Type Ia Supernova Colors and Ejecta Velocities: Hierarchical Bayesian
  Regression with Non-Gaussian Distributions
  We investigate the statistical dependence of the peak intrinsic colors of
Type Ia supernovae (SN Ia) on their expansion velocities at maximum light,
measured from the Si II 6355 spectral feature. We construct a new hierarchical
Bayesian regression model, accounting for the random effects of intrinsic
scatter, measurement error, and reddening by host galaxy dust, and implement a
Gibbs sampler and deviance information criteria to estimate the correlation.
The method is applied to the apparent colors from BVRI light curves and Si II
velocity data for 79 nearby SNe Ia. The apparent color distributions of high
(HV) and normal velocity (NV) supernovae exhibit significant discrepancies for
B-V and B-R, but not other colors. Hence, they are likely due to intrinsic
color differences originating in the B-band, rather than dust reddening. The
mean intrinsic B-V and B-R color differences between HV and NV groups are 0.06
+/- 0.02 and 0.09 +/- 0.02 mag, respectively. A linear model finds significant
slopes of -0.021 +/- 0.006 and -0.030 +/- 0.009 mag/(1000 km/s) for intrinsic
B-V and B-R colors versus velocity, respectively. Since the ejecta velocity
distribution is skewed towards high velocities, these effects imply
non-Gaussian intrinsic color distributions with skewness up to +0.3. Accounting
for the intrinsic color-velocity correlation results in corrections to A_V
extinction estimates as large as -0.12 mag for HV SNe Ia and +0.06 mag for NV
events. Velocity measurements from SN Ia spectra have potential to diminish
systematic errors from the confounding of intrinsic colors and dust reddening
affecting supernova distances.
