The Rise and Fall of Type Ia Supernova Light Curves in the SDSS-II
  Supernova Survey
  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.
