Conclusions

In our survey, we have found no true analogs of $\eta$Car. This implies that the rate of Great Eruption-like events is of order $F_e = 0.046 t_{d200}^{-1}$ ( $0.0083 < F_e t_{d200} < 0.19$) of the ccSN rate, which is roughly consistent with each $M \gtrsim 70M_\odot$ star undergoing 1 or 2 such outbursts in its lifetime. This is scaled by an estimated detection period of order $t_d = 200 t_{d200}$years. We do identify a significant population of lower luminosity dusty stars that that are likely similar to IRC$+10420$. Stars enter this phase at the rate $F_e = 0.20 t_{d500}^{-1}$ ( $0.086 < F_e t_{d500} < 0.55$) compared to the ccSN rate and for a detection period of $t_d = 500 t_{d500}$years. Here the detection period is assumed longer because the expansion velocities are likely slower. This rate is comparable to having all stars with $25 < M < 60M_\odot$ undergoing such a phase once or twice.

If the estimated detection periods and mass ranges are roughly correct, and our completeness is relatively high, there are two interesting implications for both populations. First, these high optical depth phases represent a negligible fraction of the post-main sequence lifetimes of these stars, at most lasting a few thousand years. This implies that these events have to be associated with special periods in the evolution of the stars. The number of such events a star experiences is also small, one or two, not ten or twenty. Second, while a significant amount of mass is lost in the eruptions, they cannot be a dominant contribution to mass loss. For these high mass stars, standard models (e.g., Maeder & Meynet1988; Maeder & Meynet1987; Meynet et al.1994; Maeder1981; Stothers & Chin1996) typically strip the stars of their hydrogen envelopes and beyond, implying total mass losses of all but the last $5$-$10M_\odot$. The median mass loss in Figure9 is $M_e \sim 0.5 M_\odot$ and if every star underwent two eruptions, the typical total would be $N_e M_e \sim M_\odot$. Clearly there are some examples that require significantly larger $M_e$, but we simply do not find enough heavily obscured stars for this phase to represent more than a modest fraction of the total mass loss ($\sim 10\%$ not $\sim 50\%$).

For the stars similar to IRC$+$10420, this is consistent with the picture that the photospheres of blue-ward evolving Red Super Giants (RSGs) with $\log(L_*/L_\odot)= 5.6\sim6.0$ and $T_{star} \simeq 7000$-$12500$ K, become moderately unstable, leading to periods of lower effective temperature and enhanced mass loss as the stars try to evolve into a ``prohibited'' region of the HR diagram that de Jager & Nieuwenhuijzen (1997), de Jager (1998) and Nieuwenhuijzen & de Jager (2000) termed the ``yellow void''. In this phase, the stars lose enough mass to evolve into a hotter, less massive star on the blue side of the HR diagram. This is also the luminosity regime of the ``bistability jump'' in wind speeds driven by opacity changes which Smith et al. (2004) hypothesizes can explain the absence of LBVs and the existence of YHGs with high mass loss rates and dust formation (Vink et al. 2009) in this luminosity range. In fact, Humphreys et al. (2002) propose that IRC$+10420$, which is identified by our selection criterion, is such a star. While these arguments supply a unique, short-lived evolutionary phase, there may be problems with the absolute scale of the mass loss, since estimates are that IRC$+$10420 started with a mass of $\sim 40M_\odot$ and has lost all but $6\sim15 M_\odot$ (Nieuwenhuijzen & de Jager2000).

The only other similarly unique phase in the lives of these stars is the final post-carbon ignition phase. There are now many examples of stars which have had outbursts shortly before exploding as supernovae (e.g., Pastorello et al.2013; Mauerhan et al.2013; Ofek et al.2013; Pastorello et al.2007; Prieto et al.2013) and superluminous supernovae that are most easily explained by surrounding the star with a large amount of previously ejected mass (Kozlowski et al.2010; Smith et al.2008; Ofek et al.2013; Gal-Yam et al.2007; Smith & McCray2007). Powering these supernovae requires mass ejected in the last years to decades of the stellar life (e.g., Chugai & Danziger2003; Moriya et al.2014; Smith2009; Chevalier & Fransson1994). and it seems natural to associate these events with the mass ejections of LBVs like $\eta$Car (e.g., Gal-Yam & Leonard2009; Smith & McCray2007). The statistical properties and masses of either of the classes of dusty stars we discuss are well-matched to the statistical requirements for explaining these interaction powered supernovae if the instability is associated with the onset of carbon burning (see Kochanek2011). If there is only one eruption mechanism, it must be associated with a relatively long period like carbon burning (thousands of years) rather than the shorter, later nuclear burning phases, because we observe many systems like $\eta$Car that have survived far longer than these final phases last. If the mechanism for producing the ejecta around the superluminous supernovae is associated with nuclear burning phases beyond carbon, then we must have second eruption mechanism to explain $\eta$Car or other still older LBVs surrounded by massive dusty shells. If there indeed are two mass loss mechanisms -- one commencing $\gtrsim 10^3$years from core-collapse and the other occurring in the $\sim 1$year prior to core-collapse -- then the self-obscured stars identified in this work may very well be experiencing the earlier of these two mechanisms. Otherwise, in a larger sample to $\sim100$ such stars, one should be exploding as a ccSN every $\sim10$ years.

The dusty stars can be further characterized by their variability, which will help to follow the evolution of the dust. For the optically brighter examples, it may be possible to spectroscopically determine the stellar temperatures, although detailed study may only become possible with the James Webb Space Telescope (JWST). It is relatively easy to expand our survey to additional galaxies. For very luminous sources like $\eta$Car analogs this is probably feasible to distance of $10$Mpc, while for the lower luminosity IRC$+$10420 analogs this is likely only feasible at the distances of the most distant galaxies in our sample ($\sim4$Mpc). Larger galaxy samples are needed not only to increase the sample of dusty luminous stars (and hopefully find a true $\eta$ Car analog!), but also to have a sample with a larger number of supernovae, or equivalently a higher star formation rate. Our estimate of the abundance of IRC$+$10420 analogs is limited by the small number of ccSN ($3$) in our sample more than by the number of dusty stars ($18$) identified. Finally, while we have shown that surveys for the stars are feasible using archival Spitzer data, JWST will be a far more powerful probe of these stars. The HST-like resolution (Gardner et al.2006) will be enormously useful to either greatly reduce the problem of confusion or to greatly expand the survey volume. Far more important will be the ability to carry out the survey at $24\mu$m, which will increase the time over which dusty shells can be identified from hundreds of years to thousands of years, greatly improving the statistics and our ability to survey the long term evolution of these systems and the relationship between stellar eruptions and supernovae.

We thank Hendrik Linz for helping us analyze the Herschel PACS data and John Beacom for numerous productive discussions. We extend our gratitude to the SINGS Legacy Survey and LVL Survey for making their data publicly available. This research has made use of observations made with the NASA/ESA Hubble Space Telescope, and obtained from the Hubble Legacy Archive, which is a collaboration between the Space Telescope Science Institute (STScI/NASA), the Space Telescope European Coordinating Facility (ST-ECF/ESA) and the Canadian Astronomy Data Centre (CADC/NRC/CSA). RK and KZS are supported in part by NSF grant AST-1108687.