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srodney filled in discussion of RN and LBV physics
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most consistent with RNe and LBVs. Let us now consider
the astrophysical implications of these two possible classifications.
\subsection{Physical Implications of the RN Model}
The physical limits of the RN model are best evaluated by combining
the two key observables of recurrence period and peak brightness. In
this examination we rely on a pair of papers that evaluated an
...
\citet{Yaron:2005} suggest that such systems should have a very low
peak amplitude (barely consistent with the lower limit for \spock) and
a low peak luminosity ($\sim$100 times less luminous than the \spock
events).
Thus, if The closest analog for the \spock events from the population of known
RN systems is the nova M31N\,2008a-12. \citet{Kato:2015} provided a
theoretical model that can account for the key observational
characteristics of this remarkable nova: the very rapid recurrence
timescale ($<$1 yr), fast optical light curve ($\t2\sim2$ days), and
short supersoft x-ray phase \citep[6-18 days after optical
outburst][]{Henze:2015a}. To match these observations,
\citeauthor{Kato:2015} invoke a 1.38 \Msun white dwarf primary,
drawing mass from a companion at a rate of $1.6\times10^{-7}$ \Msun
yr$^{-1}$. This is largely consistent with the theoretical
expectations derived by \citet{Yaron:2005}, and reinforces the
conclusion that a combination of a high mass white dwarf and efficient
mass transfer are the key ingredients for rapid recurrence and short
light curves. The one feature that can not be effectively explained
with this scenario is the peculiarly high luminosity of the \spock
events -- even after accounting for the very large uncertainties. If
the \spock transients are
in fact two outbursts
from caused by a single RN system, then that
progenitor system would be the most extreme WD binary yet known.
\subsection{Physical Implications of the LBV Model}
For the LBV scenario, the observed \spock events would also stand out
as quite extreme. The observed rise and decline times for \spock
...
of energy. This approach assumes that the energy released in an LBV
eruption is generated slowly in the stellar interior and is in some
way ``bottled up'' by the stellar envelope over months or years,
before being released in a rapid mass ejection. The ``build-up''
timescale to match the radiative energy release is then
\begin{equation}
\label{eqn:trad}
...
reasonable quiescent luminosity value for the massive ($M>10\Msun$)
progenitor stars expected for LBVs.
Although the above discussion shows that the observations of the
\spock transients are largely consistent with the observed
characteristics of known LBV systems, this does not mean that we have
a viable physical model to explain these events. Rapid transient
episodes in LBVs such as SN 2002kg and SN 2009ip may best be explained
by a sudden ejection of an optically thick shell
\citep[e.g.]{Smith:2010,Smith:2011b}, or by some form of S Dor-type
variability \citep{Weis:2005,VanDyk:2006,Foley:2011}, which may be
driven by stellar pulsation rather than mass ejection
\citep{VanGenderen:1997,VanGenderen:2001}.
For massive stars such as \etacar at its great eruption and the
rapidly varying SN 2009ip, the effective photospheric radius during
eruption must have been comparable to the orbit of Saturn
\citep[$10^{14}$ cm][]{Davidson:1997,Smith:2011,Foley:2011}. With
observed photospheric velocities of order 500 km s$^{-1}$ for such
events, the dynamical timescale is on the order of tens to hundreds of
days. The very rapid light curves of both \spock events will add to
the already challenging task of developing a coherent theoretical
explanation for the physical mechanisms that drive the great eruptions
and the S Dor-type variation of LBVs.
%To examine the temperature and total energy output, we first make a
%set of (admittedly unfounded) assumptions: (1) the two outbursts had a
%very similar SED; (2) the last observed epoch for each event