Implications

The advantage of surveying external galaxies with a significant supernova rate is that we can translate our results into estimates of abundances and rates. We scale our rates using the observed supernova rate of year ( at 90% confidence). As we discussed in PaperI, this is significantly higher than standard star formation rate estimates for these galaxies, but the SN rate is directly proportional to the massive star formation rate rather than an indirect indicator, and similar discrepancies, although not as dramatic, have been noted in other contexts (e.g., Horiuchi et al.2011). In this section we first outline how we will estimate rates, and then we discuss the constraints on analogs of Car and the implications of our sample of luminous dusty stars.

We are comparing a sample of supernovae observed over years
to a sample of candidate stars which are detectable by our selection procedures
for a time . In PaperI we used DUSTY to model the detection of expanding
dusty shells and found that a good estimate for the detection time period was

(5) |

The transient rate in a sample of galaxies is less interesting than comparing the rate
to the supernova rate. Let be the fraction of massive (
) stars that
create the transients, where
if we
assume a Salpeter IMF (Kennicutt1998), that all stars more massive than become
supernovae and that all stars more massive than cause the transients.
If each star undergoes an average of eruptions, then the rate of transients is related
to the rate of supernovae by
. The
interesting quantity to constrain is rather than . Poisson
statistics provide constraints on the rates,
where
for events observed over a time
period . This means that the probability of the rates given the data is

(6) |

(7) |