Conclusions

This work empirically demonstrates that true analogs of $\eta$Car -- massive stars that have undergone eruptive mass ejection in the recent past (centuries) -- are rare. Based on the discussion in Section4, our survey can detect close analogs of $\eta$ Car for roughly $t_d \simeq 200$ years, consistent with $\eta$Car meeting our selection criteria. The statistics of our present sample gives us a maximum of $N_{cand}=6 \pm 6$ candidate systems after correcting for the estimated extragalactic contamination. Aside from the three very compact, luminous star clusters, the candidates generally do not have SEDs that closely resemble the SED of $\eta$Car. Although we keep those three compact clusters in our candidate list for now, it is highly unlikely that they could hide luminous dusty stars similar to $\eta$Car. We anticipate that further analysis and follow-up observations, using HST astrometry and photometry, ground based spectroscopy and Herschel 70$\micron$ photometry, will show that most, if not all, of the remaining candidates are either non-stellar or are not truly analogous to $\eta$Car. Of the true stellar systems, they are clearly going to be a mixture of ``eruptions'' such as $\eta$Car and sources with longer lived, relatively steady dusty winds such as ObjectX.

We will carry out the detailed consideration of the candidates in PaperII, but suppose we scale conclusions about the rates to $N_{cand}=3$, 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

$$R_{erupt} = \frac{N_{cand}}{t_d} = 0.015 \left( \frac{N_{can... ...t) \left( \frac{200~\hbox{year}}{t_d} \right)~\hbox{year}^{-1}$$ (9)

for this sample of galaxies (roughly 1 per 200 years per galaxy), and fractional rates compared to the ccSN rate of order

$$f_\eta = 0.15 \left( \frac{N_{cand}}{3} \right) \left( \frac... ..._d} \right) \left( \frac{0.1~\hbox{year}^{-1}}{R_{SN}} \right)$$ (10)

that are in the appropriate regime. In fact, it seems likely that we should not find $N_{cand}=0$ at the end of PaperII, and in some senses we already have that $N_{cand}\gtrsim1$ since our present sample contains ObjectX.

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 $R_{SN}=0.15$year$^{-1}$ ( $0.05 < R_{SN} < 0.35$year$^{-1}$, 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 $R_{SN}=0.014$year$^{-1}$. $R_{SN}=0.15$year$^{-1}$ implies that the expected number of candidates in the targeted galaxies should be $\simeq6$ ( $R_{SN} \times f_\eta \times t_d$ for $f_\eta \gtrsim 0.2$ and $t_d=200$years) with a $>3\sigma$ chance of finding at least 1. On the other hand, $R_{SN}=0.014$year$^{-1}$ reduces the probability to only about 40% and implies that we need to study galaxies with an integrated star formation rate of 20$M_\odot$year$^{-1}$ (10 times greater than what we have now) to have a $>3\sigma$ 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 $S^4G$ 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$\micron$) 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 $0.1(t/4~\hbox{year})^{1/2}$ 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.