Type-Ia Supernova Rates and the Progenitor Problem: A Review

The identity of the progenitor systems of type-Ia supernovae (SNe Ia) is a major unsolved problem in astrophysics. SN Ia rates are providing some striking clues. We review the basics of SN rate measurement, preach about some sins of SN rate measurement and analysis, and illustrate one of these sins with an analogy about Martian scientists. We review the recent progress in measuring SN Ia rates in various environments and redshifts, and their use to reconstruct the SN Ia delay-time distribution (DTD) - the SN rate versus time that would follow a hypothetical brief burst of star formation. A good number of DTD measurements, using a variety of methods, appear to be converging. At delays 1 < t < 10 Gyr, these measurements show a similar, similar to t(-1), power-law shape. The DTD peaks at the shortest delays probed. This result supports the idea of a double-degenerate progenitor origin for SNe Ia. Single-degenerate progenitors may still play a role in producing short-delay SNe Ia, or perhaps all SNe Ia, if the red-giant donor channel is more efficient than is found by most theoretical models. The DTD normalization enjoys fairly good agreement (though perhaps some tension), among the various measurements, with a Hubble time-integrated DTD value of about 2 +/- 1 SNe Ia per 1000 M-circle dot (stellar mass formed with a low-mass turnover initial mass function). The local WD binary population suggests that the WD merger rate can explain the Galactic SN Ia rate, but only if sub-Chandra mergers lead to SN Ia events. We point to some future directions that should lead to progress in the field, including measurement of the bivariate (delay and stretch) SN Ia response function.