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Statistical Connections Between the Properties of Type Ia Supernovae and the B--V Colors of Their Parent Galaxies, and the Value of H$_0$

Statistical connections between the properties of Type Ia supernovae (SNe Ia) and the B--V colors of their parent galaxies are established. Compared to SNe Ia in blue galaxies [B-V$\la$0.75], SNe Ia in redder galaxies have (1) a wider dispersion in the blueshifts of their Si II $λ$6355 absorption features, ten days after maximum light; (2) more rapidly declining light curves; and (3) lower luminosities. Even when the spectroscopically peculiar, very subluminous SNe Ia such as SN 1991bg are disregarded, SNe Ia in red galaxies are less luminous than those in blue galaxies by about 0.3 magnitudes. When SNe Ia that are thought to have been significantly extinguished by dust in their parent galaxies are disregarded, those in blue galaxies have observational absolute--magnitude dispersions of only $σ_{obs}(M_B)$=0.20 and $σ_{obs}(M_V)$=0.17, which implies that their intrinsic absolute--magnitude dispersions are very small. We use six SNe Ia whose absolute magnitudes have been calibrated by means of Cepheids, which also indicate that the intrinsic absolute--magnitude dispersions of SNe Ia in blue galaxies are very small, to calibrate SNe Ia in blue galaxies and obtain $\rm H_0=57\pm4\ km\ s^{-1}\ Mpc^{-1}$. This value is in excellent agreement with that obtained by Saha et al. (1995b), in spite of the fact that they do not take into account any dependence of SN Ia absolute magnitude on the nature of the parent galaxy. Some implications of the statistical connections between SNe Ia and the colors of their parent galaxies, for identifying the progenitor binary systems of SNe Ia and for using high--redshift SNe Ia to measure q$_0$, are briefly discussed.