An Empirical Fitting Method to Type Ia Supernova Light Curves. III. A Three-parameter Relationship: Peak Magnitude, Rise Time, and Photospheric Velocity

We examine the relationship between three parameters of Type Ia supernovae (SNe Ia): peak magnitude, rise time, and photospheric velocity at the time of peak brightness. The peak magnitude is corrected for extinction using an estimate determined from MLCS2k2 fitting. The rise time is measured from the well-observed B-band light curve with the first detection at least 1 mag fainter than the peak magnitude, and the photospheric velocity is measured from the strong absorption feature of Si ii λ6355 at the time of peak brightness. We model the relationship among these three parameters using an expanding fireball with two assumptions: (a) the optical emission is approximately that of a blackbody, and (b) the photospheric temperatures of all SNe Ia are the same at the time of peak brightness. We compare the precision of the distance residuals inferred using this physically motivated model against those from the empirical Phillips relation and the MLCS2k2 method for 47 low-redshift SNe Ia (0.005 < z < 0.04) and find comparable scatter. However, SNe Ia in our sample with higher velocities are inferred to be intrinsically fainter. Eliminating the high-velocity SNe and applying a more stringent extinction cut to obtain a "low-v golden sample" of 22 SNe, we obtain significantly reduced scatter of 0.108 ±0.018 mag in the new relation, better than those of the Phillips relation and the MLCS2k2 method. For 250 km s^-1 of residual peculiar motions, we find 68% and 95% upper limits on the intrinsic scatter of 0.07 and 0.10 mag, respectively.