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The \fullmacs0416 cluster (hereafter \macs0416) is one of the most
efficient lenses in the sky, and in 2014 it was observed with high-cadence
imaging from the Hubble Space Telescope (\HST). Here we describe two
unusual transient events that appeared behind \macs0416 in a strongly lensed galaxy at
redshift
$z=1.0054\pm0.0002$. These transients---designated
\spockone and \spocktwo and collectively nicknamed ``Spock''---were
faster and fainter than any supernova (SN), but significantly more luminous
than a classical nova. They reached peak luminosities of $\sim10^{41}$
erg s$^{-1}$
(M$_{AB}<-14$) ($M_{AB}<-14$ mag) in $\lesssim$5 rest-frame days, then faded
below detectability in roughly the same time span. Models of the
cluster lens suggest that these events may be {\it spatially}
coincident at the source plane, but are most likely not {\it
diff --git a/Acknowledgments.tex b/Acknowledgments.tex
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...
The authors thank Mario Livio and Laura Chomiuk for helpful discussion
of this paper, as well as Stephen Murray and Neil Gehrels for
assistance with the \Chandra and
\SWIFT \Swift data, respectively.
Financial support for this work was provided to S.A.R., O.G., and L.G.S. by NASA
through grant HST-GO-13386 from the Space Telescope Science Institute
...
projects AYA2015-64508-P (MINECO/FEDER, UE), AYA2012-39475-C02-01 and
the consolider project CSD2010-00064 funded by the Ministerio de
Economia y Competitividad.
A.V.F. and P.L.K. are grateful for financial assistance from the
Christopher R. Redlich Fund, the TABASGO Foundation, and NASA/STScI
grants 14528, 14872, and 14922. The work of A.V.F. was conducted in
part at the Aspen Center for Physics, which is supported by NSF grant
PHY-1607611; he thanks the Center for its hospitality during the
neutron stars workshop in June and July 2017.
R.J.F. and the UCSC group is supported in part by NSF grant
AST-1518052 and from fellowships from the Alfred P.\ Sloan Foundation
and the David and Lucile Packard Foundation to R.J.F.
diff --git a/Classification.tex b/Classification.tex
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\subsection{Stellar Explosion Models}
\label{sec:Classification}
Most optical transient events observed in extragalactic surveys can be
explained as stellar explosions of one type or another. As the \spock
transients do not easily fall within familiar categories, a useful
starting point for comparing them to known stellar explosion
categories is to examine the phase space of peak luminosity versus
decline time \citep[see, e.g.,][]{Kasliwal:2010}. To infer the
luminosity and decline time for each \spock event, we combine the
linear fits to the light curves (shown in
Figure~\ref{fig:LinearLightCurveFits}) with the predicted range of
lensing magnifications (Figure~\ref{fig:LensModelContours}). For any
assumed value for the time of peak brightness, the light curve fits
give us an estimate of the ``observed'' peak magnitude and a
corresponding rise-time and decline-time measurement. We then convert
this extrapolated peak magnitude to a luminosity (e.g., $\nu L_\nu$ in
erg s$^{-1}$) by first correcting for the luminosity distance assuming
a standard \LCDM cosmology \citep{Planck:2016}, and then accounting
for an assumed lensing magnification, $\mu$. At the end of all this,
we have a grid of possible peak luminosities for each event as a
function of magnification and time of peak (or, equivalently, the
decline time).
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
\spocktwo events, respectively, and in each case they incorporate the
allowed range for time of peak (see
Figure~\ref{fig:LinearLightCurveFits}) and the lensing magnification
($10<\mu<100$) as reported in Table~\ref{tab:LensModelPredictions}.
The two events are largely consistent with each other, and if both
events are representative of a single system (or a homogeneous class)
then the most likely peak luminosity and decline time (the region with
the most overlap) would be $L_{\rm pk}\sim10^{41}$ ergs/s and
$t_2\sim1.8$ days.
%In Figure~\ref{fig:PeakLuminosityDeclineTimeWide} we also demarcate
%regions of the luminosity--decline time phase space occupied by known
%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. This includes the
familiar luminosity-decline relation of Type Ia SNe
\citep{Phillips:1993} and the broad heterogeneous class of Core
Collapse SNe, as well as less well-understood classes such as
Superluminous SNe \citep{Gal-Yam:2012,Arcavi:2016}, Type Iax SNe
\citep{Foley:2013a}, fast optical transients \citep{Drout:2014}, Ca-rich SNe \citep{Filippenko:2003,Perets:2011,Kasliwal:2012}, and
Luminous Red Novae \citep[also called intermediate luminosity red
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. Both of these
categories come closer to matching the observed characteristics of the
two \spock events, so they warrant closer scrutiny.
\subsubsection{Kilonova}
Also called a ``macronova'' or ``mini-supernova,'' this is a theorized
optical transient that may be generated by the merger of a neutron
star (NS) binary. Such 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: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.
\subsubsection{.Ia Supernova}
The dashed oval in Figure~\ref{fig:PeakLuminosityDeclineTimeWide}
represents the ``.Ia'' class of He shell explosions
\citep{Bildsten:2007}. These are theorized to 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} argued that
these systems can build up enough He on the surface of the 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 He mass transfer rate is slow enough to admit thermally
unstable burning in the WD's accreted He shell. The final He shell
flash is the brightest, and is what we refer to as the .Ia event. This
last explosion may or may not lead to a detonation of the WD core
\citep[the double detonation scenario;][]{Nomoto:1982a, Nomoto:1982b,
Woosley:1986, Woosley:1994}.
Theoretical .Ia models suggest that the light curves would be quite
bright, reaching a peak luminosity of $\sim10^{42}$ erg s$^{-1}$.
That is comparable to the brightness of a normal SN, but the .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 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 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 these cataclysmic explosion models
with the two observed \spock events is to either (a) assert that the
two events are two images of the same 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}, or (b) invoke a highly
serendipitous occurrence of two unrelated peculiar explosions in the
same host galaxy in the same year.
To evaluate scenario (a), in which a lensing time delay causes the
appearance of two separate events, 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 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 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 sources categorized as Luminous Blue Variables (LBVs)
are the result of eruptions or explosive episodes from massive stars
($>10$\Msun). The class is exemplified by well-studied examples such
as P Cygni and $\eta$ Carinae (\etacar) in the Milky Way and S Doradus
(S-Dor) in the Large Magellanic Cloud \citep[for recent overviews of
the LBV class, see][]{Smith:2011b, Kochanek:2012}. 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}. The ``Great Eruptions''
of such massive stars are sometimes labeled as ``SN impostors''
because these most prominent 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. In some cases the LBV progenitor does
indeed culminate with a final true core collapse SN event
\citep[e.g.][]{Mauerhan:2013, Tartaglia:2016}
% Foley:2007,Pastorello:2007,Smith:2010b,GalYam:2009}.
Although most giant LBV eruptions have been observed to last much
longer than the \spock events \citep{Smith:2011b}, some LBVs have
exhibited repeated rapid outbursts that are broadly consistent with
the very fast \spock light curves. Because of this commonly seen
stochastic variability, the LBV scenario does not have any trouble
accounting for the \spock events as two separate episodes.
Two well-studied LBVs in particular provide a plausible match to the
observed \spock events. The first is the transient ``SN 2009ip''
\citep{Maza:2009} which was later re-classified as an LBV as it showed
repeated brief transient episodes \citep[e.g.,][]{Miller:2009,
Li:2009, Berger:2009, Drake:2010}. Pre-eruption \HST imaging
demonstrated that the progenitor of SN 2009ip was likely a very high
mass star \citep[$\gtrsim50$ \Msun,][]{Smith:2010, Foley:2011}.
Remarkably, this star eventually did explode as a true SN event,
observed in 2012 \citep{Mauerhan:2013, Pastorello:2013, Prieto:2013}.
The second useful comparison object is NGC3432-LBV1 (also called SN
2000ch), which was first observed as a bright variable star
\citep{Papenkova:2000} and later definitively classified as an LBV
\citep{Wagner:2004}. This event exhibited at least three significant
outbursts over 2-year period, which were observed in a concerted
monitoring campaign \citep{Pastorello:2010}. The spectral
characteristics of this LBV suggest a similarity to Wolf-Rayet stars
\citep{Pastorello:2010} and the variation of the SED suggests
modulated dusty wind \citep{Wagner:2004, Kochanek:2012}. The observed
sequence of erratic transient episodes may also be indicative of
binary interactions similar to S-Dor \citep{Pastorello:2010,
Smith:2011b}.
Figure~\ref{fig:LBVLightCurveComparison} presents a direct comparison
of the observed \spock light curves against the light curves of these
two rapid-eruption LBVs, SN 2009ip and NGC3432-LBV1. The brief
outbursts of these LBVs have been less finely sampled than the two
\spock events, but the available data show a wide variety of rise and
decline times, even for a single object over a relatively narrow time
window of a few months. For each of the rapid LBV outbursts shown in
Figure~\ref{fig:LBVLightCurveComparison} we have measured the peak
luminosity and the decline time, allowing these events to be plotted
in the $L_{\rm pk}$ vs. $t_2$ space of
Figure~\ref{fig:PeakLuminosityDeclineTime} (as orange diamonds). All
of the rapid LBV eruptions of SN 2009ip and NGC3432-LBV1 provide only
upper limits on $t_2$, due to the relatively sparse photometric
sampling. The observations of both \spock events are consistent with
the observed luminosities and decline times of the fastest and
brightest of rapid LBV outbursts.
In addition to the relatively short and very bright giant eruptions
shown in Figure~\ref{fig:LBVLightCurveComparison}, most LBVs 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.
Such variation has not been detected at the \spock locations, as can
be seen from the wide views of the \spock light curves in
Figure~\ref{fig:SpockDelayPredictions}. Nevertheless, given the broad
range of light curve behaviors seen in LBV events, we can not reject
this class as a possible explanation for the \spock system.
\todo{Measure this more quantitatively: forced photometry in drz (not
diff) images at all epochs, estimate what would be the magnitude of
a quiescent eta-Car-like star, and would we be able to detect a 1-2
mag brightening over the span of the HFF campaign}
\subsubsection{Physical Implications of the LBV Model}
Considering the population of LBVs, the observed \spock events would
stand out as extreme events. The observed rise and decline times for
\spock would place both among the most rapid LBV eruptions ever
seen. The peak luminosities of both \spockone and \spocktwo are
similar to the observed luminosities of rapid, bright outbursts seen
in LBVs such as SN 2009ip and NGC3432-LBV1. However, the upper edge of
the range of plausible peak luminosities for both \spock events
reaches $10^{42}$ erg s$^{-1}$, which would be an order of magnitude
more luminous than any rapid outburst from those two nearby LBVs.
The precise physical mechanism for LBV outbursts is still not fully
understood. LBV stars such as \etacar show clear evidence of ejected
shells of gas, and very massive stars are known to undergo extensive
mass loss as they evolve toward eventual explosion as a SN. This has
led to the canonical model of LBV transient events as being the
optical signature of an eruptive mass loss episode. Such mass loss
could arise from a variety of direct mechanisms, such as
continuum-driven super-Eddingtion winds \citep{Smith:2006},
pulsational pair instability ejections \citep{Woosley:2007}, and shock
heating of stellar envelopes from internal shell-burning instabilities
\citep{Dessart:2010}. This is far from an exhaustive list, and none
of these explanations are entirely sufficient to account for all of
the observed diversity of LBV behaviors or the structural complexity
the most well-studied LBVs \citep[e.g.][]{Smith:2011b, Kochanek:2012}.
Although we do not have a complete physical model in hand, we can
nevertheless explore some of the physical implications of an LBV
classification for the two \spock events. We first make a rough
estimate of the total radiated energy, which can be computed using the
decline timescale $t_2$ and the peak luminosity $L_{\rm pk}$ following
\citet{Smith:2011b}:
\begin{equation}
\label{eqn:Erad}
E_{\rm rad} = \zeta \t2 \Lpk,
\end{equation}
\noindent where $\zeta$ is a factor of order unity that depends on the
precise shape of the light curve.\footnote{Note that
\citet{Smith:2011b} used $t_{1.5}$ instead of $t_2$, which amounts
to a different light curve shape term, $\zeta$.} Adopting
\Lpk$\sim10^{41}$ erg s$^{-1}$ and \t2$\sim$2 days (as shown in
Figure~\ref{fig:PeakLuminosityDeclineTime}), we find that the total
radiated energy isi $E_{\rm rad}\sim10^{46}$ erg. A realistic range
for this estimate would span $10^{44}
uncertainties in the magnification, bolometric luminosity correction,
decline time, and light curve shape (in roughly that order of
importance). These uncertainties notwithstanding, our crude estimate
does fall well within the range of plausible values for the total
radiated energy of a major LBV outburst.
If LBV eruptions are driven by significant mass ejection events, then
the energy budget would also include a substantial amount of kinetic
energy imparted to the ejected gas shell. Without spectroscopic
information from the \spock transients we can not place any realistic
estimate on the kinetic energy. Nevertheless, we can take the radiated
energy as a rough lower limit on the total energy release and ask what
timescale would be required for a massive star to build up that amount
of energy. This approach assumes that the energy released in an LBV
eruption is generated slowly in the stellar interior and is in some
way ``bottled up'' by the stellar envelope, before being released in a
rapid mass ejection. The ``build-up'' timescale to match the
radiative energy release is then
\begin{equation}
\label{eqn:trad}
t_{\rm rad} = \frac{E_{\rm rad}}{L_{\rm qui}} = \t2 \frac{\xi\Lpk}{L_{\rm qui}},
\end{equation}
\noindent where $L_{\rm qui}$ is the luminosity of the LBV progenitor
star during quiescence. For the \spock events we have no useful
constraint on the quiescent luminosity, but for evaluating the LBV
scenario we can assume it is similar to the local LBVs whose
progenitors have been directly observed. This gives a range for the
radiative build-up timescale between $t_{\rm rad}\sim30$ days if the
progenitor is \etacar-like ($M_V\sim-12$), or $t_{\rm rad}\sim20$
years if it is similar to the faintest known LBV progenitors (e.g. SN
2010dn, with $M_V\sim-6$).
Alternatively, a more informative approach is to assert that the
build-up timescale for \spock corresponds to the observed rest-frame
lag between the two events, roughly 120 days. Adopting $\Lpk=10^{41}$
erg s$^{-1}$ and $\t2=2$ days, if we assume $t_{\rm rad}=120$ days we
can infer that the quiescent luminosity of the \spock progenitor would
be $L_{\rm qui}\sim10^{39.5}$ erg s${-1}$ ($M_V\sim-10$). This is a
very reasonable quiescent luminosity value for the massive
($>10\Msun$) progenitor stars expected for LBVs.
Although the above discussion shows that the observations of the
\spock transients are largely consistent with the observed
characteristics of known LBV systems, this does not mean that we have
a viable physical model to explain these events. Rapid transient
episodes in LBVs such as SN 2002kg and SN 2009ip may best be explained
by a sudden ejection of an optically thick shell
\citep[e.g.,][]{Smith:2010, Smith:2011b}, or by some form of S
Dor-type variability \citep{Weis:2005, VanDyk:2006, Foley:2011}, which
may be driven by stellar pulsation rather than mass ejection
\citep{VanGenderen:1997, VanGenderen:2001}.
For massive stars such as \etacar at its great eruption and the
rapidly varying SN 2009ip, the effective photospheric radius during
eruption must have been comparable to the orbit of Saturn
\citep[$10^{14}$ cm;][]{Davidson:1997, Smith:2011b, Foley:2011}. With
observed photospheric velocities of order 500 km s$^{-1}$ for such
events, the dynamical timescale of the extended photosphere is on the
order of tens to hundreds of days. Thus, if the very rapid light
curves of both \spock events are indeed LBV eruptions, then they will
be near the extreme limits of physical models for massive stellar
eruptions.
%To examine the temperature and total energy output, we first make a
%set of (admittedly unfounded) assumptions: (1) the two outbursts had a
%very similar SED; (2) the last observed epoch for each event
%corresponds to the same phase relative to the true epoch of peak
%brightness; and (3) the lensing magnifications for the two events are
%the same. These simplifying assumptions allow us to jointly apply the
%optical observations of \spockone and the NIR observations of
%\spocktwo as constraints on the SED in any given epoch. We then set
%an assumption for the epoch of peak brightness, make another
%assumption for the magnification of both events, and then fit a
%blackbody to the resulting extrapolated SED. From this blackbody fit
%we derive a temperature and integrate to get an estimate of the
%pseudo-bolometric luminosity. The resulting inferred physical
%parameters are plotted in Figure~\ref{fig:DerivedPhysicalParameters}.
\subsection{Recurrent Nova}
Novae are represented in
Figure~\ref{fig:PeakLuminosityDeclineTimeWide} as a grey band, which
traces the maximum magnitude - rate of decline (MMRD) relation. Nova
explosions occur in binary star systems in which the more massive star
is a white dwarf that accretes matter from its companion, which may be
a main sequence dwarf or evolved giant star overfilling its Roche
Lobe. The white dwarf builds up a dense layer of H-rich material on
its surface until the high pressure and temperature triggers nuclear
fusion, resulting in a surface explosion that causes the white dwarf
to brighten by several orders of magnitude, but does not completely
disrupt the star. In a recurrent nova (RN) system, the mass transfer
from the companion to the white dwarf restarts after the explosion, so
the cycle may begin again and repeat after a period of months or
years.
The seminal work of \citet{Zwicky:1936} and \citet{McLaughlin:1939}
first showed that more luminous novae within the Milky Way tend to
have more rapidly declining light curves, which is now the basis of
the maximum-magnitude versus rate-of-decline (MMRD) relationship. The
basic form of the MMRD relation has been theoretically attributed to a
dependence of the peak luminosity on the mass of the accreting white
dwarf \citep[e.g.][]{Livio:1992}. Studies of extragalactic novae
reaching as far as the Virgo cluster have shown that the MMRD relation
is broadly applicable to all nova populations, though with significant
scatter
\citep[e.g.][]{Ciardullo:1990,DellaValle:1995,Ferrarese:2003,Shafter:2011}.
Amidst that scatter, there may also be sub-populations of novae that
deviate from the traditional MMRD form \citep{Kasliwal:2011a}, and
recurrent novae (RNe) in particular may be poorly represented by the
MMRD \citep{Shafter:2011,Hachisu:2015}
In Figure~\ref{fig:PeakLuminosityDeclineTimeWide}, the dark grey
region follows the empirical constraints on the MMRD from
\citet{DellaValle:1995}, and the wider light grey band allows for the
increased scatter about that relation that has been noted from more
extensive surveys of novae in the Milky Way \citep{Downes:2000}, M31
\citep{Shafter:2011} and elsewhere in the local group
\citep{Kasliwal:2011a}. Nova outbursts can exhibit decline times from
$\sim$1 day to many months, so the timescale of the \spock light
curves can easily be accommodated by the nova scenario. However, the
peak luminosities inferred for the \spock events are larger than any
known novae, perhaps by as much as 2 orders of magnitude.
Figure~\ref{fig:PeakLuminosityDeclineTime} shows a narrower slice of
the same phase space as in
Figure~\ref{fig:PeakLuminosityDeclineTimeWide}, zooming in on the
``fast and faint'' region from the lower left corner. The observed
constraints from the two published kilonova candidates are shown,
which provide only lower limits on the peak luminosity
\citep{Tanvir:2013}, or the decline timescale \citep{Perley:2009}.
Two .Ia candidates are also plotted, SN 2002bj \citep{Poznanski:2010}
and SN 2010X \citep{Kasliwal:2010}. The sample of observed nova
outbursts (shown as solid points) demonstrates the observed scatter
about the MMRD relation.
One primary line of evidence supporting the nova hypothesis
comes from the \spock light curves. Many RN light curves are similar
in shape to the \spock episodes, exhibiting a sharp rise ($<10$ days
in the rest-frame) and a similarly rapid decline.
Figure~\ref{fig:RecurrentNovaLightCurveComparison} compares the \spock
light curves to template light curves from RNe within our galaxy and
in M31. There are 10 known RNe in the Milky Way galaxy, and 7 of
these exhibit outbursts that decline rapidly, fading by 2 magnitudes
in less than 10 days \citep{Schaefer:2010}
% U Sco, V2487 Oph, V394 CrA, T CrB, RS Oph, V745 Sco, and V3890 Sgr.
The gray shaded region in
Figure~\ref{fig:RecurrentNovaLightCurveComparison} encompasses the V
band light curve templates for all 7 of these events, from
\citet{Schaefer:2010}. The Andromeda galaxy (M31) also hosts at least
one RN with a rapidly declining light curve. The 2014 eruption of
this well-studied nova, M31N 2008a-12, is shown as a solid black line
in Figure~\ref{fig:RecurrentNovaLightCurveComparison}, fading by 2
mags in less than 3 days. This comparison demonstrates that the
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.
Among the most luminous classical novae known, a similarly rapid
decline time is not unheard of. For example, the bright nova
M31N-2007-11d had $t_2 = 9.5$ days \citep{Shafter:2009}. The
extremely luminous nova SN 2010U had $t_2 = 3.5 \pm 0.3$
\citep{Czekala:2013}. The nova L91 required at least 4 days to rise
to maximum \citep{Shafter:2009}, and then declined with $t_2 = 6 \pm
1$ days \citep{DellaValle:1991, Williams:1994, Schwarz:2001}.
Another 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,
and the gravitational lensing time delay does not need to match the
observed 8 month separation between the January and August 2014
appearances.
Although {\it qualitatively} consistent with the 8-month separation,
the RN model is strained by a quantitative assessment of the
recurrence period. If \spock is indeed a RN at $z=1$, then the
recurrence timescale in the rest-frame is $120\pm30$ days ($3-5$
months), where the uncertainty accounts for the $1\sigma$ range of
modeled gravitational lensing time delays. This would be a singularly
rapid recurrence period, significantly faster than all 11 RNe in our
own galaxy, which have recurrence timescales ranging from 15 years (RS
Oph) to 80 years (T CrB). For the 5 galactic RNe with a rapidly
declining outburst light curve (U Sco, V2487 Oph, V394 CrA, T CrB, and
V745 Sco), the median recurrence timescale is 21 years. The fastest
measured recurrence timescale belongs to the Andromeda galaxy nova
M31N 2008a-12, which has exhibited a new outburst every year from
2009-2015
\citep{Tang:2014,Darnley:2014,Darnley:2015,Henze:2015,Henze:2015a}. Although
this M31 record-holder demonstrates that very rapid recurrence is
possible, classifying \spock as a RN would still require a very
extreme mass transfer rate to accommodate the $<1$ year recurrence.
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
reconcile the \spock luminosity more comfortably with the nova class
by assuming a significant lensing magnification for one of the two
events. This would drive down the intrinsic luminosity, perhaps to
$\sim10^{40}$ erg s${-1}$, on the edge of the nova region. However,
this assumption implicitly moves the lensing critical curve to be
closer to the \spock event in question. That pulls the critical curve
away from the other \spock position, which makes that second event
{\it more inconsistent} with observed nova peak luminosities.
\subsubsection{Physical Implications of the RN Model}
The physical limits of the RN model are best evaluated by combining
the two key observables of recurrence period and peak brightness. In
this examination we rely on a pair of papers that evaluated an
extensive grid of nova models through multiple cycles of outburst and
quiescence \citep{Prialnik:1995,Yaron:2005}.
Figure~\ref{fig:RecurrentNovaRecurrenceComparison} plots first the RN
outburst amplitude (the apparent magnitude between outbursts minus the
apparent magnitude at peak) and then the peak luminosity against the
log of the recurrence period in years.
% The observations for \spock
% are shown in comparison to observed RNe (crosses) and theoretical
% models (circles) from \citet{Yaron:2005}.
For the \spock events we can only measure a lower limit on the
outburst amplitude, since the presumed progenitor star is unresolved,
so no measurement is available at
quiescence. Figure~\ref{fig:RecurrentNovaRecurrenceComparison} shows
that a recurrence period as fast as one year is expected only for a RN
system in which the primary WD is both very close to the Chandrasekhar
mass limit (1.4 \Msun) and also has an extraordinarily rapid mass
transfer rate ($\sim10^{-6}$ \Msun yr$^{-1}$). The models of
\citet{Yaron:2005} suggest that such systems should have a very low
peak amplitude (barely consistent with the lower limit for \spock) and
a low peak luminosity ($\sim$100 times less luminous than the \spock
events).
The closest analog for the \spock events from the population of known
RN systems is the nova M31N\,2008a-12. \citet{Kato:2015} provided a
theoretical model that can account for the key observational
characteristics of this remarkable nova: the very rapid recurrence
timescale ($<$1 yr), fast optical light curve ($\t2\sim2$ days), and
short supersoft x-ray phase \citep[6-18 days after optical
outburst][]{Henze:2015a}. To match these observations,
\citeauthor{Kato:2015} invoke a 1.38 \Msun white dwarf primary,
drawing mass from a companion at a rate of $1.6\times10^{-7}$ \Msun
yr$^{-1}$. This is largely consistent with the theoretical
expectations derived by \citet{Yaron:2005}, and reinforces the
conclusion that a combination of a high mass white dwarf and efficient
mass transfer are the key ingredients for rapid recurrence and short
light curves. The one feature that can not be effectively explained
with this scenario is the peculiarly high luminosity of the \spock
events -- even after accounting for the very large uncertainties. If
the \spock transients are caused by a single RN system, then that
progenitor system would be the most extreme WD binary yet known.
\section{Non-explosive Astrophysical Transients}
There are several categories of astrophysical transients that are not
related to stellar explosions, and we find that these models cannot
accommodate the observations of the \spock transients. We may first
dismiss any of the category of {\it periodic} sources (e.g. Cepheids,
RR Lyrae, or Mira variables) that exhibit regular changes in flux due
to pulsations of the stellar photosphere. These variable stars do not
exhibit sharp, isolated transient episodes that could match the \spock
light curve shapes.
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
to infrared wavelengths \citep[e.g.][]{Gaskell:2003}. The AGN
hypothesis for \spock is disfavored for three primary reasons:
%principally due to the quiescence of the
%\spock sources between the two observed episodes.
First, AGN that exhibit short-duration transient events also typically
exhibit slower variation on much longer timescales, which is not
observed at either of the \spock locations. Second, the spectrum
of the \spock host galaxy shows none of the broad emission lines that
are often (though not always) observed in AGN. Third, an AGN would
necessarily be located at the center of the host galaxy.
%The severe distortion of the
%host galaxy images makes it impossible to identify the location of the
%host center in images 11.1 and 11.2 from the galaxy morphology. Any
%spatial reconstruction at the source plane from the lens models would
%not be not precise enough for a useful test. However, since
%gravitational lensing is achromatic, if the \spock positions are
%coincident with the host galaxy center, then the color of the galaxy
%at each \spock location in images 11.1 and 11.2 should be consistent
%with the color at the center of the less distorted image 11.3.
In Section~\ref{sec:HostGalaxy}
we saw that there are minor differences in the host galaxy properties
(i.e. rest-frame U-V color and mean stellar age) from the \spockone
and \spocktwo locations to the center of the host galaxy at image 11.3
Although by no means definitive, this suggests that the \spock events
were not located at the physical center of the host galaxy, and
therefore are not related to an AGN. \todo{Update with MUSE results}
Stellar flares provide a third very common source for optical
transient events. Relatively mild stellar flares may be caused by
magnetic activity in the stellar atmosphere, and the brightest flare
events (so-called ``superflares'') may be generated by perturbations
to the stellar atmosphere via interactions from a disk, a binary
companion, or a planet. In these circumstances the stars release a
{\em total} energy in the range of $10^{33}$ to $10^{38}$ erg over a
span of minutes to hours \citep{Balona:2012,Karoff:2016}. This falls
far short of the observed energy release from the \spock transients,
so we can also dismiss stellar flares as implausible for this source.
\subsection{Microlensing}
In the presence of strong gravitational lensing it is possible to
generate a transient event from lensing effects alone. In this case
the background source has a steady luminosity but the relative motion
of the source, lens, and observer causes the magnification of that
source to change rapidly with time.
A commonly observed example is the microlensing of a bright background
source (a quasar) by a galaxy-scale lens \citep{Wambsganss:2001,
Kochanek:2004}. In this optically thick microlensing regime, the
lensing potential along the line of sight to the quasar is composed of
many stellar-mass objects. Each compact object along the line of
sight generates a separate critical lensing curve, resulting in a
complex web of overlapping critical curves. As all of these lensing
stars are in motion relative to the background source, the web of
caustics will shift across the source position, leading to a
stochastic variability on timescales of months to years. This
scenario is inconsistent with the observed data, as the two \spock
events were far too short in duration and did not exhibit the repeated
``flickering'' variation that would be expected from optically thick
microlensing.
A second possibility is through an isolated strong lensing event with
a rapid timescale, such as a background star crossing over a lensing
critical curve. This corresponds to the optically thin microlensing
regime, and is similar to the ``local'' microlensing light curves
observed when stars within our galaxy or neighboring dwarf galaxies
pass behind a massive compact halo object \citep{Paczynski:1986,
Alcock:1993, Aubourg:1993, Udalski:1993}. In the case of a star
crossing the caustic of a smooth lensing potential, the amplification
of the source flux would increase (decrease) with a characteristic
$t^{-1/2}$ profile as it moves toward (away from) the caustic. This
slowly evolving light curve transitions to a very sharp decline (rise)
when the star has moved to the other 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}.
To generate an isolated microlensing event, the background source
would have to be the dominant source of luminosity in its environment,
meaning it must be a very bright O or B star with mass of order 10
\Msun. Depending on its age, the size of such a star would range from
a few to a few dozen times the size of the sun. The net relative
transverse velocity would be on the order of a few 100 km/s, which is
comparable to the orbital velocity of stars within a galaxy or
galaxies within a cluster. In the case of a smooth cluster potential---the
%timescale
%$\tau$ for the light curve of such a caustic crossing event is
%dictated by the radius of the source, $R$, and the net transverse
%velocity, $v$, of the source across the caustic, as:
%
%\begin{equation}
% \tau = 6\frac{R}{5\,\Rsun}\frac{300 {\rm km~ s}^{-1}}{v}~\rm{hr}
%\label{eqn:caustic_crossing_time}
%\end{equation}
%
%
%\noindent Thus, the
characteristic timescale of such an event would be on the order of
hours or days \citet{Chang:1979,Chang:1984,MiraldaEscude:1991}, which
is in the vicinity of the timescales observed for the \spock events.
However, if we apply this scenario to the \macs0416 field, we can not
plausibly generate two events with similar decay timescales at
distinct locations on the sky. This is because a caustic-crossing
transient event must necessarily appear at the location of the lensing
critical curve, but in this case the critical curve most likely passes
between the two observed \spock locations. At best, a caustic crossing
could account for only one of the \spock events, not both.
diff --git a/ColorCurves.tex b/ColorCurves.tex
index b4843b3..3f1ce78 100644
--- a/ColorCurves.tex
+++ b/ColorCurves.tex
...
\subsection{Color Curves}\label{sec:ColorCurves} Curves.}\label{sec:ColorCurves}
Atredshift $z=1$ the observed optical and infrared bands translate to
rest-frame ultraviolet (UV) and optical wavelengths, respectively. To
derive rest-frame UV and optical colors from the observed photometry,
we start with the measured magnitude in a relatively blue band (F435W
...
broad bands for each transient event at each epoch. For consistency
with past published results, we include in each K correction a
transformation from AB to Vega-based magnitudes. The resulting UV and
optical colors are plotted in
Supplementary Figure~\ref{fig:ColorCurves}. Both
\spockone and \spocktwo show little or no color variation over the
period where color information is available. This lack of color
evolution is compatible with all three of the primary hypotheses
...
If these two events are from a single source then one could construct
a composite SED from rest-frame UV to optical wavelengths by combining
the NW and SE flux measurements, but only after correcting for the
relative magnification. Figure~\ref{fig:LightCurves}
shows that the observed peak brightnesses for the two events agree to
within $\sim30\%$. This implies that for any composite SED, the
rest-frame UV to optical flux ratio is approximately equal to the
NW:SE magnification ratio, and any extreme asymmetry in the
magnification would indicate a very steep slope in the SED.
diff --git a/Discussion.tex b/Discussion.tex
index a4dd90f..514c927 100644
--- a/Discussion.tex
+++ b/Discussion.tex
...
(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
can not cannot make a definitive choice
between these hypotheses, principally due to the scarcity of
observational data and the uncertainty in 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 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
diff --git a/Figures.tex b/Figures.tex
index e877912..058c770 100644
--- a/Figures.tex
+++ b/Figures.tex
...
\end{center}
\end{figure*}
%\end{multicols}
\input{LensingSummaryTable.tex}
%\begin{multicols}{2}
\begin{figure*}[tbp]
\begin{center}
\includegraphics[width=1\textwidth]{./figures/spock_lightcurves/spock_lightcurves_flux}
\caption{ \protect\input{./figures/spock_lightcurves/caption.tex}} \includegraphics[width=\textwidth]{./figures/spock_predictions/spock_predictions}
\caption{\protect\input{./figures/spock_predictions/caption.tex}}
\end{center}
\end{figure*}
\begin{figure*}[tbp]
\begin{center}
\includegraphics[width=\textwidth]{./figures/spock_critical_curves/spock_critical_curves} \includegraphics[width=\textwidth]{./figures/spock_critical_curves/spock_critical_curves.png}
\caption{\protect\input{./figures/spock_critical_curves/caption.tex}}
\end{center}
\end{figure*}
\begin{figure*}[tbp]
\begin{center}
\includegraphics[width=1\textwidth]{./figures/spock_lightcurves/spock_lightcurves_flux}
\caption{ \protect\input{./figures/spock_lightcurves/caption.tex}}
\end{center}
\end{figure*}
\begin{figure*}[tbp]
\begin{center}
\includegraphics[width=0.48\textwidth]{./figures/peakluminosity_vs_declinetime/peakluminosity_vs_declinetime_sn}
...
\end{center}
\end{figure*}
\begin{figure*}[tbp]
\begin{center}
\includegraphics[width=\textwidth]{./figures/spock_predictions/spock_predictions}
\caption{\protect\input{./figures/spock_predictions/caption.tex}}
\end{center}
\end{figure*}
%\end{multicols}
\input{LensingSummaryTable.tex}
%\begin{multicols}{2}
diff --git a/HostGalaxy.tex b/HostGalaxy.tex
index 346969c..095076c 100644
--- a/HostGalaxy.tex
+++ b/HostGalaxy.tex
...
To examine whether the two transients originated from the same
physical location in the source plane, we looked for differences in
the properties of the \spock host galaxy at the location of each
event. We first used the technique of ``pixel-by-pixel'' SED
fitting
as described in \citet{Hemmati:2014} fitting\cite{Hemmati:2014} to determine rest-frame colors and stellar
properties in a single resolution element of the \HST imaging data.
For this purpose we used the deepest possible stacks of \HST images,
comprising all available data except those images where the transient
events were present. The resulting maps of stellar population
properties are shown in
Supplementary Figure~\ref{fig:HostProperties}.
Supplementary Table~\ref{tab:HostProperties} reports measurements of
the three derived stellar population properties (color, mass, age)
from host images 11.1, 11.2 and 11.3. In 11.1 and 11.2 these
measurements were extracted from the central pixel at the location of
each of the two \spock events. The lensing magnification here ranges
from $\mu=10$ to
100 (see Section~\ref{sec:LensingModels}), 200, corresponding to a size on the source plane
between 6 and 600 pc$^2$. For host image 11.3 we report the stellar
population properties derived from the pixel at the center of the
galaxy, because the lens models do not have sufficient precision to
map the \spock locations to specific positions in image 11.3. With a
magnification of $\sim$3 to 5, this extraction region covers roughly
2000 to 6000 pc$^2$.
\begin{deluxetable}{lccc}
\tablewidth{0.7\linewidth}
\tablecolumns{6}
\tablecaption{Properties of the local stellar population in the \spock host galaxy, from SED fitting.}
\tablehead{ {Host image:} & \colhead{11.1} & \colhead{11.2} & \colhead{11.3}\\
{Location:} & \colhead{\spocktwo} & \colhead{\spockone} & \colhead{center}}
\startdata
$(U-V)_{\rm rest}$ & 0.69$^{+0.2}_{-0.05}$ & 0.52$^{+0.15}_{-0.10}$ & 0.39$\pm$0.05 \\
$\log[\Sigma (M_*/\Msun)]$ & 7.14 $\pm$ 0.15 & 7.14 $\pm$ 0.15 & 7.04 $\pm$ 0.10 \\
Age (Gyr) & 0.292$\pm$0.5 & 0.290$\pm$0.5 & 0.292$\pm$0.5
\enddata
\label{tab:HostProperties}
\end{deluxetable}
The reported uncertainties for these derived stellar properties in
Table~\ref{tab:HostProperties} reflect only the measurement errors
...
galaxies and varies significantly across the \MACS0416 field. Such a
bias might shift the absolute values of the parameter scales for any
given host image (e.g., making the galaxy as a whole appear bluer,
more
massive massive, and younger). However, the gradients across any single
host image are unlikely to be driven primarily by such systematics.
Supplementary Figure~\ref{fig:HostProperties} and
Supplementary
Table~\ref{tab:HostProperties} show that the measured values of the
color, stellar mass, and age at the two \spock locations are mutually
consistent. Thus, it is plausible to assume that the two positions map
back to the same physical location at the source plane. Comparing
those two locations to the center of the galaxy as defined in image
11.3, we see only a mild tension in the
rest-frame U-V rest frame $U-V$ color. This
comparison therefore cannot quantitatively rule out the possibility
that the two transient events are located at the center of the
galaxy. However, the maps shown in
Supplementary Figure~\ref{fig:HostProperties} do
show a gradient in both
U-V $U-V$ color and stellar age. For both images
11.1 and 11.2 the bluest and youngest stars
(U-V$\sim$0.3, $\tau\sim$280 ($U-V\approx0.3$,
$\tau\approx280$ Myr) are localized in knots near the extreme ends of
each image, well separated from either of the \spock transient events.
In the less distorted host image 11.3 the bluer and younger stars are
concentrated near the center. Taken together, these color and age
gradients suggest that the two transients are not coincident with the
center of their host galaxy.
\input{muse_linefits}
In addition to the \HST imaging data, we also have spatially resolved
spectroscopy from the MUSE integral field data. The only significant
spectral line feature for the \spock host is the \forbidden{O}{ii}
($\lambda\lambda$ $\lambda\lambda$ 3726,
3729) 3729 doublet, observed at 7474 and 7478 \AA.
To examine this feature in detail, one-dimensional spectra were
extracted from the three-dimensional MUSE data cube at a series of
locations along the \spock
host galaxy host-galaxy arc.
Supplementary Figure~\ref{fig:MUSEOIISequence} depicts the apertures used for these
extractions, shows the observed \forbidden{O}{ii} lines at the
\spock-NW and SE positions, and compares the \forbidden{O}{ii} line
profiles to other positions along the length of the
host galaxy host-galaxy arc.
At each position the lines were extracted using apertures with a
radius of
0\farcs6, $0.6''$, so adjacent extractions are not independent,
although the two extractions centered on the \spockone and -SE
positions have no overlap.
...
emerged from independent sources. For a visual test for spectral
deviations, we first constructed a mean spectrum by averaging the 1-D
spectra from five non-overlapping apertures (apertures 1, 3, 5, 7,
9). To account for differences in magnification and
host galaxy host-galaxy
intensity across the arc, each input spectrum was normalized at the
wavelength 7477.7
$\AA$, \AA, which corresponds to the center of the
$\lambda$3729 component of the \forbidden{O}{ii} emission line. This
mean spectrum was then subtracted from the 1-D spectrum of each
aperture, producing a set of ``residual spectra,'' shown in
Supplementary Figure~\ref{fig:MUSEOIISequence} in the
lower left lower-left panel. These
spectra show no indication of a systematic trend in the wavelength
position, shape or line ratio across the arc. Similarly, a comparison
of the spectra from the \spock-NW and SE locations (right panels of
Supplementary Figure~\ref{fig:MUSEOIISequence}) reveals no significant difference in
the \forbidden{O}{ii} line shapes.
This qualitative comparison is
born borne out by a more quantitative
assessment, reported in Table~\ref{tab:MuseLineFits}. We fit a
Gaussian profile to each component of the \forbidden{O}{ii} doublet,
separately in each extracted 1-D spectrum. From these fits we measured
the integrated line flux, observed wavelength of line center
($\lambda_{\rm center}$), full width at half maximum
intensity (FWHM), and the
intensity ratio of the two components of the doublet. These
quantities--all quantities---all reported in
Table~\ref{tab:MuseLineFits}--do Table~\ref{tab:MuseLineFits}---do not
exhibit any discernible gradient across the host galaxy. Thus, the
\forbidden{O}{ii} measurements from MUSE cannot be used to distinguish
either \spock location from the other, or to definitively answer
diff --git a/HostGalaxyProperties.tex b/HostGalaxyProperties.tex
new file mode 100644
index 0000000..bdbc826
--- /dev/null
+++ b/HostGalaxyProperties.tex
...
\begin{deluxetable}{lccc}
\tablewidth{0.7\linewidth}
\tablecolumns{6}
\tablecaption{Properties of the local stellar population in the \spock host galaxy, from SED fitting.}
\tablehead{ {Host image:} & \colhead{11.1} & \colhead{11.2} & \colhead{11.3}\\
{Location:} & \colhead{\spocktwo} & \colhead{\spockone} & \colhead{center}}
\startdata
$(U-V)_{\rm rest}$ & 0.69$^{+0.2}_{-0.05}$ & 0.52$^{+0.15}_{-0.10}$ & 0.39$\pm$0.05 \\
$\log[\Sigma (M_*/\Msun)]$ & 7.14 $\pm$ 0.15 & 7.14 $\pm$ 0.15 & 7.04 $\pm$ 0.10 \\
Age (Gyr) & 0.292$\pm$0.5 & 0.290$\pm$0.5 & 0.292$\pm$0.5
\enddata
\label{tab:HostProperties}
\end{deluxetable}
diff --git a/IntroductionShort.tex b/IntroductionShort.tex
index ac89ab8..1cf4ed7 100644
--- a/IntroductionShort.tex
+++ b/IntroductionShort.tex
...
When a star explodes or a relativistic jet erupts from near the edge
of a black hole, the event can be visible across many billions of
light-years. Such extremely luminous astrophysical transients as
supernovae (SNe),
gamma ray bursts gamma-ray bursts, and quasars are powerful tools for
probing cosmic history and sampling the matter and energy content of
the universe. Less energetic transients generated by the tumultuous
atmospheres of massive stars or the interactions of close stellar
...
%maximize the area of sky covered while remaining sensitive to their
%primary targets---relatively bright Type Ia SNe.
Although recent surveys are beginning to discover
more and progressively more
categories of rapidly changing optical
transients\cite{Kasliwal:2011a,Drout:2014}, most programs remain
largely insensitive to transients with peak brightness and timescales
...
such transients, and can be expected to reveal many new categories of
astrophysical transients.
As shown in
Fig.~\ref{fig:SpockDetectionImages}, Figure~\ref{fig:SpockDetectionImages}, the \spock events
appeared in \HST imaging collected as part of
the Hubble Frontier Fields (HFF) survey\cite{Lotz:2017}, a multi-cycle
program for deep imaging of 6 massive galaxy clusters and associated
...
relatively high redshift ($z\gtrsim1$) in these fields are made
detectable by the substantial gravitational lensing magnification from
the foreground galaxy clusters. Very rapidly evolving sources are
also more likely to be found,
due owing to the necessity of a rapid cadence
for repeat imaging in the HFF program.
diff --git a/LBV.tex b/LBV.tex
index 90b63ab..098e359 100644
--- a/LBV.tex
+++ b/LBV.tex
...
\subsection{Luminous Blue Variable Light Curve Comparison}
\label{sec:LBVlightcurves}
Extended Data Fig.~\ref{fig:LBVLightCurveComparison} presents a direct
comparison of the observed \spock light curves against the light
curves of the two LBVs that have well-studied rapid eruptions: SN
2009ip and NGC3432-LBV1. The brief outbursts of these LBVs have been
less finely sampled than the two \spock events, but the available data
show a wide variety of rise and decline times, even for a single
object over a relatively narrow time window of a few months. \subsection{LBV Build-up
timescale}\label{sec:LBVbuildup} Timescale and Quiescent Luminosity.}\label{sec:LBVbuildup}
To explore some of the physical implications of an LBV classification
for the two \spock events, we first make a rough estimate of the total
...
\end{equation}
\noindent where $\zeta$ is a dimensionless factor of order unity that
depends on the precise shape of the light
curve\cite{Smith:2011b}. Note that earlier work\cite{Smith:2011b} has
used $t_{1.5}$ instead of $t_2$, which amounts to a different
light curve light-curve shape term, $\zeta$. Adopting
\Lpk$\sim10^{41}$ \Lpk$\approx10^{41}$ erg
s$^{-1}$ and
\t2$\sim$1 \t2$\approx$1 day (as shown in
Figure~\ref{fig:PeakLuminosityDeclineTime}), Fig.~\ref{fig:PeakLuminosityDeclineTime}), we find that the total
radiated energy is $E_{\rm
rad}\sim10^{46}$ rad}\approx10^{46}$ erg. A realistic range
for this estimate would span $10^{44}
uncertainties in the magnification, bolometric luminosity correction,
decline time, and
light curve light-curve shape. These uncertainties
notwithstanding, our estimate falls well within the range of plausible
values for the total radiated energy of a major LBV outburst.
The ``build-up'' timescale\citep{Smith:2011b} matches the radiative
energy released in an LBV eruption event with the radiative energy
produced during the intervening quiescent
phase: phase,
\begin{equation}
\label{eqn:trad}
...
and a gravitational lensing time delay of $\sim$40 days). Adopting
$\Lpk=10^{41}$ erg s$^{-1}$ and $\t2=2$ days (see
Figure~\ref{fig:PeakLuminosityDeclineTime}), we infer that the
quiescent luminosity of the \spock progenitor would be
$L_{\rm
qui}\sim10^{39.5}$ qui}\approx10^{39.5}$ erg s$^{-1}$
($M_V\sim-10$). ($M_V\approx-10$ mag).
%Rapid transient episodes in LBVs may
diff --git a/LBVsupplement.tex b/LBVsupplement.tex
new file mode 100644
index 0000000..7b9f402
--- /dev/null
+++ b/LBVsupplement.tex
...
\subsection{LBV Light-Curve Comparison.}
\label{sec:LBVlightcurves}
Supplementary Figure~\ref{fig:LBVLightCurveComparison} presents a direct
comparison of the observed \spock light curves against the light
curves of the two LBVs that have well-studied rapid eruptions: SN
2009ip and NGC3432-LBV1. The brief outbursts of these LBVs have been
less finely sampled than the two \spock events, but the available data
show a wide variety of rise and decline times, even for a single
object over a relatively narrow time window of a few months.
diff --git a/LensModelVariations.tex b/LensModelVariations.tex
new file mode 100644
index 0000000..4cf0f46
--- /dev/null
+++ b/LensModelVariations.tex
...
\subsection{Lens Model Variations.}\label{sec:LensModelVariations}
Supplementary Figure~\ref{fig:LensModelContours} presents probability
distributions for the three magnifications and two time delay values
of interest. These distributions were derived by combining the Monte
Carlo chains from the CATS, GLAFIC, GLEE, and ZLTM models, and
individual runs of the GRALE model, which uses a different random seed
for each run. We applied a weight to each model to account for the
different number of model iterations used by each modeling team. All
five of these models agree that host image 11.3 is the leading image,
appearing some 3--7 years before the other two images. The models do
not agree on the arrival sequence of images 11.1 and 11.2: some have
the NW image 11.2 as a leading image, and others have it as a trailing
image. However, the models do consistently predict that the
separation in time between those two images should be roughly in the
range of 1 to 60 days.
Because of the proximity of the critical curves in all models, the
predicted time delays and magnification factors are significantly
different if calculated at the model-predicted positions instead of
the observed positions. For example, in the GLEE model series (GLEE
and GLEE-var) when switching from the observed to model-predicted
positions the arrival order of the NW and SE images flips, the
expected time delay drops from tens of days to $<$1 day, and the
magnifications change by 30-60\%. However, the expected
magnifications and time delays between the events still fall within
the broad ranges summarized in Table~\ref{tab:LensModelPredictions}
and shown in Supplementary Figure~\ref{fig:LensModelContours}. Regardless of
whether the model predictions are extracted at the observed or
predicted positions of the \spock events, none of the lens models can
accommodate the observed 234-day time difference as purely a
gravitational lensing time delay.
We used variations of several lens models to investigate how the
lensing critical curves shift under a range of alternative assumptions
or input constraints. These variations highlight the range of
systematic effects that might impact the model predictions for the
\spock magnifications, time delays and proximity to the critical
curves. Figure~\ref{fig:SpockCriticalCurves} shows the critical
curves for a source at $z=1$ (the redshift of the \spock host galaxy)
predicted by our seven baseline models, plus the four variations
described below. Within a given model, variations that move a
critical curve closer to the position of \spockone\ would drive the
magnification of that event much higher (toward $\mu_{\rm
NW}\approx200$). This generally also has the effect of moving the
critical curve farther from \spocktwo, which would necessarily drive
its magnification downward (toward $\mu_{\rm SE}\approx10$).
The baseline CATS model reported in
Table~\ref{tab:LensModelPredictions} corresponds to the CATSv4.1 model
published on the STScI Frontier Fields lens model repository
(\url{https://archive.stsci.edu/pub/hlsp/frontier/macs0416/models/cats/v4.1/}).
That model uses 178 cluster member galaxies, including a galaxy $<5''$
south of the \spock host galaxy, which creates a local critical curve
that intersects the \spocktwo location. Our CATS-var model is an
earlier iteration of the model, published on the STScI repository as
CATSv4
(\url{https://archive.stsci.edu/pub/hlsp/frontier/macs0416/models/cats/v4/}),
and includes only 98 galaxies identified as cluster members. In this
variation the nearby cluster member galaxy is not included, so the
\spocktwo event is not intersected by a critical curve. However, the
\spockone event is approximately coincident with the primary critical
curve of the \macs0416 cluster. When the critical curve is close to
either \spock location, the magnifications predicted by the CATS model
are driven up to $\mu>100$. However, the time delays remain small, on
the order of tens of days, and incompatible with the observed 234-day
gap.
The WSLAP-var model evaluates whether the cluster redshift
significantly impacts the positioning of the critical curve. In this
merging cluster, the northern brightest cluster galaxy (BCG) has a
slighter higher redshift than the southern BCG. The mean redshift of
the cluster is not precisely determined, since it is likely to be
aligned somewhat along the line of sight. For the WSLAP-var model we
shift the assumed cluster redshift $z=0.4$ from the default $z=0.396$
(used in all the baseline models). The shift in the critical curve is
noticeable, but not substantial, insofar as this change does not drive
the critical curve to intersect either or both of the \spock
locations.
The GLEE-var model is a multi-plane lens model (Chiriv{\`i} et al.,~in
prep.) that incorporates 13 galaxies with spectroscopic redshifts that
place them either in the foreground or background of the \macs0416
cluster. Supplementary Figure~\ref{fig:LineOfSightLenses} marks these
13 galaxies and highlights two of them that appear in the foreground
of the \spock host galaxy and are close to the lines of sight to the
\spock transients. Both the foreground $z=0.0557$ galaxy and the
reconstructed position of the $z=0.9397$ galaxy have a projected
separation of $<$4\arcsec from the \spocktwo transient position.
Including these galaxies in the GLEE lensing model changes the
absolute value of the magnifications at the location of HFF14Spo-NW
(HFF14Spo-SE) to $\sim70$ ($\sim250$) and the time delay between the
two locations to $\sim50$ days. The line-of-sight galaxies also
result in a shift of the position of the critical curve---as can be
seen by comparing the GLEE and GLEE-var models in
Figure~\ref{fig:SpockCriticalCurves}. Nonetheless, the predicted time
delays are still incompatible with the observed gap of 234 days
between events.
The GLAFIC-var model examines whether it is plausible for a critical
curve to intersect both \spock locations---contrary to the baseline
assumption of a single critical curve subtending the \spock host
galaxy roughly midway between the two positions. This model includes
a customized constraint, requiring that the magnification factors at
the \spock positons are $>1000$. To achieve this, we independently
adjusted the mass scaling for the two nearest cluster member galaxies,
which are located just northeast and south of the \spock host galaxy
arc. The mass of the northeast member galaxy was increased by
$\sim$30\% and that of the southern one by $\sim$60\%. As a simple
check of the predicted morphology of the host galaxy, we placed a
source with a simple Sersic profile\cite{Sersic:1963} on the source
plane. The lensed image of that artificial source is an unbroken
elongated arc, reproducing the host galaxy image morphology reasonably
well.
For this modification of the GLAFIC lens model to be justified in a
statistical sense, the revised model should still accurately reproduce
the observed strong-lensing constraints across the entire cluster.
The $\chi^2$ statistic for the baseline GLAFIC model is 240, with 196
degrees of freedom ($\chi^2_\nu=1.2$), and yields an Akaike
information criterion (AIC)\citep{Akaike:1974} of 676. For the
GLAFIC-var model that forces multiple critical curves to intersect the
\spock locations, we get $\chi^2$=331 for 192 degrees of freedom
($\chi^2_\nu=1.7$) and AIC=769. This suggests that the multiple
critical curve GLAFIC-var model is strongly disfavored by the
{\it positional} strong-lensing constraints that are used for both models.
However, we note that neither model incorporates the temporal
constraints of the observed time delay.
A second variation of the CATS model (CATS-var2) was also used to test
the plausibility of multiple critical curves intersecting the \spock
locations. As in the GLAFIC-var case, this model requires that
critical curves pass very near the \spock positions. The model can
accommodate that constraint, insofar as the root mean square (RMS)
error of the best-fit model is similar to that of the CATS and
CATS-var models. However, in this CATS-var2 model the \spock host
galaxy is predicted to be multiply-imaged 5 times. The \HST images do
not exhibit any breaks or substructure in the arc that would be
generally expected in such a situation.
Moreover, this CATS-var2 model has strong implications for a separate
background galaxy in the vicinity of image 11.3 (system 14 in
\citeref{Caminha:2017}). This galaxy is strongly lensed by a pair of
spectroscopically confirmed cluster member galaxies\citep{Caminha:2017}. Comparing the observed positions of the multiple
images of System 14 against the CATS-var2 model-predicted positions,
we find that this System contributes significantly to the global RMS
error for the model---indicating that the CATS-var2 model can not
accurately reproduce the multiple images of System 14. Conversely,
when this system is removed as a model constraint, the RMS error
decreases, and the CATS-var2 model can more successfully pass the
critical line through the two \spock locations. A possible
interpretation of this is that the established strong lensing
constraints (especially System 14) are incompatible with the
requirement that multiple critical curves must intersect the two
\spock locations.
diff --git a/LensingModels.tex b/LensingModels.tex
index 866000d..c60cfc8 100644
--- a/LensingModels.tex
+++ b/LensingModels.tex
...
\subsection{Gravitational Lens
Models}\label{sec:LensingModels} Models.}\label{sec:LensingModels}
%That same transient episode would have appeared at
...
%more widely separated image 11.3.
The seven lens models used to provide estimates of the plausible range
of magnifications and time delays
are: are as follows:
\bigskip
\begin{itemize}
\item{{\it \item{\it CATS:} The model of
\citet{Jauzac:2014}, \citeref{Jauzac:2014}, version 4.1,
generated with the {\tt LENSTOOL} software
\citep{Jullo:2007},\footnote{\url{http://projects.lam.fr/repos/lenstool/wiki}}} (\url{http://projects.lam.fr/repos/lenstool/wiki})\citep{Jullo:2007}
using strong lensing constraints. This model
makes a
light-traces-mass assumption and parameterizes cluster
and galaxy components using pseudo-isothermal elliptical mass
distribution (PIEMD) density
profiles
\citep{Eliasdottir:2007, profiles\citep{Kassiola:1993,
Limousin:2007}.
\item{\it GLAFIC:} The model of
\citet{Kawamata:2016}, \citeref{Kawamata:2016}, built using
the {\tt
GLAFIC}\footnote{\url{http://www.slac.stanford.edu/~oguri/glafic/}} GLAFIC} software
\citep{Oguri:2010b} (\url{http://www.slac.stanford.edu/~oguri/glafic/})\citep{Oguri:2010b}
with strong-lensing constraints. This model assumes simply
parametrized mass distributions, and model parameters are
constrained using positions of more than 100 multiple images.
\item{\it GLEE:} A new model built using the {\tt GLEE}
software
\citep{Suyu:2010b, software\citep{Suyu:2010b, Suyu:2012} with the same strong-lensing
constraints used in
\citet{Caminha:2017}, \citeref{Caminha:2017}, representing mass
distributions with simply parameterized mass profiles.
\item{{\it \item{\it GRALE:} A free-form, adaptive grid model developed using
the GRALE software
tool \citep{Liesenborgs:2006, tool\citep{Liesenborgs:2006, Liesenborgs:2007,
Mohammed:2014, Sebesta:2016}, which implements a genetic algorithm
to reconstruct the cluster mass distribution with hundreds to
thousands of projected
\citet{Plummer:1911} Plummer\citet{Plummer:1911} density
profiles.} profiles.
\item{\it SWUnited:} The model of
\citet{Hoag:2016}, \citeref{Hoag:2016}, built using the
{\tt SWUnited} modeling
method \citep{Bradac:2005, method\citep{Bradac:2005, Bradac:2009}, in
which an adaptive pixelated grid iteratively adapts the mass
distribution to match both strong- and weak-lensing constraints.
Time delay predictions are not available for this model.
\item{\it WSLAP+:} Created with the {\tt WSLAP+} software
\citep{Sendra:2014}: (\url{http://www.ifca.unican.es/users/jdiego/LensExplorer})\citep{Sendra:2014}:
Weak and Strong Lensing Analysis Package plus member galaxies (Note:
no weak-lensing constraints were used for this \MACS0416
model).\footnote{\url{http://www.ifca.unican.es/users/jdiego/LensExplorer}}
\item{{\it model).
\item{\it ZLTM:} A model with strong- and weak-lensing constraints,
built using the ``light-traces-mass'' (LTM)
methodology
\citep{Zitrin:2009a,Zitrin:2015}, methodology\citep{Zitrin:2009a, Zitrin:2015}, first presented for
\MACS0416 in
\citet{Zitrin:2013a}.} \citeref{Zitrin:2013a}.
\end{itemize}
\bigskip
Early versions of the {\it SWUnited}, {\it CATS}, {\it ZLTM} and {\it
GRALE} models were originally distributed as part of the Hubble
Frontier Fields lens modeling
project,\footnote{For more details, see
\url{https://archive.stsci.edu/prepds/frontier/lensmodels/}} project
(\url{https://archive.stsci.edu/prepds/frontier/lensmodels/}), in
which models were generated based on data available before the start
of the HFF observations to enable rapid early investigations of lensed
sources. The versions of these models applied here are updated to
incorporate additional lensing constraints. In all cases the lens
modelers made use of strong-lensing constraints
(multiply-imaged (multiply imaged
systems and arcs) derived from \HST imaging collected as part of the
CLASH
program (PI:Postman, HST-PID:12459,
\citealt{Postman:2012}). program\cite{Postman:2012}). These
models also made use of spectroscopic redshifts in the cluster
field\cite{Mann:2012, Christensen:2012, Grillo:2015, Caminha:2017}.
Input weak-lensing constraints were derived from data collected at the
Subaru Telescope by PI K. Umetsu (in prep) and archival imaging.
%\citet{Priewe:2016} provides a more complete
%description of the methodology of model and a comparison of the
%magnification predictions and uncertainties across the entire
%\macs0416 field.
Extended Data Fig.~\ref{fig:LensModelContours} presents probability distributions
derived from these models for the three magnifications and two time
delay values of interest. These distributions were derived by
combining the Monte Carlo chains from the CATS, GLAFIC, GLEE, and ZLTM
models, and individual runs of the GRALE model, which uses a different
random seed for each run. We applied a weight to each model to
account for the different number of model iterations used by each
modeling team. All five of these models agree that host image 11.3 is
the leading image, appearing some 3--7 years before the other two
images. The models do not agree on the arrival sequence of images
11.1 and 11.2: some have the NW image 11.2 as a leading image, and
others have it as a trailing image. However, the models do
consistently predict that the separation in time between those two
images should be roughly in the range of 1 to 60 days. As shown in
Extended Data Fig.~\ref{fig:SpockDelayPredictions}, \spockone and \spocktwo are
inconsistent with these predicted time delays if one assumes that they
are delayed images of a single event. However, if these were
independent events, then a time delay on the order of tens of days
between image 11.1 and 11.2 could have resulted in time-delayed events
that were missed by the \HST imaging of this field.
%The angular separation of $1\farcs8$ between the \spock events
%corresponds to a physical separation of many tens of parsecs in the
%source plane. A star could not traverse that distance in the
%$\sim$120 rest-frame days that separate the two \spock events. Thus,
%even with a critical curve smeared out by the effects of the ICL, it
%would be impossible for a single star crossing a single caustic in the
%source plane to be responsible for both transients.
Because of the proximity of the critical curves in all models, the
predicted time delays and magnification factors are significantly
different if calculated at the model-predicted positions instead of
the observed positions. For example, in the GLEE model series (GLEE
and GLEE-var) when switching from the observed to model-predicted
positions the arrival order of the NW and SE images flips, the
expected time delay drops from tens of days to $<$1 day, and the
magnifications change by 30-60\%. However, the expected
magnifications and time delays between the events still fall within
the broad ranges summarized in Table~\ref{tab:LensModelPredictions}
and shown in Figure~\ref{fig:LensModelContours}. Regardless of
whether the model predictions are extracted at the observed or
predicted positions of the \spock events, none of the lens models can
accommodate the observed 234-day time difference as purely a
gravitational lensing time delay.
\subsection{Lens Model Variations}\label{sec:LensModelVariations}
We used variations of several lens models to investigate how the
lensing critical curves shift under a range of alternative assumptions
or input constraints. These variations highlight the range of
systematic effects that might impact the model predictions for the
\spock magnifications, time delays and proximity to the critical
curves. Figure~\ref{fig:SpockCriticalCurves} shows the critical
curves for a source at $z=1$ (the redshift of the \spock host galaxy)
predicted by our seven baseline models, plus the four variations
described below. Within a given model, variations that move a
critical curve closer to the position of \spockone\ would drive the
magnification of that event much higher (toward $\mu_{\rm
NW}\sim200$). This generally also has the effect of moving the
critical curve farther from \spocktwo, which would necessarily drive
its magnification downward (toward $\mu_{\rm SE}\sim10$).
The baseline CATS model reported in
Table~\ref{tab:LensModelPredictions} corresponds to the CATSv4.1 model
published on the STScI Frontier Fields lens model
repository\footnote{\url{https://archive.stsci.edu/pub/hlsp/frontier/macs0416/models/cats/v4.1/}}.
That model uses 178 cluster member galaxies, including a galaxy $<$5
arcsec south of the \spock host galaxy, which creates a local critical
curve that intersects the \spocktwo location. Our CATS-var model is
an earlier iteration of the model, published on the STScI repository
as
CATSv4\footnote{\url{https://archive.stsci.edu/pub/hlsp/frontier/macs0416/models/cats/v4/}},
and includes only 98 galaxies identified as cluster members. In this
variation the nearby cluster member galaxy is not included, so the
\spocktwo event is not intersected by a critical curve. However, the
\spockone event is approximately coincident with the primary critical
curve of the \macs0416 cluster. When the critical curve is close to
either \spock location, the magnifications predicted by the CATS model
are driven up to $\mu>100$. However, the time delays remain small, on
the order of tens of days, and incompatible with the observed 234-day
gap.
The WSLAP-var model evaluates whether the cluster redshift
significantly impacts the positioning of the critical curve. In this
merging cluster, the northern brightest cluster galaxy (BCG) has a
slighter higher redshift than the southern BCG. The mean redshift of
the cluster is not precisely determined, since it is likely to be
aligned somewhat along the line of sight. For the WSLAP-var model we
shift the assumed cluster redshift $z=0.4$ from the default $z=0.396$
(used in all the baseline models). The shift in the critical curve is
noticeable, but not substantial, insofar as this change does not drive
the critical curve to intersect either or both of the \spock
locations.
The GLEE-var model is a multi-plane lens model (Chiriv{\`i} et al.~in
prep.) that incorporates 13 galaxies with spectroscopic redshifts that
place them either in the foreground or background of the \macs0416
cluster. Figure~\ref{fig:LineOfSightLenses} marks these 13 galaxies
and highlights two of them that appear in the foreground of the \spock
host galaxy and are close to the lines of sight to the \spock
transients. Both the foreground $z=0.0557$ galaxy and the
reconstructed position of the $z=0.9397$ galaxy have a projected
separation of $<$4\arcsec from the \spocktwo transient position.
Including these galaxies in the GLEE lensing model changes the
absolute value of the magnifications at the location of HFF14Spo-NW
(HFF14Spo-SE) to $\sim70$ ($\sim250$) and the time delay between the
two locations to $\sim50$ days. The line-of-sight galaxies also
result in a shift of the position of the critical curve--as can be
seen by comparing the GLEE and GLEE-var models in
Figure~\ref{fig:SpockCriticalCurves}. Nonetheless, the predicted time
delays are still incompatible with the observed gap of 234 days
between events.
The GLAFIC-var model examines whether it is plausible for a critical
curve to intersect both \spock locations---contrary to the baseline
assumption of a single critical curve subtending the \spock host
galaxy roughly midway between the two positions. This model includes
a customized constraint, requiring that the magnification factors at
the \spock positons are $>1000$. To achieve this, we independently
adjusted the mass scaling for the two nearest cluster member galaxies,
which are located just northeast and south of the \spock host galaxy
arc. The mass of the northeast member galaxy was increased by
$\sim$30\% and that of the southern one by $\sim$60\%. As a simple
check of the predicted morphology of the host galaxy, we placed a
source with a simple \citet{Sersic:1963} profile on the source
plane. The lensed image of that artificial source is an unbroken
elongated arc, reproducing the host galaxy image morphology reasonably
well.
For this modification of the GLAFIC lens model to be justified in a
statistical sense, the revised model should still accurately reproduce
the observed strong-lensing constraints across the entire cluster.
The $\chi^2$ statistic for the baseline GLAFIC model is 240, with 196
degrees of freedom ($\chi^2_\nu=1.2$), and yields an Akaike
information criterion (AIC)\citep{Akaike:1974} of 676. For the
GLAFIC-var model that forces multiple critical curves to intersect the
\spock locations, we get $\chi^2$=331 for 192 degrees of freedom
($\chi^2_\nu=1.7$) and AIC=769. This suggests that the multiple
critical curve GLAFIC-var model is strongly disfavored by the
{\it positional} strong-lensing constraints that are used for both models.
However, we note that neither model incorporates the temporal
constraints of the observed time delay.
A second variation of the CATS model (CATS-var2) was also used to test
the plausibility of multiple critical curves intersecting the \spock
locations. As in the GLAFIC-var case, this model requires that
critical curves pass very near the \spock positions. The model can
accommodate that constraint, insofar as the root mean square (RMS)
error of the best-fit model is similar to that of the CATS and
CATS-var models. However, in this CATS-var2 model the \spock host
galaxy is predicted to be multiply-imaged 5 times. The \HST images do
not exhibit any breaks or substructure in the arc that would be
generally expected in such a situation.
Moreover, this CATS-var2 model has strong implications for a separate
background galaxy in the vicinity of image 11.3 (system 14 in
\citet{Caminha:2017}). This galaxy is strongly lensed by a pair of
spectroscopically confirmed cluster member galaxies
\citep{Caminha:2017}. Comparing the observed positions of the multiple
images of System 14 against the CATS-var2 model-predicted positions,
we find that this System contributes significantly to the global RMS
error for the model--indicating that the CATS-var2 model can not
accurately reproduce the multiple images of System 14. Conversely,
when this system is removed as a model constraint, the RMS error
decreases, and the CATS-var2 model can more successfully pass the
critical line through the two \spock locations. A possible
interpretation of this is that the established strong lensing
constraints (especially System 14) are incompatible with the
requirement that multiple critical curves must intersect the two
\spock locations.
diff --git a/LensingSummaryTable.tex b/LensingSummaryTable.tex
index 7a11bfb..af48c77 100644
--- a/LensingSummaryTable.tex
+++ b/LensingSummaryTable.tex
...
\begin{deluxetable}{lccccc}
\tablewidth{\linewidth} \tablewidth{0.7\textwidth}
\tablecolumns{6}
\tablecaption{Lens model predictions for time delays and
magnifications at the observed locations of the \spock
diff --git a/LightCurves.tex b/LightCurves.tex
index 415dd13..795d31e 100644
--- a/LightCurves.tex
+++ b/LightCurves.tex
...
\subsection{Light Curve
Fitting}\label{sec:LightCurves} Fitting.}\label{sec:LightCurves}
Due to the rapid decline timescale, no observations were collected for
either event that unambiguously show the declining portion of the
light curve. Therefore, we must make some assumptions for the shape of
the light curve in order to quantify the peak luminosity and the
corresponding timescales for the rise and the decline. We first
approach this with a simplistic model that is
piece-wise piecewise linear in
magnitude vs time.
Supplementary Figure~\ref{fig:LinearLightCurveFits} shows
examples of the resulting fits for the two events. For each fit we
use only the data collected within 3 days of the brightest observed
magnitude, which allows us to fit a linear rise separately for the
...
\begin{enumerate}
\item make an assumption for the date of peak, $t_{\rm pk}$;
\item measure the peak magnitude at $t_{\rm pk}$ from the linear fit
to the rising
light curve light-curve data;
\item assume the source reaches a minimum brightness (maximum
magnitude) of 30 AB mag at the epoch of first observation after the
peak;
\item draw a line for the declining light curve between the assumed
peak and the assumed minimum brightness;
\item use that declining
light curve light-curve line to measure the timescale for
the event to drop by 2
magnitudes, mag, $t_2$;
\item make a new assumption for $t_{\rm pk}$ and repeat.
\end{enumerate}
As shown in
Supplementary Figure~\ref{fig:LinearLightCurveFits}, the resulting
piece-wise piecewise linear fits are simplistic, but nevertheless approximately
capture the observed behavior for both events. Furthermore, since
this toy model is not physically motivated, it allows us to remain
agnostic for the time being as to the astrophysical source(s) driving
these transients. From these fits we can see that \spockone most
likely reached a peak magnitude between 25 and 26.5 AB mag in both
F814W and F435W, and had a decline timescale $t_2$ of less than 2 days
in the
rest-frame. rest frame. The observations of \spocktwo provide less
stringent constraints, but we see that it had a peak magnitude between
23 and 26.5 AB mag in F160W and exhibited a decline time of less than
seven days. These fits also illustrate the generic fact that a higher
...
correcting for the luminosity distance assuming a standard \LCDM
cosmology, and then accounting for an assumed lensing magnification,
$\mu$. The range of plausible lensing magnifications ($10<\mu<100$)
is derived from the union of our
six seven independent lens
models (Methods,
Figure~\ref{fig:LensModelContours}). models. This
results in a grid of possible peak luminosities for each event as a
function of magnification and time of peak. As we are using linear
light curve fits, the assumed time of peak is equivalent to an
assumption for the decline time, which we quantify as $t_2$, the time
over which the transient declines by 2 magnitudes.
diff --git a/MicroLensing.tex b/MicroLensing.tex
index 7d757bf..659e0a5 100644
--- a/MicroLensing.tex
+++ b/MicroLensing.tex
...
\subsection{Intracluster
Light}\label{sec:ICL} 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) \citeref{Kelly:2017} 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
\cite{Chabrier:2003} Chabrier\cite{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 $\log
(\Sigma_{\star} /
(M_{\odot}\,{\rm (\Msun\,{\rm kpc}^{-2})) = 6.9\pm0.4$. 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). M1149 LS1\cite{Kelly:2017}.
\subsection{Expected Timescale for Microlensing Events}\label{sec:Microlensing}
A commonly observed example of microlensing-induced transient effects
is when a bright background source (a quasar) is magnified by a
galaxy-scale lens \citep{Wambsganss:2001, Kochanek:2004}. In this
optically thick microlensing regime, the lensing potential along the
line of sight to the quasar is composed of many stellar-mass objects.
Each compact object along the line of sight generates a separate
critical lensing curve, resulting in a complex web of overlapping
critical curves. As all of these lensing stars are in motion relative
to the background source, the web of caustics will shift across the
source position, leading to a stochastic variability on timescales of
months to years. This scenario is inconsistent with the observed
data, as the two \spock events were far too short in duration and did
not exhibit the repeated ``flickering'' variation that would be
expected from optically thick microlensing.
For the cluster-scale lens relevant in the case of \spock, we should
expect to be in the optically thin microlensing regime. This
situation is similar to the ``local'' microlensing light curves
observed when stars within our galaxy or neighboring dwarf galaxies
pass behind a massive compact halo object \citep{Paczynski:1986,
Alcock:1993, Aubourg:1993, Udalski:1993}. In this case, an isolated
microlensing event can occur if there is a background star (i.e., in
the \spock host galaxy) that is the dominant source of luminosity in
its environment. In practice this means that the source must be a very
bright O or B star with mass of order 10 \Msun. Depending on its age,
the size of such a star would range from a few to a few dozen times
the size of the sun. The net relative transverse velocity would be on
the order of a few 100 km s$^{-1}$, which is comparable to the orbital
velocity of stars within a galaxy or galaxies within a cluster.
In the case of a smooth cluster potential, the timescale $\tau$ for
the light curve of such a caustic crossing event is dictated by the
radius of the source, $R$, and the net transverse velocity, $v$, of
the source across the caustic
\citep{Chang:1979,Chang:1984,MiraldaEscude:1991}:
\begin{equation}
\tau = 6\frac{R}{5\,\Rsun}\frac{300 {\rm km~ s}^{-1}}{v}~\rm{hr}
\label{eqn:caustic_crossing_time}
\end{equation}
\noindent Thus, for reasonable assumptions about the star's radius and
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/MicroLensingSupplement.tex b/MicroLensingSupplement.tex
new file mode 100644
index 0000000..af95fac
--- /dev/null
+++ b/MicroLensingSupplement.tex
...
\subsection{Expected Timescale for Microlensing Events.}\label{sec:Microlensing}
A commonly observed example of microlensing-induced transient effects
is when a bright background source (a quasar) is magnified by a
galaxy-scale lens\citep{Wambsganss:2001, Kochanek:2004}. In this
optically thick microlensing regime, the lensing potential along the
line of sight to the quasar is composed of many stellar-mass objects.
Each compact object along the line of sight generates a separate
critical lensing curve, resulting in a complex web of overlapping
critical curves. As all of these lensing stars are in motion relative
to the background source, the web of caustics will shift across the
source position, leading to a stochastic variability on timescales of
months to years. This scenario is inconsistent with the observed
data, as the two \spock events were far too short in duration and did
not exhibit the repeated ``flickering'' variation that would be
expected from optically thick microlensing.
For the cluster-scale lens relevant in the case of \spock, we should
expect to be in the optically thin microlensing regime. This
situation is similar to the ``local'' microlensing light curves
observed when stars within our Galaxy or neighboring dwarf galaxies
pass behind a massive compact halo object\citep{Paczynski:1986,
Alcock:1993, Aubourg:1993, Udalski:1993}. In this case, an isolated
microlensing event can occur if there is a background star (i.e., in
the \spock host galaxy) that is the dominant source of luminosity in
its environment. In practice this means that the source must be a very
bright O or B star with mass of order 10 \Msun. Depending on its age,
the size of such a star would range from a few to a few dozen times
the size of the Sun. The net relative transverse velocity would be on
the order of a few 100 km s$^{-1}$, which is comparable to the orbital
velocity of stars within a galaxy or galaxies within a cluster.
In the case of a smooth cluster potential, the timescale $\tau$ for
the light curve of such a caustic crossing event is dictated by the
radius of the source, $R$, and the net transverse velocity, $v$, of
the source across the caustic\citep{Chang:1979,Chang:1984,MiraldaEscude:1991} as
\begin{equation}
\tau = \frac{6 R}{5\,\Rsun}\frac{300~{\rm km~ s}^{-1}}{v}~\rm{hr.}
\label{eqn:caustic_crossing_time}
\end{equation}
\noindent Thus, for reasonable assumptions about the star's radius and
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/Observations.tex b/Observations.tex
index 655cc07..9b198e6 100644
--- a/Observations.tex
+++ b/Observations.tex
...
\subsection{Discovery}\label{sec:Discovery} \subsection{Discovery.}\label{sec:Discovery}
The transient \spock\ was discovered in \HST imaging collected as part
of the Hubble Frontier Fields (HFF) survey
(HST-PID:13496, PI:Lotz), (HST-PID: 13496, PI: Lotz),
a multi-cycle program observing 6 massive galaxy clusters and
associated ``blank sky'' parallel
fields. fields\cite{Lotz:2017}. Several
\HST observing programs have provided additional observations
supplementing the core HFF program. One of these is the FrontierSN
program
(HST-PID:13386, PI:Rodney), (HST-PID: 13386, PI: Rodney), which aims to identify and study
explosive transients found in the HFF and related
programs. programs\citet{Rodney:2015a}. The FrontierSN team discovered
\spock\ in two separate HFF observing campaigns on the galaxy cluster
\MACS0416. The first was an imaging campaign in January, 2014 during
which the MACS0416 cluster field was observed in the F435W, F606W, and
F814W optical bands using the Advanced Camera for Surveys Wide Field
Camera (ACS-WFC). The second concluded in August, 2014, and imaged
the cluster with the infrared detector of \HST's Wide Field Camera 3
(WFC3-IR) using the F105W, F125W, F140W, and F160W bands.
To discover transient sources, the FrontierSN team processes each new
epoch of \HST data through a
difference imaging
pipeline,\footnote{\url{https://github.com/srodney/sndrizpipe}} difference-imaging
pipeline (\url{https://github.com/srodney/sndrizpipe}), using
archival \HST images to provide reference images (templates) which are
subtracted from the astrometrically registered HFF images. In the case
of MACS0416, the templates were constructed from images collected as
part of the Cluster Lensing And Supernova survey with Hubble (CLASH,
HST-PID:12459,
PI:Postman). PI:Postman)\cite{Postman:2012}. The resulting difference images are
visually inspected for new point sources, and any new transients of
interest (primarily
supernovae, SNe) are
followed up monitored with additional
\HST imaging or ground-based spectroscopic observations as needed.
For
a more complete description of the operations of the FrontierSN
program\citet{Rodney:2015a}.
\subsection{Photometry}\label{sec:Photometry} \subsection{Photometry.}\label{sec:Photometry}
The follow-up observations for \spock\ included \HST imaging
observations in infrared and optical bands using the WFC3-IR and
...
P330E, observed in a separate calibration program. A separate PSF
model was defined for each filter, but owing to the long-term
stability of the \HST PSF we used the same model in all epochs. All
of the aperture and
PSF fitting PSF-fitting photometry was carried out using the
{\tt PythonPhot} software
package\citep{Jones:2015}.\footnote{\url{https://github.com/djones1040/PythonPhot}} package
(\url{https://github.com/djones1040/PythonPhot})\citep{Jones:2015}.
\subsection{Host Galaxy Spectroscopy}\label{sec:Spectroscopy} \subsection{Host-Galaxy Spectroscopy.}\label{sec:Spectroscopy}
Spectroscopy of the \spock\ host galaxy was collected using three
instruments on the Very Large Telescope (VLT). Observations with the
VLT's X-shooter cross-dispersed echelle spectrograph\citep{Vernet:2011} were taken on October
19th, 21st 19, 21 and
23rd, 23, 2014
(Program 093.A-0667(A), PI: J. Hjorth) with the slit centered on the
position of \spocktwo. The total integration time was 4.0 hours for
the NIR arm of X-shooter, 3.6 hours for the VIS arm, and 3.9 hours for
...
field\citep{Grillo:2015,Balestra:2016}. These massively multi-object
observations could potentially have provided confirmation of the
redshift of the \spock host galaxy with separate spectral line
identifications in each of the three
host galaxy host-galaxy images. For the
\macs0416 field the CLASH-VLT program collected 1 hour of useful
exposure time in good seeing conditions with the Low Resolution Blue
grism. Unfortunately, the wavelength range of this grism (3600-6700
\AA) does not include any strong emission lines for a source at
z=1.0054, $z=1.0054$, and the signal-to-noise
ratio (S/N) was not sufficient to provide
any clear line identifications for the three images of the \spock host
galaxy.
...
\forbidden{O}{ii} doublet. Importantly, since MUSE is an integral
field spectrograph, these observations also provided a confirmation of
the redshift of the third image of the host galaxy, 11.3, with a
matching \forbidden{O}{ii} line at the same
wavelength
(\citealt{Caminha:2017}, Richard et al. in prep). wavelength\cite{Caminha:2017}.
A final source of spectroscopic information relevant to \spock is the
Grism Lens Amplified Survey from Space (GLASS; PID:
...
data, the three sources identified as images of the \spock host galaxy
are too faint in the GLASS data to provide any useful line
identifications. There are also no other sources in the GLASS
redshift
catalog\footnote{\url{http://glass.astro.ucla.edu/}} catalog (\url{http://glass.astro.ucla.edu/}) that
have a spectroscopic redshift consistent with
z=1.0054. $z=1.0054$.
diff --git a/RN.tex b/RN.tex
index 846d837..9dc0b09 100644
--- a/RN.tex
+++ b/RN.tex
...
\subsection{RN
Light Curve Comparison}\label{sec:RNLightCurves} Light-Curve Comparison.}\label{sec:RNLightCurves}
%Nova outbursts can exhibit decline times from
%$\sim$1 day to many months, so the timescale of the \spock light
...
There are ten known RNe in the Milky Way galaxy, and seven of
these exhibit outbursts that decline rapidly, fading by two magnitudes
in less than ten
days \citep{Schaefer:2010}. days\citep{Schaefer:2010}.
% U Sco, V2487 Oph, V394 CrA, T CrB, RS Oph, V745 Sco, and V3890 Sgr.
Supplementary Figure~\ref{fig:RecurrentNovaLightCurveComparison}
compares the \spock light curves to a composite light curve (the gray
shaded region), which encompasses the V band light curve
templates
\citep{Schaefer:2010} templates\citep{Schaefer:2010} for all seven of these galactic RN
events. The Andromeda galaxy (M31) also hosts at least one RN with a
rapidly declining light curve. The 2014 eruption of this well-studied
nova, M31N 2008-12a, is shown as a solid black line in
Supplementary
Figure~\ref{fig:RecurrentNovaLightCurveComparison}, fading by 2
mags mag in
less than 3 $<3$ days. This comparison demonstrates that the rapid decline of
both of the \spock transient events is fully consistent with the
eruptions of known RNe in the local universe.
%Among the most luminous classical novae known, a similarly rapid
%decline time is not unheard of. For example, the bright nova
...
%1$ days \citep{DellaValle:1991, Williams:1994, Schwarz:2001}.
\subsection{RN Luminosity and Recurrence
Period}\label{sec:RNLuminosityRecurrence} Period.}\label{sec:RNLuminosityRecurrence}
To examine the recurrence period and peak brightness of the \spock
events relative to RNe, we rely on a pair of papers that evaluated an
extensive grid of nova models through multiple cycles of outburst and
quiescence \citep{Prialnik:1995,Yaron:2005}. quiescence\citep{Prialnik:1995,Yaron:2005}. Supplementary
Figure~\ref{fig:RecurrentNovaRecurrenceComparison} plots first the RN
outburst amplitude (the apparent magnitude between outbursts minus the
apparent magnitude at peak) and then the peak luminosity against the
...
% models (circles) from \citet{Yaron:2005}.
For the \spock events we can only measure a lower limit on the
outburst amplitude, since the presumed progenitor star is unresolved,
so no measurement is available at quiescence.
Supplementary
Figure~\ref{fig:RecurrentNovaRecurrenceComparison} shows that a
recurrence period as fast as one year is expected only for a RN system
in which the primary white dwarf is both very close to the
Chandrasekhar mass limit (1.4 \Msun) and also has an extraordinarily
rapid mass transfer rate ($\sim10^{-6}$ \Msun yr$^{-1}$). The models
of
\citet{Yaron:2005} \citeref{Yaron:2005} suggest that such systems should have a very
low peak amplitude (barely consistent with the lower limit for \spock)
and a low peak luminosity ($\sim$100 times less luminous than the
\spock events).
The closest analog for the \spock events from the population of known
RN systems is the nova M31N\,2008-12a.
\citet{Kato:2015} \citeref{Kato:2015} provided a
theoretical model that can account for the key observational
characteristics of this remarkable nova: the very rapid recurrence
timescale ($<$1 yr), fast optical light curve ($\t2\sim2$ days), and
short supersoft x-ray phase (6-18 days after optical
outburst)\citep{Henze:2015a}. To match these observations,
\citet{Kato:2015} \citeref{Kato:2015} invoke a 1.38 \Msun white dwarf primary,
drawing mass from a companion at a rate of $1.6\times10^{-7}$ \Msun
yr$^{-1}$. This is largely consistent with the theoretical
expectations derived by
\citet{Yaron:2005}, \citeref{Yaron:2005}, and reinforces the
conclusion that a combination of a
high mass high-mass white dwarf and efficient
mass transfer are the key ingredients for rapid recurrence and short
light curves. The one feature that cannot be effectively explained
with this hypothesis is the peculiarly high luminosity of the \spock
diff --git a/Rates.tex b/Rates.tex
index dbdbf84..4354489 100644
--- a/Rates.tex
+++ b/Rates.tex
...
\subsection{Rates}\label{sec:RatesMethods} \subsection{Rates.}\label{sec:RatesMethods}
To derive a rough estimate of the rate of \spock-like transients, we
first define the set of strongly lensed galaxies in which a similarly
...
the host galaxy must be amplified by strong lensing with a
magnification $\mu>20$ at $z\sim1$, growing to $\mu>100$ at $z\sim2$.
Using photometric redshifts and magnifications derived from the GLAFIC
lens models
of the six HFF clusters, we find $N_{\rm gal}=6$ galaxies
that satisfy this criterion, with
redshifts $0.5(Extended Data
Fig.~\ref{fig:StronglyLensedGalaxies}). (Supplementary
Figure~\ref{fig:StronglyLensedGalaxies}).
We then define the {\it control time}, $t_{c}$, for the HFF survey,
which gives the span of time over which each cluster was observed with
a cadence sufficient for detection of such rapid transients. We
define this as any period in which at least two \HST observations were
collected within every
ten 10 day span. This effectively includes the
entirety of the primary HFF campaigns on each cluster, but excludes
all of the ancillary data collection periods from supplemental \HST
imaging programs. The average control time for an HFF cluster is
$t_{c}$=0.22 $t_{c} = 0.22$ years (80 days). Treating each \spock event as a
separate detection, we can derive a rate estimate using $R = 2 /
(N_{\rm gal}\,t_c)$. This yields $R=1.5$ events galaxy$^{-1}$
year$^{-1}$.
Future examination of the rate of such transients should consider the
total stellar mass and the
star formation star-formation rates of the galaxies
surveyed, or use a projection of the lensed background area onto the
source plane to derive a volumetric rate. Such analyses would require
a more detailed exploration of the impact of lensing uncertainties on
derived properties of the lensed galaxies and the lensed volume, and
this is beyond the scope of
the current work.
diff --git a/Results.tex b/Results.tex
index 988e0ae..b8f0ee0 100644
--- a/Results.tex
+++ b/Results.tex
...
\spockone location and the \spocktwo location is $<$60 days
(Table~\ref{tab:LensModelPredictions}). This falls far short of the
observed 223 day span between the two events, suggesting that
\spocktwo is not a time-delayed image of the \spockone event.
As
shown in Figure~\ref{fig:SpockDelayPredictions}, \spockone and
\spocktwo are inconsistent with these predicted time delays if one
assumes that they are delayed images of a single event. However, if
these were independent events, then a time delay on the order of tens
of days between image 11.1 and 11.2 could have resulted in
time-delayed events that were missed by the \HST imaging of this
field.
The models also predict absolute magnification values between about
$\mu=10$ and $\mu=200$ for both events. This wide range is due
...
The lensing configuration consistently adopted for this cluster
assumes that the arc comprises two mirror images of the host galaxy
(labeled 11.1 and 11.2 in
Fig.~\ref{fig:SpockDetectionImages})\cite{Zitrin:2013a, Figure~\ref{fig:SpockDetectionImages})\cite{Zitrin:2013a, Jauzac:2014,
Johnson:2014, Richard:2014, Diego:2015a, Grillo:2015, Hoag:2016,
Sebesta:2016, Caminha:2017}. This implies that a single critical
curve passes roughly
mid-way midway between the two \spock locations. The
location of the critical curve varies significantly among the models
(Fig.~\ref{fig:SpockCriticalCurves}), (Figure~\ref{fig:SpockCriticalCurves}), and is sensitive to many
parameters that are poorly constrained. We find that it is possible to
make reasonable adjustments to the lens model parameters so that the
critical curve does not bisect the \spock host arc, but instead
intersects both of the \spock
locations. locations (see Supplementary
Note~\ref{sec:LensModelVariations}). 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.
\subsection{Ruling Out Common Astrophysical
Transients} Transients.}
There are several categories of astrophysical transients that can be
rejected, rejected based solely on
the light curve characteristics of
the \spockone and
\spocktwo. \spocktwo light curves, shown in Figure~\ref{fig:LightCurves}. Neither
of the \spock events
are is {\it periodic}, as expected for stellar
pulsations such as Cepheids, RR Lyrae, or Mira variables. Stellar
flares can produce rapid optical transient phenomena, but the total
energy released by even the most extreme stellar
flare\cite{Karoff:2016} falls far short of the observed energy release
from the \spock transients. We can also rule out active galactic
nuclei (AGN), which are 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 observed in AGN.
Additionally, no x-ray emitting point source was detected in 7 epochs
from 2009 to 2014, including \Chandra X-ray Space Telescope imaging
that was coeval with the peak of
IR infrared emission from \spocktwo.
Many types of stellar explosions can generate isolated transient
events, and a useful starting point for classification of such objects
is to examine their position in the phase space of peak luminosity
(\Lpk) versus decline
time \cite{Kulkarni:2007}. time\cite{Kulkarni:2007}.
Figure~\ref{fig:PeakLuminosityDeclineTime} shows our two-dimensional
constraints on \Lpk and the decline timescale \t2 (the time over which
the transient declines by 2
magnitudes) mag) for the \spock events,
accounting for the range of lensing magnifications ($10<\mu<200$)
derived from the cluster lens models. The \spockone and \spocktwo
events are largely consistent with each other, and if both events are
representative of a single system (or a homogeneous class) then the
most likely peak luminosity and decline time (the region with the most
overlap) would be $L_{\rm
pk}\sim10^{41}$ pk}\approx10^{41}$ erg s$^{-1}$ and
$t_2\sim1$ $t_2\approx1$
day.
The relatively low peak luminosities and the very rapid rise and fall
of both \spock light curves are incompatible with all categories of
stellar explosions for which a significant sample of observed events
exists. This includes the common Type Ia SNe and
core collapse core-collapse SNe,
as well as the less well-understood classes of
Superluminous superluminous
SNe\cite{Gal-Yam:2012}, Type Iax SNe\citep{Foley:2013a}, fast optical
transients\cite{Drout:2014}, Ca-rich SNe\cite{Kasliwal:2012}, and
Luminous Red Novae\cite{Kulkarni:2007}. luminous red novae\cite{Kulkarni:2007}.
The SN-like transients that come closest to matching the observed
light curves of the two \spock events are the ``kilonova'' class and
the ``.Ia'' class. Kilonovae are a theorized category of
optical/near-infrared transients that may be generated by the merger
of a neutron star (NS)
binary\cite{Li:1998,Kulkarni:2005}. binary\cite{Li:1998}. The .Ia class is
due to produced by He shell explosions that are expected to arise from AM
Canum Venaticorum (AM CVn) binary star systems undergoing He mass
transfer onto a white dwarf primary star\cite{Warner:1995,
Nelemans:2005,Bildsten:2007}. Bildsten:2007}. The \spock light curves exhibited a slower rise
time than is expected for a kilonova
event\cite{Metzger:2010,Barnes:2013,Kasen:2015}, event\cite{Metzger:2010, Barnes:2013, Kasen:2015}, and a faster decline
time than is anticipated for a .Ia event\cite{Shen:2010}.
Another problem for all of these catastrophic stellar explosion models
...
events. The kilonova progenitor systems are completely disrupted at
explosion, as is the case for all normal SN explosions. For .Ia
events, even if an AM CVn system could produce repeated He shell
flashes of similar luminosity, the period of recurrence would be
of
order $10^5$ $\sim10^5$ yr, making these effectively non-recurrent sources.
%Thus, to reconcile any such cataclysmic explosion model with the two
%observed \spock events we would need to invoke a highly serendipitous
%occurrence of two unrelated peculiar explosions in the same host
...
Although the two events were most likely not {\it temporally}
coincident, all of our lens models indicate that it is entirely
plausible for the two \spock events to be {\it spatially} coincident:
a single location at the source plane can be mapped to both \spock
locations to within the positional accuracy of the model
reconstructions ($\sim$0.6\arcsec in the lens plane). This is
supported by the fact that the
host galaxy host-galaxy colors and spectral indices
at each \spock location are indistinguishable within the
uncertainties. uncertainties
(see Supplementary Figure~\ref{fig:HostProperties} and Supplementary Table~\ref{tab:HostProperties}). Thus,
to accommodate all of the observations of the \spock events with a
single astrophysical source, we turn to two categories of stellar
explosion that are sporadically recurrent: luminous blue variables
(LBVs) and recurrent novae (RNe).
\subsection{Luminous Blue
Variable} Variable.}
The transient sources categorized as LBVs are the result of eruptions
or explosive episodes from massive stars
($>10$\Msun). ($>10$ \Msun).
%\footnote{We use
% the term LBV to encompass any massive stars producing sporadic
% bright optical transient events. Such
...
most giant LBV eruptions have been observed to last much longer than
the \spock events\cite{Smith:2011b}, some LBVs have exhibited repeated
rapid outbursts that are broadly consistent with the very fast \spock
light curves (see
SI Fig.~\ref{fig:LBVLightCurveComparison}). Supplementary
Figure~\ref{fig:LBVLightCurveComparison}). Because of this common
stochastic variability, the LBV hypothesis does not have any trouble
accounting for the \spock events as two separate episodes.
Two well-studied LBVs that provide a plausible match to the observed
\spock events are ``SN 2009ip''\cite{Maza:2009} and
NGC3432-LBV1\cite{Pastorello:2010}. Both exhibited multiple brief
transient episodes over a span of months to years\cite{Miller:2009,
Li:2009, Berger:2009,
Drake:2010, Pastorello:2010}. Unfortunately,
for these outbursts we have only upper limits on the decline
timescale, $t_2$,
due owing to the relatively sparse photometric sampling.
Recent studies have shown that
SN 2009ip-like LBV transients have remarkably
similar light curves, leading up to a final terminal SN
explosion\cite{Kilpatrick:2017, Pastorello:2017}.
Figure~\ref{fig:PeakLuminosityDeclineTime}b shows that both \spock
...
$\sim$1 to 2 mag over a timespan of several years before and after
their historic giant eruptions. Such variation has not been detected
at the \spock locations. Nevertheless, given the broad
range of
light curve light-curve behaviors seen in LBV events, we cannot reject
this class as a possible explanation for the \spock system.
The total radiated energy of the \spock events is in the range
...
slowly in the stellar interior and is in some way ``bottled up'' by
the stellar envelope, before being released in a rapid mass ejection
(see Methods). With this approach we a quiescent luminosity of
$L_{\rm
qui}\sim10^{39.5}$~erg~s$^{-1}$ ($M_V\sim-10$). qui}\approx10^{39.5}$~erg~s$^{-1}$ ($M_V\approx-10$ mag). This value is
fully consistent with the expected range for LBV progenitor stars
(e.g., \etacar has
$M_V\sim-12$ $M_V\approx-12$ mag and the faintest known LBV progenitors
such as SN 2010dn have
$M_V\sim-6$). $M_V\approx-6$ mag).
\subsection{Recurrent
Nova}\label{sec:RNe} Nova.}\label{sec:RNe}
Novae occur in binary systems in which a white dwarf star accretes
matter from a less massive companion, leading to a burst of nuclear
...
The light curves of many RN systems in the Milky Way are similar in
shape to the \spock episodes, exhibiting a sharp rise ($<10$ days in
the rest-frame) and a similarly rapid decline (see
Supplemental
Information). Supplementary
Information and Supplementary
Figure~\ref{fig:RecurrentNovaLightCurveComparison}). This is
reflected in Figure~\ref{fig:PeakLuminosityDeclineTime}, where novae
are represented by a grey band that traces the empirical constraints
on the maximum magnitude
- vs.\ rate of decline (MMRD) relation for
classical novae\cite{DellaValle:1995, Downes:2000, Shafter:2011,
Kasliwal:2011a}.
The RN model can provide a natural explanation for having two separate
explosions that are coincident in space but not in time. However, the
recurrence timescale for \spock in the
rest-frame rest frame is $120\pm30$ days,
which would be a singularly rapid recurrence period for a RN system.
The RNe in our own
galaxy Galaxy have recurrence timescales
from of 10--98
years\cite{Schaefer:2010}. The fastest measured recurrence timescale
belongs to M31N 2008-12a, which has exhibited a new outburst every
year from
2008-2016\cite{Tang:2014, 2008 through 2016\cite{Tang:2014, Darnley:2014,
Darnley:2015, Henze:2015,
Henze:2015a, Darnley:2016}. Although this
M31 record-holder demonstrates that very rapid recurrence is possible,
classifying \spock as a RN would still require a very extreme
mass
transfer mass-transfer rate to accommodate the $<1$ year recurrence.
Another major concern with the RN hypothesis is that the two \spock
events are substantially brighter than all known
novae -- perhaps novae---perhaps by as
much as 2 orders of magnitude. This is exacerbated by the
observational and theoretical evidence indicating that
rapid-recurrence novae have less energetic
eruptions\cite{Yaron:2005}. eruptions\cite{Yaron:2005}
(see Supplementary Information and Supplementary Figure
\ref{fig:RecurrentNovaRecurrenceComparison}).
%One might
%attempt to reconcile the \spock luminosity more comfortably with the
%nova class by assuming a significant lensing magnification for one of
...
\subsection{Microlensing}\label{sec:MicroLensing} \subsection{Microlensing.}\label{sec:MicroLensing}
In the presence of strong gravitational lensing it is possible to
generate a transient event from lensing effects alone. In this case
...
sharp decline (rise) when the star has moved to the other side of the
caustic\cite{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\cite{Lewis:1993}. peaks\cite{Lewis:1993, Diego:2017}.
The peculiar transient MACS J1149 LS1, observed behind the Hubble
Frontier Fields cluster MACS J1149.6+2223, has been proposed as the
first observed example of such a stellar caustic crossing
event\cite{Kelly:2017}. 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 microlenses 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 caustic-crossing event.
On this basis the \spock
host galaxy host-galaxy images are suitably positioned
for
caustic crossing caustic-crossing transients, as they are seen through a relatively
high density of intracluster
stars---comparable stars (see Methods)---comparable to that
observed for the MACS J1149 LS1 transient.
The characteristic timescale of a canonical
caustic crossing caustic-crossing event
would be on the order of hours or
days, days (see Supplementary
Information), which is comparable to the timescales observed for the
\spock events. Gravitational lensing is achromatic as long as the size
of the source is consistent across the spectral energy distribution
(SED). This means that the color of a
caustic crossing caustic-crossing transient will
be roughly constant. Using simplistic linear interpolations of the
observed light curves (see
Methods) Methods), we find that the inferred color
curves for both \spock events are marginally consistent with this
expectation of an unchanging
color. color (Supplementary
Figure~\ref{fig:ColorCurves}).
In the baseline lensing configuration adopted above---where a single
critical curve subtends the \spock host galaxy arc---these events
cannot plausibly be explained as stellar caustic crossings, because
neither transient is close enough to the single critical curve to
reach the required magnifications of
$\mu\sim10^6$. $\mu\approx10^6$. Some of our lens
models can, however, be modified so that instead of just two host
images, the lensed galaxy arc is made up of many more images of the
host, with multiple critical curves subtending the arc where the
\spock events appeared
(Fig.~\ref{fig:SpockCriticalCurves}). (Figure~\ref{fig:SpockCriticalCurves}).
If this alternative lensing
situation is correct, then similar microlensing transients would be
expected to appear at different locations along the
host galaxy host-galaxy arc,
instigated by new
caustic crossing caustic-crossing episodes from different stars in
the host galaxy.
\subsection{The Rate of Similar
Transients}\label{sec:Rates} Transients.}\label{sec:Rates}
Although we lack a definitive classification for these events, we can
derive a simplistic estimate of the rate of \spock-like transients by
counting the number of strongly lensed galaxies in the HFF clusters
that have sufficiently high magnification that a source with
$M_{V}=-14$ mag would be detected in \HST imaging. There are only six
galaxies that satisfy that criteria, all with
redshift $0.5
for an average of 80 days. Treating \spockone and \spocktwo as
separate events leads to a very rough rate estimate of 1.5 \spock-like
...
Derivation of a volumetric rate for such events would require a
detailed analysis of the lensed volume as a function of redshift, and
is beyond the scope of this work.
A Nevertheless, a comparison to rates
of similar transients in the local universe can inform our assessment
of the likelihood that the \spock events are unrelated. A study of
very fast optical transients with the Pan-STARRS1 survey derived a
rate limit of $\lesssim0.05$ Mpc$^{-3}$ yr$^{-1}$ for transients
reaching $M\approx -14$ mag on a timescale of $\sim$1
day\citet{Berger:2013b}. This limit, though several orders of
magnitude higher than the constraints on novae or SNe, is sufficient
to make it exceedingly unlikely that two unrelated fast optical
transients would appear in the same galaxy in a single year.
Furthermore, we have observed no other transient events with similar
luminosities and light curve shapes in high-cadence surveys of five
other Frontier Fields clusters. Indeed, all other transients detected
in the primary HFF survey have been fully consistent with normal SNe.
Thus, we have no evidence to suggest that transients of this kind are
common enough to be observed twice in a single galaxy in a single
year.
diff --git a/Supplemental.tex b/Supplementary.tex
similarity index 90%
rename from Supplemental.tex
rename to Supplementary.tex
index 257aea0..7c0ab64 100644
--- a/Supplemental.tex
+++ b/Supplementary.tex
...
\input{LensModelVariations}
\input{HostGalaxy}
\input{LBVsupplement}
\input{RN}
\input{MicroLensingSupplement}
\begin{figure*}[tbp]
\begin{center}
\includegraphics[width=\textwidth]{./figures/composite_lens_model_contours/composite_lens_model_contours}
...
\end{center}
\end{figure*}
\begin{figure*}[tbp]
\begin{center}
\includegraphics[width=\textwidth]{./figures/LineOfSightLenses/macs0416_lineofsight_lensing} \includegraphics[width=\textwidth]{./figures/LineOfSightLenses/macs0416_lineofsight_lensing.png}
\caption{\protect\input{./figures/LineOfSightLenses/caption.tex}}
\end{center}
\end{figure*}
...
\begin{figure*}[tbp]
\begin{center}
\includegraphics[width=\textwidth]{./figures/spock_hostgalaxy_properties/spock_hostgalaxy_properties} \includegraphics[width=\textwidth]{./figures/spock_hostgalaxy_properties/spock_hostgalaxy_properties.png}
\caption{\protect\input{./figures/spock_hostgalaxy_properties/caption.tex}}
\end{center}
\end{figure*}
...
\end{center}
\end{figure*}
\input{HostGalaxyProperties}
\input{LongTables}
diff --git a/TitleAndAuthors.tex b/TitleAndAuthors.tex
index e7db299..7792f08 100644
--- a/TitleAndAuthors.tex
+++ b/TitleAndAuthors.tex
...
%%\author{Aauthor$^{1,2}$, Bauthor$^2$ \& LastAuthor$^2$}
\author{
S.~A.~Rodney\altaffilmark{\affilref{JHU},\affilref{USC}}, S.~A.~Rodney\altaffilmark{\affilref{USC}},
I.~Balestra\altaffilmark{\affilref{Munich}},
M.~Brada\v{c}\altaffilmark{\affilref{UCDavis}},
G.~Brammer\altaffilmark{\affilref{STScI}},
...
B.~Mobasher\altaffilmark{\affilref{UCRiverside}},
A.~Molino\altaffilmark{\affilref{SaoPaulo},\affilref{Andalucia}},
M.~Oguri\altaffilmark{\affilref{TokyoRCEU},\affilref{TokyoPhys},\affilref{TokyoIPMU}},
A.~G.~Riess\altaffilmark{\affilref{JHU},\affilref{STScI}},
J.~Richard\altaffilmark{\affilref{Lyon}},
A.~G.~Riess\altaffilmark{\affilref{JHU},\affilref{STScI}},
P.~Rosati\altaffilmark{\affilref{Ferrara}},
K.~B.~Schmidt\altaffilmark{\affilref{UCSB},\affilref{AIP}},
J.~Selsing\altaffilmark{\affilref{DARK}},
...
T.~Treu\altaffilmark{\affilref{UCLA},\affilref{Packard}},
B.~J.~Weiner\altaffilmark{\affilref{Arizona}},
L.~L.~R.~Williams\altaffilmark{\affilref{Minnesota}} \&
A.~Zitrin\altaffilmark{\affilref{CalTech},\affilref{BenGurion}} A.~Zitrin\altaffilmark{\affilref{BenGurion}}
}
\def\makeaffil{
\begin{affiliations}
\item \JHU
\item \USC
\item \Munich
\item \UCDavis
...
\item \TokyoPhys
\item \TokyoIPMU
\item \Lyon
\item \JHU
\item \AIP
\item \Michigan
\item \ASIAA
diff --git a/Xray.tex b/Xray.tex
index 03837b4..a6020ab 100644
--- a/Xray.tex
+++ b/Xray.tex
...
\subsection{X-ray
Non-detections}\label{sec:Xray} Nondetections.}\label{sec:Xray}
The \MACS0416 field was observed by the
SWIFT \Swift X-Ray Telescope
(XRT)
and UltraViolet/Optical Telescope
(UVOT) in April 2013. No source was
detected near the locations of the \spock events (N. Gehrels, private
communication). The field was also observed by \Chandra with the
ACIS-I instrument for three separate programs. On June 7, 2009 it was
diff --git a/bibliography/biblio.bib b/bibliography/biblio.bib
index bf76244..2da74a7 100644
--- a/bibliography/biblio.bib
+++ b/bibliography/biblio.bib
...
%% This BibTeX bibliography file was created using BibDesk.
%% http://bibdesk.sourceforge.net/
%% Created for rodney at
2017-07-06 10:26:06 2017-07-07 14:16:04 -0400
%% Saved with string encoding Unicode (UTF-8)
...
@article{Pastorello:2017,
Author = {{Pastorello}, A. and {Kochanek}, C.~S. and {Fraser}, M. and {Dong}, S. and {Elias-Rosa}, N. and {Benetti}, S. and {Cappellaro}, E. and {Tomasella}, L. and {Drake}, A.~J. and {Hermanen}, J. and {Reynolds}, T. and {Shappee}, B.~J. and {Smartt}, S.~J. and {Chambers}, K.~C. and {Huber}, M.~E. and {Smith}, K. and {Stanek}, K.~Z. and {Filippenko}, A.~V. and {Christensen}, E.~J. and {Denneau}, L. and {Djorgovski}, S.~G. and {Flewelling}, H. and {Gall}, C. and {Gal-Yam}, A. and {Geier}, S. and {Heinze}, A. and {Holoien}, T.~W.-S. and {Isern}, J. and {Kangas}, T. and {Kankare}, E. and {Koff}, R.~A. and {Llapasset}, J.-M. and {Lowe}, T.~B. and {Lundqvist}, P. and {Magnier}, E.~A. and {Mattila}, S. and {Morales-Garoffolo}, A. and {Mutel}, R. and {Nicolas}, J. and {Ochner}, P. and {Ofek}, E.~O. and {Prosperi}, E. and {Rest}, A. and {Sano}, Y. and {Stalder}, B. and {Stritzinger}, M.~D. and {Taddia}, F. and {Terreran}, G. and {Tonry}, J.~L. and {Wainscoat}, R.~J. and {Waters}, C. and {Weiland}, H. and {Willman}, M. and {Young}, D.~R. and {Zheng}, W.},
Journal =
{ArXiv e-prints}, {arXiv: 1707.00611},
Month = jul,
Title = {{Supernovae 2016bdu and 2005gl, and their link with SN 2009ip-like transients: another piece of the puzzle}},
Year = 2017}
@article{Kilpatrick:2017,
Author = {{Kilpatrick}, C.~D. and {Foley}, R.~J. and {Drout}, M.~R. and {Pan}, Y.-C. and {Panther}, F.~H. and {Coulter}, D.~A. and {Filippenko}, A.~V. and {Marion}, G.~H. and {Piro}, A.~L. and {Rest}, A. and {Seitenzahl}, I. and {Strampelli}, G. and {Wang}, X.~E.},
Journal =
{ArXiv e-prints}, {arXiv: 1706.09962},
Month = jun,
Title = {{Connecting the progenitors, pre-explosion variability, and giant outbursts of luminous blue variables with Gaia16cfr}},
Year = 2017}
@article{Kelly:2017,
Author = {{Kelly}, P.~L. and {Diego}, J.~M. and {Rodney}, S. and {Kaiser}, N. and {Broadhurst}, T. and {Zitrin}, A. and {Treu}, T. and {Perez-Gonzalez}, P.~G. and {Morishita}, T. and {Jauzac}, M. and {Selsing}, J. and {Oguri}, M. and {Pueyo}, L. and {Ross}, T.~W. and {Filippenko}, A.~V. and {Smith}, N. and {Hjorth}, J. and {Cenko}, S.~B. and {Wang}, X. and {Howell}, D.~A. and {Richard}, J. and {Frye}, B.~L. and {Jha}, S.~W. and {Foley}, R.~J. and {Norman}, C. and {Bradac}, M. and {Zheng}, W. and {Brammer}, G. and {Molino Benito}, A. and {Cava}, A. and {Christensen}, L. and {de Mink}, S.~E. and {Graur}, O. and {Grillo}, C. and {Kawamata}, R. and {Kneib}, J.-P. and {Matheson}, T. and {McCully}, C. and {Nonino}, M. and {Perez-Fournon}, I. and {Riess}, A.~G. and {Rosati}, P. and {Borello Schmidt}, K. and {Sharon}, K. and {Weiner}, B.~J.},
Journal =
{ArXiv e-prints}, {arXiv:1706.10279},
Month = jun,
Title = {{An individual star at redshift 1.5 extremely magnified by a galaxy-cluster lens}},
Year = 2017}
@article{Diego:2017,
Author = {{Diego}, J.~M. and {Kaiser}, N. and {Broadhurst}, T. and {Kelly}, P.~L. and {Rodney}, S. and {Morishita}, T. and {Oguri}, M. and {Ross}, T.~W. and {Zitrin}, A. and {Jauzac}, M. and {Richard}, J. and {Williams}, L. and {Vega}, J. and {Frye}, B. and {Filipenko}, A.~V.},
Journal =
{ArXiv e-prints}, {arXiv:1706.10281},
Month = jun,
Title = {{Dark matter under the microscope: Constraining compact dark matter with caustic crossing events}},
Year = 2017}
...
@article{Eliasdottir:2007,
Author = {{El{\'{\i}}asd{\'o}ttir}, {\'A}. and {Limousin}, M. and {Richard}, J. and {Hjorth}, J. and {Kneib}, J.-P. and {Natarajan}, P. and {Pedersen}, K. and {Jullo}, E. and {Paraficz}, D.},
Journal =
{ArXiv e-prints}, {arXiv:0710.5636},
Month = oct,
Title = {{Where is the matter in the Merging Cluster Abell 2218?}},
Year = 2007}
...
@article{Hogg:2002,
Author = {Hogg, David W. and Baldry, Ivan K. and Blanton, Michael R. and Eisenstein, Daniel J.},
Journal =
{ArXiv Astrophysics e-prints}, {arXiv:astro-ph/0210394},
Title = {The K correction},
Year = {2002}}
diff --git a/figures/LineOfSightLenses/caption.tex b/figures/LineOfSightLenses/caption.tex
index c3e3972..2c02359 100644
--- a/figures/LineOfSightLenses/caption.tex
+++ b/figures/LineOfSightLenses/caption.tex
...
model that accommodates multi-plane lensing. The larger panel at left
marks nine galaxies with spectroscopic redshifts greater than the
cluster redshift (magenta circles) and four galaxies in the cluster
foreground
(light blue (light-blue circles). The inset panel at right zooms in on
the \spock host galaxy (enclosed by the orange ellipse in each panel).
Cluster member galaxies with spectroscopic redshifts that were
included in the GLEE models are marked with black diamonds. The
magenta circle marks a spiral galaxy at $z=0.9397$, which is also
strongly lensed by the \macs0416 cluster into three highly distorted
images (System 12 in
\citet{Caminha:2017}). \citeref{Caminha:2017}). This image of the System
12 galaxy is further strongly lensed into arcs around a cluster member
galaxy, which is marked by the black diamond near the center of the
magenta circle. The galaxy in the foreground of the cluster at
diff --git a/figures/LineOfSightLenses/macs0416_lineofsight_lensing.pdf b/figures/LineOfSightLenses/macs0416_lineofsight_lensing.pdf
new file mode 100644
index 0000000..c887d39
Binary files /dev/null and b/figures/LineOfSightLenses/macs0416_lineofsight_lensing.pdf differ
diff --git a/figures/LineOfSightLenses/macs0416_lineofsight_lensing.png b/figures/LineOfSightLenses/macs0416_lineofsight_lensing.png
index 608fedc..93f41b9 100644
Binary files a/figures/LineOfSightLenses/macs0416_lineofsight_lensing.png and b/figures/LineOfSightLenses/macs0416_lineofsight_lensing.png differ
diff --git a/figures/composite_lens_model_contours/caption.tex b/figures/composite_lens_model_contours/caption.tex
index 8908fe3..d8131c2 100644
--- a/figures/composite_lens_model_contours/caption.tex
+++ b/figures/composite_lens_model_contours/caption.tex
...
Probability distributions for the five primary magnification and
time
delay time-delay observables, drawn from a combination of results from five
of our seven baseline lens models: CATS, GLAFIC, GLEE, GRALE, and
ZLTM. Contours shown in the ten panels at the lower left mark the
1-$\sigma$ 1$\sigma$ and
2-$\sigma$ 2$\sigma$ confidence regions in each two-dimensional
slice of the parameter space. Histograms at the top of each column
show the marginalized
one-dimensional 1-D probability distributions, with
dashed vertical lines marking the mean and 1$\sigma$ confidence
region. These mean values and uncertainties are also reported in the
table of values at the upper right. The final line in the table
reports the observed time gap in days between \spockone in January,
2014 and \spocktwo in August, 2014.
\label{fig:LensModelContours}
diff --git a/figures/detection_image/caption.tex b/figures/detection_image/caption.tex
index eafd144..2462ad3 100644
--- a/figures/detection_image/caption.tex
+++ b/figures/detection_image/caption.tex
...
\label{fig:SpockDetectionImages}
The detection of \spockone and \spocktwo in
HST \HST imaging from the
Hubble Frontier Fields. The central panel shows the full field of the
MACSJ0416 cluster, in a combined image using optical and infrared
bands from
HST. \HST. Two boxes within the main panel demarcate the regions
where the \spock
host galaxy host-galaxy images appear. These regions are shown as
two inset panels on the left, highlighting the three images of the
host galaxy (labeled 11.1, 11.2, and 11.3), which are caused by the
gravitational lensing of the cluster. Two columns on the right side
diff --git a/figures/detection_image/detection_image.pdf b/figures/detection_image/detection_image.pdf
new file mode 100644
index 0000000..b774d22
Binary files /dev/null and b/figures/detection_image/detection_image.pdf differ
diff --git a/figures/detection_image/detection_image.png b/figures/detection_image/detection_image.png
index da22531..580d473 100644
Binary files a/figures/detection_image/detection_image.png and b/figures/detection_image/detection_image.png differ
diff --git a/figures/lbv_lightcurve_comparison/caption.tex b/figures/lbv_lightcurve_comparison/caption.tex
index 1e30905..12bd0af 100644
--- a/figures/lbv_lightcurve_comparison/caption.tex
+++ b/figures/lbv_lightcurve_comparison/caption.tex
...
Comparison of observed \spock light curves against rapid outbursts
from two LBVs. Colored markers show the \spock
light curve light-curve data, as in
Figure~\ref{fig:LightCurves}, with downward arrows marking
3-$\sigma$ 3$\sigma$
upper limits in epochs with no detection of the \spock source. The LBV
comparison light curves have been shifted in time and magnitude to
match up with the peak of the observed light curves.
diff --git a/figures/light_curve_linear_fits/caption.tex b/figures/light_curve_linear_fits/caption.tex
index 867f0ff..d368183 100644
--- a/figures/light_curve_linear_fits/caption.tex
+++ b/figures/light_curve_linear_fits/caption.tex
...
Piece-wise Piecewise linear fits to the \spock light curves, used to measure the
rise time and decay time of the two events. The \spockone light curve
is shown in the top panel, and \spocktwo in the bottom. Filled points
with error bars plot the observed brightness of each event in AB
magnitudes as a function of rest-frame time (for
$z=1.0054$).
Piece-wise Piecewise linear fits are shown for the four bands that
have enough points for fitting: in the top panel fits are plotted for
the F814W band (solid green lines) and the F435W band (dashed cyan
lines), while in the bottom panel fits are shown for F160W (solid
maroon) and F125W (dashed scarlet). Open diamonds in each panel show
three examples of assumptions for the time of peak brightness, $t_{\rm
pk}$
(i.e. (i.e., the position where the rising piece of the linear fit
ends). Open circles mark the corresponding point, $t_{\rm pk} + t_3$,
at which the fading transient would have declined in brightness by 3
magnitudes. mag. See text for details on the fitting procedure.
\label{fig:LinearLightCurveFits}
diff --git a/figures/muse_oii_sequence/caption.tex b/figures/muse_oii_sequence/caption.tex
index 7251a1c..46385d7 100644
--- a/figures/muse_oii_sequence/caption.tex
+++ b/figures/muse_oii_sequence/caption.tex
...
\label{fig:MUSEOIISequence}
Measurements of the \forbidden{O}{ii}
$\lambda\lambda$3726,3729 $\lambda\lambda$3726, 3729
doublet, observed with MUSE after both \spock events had faded. The
upper left upper-left panel shows the 12 apertures with radius 0.6\arcsec that
were used for the extractions reported in
Table~\ref{tab:MuseLineFits}. Odd-numbered apertures are plotted with
solid lines, while even-numbered apertures are shown as unlabeled
dashed circles. The apertures centered on the \spock-NW and SE
locations are highlighted in orange and magenta, respectively. The
1-D spectra extracted from these \spock locations are shown in the
upper right upper-right and
lower right lower-right panels, centered around the observed
wavelength of the \forbidden{O}{ii} doublet, and normalized to reach a
value of unity at the peak of the $\lambda$3729 line. Dashed vertical
lines mark the vacuum wavelengths of the doublet, redshifted to
$z=1.0054$. The width of the shaded region indicates the $1\sigma$
uncertainty in the measured flux. Below each spectrum, a residual
plot shows the flux that remains after subtracting off a mean spectrum
constructed from the normalized spectra of the odd-numbered apertures.
The
lower left lower-left panel shows the same residual spectra constructed for
the odd-numbered apertures, demonstrating that the \forbidden{O}{ii}
line profile does not exhibit any significant gradients across the
length of the
host galaxy host-galaxy arc.
diff --git a/figures/peakluminosity_vs_declinetime/caption.tex b/figures/peakluminosity_vs_declinetime/caption.tex
index 044bfcd..60517bf 100644
--- a/figures/peakluminosity_vs_declinetime/caption.tex
+++ b/figures/peakluminosity_vs_declinetime/caption.tex
...
class from neutron star mergers. Grey bands in both panels show the
MMRD relation for classical novae. In the right panel, circles mark
the observed peak luminosities and decline times for classical novae,
while black `+' symbols mark recurrent novae from our own
galaxy. Galaxy. The
large cross labeled at the bottom shows the rapid recurrence nova M31N
2008-12a. Each orange diamond marks a separate short transient event
from the two rapid LBV outburst systems, SN
2009ip\cite{Pastorello:2013} and NGC3432-LBV1
(a.k.a. (also known as SN
2000ch)\cite{Pastorello:2010}. These LBV events provide only upper
limits on the decline time
due owing to limited photometric sampling.
diff --git a/figures/recurrent_nova_lightcurve_comparison/caption.tex b/figures/recurrent_nova_lightcurve_comparison/caption.tex
index 64a1dd2..8f045a1 100644
--- a/figures/recurrent_nova_lightcurve_comparison/caption.tex
+++ b/figures/recurrent_nova_lightcurve_comparison/caption.tex
...
\label{fig:RecurrentNovaLightCurveComparison}
Comparison of the \spock light curves against template light curves
for RN outbursts. Colored markers show the \spock
light curve light-curve data,
as in Figure~\ref{fig:LightCurves}, plotting the apparent magnitude as
a function of time in the rest frame (bottom axis) and observer frame
(top axis). The gray shaded regions encompass the outburst
light curve light-curve
shapes of 5 of the 11 known
galactic Galactic RNe (U Sco, V2487 Oph, V394 CrA,
T CrB, and V745 Sco), selected because they exhibit a rapid decline in
their light
curves \citep{Schaefer:2010}. curves\citep{Schaefer:2010}. The solid black line traces
the 2014 outburst
light curve light-curve shape for the rapid-recurrence nova M31N
2008a-12 \citep{Darnley:2014}. 2008a-12\citep{Darnley:2014}. All template light curves have been
normalized to match the observed peaks of the \spock events.
diff --git a/figures/recurrent_nova_recurrence_comparison/caption.tex b/figures/recurrent_nova_recurrence_comparison/caption.tex
index 050edf4..f1b8949 100644
--- a/figures/recurrent_nova_recurrence_comparison/caption.tex
+++ b/figures/recurrent_nova_recurrence_comparison/caption.tex
...
Comparison of the inferred \spock recurrence timescale against
observed RNe and models. In the left panel the outburst amplitude in
magnitudes is plotted against the recurrence timescale, while in the
right panel the
y ordinate axis shows the peak luminosity (or absolute
magnitude). In both
panels panels, the joint constraints on \spock from both
transient episodes are plotted as large open diamonds, observed
constraints from the 10
galactic Galactic RNe appear as black
`x' ``x'' points, and
the rapid-recurrence nova M31N 2008a-12 is shown with a thick black
`+' ``+'' marker. Colored circles show the results from a suite of
numerical hydrodynamic
simulations from \citet{Yaron:2005}. simulations\citet{Yaron:2005}. The size
of each circle indicates the mass of the primary white dwarf (WD) star
over the range 0.4-1.4
M$_\odot$, \Msun, as indicated in the legend of the
left panel. The color of each circle denotes the rate of mass
transfer from the secondary onto the WD, as given in the right panel's
legend.
diff --git a/figures/spock_colorcurves_observerframe/caption.tex b/figures/spock_colorcurves_observerframe/caption.tex
index daa5e17..31204d2 100644
--- a/figures/spock_colorcurves_observerframe/caption.tex
+++ b/figures/spock_colorcurves_observerframe/caption.tex
...
Observed colors for the \spock events. Filled points plotted in the
top panels show observed AB magnitudes for the \spockone and \spocktwo
events from
-3 3 rest-frame days before the date of observed peak
brightness. Solid lines and shaded regions show linear fits to the
data in the F814W and F160W bands. Open points in the bottom panels
show observed colors in the rest-frame bands. For each color the
diff --git a/figures/spock_critical_curves/caption.tex b/figures/spock_critical_curves/caption.tex
index 3bb6e30..b0bfd72 100644
--- a/figures/spock_critical_curves/caption.tex
+++ b/figures/spock_critical_curves/caption.tex
...
\label{fig:SpockCriticalCurves}
Locations of the lensing critical curves relative to the positions of
the two \spock sources. Panel (a) shows the
HST \HST Frontier Fields
composite near-infrared image of the full \macs0416 field. The
magnification map
from the \citet{Caminha:2017} model for a source at $z=1$ is overlaid with orange and
black
contours. contours\citet{Caminha:2017}. The white box marks the region
that is shown in panel (b) with a closer view of the \spock host
galaxy. Panel (c) shows a trace of the lensing critical curve from
the GRALE model, and panels (d)-(i) show magnification maps for the
six other primary models, all for a source at the \spock redshift.
The magnification maps are plotted with log scaling, such that white
is $\mu=1$ and black is $\mu=10^3$. Panels j-m show the same
magnification maps, extracted from the lens model variations
described
in \ref{sec:LensModelVariations}. (see
Methods).
diff --git a/figures/spock_critical_curves/spock_critical_curves.pdf b/figures/spock_critical_curves/spock_critical_curves.pdf
new file mode 100644
index 0000000..f9d8507
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diff --git a/figures/spock_critical_curves/spock_critical_curves.png b/figures/spock_critical_curves/spock_critical_curves.png
index 159e0c1..ca25e41 100644
Binary files a/figures/spock_critical_curves/spock_critical_curves.png and b/figures/spock_critical_curves/spock_critical_curves.png differ
diff --git a/figures/spock_hostgalaxy_properties/caption.tex b/figures/spock_hostgalaxy_properties/caption.tex
index 3141efb..103672d 100644
--- a/figures/spock_hostgalaxy_properties/caption.tex
+++ b/figures/spock_hostgalaxy_properties/caption.tex
...
Stellar population properties of the \spock host galaxy, derived from
``pixel-by-pixel'' SED fitting. The top row shows maps for the adjacent
host images 11.1 and 11.2, and the bottom panels show image 11.3.
From left to right the panels present the rest-frame
(U-V) ($U-V$) color, the
stellar surface mass
density, density $\Sigma$, and the mean age of the
stellar population in Gyr. Markers in the top row denote the
positions of the two \spock transient events. Markers in the bottom
panels are at the center of host image 11.3.
diff --git a/figures/spock_predictions/caption.tex b/figures/spock_predictions/caption.tex
index e740cb0..27b04cd 100644
--- a/figures/spock_predictions/caption.tex
+++ b/figures/spock_predictions/caption.tex
...
Predictions for the reappearance episodes of both \spockone
and \spocktwo due to gravitational lensing time delays, as listed in
Table~\ref{tab:LensModelPredictions}. The top panel shows photometry
collected at the NW position
(host galaxy (host-galaxy image 11.2) where the first
event (\spockone) appeared in January, 2014. Optical
measurements from ACS are in blue and green, and infrared observations
from WFC3-IR are in red and
orange, as in
Figure~\ref{fig:LightCurves}. orange. Each blue bar in the lower panel shows
one lens model prediction for the dates when that same physical event
(\spockone) would have also appeared in the SE location (galaxy image
11.1), due to gravitational lensing time delay. The lower panel plots
diff --git a/nature_arxiv.cls b/nature_arxiv.cls
index a97088c..3e45d32 100644
--- a/nature_arxiv.cls
+++ b/nature_arxiv.cls
...
%% make citations be superscripts, taken from citesupernumber.sty
\def\@cite#1#2{$^{\mbox{\scriptsize #1\if@tempswa , #2\fi}}$}
\newcommand{\citeref}[1]{[Ref.~{\citenum{#1}}]}
\providecommand\citealt{\cite}
\providecommand\citep{\cite}
\providecommand\citet{\cite}
%% Some style parameters
\setlength{\parindent}{0.39in}
\setlength{\parskip}{1pt}
...
\setlength{\parskip}{12pt}%
}{}
%% Define the Supplemental Information environment. Use \subsection to separate.
\newenvironment{supplementary}{%
\section*{Supplementary Information}%
\setlength{\parskip}{12pt}%
\renewcommand{\figurename}{Supplementary Figure}
\renewcommand{\tablename}{Supplementary Table}
\setcounter{figure}{0}
\setcounter{table}{0}
}{}
%% No heading for References section, but eat up the extra space from \section command
\renewcommand\refname{\vspace{-48pt}\setlength{\parskip}{12pt}}
diff --git a/preamble_nature.tex b/preamble_nature.tex
index df717ef..29dafb8 100644
--- a/preamble_nature.tex
+++ b/preamble_nature.tex
...
\usepackage{cite}
\usepackage{graphicx}
\usepackage[space]{grffile}
\usepackage{latexsym}
...
{\endminipage\par\medskip}
\providecommand\citet{\cite}
\providecommand\citep{\cite}
\providecommand\citealt{\cite}
\def\dataset[#1]#2{#2}%
...
\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\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}
...
\def\Chandra{{\it Chandra}\xspace}
\def\Herschel{{\it Herschel}\xspace}
\def\XMM{{\it XMM}\xspace}
\def\SWIFT{{\it SWIFT}\xspace} \def\Swift{{\it Swift}\xspace}
% Specific to this paper:
diff --git a/spock_arxiv.pdf b/spock_arxiv.pdf
index 51775fb..346d86e 100644
Binary files a/spock_arxiv.pdf and b/spock_arxiv.pdf differ
diff --git a/spock_arxiv.tex b/spock_arxiv.tex
index dbb7310..a4f2232 100644
--- a/spock_arxiv.tex
+++ b/spock_arxiv.tex
...
%% Template for a preprint Letter or Article for submission
%% to the journal Nature.
%% Written by Peter Czoschke, 26 February 2004
%%
%Sections can only be used in Articles. Contributions should be
%organized in the sequence: title, text, methods, references,
%Supplementary Information line (if any), acknowledgements,
%interest declaration, corresponding author line, tables, figure
%legends.
\documentclass{nature_arxiv}
\input{preamble_nature}
%% make sure you have the nature.cls and naturemag.bst files where
%% LaTeX can find them
\bibliographystyle{naturemag}
\input{TitleAndAuthors}
...
\makeaffil
\begin{multicols}{2} %\begin{multicols}{2}
\input{IntroductionShort}
\input{Figures}
\input{Results}
\input{Discussion}
\end{multicols}
\input{Figures} %\end{multicols}
\clearpage
\begin{methods}
%Put methods in here. If you are going to subsection it, use
%\verb|\subsection| commands. Methods section should be less than
...
\input{LensingModels}
\input{Xray}
\input{LightCurves}
\input{HostGalaxy}
\input{LBV}
\input{RN}
\input{Microlensing}
...
\end{methods}
% Supplemental figures
\input{Supplemental}
%% Put the bibliography here, most people will use BiBTeX in
%% which case the environment below should be replaced with
...
\bibliography{./bibliography/biblio}{}
%% Here is the endmatter stuff: Supplementary Info, etc.
%% Use \item's to separate, default label is "Acknowledgements"
\begin{addendum}
%\item[Supplementary \item[Supplementary Information]
Supplementary figures, tables and notes are included at the end of this document.
\item \input{Acknowledgments}
% \item[Competing Interests] The authors declare that they have no
% competing financial interests.
...
should be addressed to S.A.R.~(email:
[email protected]).
\end{addendum}
%%
%% TABLES
%%
%% If there are any tables, put them here.
%%
\input{LongTables} % Supplemental figures, notes and tables
\clearpage
\begin{supplementary}
\input{Supplementary}
\end{supplementary}
\end{document}
diff --git a/spockone_photometry.tex b/spockone_photometry.tex
index fc48447..32ab8db 100644
--- a/spockone_photometry.tex
+++ b/spockone_photometry.tex
...
\begin{deluxetable}{cccc}
\tablewidth{\linewidth} \tablewidth{0.7\textwidth}
\tablecolumns{12}
\tablecaption{Photometry of the \spockone event.\label{tab:spockonephot}}
\tablehead{ \colhead{Date} & \colhead{Filter} &
\colhead{Flux} \colhead{Flux Density} & \colhead{AB Mag}\\
\colhead{(MJD)} & \colhead{} & \colhead{(10$^{30}$ erg\,s$^{-1}$\,cm$^{-2}$\,Hz$^{-1}$)} & \colhead{} }
\startdata
56144.86 & F105W & 0.063$\pm$0.119 & $<$29.39\\
...
56916.98 & F814W & 0.007$\pm$0.093 & $<$31.86\\
\enddata
\end{deluxetable}
diff --git a/spocktwo_photometry.tex b/spocktwo_photometry.tex
index 6675959..86240de 100644
--- a/spocktwo_photometry.tex
+++ b/spocktwo_photometry.tex
...
\begin{deluxetable}{cccc}
\tablewidth{\linewidth} \tablewidth{0.7\textwidth}
\tablecolumns{12}
\tablecaption{Photometry of the \spocktwo event.\label{tab:spocktwophot}}
\tablehead{ \colhead{Date} & \colhead{Filter} &
\colhead{Flux} \colhead{Flux Density} & \colhead{AB Mag}\\
\colhead{(MJD)} & \colhead{} & \colhead{(10$^{30}$ erg\,s$^{-1}$\,cm$^{-2}$\,Hz$^{-1}$)} & \colhead{} }
\startdata
56144.86 & F105W & -0.127$\pm$0.206 & $<$26.92\\
...
56916.98 & F814W & -0.028$\pm$0.089 & $<$27.83\\
\enddata
\end{deluxetable}
