deletions | additions       diff --git a/Authors.tex b/Authors.tex  index 6290c3d..c1d56fd 100644  --- a/Authors.tex  +++ b/Authors.tex 
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%\author{All of Us, In Some Order}  \author{S.~A.~Rodney\altaffilmark{\affilref{JHU},\affilref{HubbleFellow},\affilref{USC}}} \author{S.~A.~Rodney\altaffilmark{\affilref{JHU},\affilref{USC}}}  \affilreftxt{JHU}{\JHU}  \affilreftxt{HubbleFellow}{\HubbleFellow}  \affilreftxt{USC}{\USC}  diff --git a/Discussion.tex b/Discussion.tex  index ca6474a..3287e5d 100644  --- a/Discussion.tex  +++ b/Discussion.tex 
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\section{Discussion}\label{sec:Discussion}  We have examined three plausible explanations for the \spock events: (1) these transients are due to they were surface explosions from  a single  RN that reaches an extraordinarily high peak luminosity, (2) they are were  separate rapid outbursts of an LBV star, or (3) they are were  each the result of caused by  the rapidly changing magnification of a as two unrelated  massive star crossing stars crossed  overone or  more  lensing caustics. Our We can not make a definitive choice between these  hypotheses, principally due to the scarcity of observational data and  the uncertainty in the the location of the lensing critical curves.  If there is just a single critical curve for a source at $z=1$ passing  between the two \spock locations then our  preferred explanation for the \spock events is that we have observed two distinct eruptive episodes from a massive LBV star. The light curve shape is consistent with rapid LBV eruptions seen in systems such as SN 2009ip and NGC 3432-LBV1. The peak luminosity and recurrence timescale are also within the bounds of what has been observed from nearby LBVs. The In this  case, the  \spock episodes may have been among the fastest and most luminous of any rapid LBV events yet observed. However, the rapid outbursts of LBV stars in the local universe have never yet been observed with such a high cadence, so the detailed light curve shape of the \spock events cannot be rigorously compared against other events. In this scenario, the \spock LBV system would most likely have exhibited multiple eruptions over the last few years, but most of them were missed, as they landed within the large gaps of the \HST Frontier Fields imaging program. We speculate that the very luminous and very fast \spock transients  may be driven by extreme mass eruption events or an extreme form of 
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events are extreme in several dimensions, and should add a useful  benchmark for this theoretical challenge.  If instead the \macs0416 lens has multiple critical curves that  intersect both \spock locations, then the third proposal of a  microlensing-generated transient would be preferred. Stellar caustic  crossings have not been observed before, but the analysis of a likely  candidate behind the MACSJ1149 cluster suggests that massive cluster  lenses may generate such events more frequently than previously  expected \citep{Kelly:2017}. To resolve the uncertainty of the \spock  classification will require refinement of the lens models to more  fully address systematic biases. High-cadence monitoring of the  \macs0416 field may also be important, as it could catch future LBV  eruptions or microlensing transients at or near these locations.  diff --git a/Introduction.tex b/Introduction.tex  index c710939..43008dd 100644  --- a/Introduction.tex  +++ b/Introduction.tex 
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clusters and associated ``blank sky'' fields observed in parallel  (Methods \ref{sec:Discovery}).  Combining the \HST imaging and lens models of the \MACS0416 gravitational lens leads to three key observables for the \spock events: (1) they are both more luminous than a classical nova, but less luminous than almost all supernovae (SNe), reaching a peak luminosity of roughly $10^{41}$ erg s$^{-1}$ ($M_V=−14$); (2) both transients exhibited fast light curves, with rise and decline timescales of $\sim$2--5 days in the rest frame; and (3) it is likely possible  that both events arose from the same physical location but highly unlikely that they  werenot  coincident in time---they were probably separated by 3-5 months in the rest frame. Thesepeculiar  transients thus present an intriguing a  puzzle: they are broadly consistent with the expected behavior of stellar explosions (they each exhibit a single isolated rise and decline in brightness), but they can not be trivially classified into anyof the  common categories category  of explosiveor eruptive  astrophysical transients. The HFF survey was not designed with the discovery of peculiar  extragalactic transients as a core objective, but it has  diff --git a/Results.tex b/Results.tex  index 5c4d8f0..e526232 100644  --- a/Results.tex  +++ b/Results.tex 
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\section{Results}\label{sec:Results}  Photometry collected from the \HST images (Methods  \ref{sec:Photometry}), reveals thatthe the two \spock\  both \spock events  exhibited very rapid light curves, as shown in Figure \ref{fig:LightCurves}. curves (Figure \ref{fig:LightCurves}).  Both events reached a peak luminosity of $\sim$0.08 \microjansky, with the entire observable rise and fall occurring in $<20$ days. The host galaxy for both the  \spock events is at a redshift of $z=1.0054\pm0.0002$ (Methods \ref{sec:Spectroscopy}). After dividing the observed  timescales by ($1+z$) to correct \ref{sec:Spectroscopy}), so after correcting  for cosmic time dilation, we see that  both dilation  these  events lasted $<$10 days in the rest frame. To interpret the observed light curves and the timing of these two  events, we use seven independently constructed cluster mass models to 
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In Table~\ref{tab:LensModelPredictions} we report model-predicted time  delays relative to the \spockone event, which appeared in January 2014  in host image 11.2. We also report absolute magnification values  between about $\mu=10$ and $\mu=300$ $\mu=200$  for both events. This wide range is due primarily to the close proximity of the \spock events to the  lensing critical curve (the region of theoretically infinite  magnification) for sources at $z=1$. The location of the critical  curverelative to each \spock event  varies significantly among the models, and is sensitive to many parameters that are poorly constrained. We have explored model variations (described in Methods (Methods  \ref{sec:LensModelVariations}) that adjust the cluster redshift and the masses of cluster member galaxies, and that account for the impact of lensing perturbations from galaxies along the line of sight. Most variations that move a critical curve closer to the position of \spockone\ would drive the magnification of that event much higher (toward $\mu_1\sim300$). $\mu_{\rm NW}\sim200$).  This generally also has the effect of moving the critical curve farther from \spocktwo, which would necessarily drive its magnification downward (toward $\mu_2\sim10$). $\mu_{\rm SE}\sim10$).  Our model variations also show that it is possible to make reasonable adjustments to the lens model parameters in order to ensure that a critical curve intersects both of the \spock locations. Such lensing configurations can qualitatively reproduce the observed morphology of the \spock host galaxy, but they are disfavored by a purely quantitative assessment of the positional strong-lensing constraints. Figure~\ref{fig:LightCurves} shows that the observed peak brightnesses  for the two events agree to within $\sim30\%$, which means that if 
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%CATS-A2 & & 491 $^{+197}_{-126}$ & 859 $^{+149}_{-105}$ & 3.2 $^{+0.1}_{-0.1}$ & 4.0 $^{+0.6}_{-0.8}$ & -4.3 $^{+0.1}_{-0.1}$\\[0.5em]  \enddata  \tablecomments{  Each lens model is identified by the name of the modeling method. method  (described in Methods~\ref{sec:LensingModels}).  Time delays give the predicted delay relative to an appearance in the NW host image, 11.2. Positive (negative) values indicate the NW image is the leading (trailing) image of the pair. }  \end{deluxetable}  %\renewcommand{\arraystretch}{1.}  \subsection{Ruling Out Common Astrophysical Transients}  There are several categories of astrophysical transients that cannot accommodate the light curve characteristics of the \spock transients. We may first dismiss any of the category of {\it periodic} sources (e.g. (e.g.,  Cepheids, RR Lyrae, or Mira variables) that exhibit regular changes in flux due to pulsations of the stellar photosphere. These variable stars photosphere and  do not exhibit sharp, isolated transient episodes that could match like  the \spock light curve  shapes. events.  Stellar flares provide another very common source for optical transient events, transients,  but the total energy released by even the most extreme stellar flare falls far short of the observed energy release  from the \spock transients \citep{Balona:2012,Karoff:2016} .  We can also rule out active galactic nuclei (AGN), in which brief transient episodes (a few days in duration) may be observed from X-ray x-ray  to infrared wavelengths \citep[e.g.][]{Gaskell:2003},  principally due to \citep[e.g.][]{Gaskell:2003}. An AGN explanation is   disfavored by  the quiescence of the \spock sources between the two observed episodes and the absence of any of the broad emission lines that are often(though not always)  observed in AGN. No x-ray emitting point source was detected in 7 epochs of imaging from the Swift and Chandra x-ray space telescopes, collected from 2009 to 2014 (Methods~\ref{sec:Xray}). This includes the Chandra imaging on August 31, 2014 (MJD=56900), which was coeval with the peak of IR emission from \spocktwo, observed with \HST. Many types of stellar explosions can generate isolated  transient events, and a useful starting point for classification of 
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interpolation of the observed photometry (Methods  \ref{sec:LightCurves}), with corrections for the luminosity distance  (assuming a standard \LCDM cosmology), and accommodating the range of  viable lensing magnifications ($10<\mu<100$) ($10<\mu<200$)  derived from the cluster lens models. This results in two-dimensional constraints on \Lpk and  the decline timescale \t2 (the time over which the transient declines  by 2 magnitudes). The \spockone and \spocktwo events are largely  diff --git a/figures/peakluminosity_vs_declinetime/peakluminosity_vs_declinetime.pdf b/figures/peakluminosity_vs_declinetime/peakluminosity_vs_declinetime.pdf  index 3e4b6c8..c05c139 100644  Binary files a/figures/peakluminosity_vs_declinetime/peakluminosity_vs_declinetime.pdf and b/figures/peakluminosity_vs_declinetime/peakluminosity_vs_declinetime.pdf differ diff --git a/figures/peakluminosity_vs_declinetime/peakluminosity_vs_declinetime.png b/figures/peakluminosity_vs_declinetime/peakluminosity_vs_declinetime.png  index a519df4..1ba0876 100644  Binary files a/figures/peakluminosity_vs_declinetime/peakluminosity_vs_declinetime.png and b/figures/peakluminosity_vs_declinetime/peakluminosity_vs_declinetime.png differ diff --git a/spock_localbuild.pdf b/spock_localbuild.pdf  index 68621be..451d507 100644  Binary files a/spock_localbuild.pdf and b/spock_localbuild.pdf differ