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\section{Conclusions} \section{Summary and Conclusions}  \label{sec:Conclusions}  The peculiar transients \spockone and \spocktwo behind \macs0416 have 
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took to decline by 2 magnitudes to $\t2<6$ days---significantly  faster than almost all categories of explosive stellar phenomena.  %The lens models used here are diverse, but deliver a consistent  %story for the plausible range of time delays The diverse lens models analyzed here all agree that the gravitational  lensing time delay between the two positions of the luminosities and rapid light curves for both  \spock events is  far shorter than the observed time difference are  marginally compatible with two categories  of $\sim$8 months. This  leads to theorized optical  transients:  the conclusion kilonova and .Ia classes. A key problem with these  models is  that the two events both  are from a single {\em  recurrent} source. This conclusion could expected to  be assailed by moving the  location of the lensing critical curve, so intrinsically quite rare, with  a rate  thatit  is significantly  closer to one or the other orders  of magnitude less than  the two rate for normal SN  events. This would drive up the  difference in the lensing potential between the two \spock positions,  and could lengthen Either  the lensing time delay, which is directly  proportional merger of a NS binary (leading  to a kilonova) or  the lensing potential difference. However, this would  also substantially increase the inferred lensing magnification final shell explosion  of one  event, and simultaneously decrease $\mu$ an AM CVn system (causing a .Ia event)  would be a terminal event---there would be no opportunity  for a second  transient event. This conflicts with  the other event, making third of our primary  observational constraints, that  theinferred luminosities for  two transient episodes incompatible. \spock transients were  probably caused by two separate events at the source plane.  That inference that the two events are from a single {\em recurrent}  source is derived from analysis of our diverse set of lens models.  All agree that the gravitational lensing time delay between the two  positions of the \spock events is far shorter than the observed time  difference of $\sim$8 months. This conclusion could be assailed by  moving the location of the lensing critical curve, so that it is  significantly closer to one or the other of the two events. This  would drive up the difference in the lensing potential between the two  \spock positions, and could lengthen the lensing time delay, which is  directly proportional to the lensing potential difference. However,  this would also substantially increase the inferred lensing  magnification of one event, and simultaneously decrease $\mu$ for the  other event, making the inferred luminosities for the two transient  episodes less compatible with each other.  \todo{quickly summarize the exclusion Having ruled out most  of the kN and .Ia models based  on recurrence}  From these constraints   We have examined these usual suspects for extragalactic  transient events, we are left with  two models in comparison to models: the \spock system  is either a RN or an LBV. There are observed examples from both of  these classes that can separately match the  three primary observational constraints: characteristics:  the peak luminosity (\Lpk),  light curve decline time (\t2),the  peak luminosity (\Lpk),  andthe  recurrence timescale (\trec). We However, we  have found that the RN model is physically untenable. The light  curve shape is consistent with RN systems in our own galaxy and M31,  but the peak luminosity and recurrence timescale are at (or beyond)  the limits when we bring all three  of those constraints together  theknown  RN population. Indeed, these latter two  observables are, at best, only barely compatible with the model must be stretched to extreme  physical limits of the RN model. limits.  The inferred peak luminosity of the \spock events would require a primary white dwarf that is extraordinarily close to the Chandresekhar limit. The uniquely rapid recurrence timescale would imply a mass transfer rate from the secondary star that is remarkably fast ($>10{-7} \Msun$ yr${-1}$). It is unclear whether thesetwo  extremes are even physically compatible as a RN system, as such a rapid mass transfer onto such a massive white dwarf would likely result in stable nuclear burning at the surface, and would therefore not lead to explosive burning episodes that could be observed as rapid transient events. Our preferred explanation for the \spock events is that we have  observed two distinct eruptive episodes from a massive LBV star. \todo{Reiterate 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 phenomenoligical consistency}  We bounds of what has been  observed from nearby LBVs. The \spock episodes may  have found that been among  the \spock fastest and most luminous of any rapid LBV  events are compatible yet  observed. However, no other rapid LBV outbursts have yet been observed  with such a high cadence, so  the observed  properties of known detailed light curve shape can not be  rigorously compared against other events. In this scenario, the  \spock  LBV system would most likely have exhibited multiple  eruptions from over  the local universe.  \todo{Reiterate last few years, but most of them were missed, as they landed  within  the observational and physical consistency}  The very luminous and very fast \spock  transients may be driven by extreme mass eruption events, an extreme  form large gaps  of stellar pulsation, or may be caused by a different mechanism  entirely. the \HST Frontier Fields imaging program.  These We speculate that the very luminous and very fast \spock transients  may be driven by extreme mass eruption  events will only add or an extreme form of  stellar pulsation. Both of these mechanisms are likely  to the theoretical challenge occur in  LBV progenitor stars, but we do not have a robust model for precisely  how LBV eruptions are generated. This is a topic in need  of deriving significant theoretical work, with the end goal being  a comprehensive  physical model that accommodates both the \etacar-like  great eruptions and the S Dor-type variation of LBVs. The \spock events are extreme  in several dimensions, and will only add to this theoretical  challenge.  \todo{Close with a prescription for resolving The theoretical objective could be aided by additional observational  constraints on  the classification with  regular monitoring \spock system. If, as we have argued, this source  is indeed a recurrent system, then an observing campaign over $\sim$4  months should reveal at least one more transient event in one  of the field, and getting measurable time delays  that three host galaxy images. Capturing another transient episode with  similarly high cadence imaging  could provide definitively resolve our  remaining classification ambiguities. If the \spock source is  a rigorous test of RN,  then we would expect the recurrence timescale, the light curve shape,  and  the cluster mass models} peak luminosity to all be relatively consistent from episode  to episode (as is the case for the rapid recurrence RN M31N 2008a-12).  In contrast, for an LBV system we would expect to see much more  variety in all of those observational characteristics.  An observing campaign that catches additional transient episodes would  have another significant windfall. If multiple events in separate  images of the host galaxy can be definitively matched, then we could  extract a measure of the gravitational lensing time delay. Given the  very sharp structure of the light curve, we anticipate that these time  delay measurements could be extremely precise, perhaps constraining  the delay to within a few hours. This would offer a powerful test of  the lens models for this cluster, and in particular could be a very  sensitive check for systematic biases. When a suitable observational  program is enacted, we would urge lens modelers to make a concerted  effort to optimize their time delay estimates in advance of any time  delay measurements, in order to provide blind predictions for the most  robust empirical test.