It is immediately obvious from Figure9 that none of the sources we identified closely
resemble Car. Their typical luminosities of
correspond
to
stars
(Maeder & Meynet1988; Maeder & Meynet1987; Meynet et al.1994; Maeder1981; Stothers & Chin1996)
rather than the higher masses usually associated with
LBV outbursts. Since we identify a significant population of fainter stars, this is
unlikely to be a selection effect, and we conclude that these galaxies contain no analogs
of
Car.
There are two ways we can interpret the result. First, we
can ignore the existence of Car, and set
. Alternatively, we can
acknowledge the existence of
Car, in which case
, since
Car
passes our selection criterion and mid-IR surveys of our Galaxy for objects as luminous
as
Car are probably complete.
For the first case, the 90% confidence upper limit is
where the period over which such
systems can be detected is scaled to
years.
For the second case, where we include
Car, we find that
with
at 90% confidence.
In either case, the rate of transients comparable to
Car is a small
fraction of the supernova rate.
Stars as massive as Car are also rare, representing only
to
of all massive stars for a mass range from
/
to
. If every sufficiently massive star had one eruption, the
results including
Car correspond to a minimum mass of
(
). If every star has an
average of two eruptions, the mass limits rise to
(
). Similarly the upper limit from
ignoring the existence of
Car corresponds to
for an average of one eruption or
for an average
of two. Kochanek (2011) estimated that the abundance of lower optical
depth shells found at
m around massive stars in the Galaxy was
roughly consistent with all stars more massive than
having an average of two eruptions, corresponding to
,
which is consistent with the present results, but close to the upper limits.