  The spectrum of radiation emitted following shock breakout from a star's
surface with a power-law density profile $\rho \propto x^n$ is investigated.
Assuming planar geometry, local Compton equilibrium and bremsstrahlung emission
as the dominant photon production mechanism, numerical solutions are obtained
for the photon number density and temperature profiles as a function of time,
for hydrogen-helium envelopes. The temperature solutions are determined by the
breakout shock velocity $v_0$ and the pre-shock breakout density $\rho_0$, and
depend weakly on the value of n. Fitting formulas for the peak surface
temperature at breakout as a function of $v_0$ and $\rho_0$ are provided, with
$T_{peak}\approx 9.44\exp{[12.63(v_0/c)^{1/2}]}$ eV, and the time dependence of
the surface temperature is tabulated. The time integrated emitted spectrum is a
robust prediction of the model, determined by $\mathcal{T}_{\rm peak}$ and
$v_0$ alone and insensitive to details of light travel time or slight
deviations from spherical symmetry. Adopting commonly assumed progenitor
parameters, breakout luminosities of ~10^45 erg/s and ~10^44 erg/s in the
0.3-10 keV band are expected for BSG and RSG/He-WR progenitors respectively
(T_{peak} is well below the band for RSGs, unless their radius is ~10^13 cm).
>30 detections of SN1987A-like (BSG) breakouts are expected over the lifetime
of ROSAT and XMM-Newton. An absence of such detections would imply that either
the typical parameters assumed for BSG progenitors are grossly incorrect or
that their envelopes are not hydrostatic. The observed spectrum and duration of
XRF 080109/SN2008D are in tension with a non-relativistic breakout from a
stellar surface interpretation.
