srodney Lpk vs t fig update. LBV text  almost 8 years ago

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luminosities for each event as a function of magnification and time of  peak (or, equivalently, the decline time).  Figure~\ref{fig:PeakLuminosityDeclineTimeWide} shows Figures~\ref{fig:PeakLuminosityDeclineTimeWide} and  \ref{fig:PeakLuminosityDeclineTime} show  the resulting constraints on the peak luminosity and the decline time, which we  quantify as $t_2$, the time over which the transient declines by 2  magnitudes. Shaded green and red bands represent the \spockone and 

the most overlap) would be $L_{\rm pk}\sim10^{41}$ ergs/s and  $t_3\sim1.8$ days.  \subsection{Comparison to SN and SN-like Explosion Models}  In %In  Figure~\ref{fig:PeakLuminosityDeclineTimeWide} we also demarcate regions %regions  of the luminosity - decline luminosity--decline  time phase space occupied by known or %or  theorized SN-like  transients. \subsection{Supernova-like Transients}  The colored regions along the right side of Figure~\ref{fig:PeakLuminosityDeclineTimeWide} mark the luminosity and decline times for SNe and SN-like transients, showing  that the very rapid rise and fall of both \spock light curves is  incompatible with any of the normal SN classes. For both  thermonuclear white dwarf explosions (Type Ia) and the core-collapse  explosions of massive stars (Type Ib, Ic, and II) the optical light  curve after reaching peak brightness is primarily powered by transients. This includes  the decay familiar luminosity-decline relation  ofradioactive \NiFiftySix to \CoFiftySix, which leads to a minimum  decline rate of $\sim$0.1 mag day$^{-1}$. For  Type II Ia  SNe this decay  time can be extended into a plateau phase by the recession of the  photosphere via a recombination wave propagating inward through the  ionized H of the expanding outer shell. In no case can a normal SN  powered by the \NiFiftySix decay chain exhibit the decline rate of  $t_3<8$ days that has been observed for \spock. Furthermore, the  observed peak luminosities for both \spock events are too low for most  Type I or Type II SN, which peak at $\sim10^{42}$ to $10^{43}$ erg  s$^{-1}$.  Figure~\ref{fig:PeakLuminosityDeclineTimeWide} also shows that the  \spock events are far too faint \citep{Phillips:1993}  andfar too fast to belong to  the broad heterogeneous class of Core  Collapse SNe, as well as  less well-understood classes of such as  Superluminous SNe \citep{Gal-Yam:2012,Arcavi:2016},which have peak luminosities  $>10^{43}$ erg s$^{-1}$ and take at least 10's of days to decline by 2  magnitudes. \spockone and \spocktwo also decline too rapidly to match  the most common categories of peculiar SNe and ``SN-like'' transients  such as  Type Iax SNe \citep{Foley:2013a}, fast optical transients \citep{Drout:2014}, and  Ca-rich SNe \citep{Filippenko:2003,Perets:2011,Kasliwal:2012}, or Luminous Red Novae \citep[also called intermediate luminosity red transients][]{Munari:2002,Kulkarni:2007,Kasliwal:2011}. transients][]{Munari:2002,Kulkarni:2007,Kasliwal:2011b}. The \spock  events are incompatible with all of these explosion categories,  owing to the very rapid rise and fall of both \spock light curves, and  their relatively low peak luminosities of $\sim10^{41}$ erg s$^{-1}$.  Dashed boxes in Figure~\ref{fig:PeakLuminosityDeclineTimeWide}  represent categories of ``SN-like''  stellar explosions that have been theoretically predicted and extensively modeled, but for which very  few viable candidates have actually been observed. One Both  of these is  the ``.Ia'' class, due categories come closer  to explosions of a He shell on the surface of a  white dwarf \citep{Bildsten:2007}. Theoretical .Ia models suggest  that after an initial short peak (3-5 days) driven by the rapid  radioactive decay of \ion{Cr}{48} and \ion{Fe}{52} at matching  the exterior observed characteristics  of theejecta, a secondary decline phase kicks in, powered by the slower  \ion{Ni}{56} decay chain \citep{Shen:2010}. There are only  two.Ia  candidates in the literature \citep{Poznanski:2010,Kasliwal:2010}, so  we do not have enough objects to empirically constrain the range of  .Ia light curve shapes. The best we can do is to conclude from the  available models that a .Ia light curve would be brighter and slower  than the observed  \spock light curves.  A second dashed box in Figure~\ref{fig:PeakLuminosityDeclineTimeWide}  represents the ``kilonova'' class (also events, so they warrant closer scrutiny.  \subsubsection{Kilonova}  Also  called ``Macronovae'' a ``macronova''  or ``mini-supernovae''), which are ``mini-supernova,'' this is  theorized to optical transients that may  be generated by the merger of two a  neutron stars (NSs). star (NS) binary.  A NS+NS merger can drive a relativistic jet that may be observed as a Gamma Ray Burst (GRB) and would emit gravitational waves. These may also be accompanied by a very rapid optical light curve (the kilonova component) that is driven by the radioactive decay of r-process elements in the ejecta \citep{Li:1998a,Kulkarni:2005}. \citep{Li:1998,Kulkarni:2005}.  To date there are two cases of fast optical transients associated with GRB events, which have been interpreted as possible kilonovae \citep{Perley:2009,Tanvir:2013}. The \spock transients fall within the range of theoretically predicted peak luminosity and decline times for kilonovae. However, the rise time for the \spockone event is at least 5 days in the rest-frame, which is significantly longer than the $<1$ day rise expected for a kilonova \citep[e.g.][]{Metzger:2010,Barnes:2013,Kasen:2015}. Furthermore, both \spock events are either significantly fainter or faster than the optical light curves for the two existing kilonova candidates. An additional challenge to all of \subsubsection{.Ia Supernova}  The dashed oval in Figure~\ref{fig:PeakLuminosityDeclineTimeWide}  represents  the models discussed above, from  supernova to .Ia ``.Ia'' class of He shell explosion  \citep{Bildsten:2007}. These are theorized  to kilonova, is arise from AM Canum  Venaticorum (AM CVn) systems, which are binary star systems  transferring He onto a C/O or O/Ne WD primary  \citep{Warner:1995,Nelemans:2005}. \citet{Bildsten:2007} showed  thatall of  these stellar explosions  are one-time events. For systems can build up enough He on  the common categories surface  ofType Ia, Type Iax,  Core Collapse, and Superluminous SNe,  the progenitor stars are  completely destroyed by WD to  trigger a thermonuclear runaway and possibly a detonation. A typical  AM CVn system could produce $\sim$10 He shell flashes over $\sim10^6$  yr, while  the explosion. Some SN-like explosions --  such as He mass transfer rate is slow enough to admit thermally  unstable burning in  the WD's accreted He shell. The final  He shell explosions in flash is  the .Ia SN model -- could leave brightest, and is what we refer to as  the progenitor star at least partially intact. However, even then .Ia event. This  last explosion may or may not lead to a detonation of  the mass lost from WD core  \citep[the double detonation  scenario][]{Nomoto:1982a,Nomoto:1982b,Woosley:1986;Woosley:1994}.  Theoretical .Ia models suggest that  the system light curves  would be sufficient quite  bright, reaching a peak luminosity of $\sim10^{42}$ erg s$^{-1}$.  That is comparable  tofatally disrupt  the mass accretion process, preventing brightness of a normal SN, but  the system from evolving back to  generate another similar explosion. These catastrophic stellar  explosions are also intrinsically rare (fewer than 1 event per century  per 10$^11$ \Msun), as they require progenitor systems .Ia light  curves would decline much more quickly. After an initial short peak  (3-5 days) driven by the rapid radioactive decay of \isotope{48}{Cr}  and \isotope{52}{Fe} at the exterior of the ejecta, a secondary  decline phase kicks in, powered by the slower \isotope{56}{Ni} decay chain  \citep{Shen:2010}. The optical emission is expected to fade by 2  magnitudes after $\sim10$ days. There have been a few viable .Ia  candidates presented in the literature  \citep{Kasliwal:2010,Perets:2010,Poznanski:2010}, but we do not have  enough objects to empirically constrain .Ia light curve shapes.  Although the \spock light curves were somewhat fainter and faster than  the expectations for a .Ia event, there is enough uncertainty about  the diversity of .Ia light curves  that start as high  mass stars and/or close binary systems this model should not be  dismissed on those merits alone.  \subsubsection{The Recurrence Problem}  An additional challenge for applying any SN-like transient model to  explain the \spock events is the problem of the apparent  recurrence. For all of these catastrophic stellar explosions we do  not expect to see repeated transient events: the kilonova progenitor  system is completely destroyed by the merger, and for the .Ia  explosions the principal observed transient event is the last  transient episode  that can sustain mass transfer. system produces. Even if we suppose that an AM  CVn system could produce repeated He shell flashes of similar  luminosity, the period of recurrence would be of order $10^5$ yr,  making these effectively non-recurrent sources.  Thus, the only way to reconcile a these  cataclysmic explosion model models  with the two observed \spock events is to either (a)invoke a highly  serendipitous occurrence of two unrelated explosions in the same host  galaxy in the same year, or (b)  assert that the two events are two images of the same explosive event, explosion,  appearing to us separately only because of a gravitational lensing time delay \citep[as was the case for the 5 images of SN Refsdal][]{Kelly:2015a,Kelly:2016}.  For the former scenario of two unrelated explosions, we have already  ruled out all of the most common categories of stellar explosions  based on the properties of the light curve. The only models that can  accommodate the observed rapid light curves are the kilonova model and  perhaps the .Ia scenario. As there are no measured rates of .Ia Refsdal][]{Kelly:2015a,Kelly:2016},  or kilonovae, it is difficult to accurately quantify the likelihood of  detecting such rare events. However, we have observed no other  transients with similar luminosity and light curve shapes in the  high-cadence surveys (b) invoke a highly  serendipitous occurrence  of5 other Frontier Fields clusters. Thus, it  appears unreasonable to allow that  two such unrelated peculiar  explosionswould occur  in the same host  galaxy in a single the same  year. Scenario (b), To evaluate scenario (a),  in which a lensing time delay causes the appearance of  two separate  events, is  also highly implausible. we must rely on the available lens  modeling.  We have seen in Section~\ref{sec:LensingModels} that none of the \macs0416 lens models predict an 8 month time delay between appearances in image 11.1 and 11.2. This is represented in Figure~\ref{fig:SpockDelayPredictions}, where we have plotted the light curves for the two transient events, along with shaded vertical bars marking the time delay predictions of all models. %The lens models are broadly consistent with each other, predicting  %that the lensing time delay between images 11.1 and 11.2 is on the  %order of $\pm$60 days, far short of the 238 day lag that was observed  %between \spockone\ and \spocktwo.  To accept the alternative single-explosion this time-delayed single explosion  explanation for \spock, we would have to assume that a large systematic bias is similarly affecting all of the lens models. While we cannot rule out such a  bias, the consistency of the lens modeling makes any catastrophic  (i.e., non-repeating) explosion model this scenario  less tenable. For the latter scenario of two unrelated explosions, it is difficult  to assess the likelihood of such an occurrence quantitatively, as  there are no measured rates of .Ia or kilonovae. In a study of very  fast optical transients with the Pan-STARRS1 survey,  \citet{Berger:2013b} derived a limit of $\lesssim0.05$ Mpc$^{-3}$  yr$^{-1}$ for transients reaching $M\approx -14$ mag on a timescale of  $\sim$1 day. This limit, though several orders of magnitude higher  than the constraints on novae or SNe, is sufficient to make it  exceedingly unlikely that two such transients would appear in the same  galaxy in a single year. Furthermore, we have observed no other  transients with similar luminosities and light curve shapes in our  high-cadence surveys of 5 other Frontier Fields clusters. Indeed, all  other transients detected in the core Frontier Fields survey have been  fully consistent with normal SNe. Thus, we have no evidence to  suggest that transients of this kind are much more common at $z\sim1$.  \subsection{Luminous Blue Variable}  The transient events labeled as luminous blue variables (LBVs) are the  result of eruptions or explosive episodes on massive stars  ($>10$\Msun) \citep[for an overview of recent work,  see][]{Smith:2011b}. Although the association with massive stars is  well established, this class is very heterogeneous and there is  currently a vigorous debate over the precise nature of the progenitor  pathway \citep{Smith:2015,Humphreys:2016,Smith:2016}. Examplified by  the well-studied galactic examples of P Cygni and $\eta$ Carinae  (\etacar), the ``Great Eruptions'' of such massive stars are sometimes  labeled as ``SN impostors.''  The transient episodes can exhibit light  curves reminiscent of core collapse SNe, reaching peak absolute  magnitudes of $\sim$-7 to -16 mag in optical bands, and lasting for  tens to hundreds of days.  The peak absolute magnitudes of observed giant LBV events span a range  of -10 to -18 mag, so the luminosities of the two \spock transients  are fully compatible. Most giant LBV eruptions have been  consistently observed to last much longer than the \spock events,  requiring tens to hundreds of days to fade by 2 magnitudes  \citep{Smith:2011b}. Some LBV stars   These stars commonly exhibit repeated  variability, with stochastic episodes of minor eruptions punctuated by  major SN impostor episodes, in some cases culminating with a final  true core collapse SN event  \citep[e.g.]{Mauerhan:2013,Tartaglia:2016}  Foley:2007,Pastorello:2007,Smith:2010b,GalYam:2009,}.  The LBV scenario does not  have any trouble accounting for the \spock events as two separate  episodes. However, in addition to the relatively short and very  bright giant eruptions, these massive stars also commonly exhibit a  slower underlying variability that has not been observed at the \spock  locations. P Cygni and \etaCar, for example, slowly rose and fell in  brightness by $\sim$1 to 2 mag over a timespan of several years before  and after their historic giant eruptions. Given the wide variation in  light curve properties for LBV events, this class must be held up as a possible   explanation for the \spock system, though the observed \spock events would stand out as the most rapid LBV major eruptions  \subsection{Recurrent Nova Model} Nova}  Novae are represented in  Figure~\ref{fig:PeakLuminosityDeclineTimeWide} as a grey band, which 

constraints from the two published kilonova candidates are shown,  which provide only lower limits on the peak luminosity  \citep{Tanvir:2013}, or the decline timescale \citep{Perley:2009}.  Two .Ia candidates are also plotted, SN 2002bj \citep{Poznanski:2010}  and SN 2010X \citep{Kasliwal:2010}.  The sample of observed nova outbursts (shown as solid points) demonstrates the observed scatter about the MMRD relation. One primaryfirst  line of evidence supporting the nova hypothesis comes from the \spock light curves. Some Many  RN light curves are similar in shape to the \spock episodes, exhibiting a sharp rise ($<10$ days  in the rest-frame) and a similarly rapid decline.  Figure~\ref{fig:RecurrentNovaLightCurveComparison} compares the \spock 

sudden disappearance of both of the \spock transient events is fully  consistent with the eruptions of known RNe in the local universe.  The rise time of the \spock events is somewhat out of the ordinary for  nova outbursts. In particular, for recurrent nova eruptions that  decline rapidly ($t_2<10$ days) they tend to also reach peak  brightness very quickly, on timescales $<1$ day  \citep{Schaefer:2010}. The 2014 eruption of the rapid-recurrence nova  M31N 2008a-12 reached maximum brightness in a little under 1 day  \citep{Darnley:2015}. However, the rise time for nova eruptions is  poorly constrained, as rapid-cadence imaging is rarely secured until  after an initial detection near peak brightness. Unlike the situation  with a kilonova light curve, there is no a priori physical expectation  for an especially rapid rise to peak in nova light curves.  A  second reason to consider the RN model is that it provides a natural explanation for having two separate explosions that are  coincident in space but not in time. If \spock is a RN, then the two  observed episodes can be attributed to two distinct nova eruptions, 

possible, classifying \spock as a RN would still require a very  extreme mass transfer rate to accommodate the $<1$ year recurrence.  A second Another  major concern with the RN hypothesis for \spock is apparent in Figure~\ref{fig:PeakLuminosityDeclineTime}, which shows that the  two \spock events are substantially brighter than all known novae --  perhaps by as much as 2 orders of magnitude. One might attempt to 

{\rm more inconsistent} with observed nova peak luminosities.   \todo{Lpk vs recurrence period}  \subsection{Non-explosive \section{Non-explosive  Astrophysical Transients} There are several categories of astrophysical transients that we have  neglected so far, but which cannot accommodate the observations of the         

originated from the same physical location in the source plane. One  way to test this is to compare the properties of the \spock host  galaxy at the location of each event. To that end, we used the  techniques technique  of ``pixel-by-pixel'' SED fitting as described in \citet{Hemmati:2014} to determine rest-frame colors and stellar  properties in a single resolution element centered at each transient  location. For this purpose we used the deepest possible stacks of HST         

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\label{fig:PeakLuminosityDeclineTime}  Peak luminosity vs. decline time for \spock and other rapidly evolving declining  transients. Constraints for \spockone and \spocktwo  are plotted as overlapping cyan and blue colored  bands, corresponding to independent constraints drawn from the F435W and F814W light curves, respectively. For \spocktwo the scarlet as in  Figure~\ref{fig:PeakLuminosityDeclineTimeWide}. Two .Ia candidates  are shown as stars \citep{Kasliwal:2010,Poznanski:2010},  and maroon arrows  indicate lower limits for two kilonova  candidates \citep{Perley:2009,Tanvir:2013}. Grey  bands showconstraints from  the F125W and F160W light curves, respectively. Each band encompass MMRD  relation for classical novae, as in  Figure~\ref{fig:PeakLuminosityDeclineTimeWide}. Circles mark  the range of possible observed  peak luminosities andtime to  decline by 3 magnitudes. The width and height of these bands incorporates the uncertainty due to magnification (we adopt $10<\mu<100$) and the time of peak (using linear fits as shown in Figure~\ref{fig:LinearLightCurveFits}). Other examples of rapidly evolving transients are shown times  for comparison, with the "optical fast transients" classical novae  from the Pan-STARRS1 survey appearing as circles in the upper right \citep{Drout:2014a}, Milky Way \citep{Downes:2000}, M31 \citep{Shafter:2011},  andvarious novae in  the lower portion of local group \citep{Kasliwal:2011}. Black '+' symbols mark  the figure. Classical novae appear as cyan squares \citep{Downes:2000}, galactic recurrent novae as blue and cyan diamonds 7 rapidly declining Recurrent Novae from our own galaxy  \citep{Schaefer:2010}, and therapid recurrence nova M31N200812a as  large cyan and orange diamonds. For all of these points the marker color indicates the band-pass of cross labeled at  the light curve used to derive bottom shows  the luminosity and decline time: blue indicates B band, cyan is V band, green is g band, and orange corresponds to r or R band.  \label{fig:PeakLuminosityDeclineTime} rapid recurrence nova  M31N 2008-12a \citep{Tang:2014,Darnley:2015}.      Binary files a/figures/peakluminosity_vs_declinetime/peakluminosity_vs_declinetime.pdf and b/figures/peakluminosity_vs_declinetime/peakluminosity_vs_declinetime.pdf differ     Binary files a/figures/peakluminosity_vs_declinetime/peakluminosity_vs_declinetime.png and b/figures/peakluminosity_vs_declinetime/peakluminosity_vs_declinetime.png differ        

\label{fig:PeakLuminosityDeclineTimeWide}  Peak luminosity vs. decline time for \spock and other astrophysical  transients. Constraints for \spockone are plotted as overlapping cyan  and blue bands, corresponding to independent constraints drawn from 

significant sample size: the ``.Ia'' class of white dwarf He shell  detonations \citep{Bildsten:2007,Shen:2010} and the kilonova class  from neutron star  mergers \citep{Kulkarni:2005,Tanvir:2013,Kasen:2015}.  \label{fig:PeakLuminosityDeclineTimeWide} \citep{Li:1998,Kulkarni:2005,Kasen:2015}.         

\def\Rv{\mbox{$R_V$}\xspace}  \def\Ha{\mbox{H$\alpha$}\xspace}  \newcommand\ionline[2]{#1{\scshape{#2}}}  \newcommand{\isotope}[2]{${}^{#1}$#2}  % Supernovae :   \def\CCSN{CC\,SN\xspace} 

\def\dmfifteen{\ensuremath{\Delta\mbox{m}_{15}}\xspace}  \def\deltamfifteen{\ensuremath{\Delta\mbox{m}_{15}}\xspace}  % Other explosions:  \def\etacar{\ensuremath{\eta\,\mbox{Car}\xspace}  \def\etaCar{\ensuremath{\eta\,\mbox{Car}\xspace}  \def\m31n{M31N\,2008-12a\xspace}  \def\M31N{M31N\,2008-12a\xspace}  % Missions:  \def\HST{{\it HST}\xspace}  \def\Hubble{{\it Hubble}\xspace}