deletions | additions       diff --git a/Makefile b/Makefile  index f529136..4152fc2 100644  --- a/Makefile  +++ b/Makefile 
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# Set the variable PAPER to the root name of your .tex document  PAPER= spock_localbuild  default: local nature  all: clean local  clean:  diff --git a/spock_natureastronomy_finalsubmission.pdf b/spock_natureastronomy_finalsubmission.pdf  index 94dec26..fe6dabf 100644  Binary files a/spock_natureastronomy_finalsubmission.pdf and b/spock_natureastronomy_finalsubmission.pdf differ diff --git a/spock_natureastronomy_finalsubmission.tex b/spock_natureastronomy_finalsubmission.tex  index 4e60d4d..f022881 100644  --- a/spock_natureastronomy_finalsubmission.tex  +++ b/spock_natureastronomy_finalsubmission.tex 
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observatories such as the Large Synoptic Survey  Telescope\cite{Tyson:2002} are expected to reveal many new examples of  such astrophysical transients. \HST is not an efficient wide-field  survey telescope, but in  the HFF program nevertheless opened a small  window the combination  ofdiscovery for such events. Very faint sources at relatively  high redshift ($z\gtrsim1$) in these fields are made detectable by  gravitational lensing magnification from the foreground galaxy  clusters. The necessity of and  a rapid observation  cadencefor repeat imaging in the  HFF program also  made it more likely possible  to catch very intrinsically faint and  rapidly evolving transient  sources. With In  this confluence of factors, way  the HFF survey provides has provided  a glimpse of the potential discovery space available to high-cadence imaging surveys in the future. % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
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galaxies that satisfy that criterion, all with $0.5  (Methods). Each galaxy was observed by the high-cadence HFF program  for an average of 80 days. Treating \spockone and \spocktwo as  separate events leads to avery  rough rate estimate of 1.5 \spock-like events per galaxy per year.  Derivation of a volumetric rate for such events would require a 
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\section{Discussion}\label{sec:Discussion}  We have examined three plausible explanations for the \spock events:  (1) they were separate rapid outbursts of an LBV star, (2) they were  surface explosions from a single RN, or (3) they were each caused by  the rapidly changing magnification as two unrelated massive stars  crossed over lensing caustics. We events,  but we  cannot make a definitive choice between these hypotheses, principally owing to them, because of  the scarcity of observational data and the uncertainty in the location of the lensing critical curves. If there is just a single critical curvefor 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. 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. The \spock  events These  would be extreme LBV outbursts in several dimensions, and should add a useful benchmark for theoutstanding  theoretical challenge of developing a comprehensive physical model that accommodates both the \etacar-like great eruptions and the S Dor-type variation of LBVs. If instead the \macs0416 lens has multiple critical curves that  intersect both \spock locations, then the our  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\citep{Kelly:2017} suggests that massive cluster lenses may generate such events more frequently than previously expected\citep{Kelly:2017, Diego:2017}. To resolve the uncertainty of the \spock classification will require refinement of the lens models to more fully address systematic biases and more tightly constrain the path of the critical curve. High-cadence monitoring of the \macs0416 field would also be valuable, as it could catch future LBV eruptions or microlensing transients at or near these locations. % END MAIN TEXT  % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%