We will carry out the detailed consideration of the candidates in PaperII,
but suppose we scale conclusions about the rates to ,
which would also correspond to the 95% confidence upper limit
we would use for estimating rate limits if we were to eliminate
all the remaining candidates. This implies that we are
probing eruption rates of order
Alternatively, we could estimate the expected number of candidates from ccSN rate and the statistics of Galactic shells as discussed in Section4. For the galaxies in our pilot study, we have two rather inconsistent estimates of the ccSN rate. Empirically, there were three ccSN over the last 20 years, which implies a rate of year ( year, at 90% confidence). On the other hand, the integrated star formation rate of the targeted galaxies implies a massive star formation rate, which is equivalent to the ccSN rate, of roughly year. year implies that the expected number of candidates in the targeted galaxies should be ( for and years) with a chance of finding at least 1. On the other hand, year reduces the probability to only about 40% and implies that we need to study galaxies with an integrated star formation rate of 20year (10 times greater than what we have now) to have a chance of finding at least 1 massive dust obscured star.
In either case, our survey can be easily expanded to at least 10 times as many galaxies (and integrated star formation rate) simply using archival data from the SINGS, LVL, and surveys, which then probes rates far below those necessary to explain the Galactic sources. In such an expanded survey, additional means of suppressing contamination are important. The simplest method is to use the time variability of the mid-IR emission, since expanding shells of ejecta will also show a well defined pattern of fading (see Kochanek et al.2012a) in the warm Spitzer bands (3.6 and 4.5) and new Spitzer observations would provide a time baseline of 5-10 years to search for such changes. Since the principle background in our present survey appears to be extragalactic, time variability is a powerful means of suppressing it. Galaxies are not variable, and the mid-IR variability of quasars is both relatively weak and stochastic, with a structure function of roughly mag (Kozowski et al.2010). Two epochs separated by 6-12 months would further help to separate source classes by constraining variability on shorter time scales.
We thank John Beacom for numerous helpful disucssions, and Jose Prieto, Todd Thompson, Shunsaku Horiuchi and Joe Antognini for helpful comments. We extend our gratitude to the SINGS Legacy Survey and LVL Survey for making their data publicly available. This research has made use of NED, which is operated by the JPL and Caltech, under contract with NASA and the HEASARC Online Service, provided by NASA's GSFC. RK and KZS are supported in part by NSF grant AST-1108687. KZS and CSK are supported in part by NSF grant AST-0908816.Rubab Khan 2012-10-28