deletions | additions
diff --git a/AstrophysicalModels.tex b/AstrophysicalModels.tex
index 369ed65..a27938d 100644
--- a/AstrophysicalModels.tex
+++ b/AstrophysicalModels.tex
...
\subsection{Microlensing}
In
a strong-lensing regime the presence of strong gravitational lensing it is possible to
generate a transient event from lensing effects alone
(Scenario~\ref{case:microlensing}). In this case the background
source has a steady luminosity but the relative motion of the source,
lens lens, and observer causes the magnification of that source to change
rapidly with time.
A commonly observed example is the microlensing of a background quasar
by a galaxy-scale lens \citep{Wambsganss:2001, Kochanek:2004}. In
...
duration and did not exhibit the repeated ``flickering'' variation
that would be expected from optically thick microlensing.
A second possibility is through an isolated
transient strong lensing
event, event with
a rapid timescale, such as a background star crossing over a lensing
critical curve. This corresponds to the optically thin microlensing
regime, and is similar to the ``local'' microlensing light curves
observed when stars within our galaxy or neighboring dwarf galaxies
pass behind a massive compact halo object \citep{Paczynski:1986,
Alcock:1993, Aubourg:1993, Udalski:1993}. In the case of a star
crossing the caustic of a smooth lensing potential, the amplification
of the source flux would rise (fall) with a characteristic $t^{-1/2}$
profile, and would exhibit a very sharp decline (increase) on the
other side of the caustic \citep{Schneider:1986,MiraldaEscude:1991}.
With a more complex lens comprising many compact objects, the light
curve would exhibit a superposition of many such sharp peaks
\citep{Lewis:1993}.
To generate an isolated microlensing event, the background source
would have to be the dominant source of luminosity in its environment,
...
transverse velocity would be on the order of a few 100 km/s, which is
comparable to the orbital velocity of stars within a galaxy or
galaxies within a cluster. \citet{MiraldaEscude:1991} showed
that---in the case of a smooth cluster potential---the
timescale
$\tau$ %timescale
%$\tau$ for the light curve of such a caustic crossing event is
dictated %dictated by the radius of the source, $R$, and the net transverse
velocity, %velocity, $v$, of the source across the caustic, as:
\begin{equation} %
%\begin{equation}
% \tau = 6\frac{R}{5\,\Rsun}\frac{300 {\rm km~ s}^{-1}}{v}~\rm{hr}
\label{eqn:caustic_crossing_time}
\end{equation}
\noindent %\label{eqn:caustic_crossing_time}
%\end{equation}
%
%
%\noindent Thus, the
characteristic timescale of such an event would be on the order of
hours or days, which is in the vicinity of the timescales observed for
the \spock events. However, this scenario could not plausibly
generate two events with similar decay timescales at distinct
locations on the sky.
To invoke This is because a
caustic crossing for
\spockone, caustic-crossing transient
event must necessarily appear at the location of the lensing critical
curve would have to be coincident with
the \spockone position, curve, but in
which this case the
critical curve most likely passes between
the two \spock locations. At best, a caustic
crossing could
not also
intersect account
for only one of the
\spocktwo location. \spock events, not both.
\subsection{Single Explosion, Time Delayed}
...
is problematic. All five lens models indicate that the locations of
the two events are within \TODO{How many arcsec? how many pc?}.
\TODO{Evaluate \TODO{Make a figure that plots the SED of this host galaxy
pixel by pixel to determine
whether at the
two
spock locations
and at the center of the host galaxy image 11.3.
Quantitatively assess the probability that the three SEDs are
consistent with being
at the same location on the source plane. }
Having two unrelated explosions occurring in the same
year within such a small physical area would be plausible if the
explosions were from a very common source, but the rapid light curve
already rules out all
normal of the common categories of supernova explosions.
Since we have not observed any similar fast transients in any other
galaxy throughout the Frontier Fields survey, to accept this scenario
we would have to conclude that the \spock host galaxy is a very
...
\TODO{Evaluate kilonova, .Ia and Fast Optical transient light curves
compared to the Spock light curves}
\TODO{Evaluate the likelihood of two rare explosions appearing in the
same lensed host galaxy, comparing to rates from PS1, etc.}
\subsection{Two Events from the Same Source}
An The final alternative is to allow two separate explosive events
powered by the same astrophysical source (Scenario
\ref{case:recurrent}). In this case the observed events must be
spatially coincident but not coincident in time, which is fully
consistent with all lens model constraints.
The two \spock events would each have been repeated
(either before or after we observed it) Any transient event that
appears at the
other position due to \spockone\ location must also appear at the
\spocktwo\ location, separated in time by a gravitational lensing time
delay.
This hypothesis Our lens models suggest that the time delay would be on the
order of 10--50 days, so this scenario supposes that those
``gravitational echoes'' were simply not observed, as they landed in
one of the long periods without
HST \HST observations on this field.
Adopting this hypothesis immediately rules out any catastrophic
explosive events---such as a supernova or neutron star merger---in
