core-collapse SNe types. (iii) The light curve and spectrum
of the initial breakout pulse holds information on the explosion geometry and
progenitor wind opacity. Its spectrum in compact progenitors shows a
(non-thermal) power-law.
