  To date, the question of which progenitor channel can reproduce the observed
rate of Type Ia supernovae (SNe Ia) remains unresolved, with the single and
double degenerate scenarios remaining the leading contenders. The former
implies a large population of hot accreting white dwarfs with photospheric
temperatures of T ~ 10^5-10^6 K during some part of their accretion history. We
show that in early-type galaxies, a population of accreting white dwarfs large
enough to reproduce the SN Ia rate would contribute significantly to the
ionizing UV radiation expected from the stellar population. For mean stellar
ages < ~5 Gyr, single degenerate progenitors would dominate the ionizing
background produced by stars, increasing the continuum beyond the He
II-ionizing limit more than ten-fold. This opens a new avenue for constraining
the progenitors of SNe Ia, through consideration of the spatially extended
low-ionization emission-line regions now found in many early-type galaxies.
Modelling the expected emission, we show that one can constrain the
contribution of the single degenerate channel to the SN Ia rate in E/S0
galaxies from upper limits on the luminosity of He II recombination lines in
the optical and FUV. We discuss future directions, as well as possible
implications for the evolution of SNe Ia in old stellar populations.
