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We examine the relationship between three parameters of Type Ia supernovae(SNe~Ia): peak magnitude, rise time, and photospheric velocity at the time ofpeak brightness. The peak magnitude is corrected for extinction using anestimate determined from MLCS2k2 fitting. The rise time is measured from thewell-observed $B$-band light curve with the first detection at least 1~magfainter than the peak magnitude, and the photospheric velocity is measured fromthe strong absorption feature of Si~II~$\lambda$6355 at the time of peakbrightness. We model the relationship among these three parameters using anexpanding fireball with two assumptions: (a) the optical emission isapproximately that of a blackbody, and (b) the photospheric temperatures ofSNe~Ia are similar to each other at the time of peak brightness. We compare theprecision of the distance residuals inferred using this physically motivatedmodel against those from the empirical Phillips relation and the MLCS2k2 methodfor 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 beintrinsically fainter. Eliminating the high-velocity SNe and applying a morestringent extinction cut to obtain a "low-v-golden sample" of 22 SNe, we obtainsignificantly reduced scatter in the new relation, better than those of thePhillips relation and the MLCS2k2 method. After removing model peculiarvelocities, our final scatter for the new relation is $0.108 \pm 0.018$~mag.

astrophysical journal/the astrophysical journal

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