Single or Double Degenerate Progenitors? Searching for Shock Emission in
  the SDSS-II Type Ia Supernovae
  From the set of nearly 500 spectroscopically confirmed type~Ia supernovae and
around 10,000 unconfirmed candidates from SDSS-II, we select a subset of 108
confirmed SNe Ia with well-observed early-time light curves to search for
signatures from shock interaction of the supernova with a companion star. No
evidence for shock emission is seen; however, the cadence and photometric noise
could hide a weak shock signal. We simulate shocked light curves using SN Ia
templates and a simple, Gaussian shock model to emulate the noise properties of
the SDSS-II sample and estimate the detectability of the shock interaction
signal as a function of shock amplitude, shock width, and shock fraction. We
find no direct evidence for shock interaction in the rest-frame $B$-band, but
place an upper limit on the shock amplitude at 9% of supernova peak flux ($M_B
> -16.6$ mag). If the single degenerate channel dominates type~Ia progenitors,
this result constrains the companion stars to be less than about 6 $M_{\odot}$
on the main sequence, and strongly disfavors red giant companions.
