In our survey, we have found no true analogs of Car.
This implies that the rate of Great Eruption-like
events is of order
(
)
of the ccSN rate, which is roughly consistent with each
star undergoing 1 or 2 such outbursts in its lifetime. This is scaled by
an estimated detection period of order
years.
We do identify a significant population of lower luminosity dusty stars that
that are likely similar to IRC
.
Stars enter this phase at the rate
(
) compared to the ccSN rate and for a
detection period of
years. Here the
detection period is assumed longer because the expansion velocities
are likely slower. This rate is comparable to
having all stars with
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 -
.
The median mass loss in Figure9 is
and
if every star underwent two eruptions, the typical total would
be
. Clearly there are some examples that
require significantly larger
, 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 (
not
).
For the stars similar to IRC10420, this is consistent with the
picture that the photospheres of blue-ward evolving Red Super Giants (RSGs) with
and
-
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
,
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
and has lost all but
(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
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
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
Car or other still older LBVs surrounded by massive dusty
shells. If there indeed are two mass loss mechanisms -- one commencing
years from core-collapse and the other occurring in
the
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
such stars, one should be
exploding as a ccSN every
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 Car analogs this is probably
feasible to distance of
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 (
Mpc). Larger galaxy
samples are needed not only to increase the sample of dusty luminous
stars (and hopefully find a true
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
(
) in our sample more than by the number of dusty stars (
) 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
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.