  The dependence of the Type Ia supernova (SN Ia) rate on galaxy type is
examined for three currently proposed scenarios: merging of a
Chandrasekhar--mass CO white dwarf (WD) with a CO WD companion, explosion of a
sub--Chandrasekhar mass CO WD induced by accretion of material from a He star
companion, and explosion of a sub--Chandrasekhar CO WD in a symbiotic system.
The variation of the SNe Ia rate and explosion characteristics with time is
derived, and its correlation with parent population age and galaxy redshift is
discussed. Among current scenarios, CO + He star systems should be absent from
E galaxies. Explosion of CO WDs in symbiotic systems could account for the SNe
Ia rate in these galaxies. The same might be true for the CO + CO WD scenario,
depending on the value of the common envelope parameter. A testable prediction
of the sub--Chandrasekhar WD model is that the average brightness and kinetic
energy of the SN Ia events should increase with redshift for a given Hubble
type. Also for this scenario, going along the Hubble sequence from E to Sc
galaxies SNe Ia events should be brighter on average and should show larger
mean velocities of the ejecta. The observational correlations strongly suggest
that the characteristics of the SNe Ia explosion are linked to parent
population age. The scenario in which WDs with masses below the Chandrasekhar
mass explode appears the most promising one to explain the observed variation
of the SN Ia rate with galaxy type together with the luminosity--expansion
velocity trend.
