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.
We analyze the rise and fall times of type Ia supernova (SN Ia) light curves discovered by the SDSS-II Supernova Survey. From a set of 391 light curves k-corrected to the rest frame B and V bands, we find a smaller dispersion in the rising portion of
the light curve compared to the decline. This is in qualitative agreement with computer models which predict that variations in radioactive nickel yield have less impact on the rise than on the spread of the decline rates. The differences we find in the rise and fall properties suggest that a single stretch correction to the light curve phase does not properly model the range of SN Ia light curve shapes. We select a subset of 105 light curves well-observed in both rise and fall portions of the light curves and develop a 2-stretch fit algorithm which estimates the rise and fall times independently. We find the average time from explosion to B-band peak brightness is 17.38 +/- 0.17 days. Our average rise time is shorter than the 19.5 days found in previous studies; this reflects both the different light curve template used and the application of the 2-stretch algorithm. We find that slow declining events tend to have fast rise times, but that the distribution of rise minus fall time is broad and single-peaked. This distribution is in contrast to the bimodality in this parameter that was first suggested by Strovink (2007) from an analysis of a small set of local SNe Ia. We divide the SDSS-II sample in half based on the rise minus fall value, tr-tf <= 2 days and tr-tf>2 days, to search for differences in their host galaxy properties and Hubble residuals; we find no difference in host galaxy properties or Hubble residuals in our sample.
