deletions | additions       diff --git a/MicroLensing.tex b/MicroLensing.tex  index 3a9c0ba..647520e 100644  --- a/MicroLensing.tex  +++ b/MicroLensing.tex 
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\subsection{Intracluster Light}\label{sec:ICL}  To estimate the mass of intracluster stars along the line of sight to  the \spock events, we follow the procedure of Kelly et al. (in prep)  and Morishita et al. (in prep). This entails fitting and removing the  surface brightness of individual galaxies in the field, then fitting a  smooth profile to the residual surface brightness of intracluster  light (ICL). The surface brightness is then converted to a projected  stellar mass surface density by assuming a Chabrier  \citeyear{Chabrier:2003} initial mass function and an exponentially  declining star formation history. For further details, see Kelly et  al. (in prep). This procedure leads to an estimate for the  intracluster stellar mass of  $\log (\Sigma_{\star} / (M_{\odot}\,{\rm kpc}^{-2})) = 6.9\pm0.4$.  This is very similar to the value of $6.8^{+0.4}_{-0.3}$ inferred for  the probable caustic crossing star {\it Icarus} (Kelly et al., in  prep).  \subsection{Expected Timescale for Microlensing Events}\label{sec:Microlensing}  A commonly observed example of microlensing-induced transient effects 
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velocity, the timescale $\tau$ is on the order of hours to days, which is well  matched to the observed rise and decline timescales of the \spock  events.  diff --git a/Results.tex b/Results.tex  index 79692b2..d3139ad 100644  --- a/Results.tex  +++ b/Results.tex 
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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}. The peculiar transient {\it Icarus}, observed in  another of behind  the Hubble Frontier Fields, Fields cluster MACS J1149.6+2223,  has been proposed as the first observed example of such a stellar caustic crossing event (P. Kelly et al., in prep). Kelly et al. find that such events may be  expected to appear more frequently in strongly lensed galaxies that  have small angular separation from the center of a massive cluster. In  such a situation, our line of sight to the lensed background galaxy  passes through a dense web of overlapping micro-lenses caused by the  intracluster stars distributed around the center of the cluster. This  has the effect of ``blurring'' the magnification profile across the  cluster critical curve, making it more likely that a single (and rare)  massive star in the background galaxy gets magnified by the required  factor of $\sim10^5$ to become visible as a transient caustic crossing  event. On this basis the \spock host galaxy images are suitably  positioned for caustic crossing transients, as they are seen through a  relatively high density of intracluster stars---comparable to that  observed for the {\it Icarus} transient (Methods \ref{sec:ICL}).  The characteristic timescale ofsuch  a canonical  caustic crossing event would be on the order of hours or days (Methods \ref{sec:Microlensing}), which is comparable to the timescales observed for the \spock events. Furthermore, since gravitational lensing is achromatic, the color of a caustic crossing transient will be constant. Using simplistic linear interpolations of the observed light curves (Methods \ref{sec:LightCurves}) we find that the inferred color curves for both \spock events are marginally consistent with this expectation of an unchanging color (Methods \ref{sec:ColorCurves}). Although the phenomenology of each \spock event is compatible with a  microlensing explanation, when applying this scenario to the MACS0416  field it is still difficult to explain {\it two} events with similar  decay timescales at such distinct locations on the sky. This is primarily because a caustic-crossing transient event must appear at the location of the lensing critical curve. It is possible for such  microlensing transients to appear offset from the central spine of the  critical curve, and this may in fact be observed in the case of {\it Icarus}  due to a ``blurring'' of the curve caused by the intracluster stars   It is possible to ubstantial clumping of mass along the line of sight through the lensing cluster (from the  The consensus from our six lens models is that there is only a single critical curve passing  roughly mid-way between the two observed \spock locations.  The lens models could, however, be modified so that instead of just  two host images (11.1 and 11.2 in Figure~\ref{fig:Discovery}), the  diff --git a/spock_localbuild.pdf b/spock_localbuild.pdf  index 461334a..21f9538 100644  Binary files a/spock_localbuild.pdf and b/spock_localbuild.pdf differ