Precursors prior to Type IIn supernova explosions are common: precursor rates, properties, and correlations

1.1 MB·

by  E. O. Ofek

SUBMITTEDTOAPJ
PreprinttypesetusingLATEXstyleemulateapjv.5/2/11
PRECURSORSPRIORTOTYPEIINSUPERNOVAEXPLOSIONSARECOMMON:PRECURSORRATES,PROPERTIES,
ANDCORRELATIONS
ERANO.OFEK1,MARKSULLIVAN2,NIRJ.SHAVIV3,AVIRAMSTEINBOK1,IAIRARCAVI1,AVISHAYGAL-YAM1,DAVIDTAL1,
SHRINIVASR.KULKARNI4,PETERE.NUGENT5,6,SAGIBEN-AMI1,MANSIM.KASLIWAL7,S.BRADLEYCENKO8,RUSSLAHER9,
JASONSURACE9,JOSHUAS.BLOOM6,ALEXEIV.FILIPPENKO6,ANDOFERYARON1
SubmittedtoApJ
4 ABSTRACT
1 There is a growing number of supernovae (SNe), mainly of Type IIn, which present an outburst prior to
0 theirpresumablyfinalexplosion. These precursorsmayaffectthe SN display,and arelikely relatedto some
2 poorlychartedphenomenainthefinalstagesofstellarevolution.Herewepresentasampleof16nearbyType

n IInSNeforwhichwehavePalomarTransientFactory(PTF)observationsobtainedpriortotheSNexplosion.
a By coaddingthese imagestaken priorto theexplosionin time bins, we searchforprecursorevents. We find
J five Type IInSNe thatlikely have atleast one possible precursorevent(PTF10bjb; SN2010mc[PTF10tel];

1 PTF10weh; SN2011ht; PTF12cxj), three of which are reported here for the first time. For each SN we
2 calculatethecontroltime(i.e.,theamountoftimeoursurveywasabletodetectaneventbrighterthanagiven
luminosity). Based on this analysis we find that precursor events among SNe IIn are common: assuming a

] homogeneouspopulation,attheone-sided99%confidencelevel,morethan50%ofSNeIInhaveatleastone
E
pre-explosionoutburstthatisbrighterthan3 107L (absolutemagnitude 14)takingplaceupto1/3yrprior
H to the SN explosion. The average rate of su×ch prec⊙ursorevents duringthe−year prior to the SN explosionis
. likelylargerthanoneperyear(i.e.,multipleeventsperSNperyear),andfainterprecursorsarepossiblyeven
h
morecommon. Wealsofindpossiblecorrelationsbetweentheintegratedluminosityoftheprecursor,andthe
p
SNtotalradiatedenergy,peakluminosity,andrisetime. Thesecorrelationsareexpectediftheprecursorsare
-
o mass-ejectionevents, and the early-timelight curveof these SNe is poweredby interactionof the SN shock
r andejectawithopticallythickcircumstellarmaterial.
t
s Subjectheadings: stars:mass-loss—supernovae:general—supernovae:individual:SN2010mc,PTF10bjb,
a SN2011ht,PTF10weh,PTF12cxj,SN2009ip
[

1
v 1. INTRODUCTION eral theoretical mechanisms have been suggested to explain
8 Influx-limitedsynopticsurveys,afewpercentofalldiscov- thishighmasslossinthefinalstagesofstellarevolution(e.g.,
6 ered supernovae (SNe) show narrow- to intermediate-width Rakavy et al. 1967; Woosley et al. 2007; Arnett & Meakin
4 ( 30–3000kms 1) hydrogen and helium emission lines. 2011; Chevalier 2012; Quataert & Shiode 2012; Shiode &
5 ∼ − Quataert2013;Soker&Kashi2013).
These are dubbed Type IIn SNe (Schlegel 1990; Filippenko
. Recently, five SNe with candidate pre-explosionoutbursts
1 1997;Kieweetal. 2012)andprobablyhavemassiveprogen-
(precursors)have been detected a few months to years prior
0 itors (e.g., Gal-Yam & Leonard 2009). Their emission lines
totheSNexplosion(Foleyetal. 2007;Pastorelloetal. 2007;
4 likely originatefrom relativelyabundantcircumstellarmate-
Mauerhan et al. 2013a; Pastorello et al. 2013; Ofek et al.
1 rial (CSM) aroundthe SN progenitorstar (e.g., Chevalier &
2013b;Corsiet al. 2013; Fraser etal. 2013). In mostcases
: Fransson1994;Chugai&Danziger1994;Chugaietal. 2003;
v these precursors were detected from SNe IIn, or closely re-
Ofek et al. 2007, 2010, 2014a; Smith et al. 2008, 2009),
i latedevents.
X ejectedonlyashorttime(oftheorderofmonthstodecades)
Thefrequencyandpropertiesofthese precursorsarecriti-
r prior to the SN explosion (Dessart et al. 2009; Gal-Yam & calforpinpointingtheeruptionmechanismsandunderstand-
a Leonard 2009; Ofek et al. 2010; Ofek et al. 2013b). Sev-
ing their effect on the eventualSN optical display, and may
changeourviewofthefinalstagesofmassivestarevolution.
1Benoziyo Center for Astrophysics, Weizmann Institute of Science, Therefore,wehaveconductedasearchforprecursoreventsin
76100Rehovot,Israel asampleofnearbySNeIInforwhichwehavepre-explosion
2School of Physics and Astronomy, University of Southampton,
observationsfromthePalomarTransientFactory(PTF10;Law
SouthamptonSO171BJ,UK
3RacahInstituteofPhysics,TheHebrewUniversity,91904Jerusalem, etal. 2009;Rauetal. 2009).Oursamplecontains16SNeIIn
Israel andwefoundprecursorseventsforfiveoftheSNeinoursam-
4CahillCenterforAstronomyandAstrophysics,CaliforniaInstituteof ple.Forthefirsttime,weestimatetherateofsucheventsand
Technology,Pasadena,CA91125,USA
showthattheyarecommon.Furthermore,weinvestigatepos-
5LawrenceBerkeleyNationalLaboratory,1CyclotronRoad,Berkeley,
siblecorrelationsbetweenthepropertiesoftheprecursorsand
CA94720,USA
6Department of Astronomy, University of California, Berkeley, CA theSNe.
94720-3411,USA Thepaperisorganizedasfollows.WedescribetheSNsam-
7ObservatoriesoftheCarnegieInstitutionforScience,813SantaBar-
ple in 2, while the observations are presented in 3. The
baraSt.,Pasadena,CA91101,USA § §
8AstrophysicsScienceDivision,NASA/GoddardSpaceFlightCenter, methodologyofprecursorselectionisdiscussedin 4andour
§
MailCode661,Greenbelt,MD,20771,USA
9SpitzerScienceCenter,CaliforniaInstituteofTechnology,M/S314-6,
Pasadena,CA91125,USA 10http://ptf.caltech.edu/iptf/
2 Ofeketal.
candidatesarepresentedin 5. We giveourcontrol-timees- 4.1. DetectionMethods
§
timate in 6, and the precursor rate in 7. The CSM mass
Ourcandidateprecursorselectionisbasedontwochannels.
§ §
estimateisdiscussedin 8,thecorrelationsbetweentheSNe
Thefirstchannelidentifiesprecursorsthatweredetectedina
§
andprecursorpropertiesin 9,andtheresultsin 10. singleimagepriortotheSNexplosion,atthe6s level,with-
§ §
outtheneedtocoadddata.Thesecondchannelidentifiespre-
2. SAMPLE cursorsthat were detected in the coadd data at the 5s level,
Our sample is based on SNe IIn that show intermediate- using15-daybinsandusingonlybinsthatcontainmorethan
widthBalmeremission lines. FrominspectionofmanySNe fivefluxmeasurements.
spectra obtained by PTF, we find that some SNe show this The second channel significantly increases the sensitivity
hallmarkofSNeIInatearlytimes(afewdaysaftertheexplo- of PTF to precursor events by effectively coadding images
sion),buttheselinesdisappearonatimescaleofaweek. Itis of a SN location in time bins of 15days. These time bins
possiblethattheseSNealsosufferfromamoderatemass-loss often include a large number of observations, extending to
ratepriorto theexplosion(e.g.,Gal-Yametal. 2014;Yaron depths beyond the nominal PTF survey limiting magnitude,
et al. 2014). However, we excludefrom our sample objects andreachinganR-bandlimitingmagnitudeof<23.5. How-
for which the spectra evolve into those of normal SNe II a ever,coaddingimagesthemselvesinarbitrarytimebins,and
fewweeksafterexplosion.Examplesforsuchobjectsinclude thenconductingimage-subtractionanalysisoneachtrialbin,
PTF11iqbandPTF10uls(Ofeketal. 2013a). isa relativelyexpensiveoperation. Instead,we carefullyap-
Another important criterion for our SNe selection is that plyimagesubtractiontoindividualimages,andforeachim-
they have a large number of pre-explosion images from the agewesavethefluxresidual(negativeorpositive)attheloca-
PTF survey (Law et al. 2009; Rau et al. 2009). The exis- tionoftheSN.Wecanthencoaddthescalarfluxresidualsin
tence of a large number of images is critical, as precursors anytemporalcombinationwe desire. Thismethodwas used
mayberelativelyfaintanditisdesirabletocoaddimagesin inthecaseofSN2010mc(PTF10tel;Ofeketal. 2013b)and
order to get a limiting magnitude that is deeper than that of PTF11qcj(Corsietal. 2013).
the nominal survey. The SNe in our sample were found by Inthe firstchannel,theuncertainty(i.e.,s ) wasestimated
thePTFaswellasamateurastronomers,theLickObservatory based on the Poisson noise propagated through the image-
SNSearch(LOSS;Lietal.2000;Filippenkoetal. 2001),and subtractionpipeline,whileforthesecondchannel,wecalcu-
theCatalinaReal-timeTransientSurvey(CRTS;Drakeetal. latederrorsin each binusing the bootstraptechnique(Efron
2009). WeselectedonlynearbySNe,foundwithin400Mpc, 1982).Wenotethatinmostcasesthebootstraperrorsarecon-
forwhichwehaveadecentnumberofpre-explosionobserva- sistent with the uncertainties derived based on the standard
tions. Table1listthe16SNeinoursample. deviation of the points in each bin, and the expected Pois-
son noise. Therefore, our bootstrap error estimate suggests
that the statistical uncertainties produced by the subtraction
3. OBSERVATIONS
pipelinearerealistic.
We usedPTFobservationsofthe SNe in oursample. The
InordertokeepoursearchuniformweuseonlythePTFR-
PTFdatareductionisdescribedbyLaheretal. (inprep.),and
banddata for oursearch and analysis, as PTF was primarily
thephotometriccalibrationisdiscussedbyOfeketal. (2012a,
anR-bandsearch. However,wealsoshowtheg-banddatain
2012b).Oursearchisbasedonimagesubtraction,andtheflux
thevariousplotswhereavailable;theamountofg-banddata
residualsintheindividualimagesubtractionsforalltheSNe
issmallincomparisontotheR-band.
inoursamplearelistedinTable2.
Candidateprecursoreventsdetectedviaoneofthechannels
Figures 1–2 show the light curves before explosion (first
arediscussedin 5. Intheinitialsearchwedonotattemptto
and third columns) and after explosion (second and fourth §
use different time bins. This decision was made in order to
columns) of all the SNe in our sample. The pre-explosion
limitthenumberofstatisticalexperiments,whichmayaffect
light curve shows the median flux, relative to the reference
the significance of our results. We note, however, that care-
image flux, in 15-daysbins. Only binscontaining 6 mea-
fulexaminationofspecificeventswithlongertimebinsmay
≥
surementsarepresented. The“+”signsshowsthelowerand
containprecursoreventsthatarenotdiscussedhere. Forex-
upper5s errorrelativetothereferenceimage,whilethesolid
ample, in Corsi et al. (2013) we report on a possible faint
lines connect consecutive bins. The errors where calculated
(absolutemagnitude 13), severalmonthslong, brightening
using the bootstrap error on the mean. The vertical dashed −
inthelightcurveoftheTypeIcPTF11qcjabout2.5yrprior
lines show the estimated explosion time and time of maxi-
toitsexplosion.
mumlight(seeTable1).
Wenotethatseveralobjectsshowpointsthataremarginally
We obtained spectra of our SNe using various telescopes, belowthelower5s errorthreshold. Itispossiblethatthisis
and the log of selected observationsis presented in Table 3.
causedbyrealvariabilityoftheprogenitor(e.g.,Szczygiełet
Some of the spectra are presented in this paper, while the
al.2012),buthereweconcentrateontheoutburstsratherthan
restareavailableelectronicallyfromtheWISeREPwebsite11 possibledimmings(seealso 5.6).
(Yaron&Gal-Yam2012). §
4.2. Tests
4. PRECURSORCANDIDATESELECTION
We performed several tests to verify the reliability of our
Inthissectionwedescribethemethodsweusedtofindthe
methodology,especiallyagainstfalsealarms. Inordertotest
precursorcandidates. In 4.1wepresentthesearchmethods,
detectionsmadebythefirstchannel(i.e.,precursorsdetected
§
while in 4.2 we discuss the reliability of our methodology
insingleimages)weextractedthelightcurvesatrandompo-
§
andthefalse-alarmprobabilityoftheprecursorcandidates.
sitions on top of the same host galaxy, but shifted in posi-
tionrelativeto theSN.We foundthattypicallytheprobabil-
11http://www.weizmann.ac.il/astrophysics/wiserep/ ity to get a 6s detection is less than 0.1% per image. This
Supernovaprecursors 3
400 16
150 13.4
100 2213.6 200 22
50 2313.8 2316.5
0 14 0
−50 14.2 17
−100 14.4 −200
−150 PTF10aaxf 14.6 PTF10aaxf −400PTF10aazn 17.5 PTF10aazn
−200 −150 −100 −50 0 0 20 40 60 80 100 −300 −200 −100 0 0 20 40 60 80 100
17.5
300 600
19.5
18
200
400
100 2218.5 20
23
0 200
−100 19 222320.5
0
−200
19.5
−300PTF10achk PTF10achk −200PTF10bjb 21 PTF10bjb
20
−500 −400 −300 −200 −100 0 0 20 40 60 80 100 −400 −300 −200 −100 0 0 20 40 60 80 100
100 2217 18.5
300
e 19
d
agnitu 50 231189 120000 2223192.05
M 0 0
x/ 20 −100 20.5
Flu −50 −200 21
21
21.5
−300
−100PTF10fjh 22 PTF10fjh PTF10gvf 22 PTF10gvf
−300 −200 −100 0 0 20 40 60 80 100 −400 −300 −200 −100 0 0 20 40 60 80 100
200 17 18
22 100 2218.5
100 18
23 50 2319
19
0 0 19.5
20 −50 20
−100
−100 20.5
21
PTF10tel PTF10tel PTF10weh PTF10weh
−200 21
−300 −200 −100 0 0 20 40 60 80 100 −400 −300 −200 −100 0 0 20 40 60 80 100
18.5
600 2000
18
400 19
1000
200 19 19.5
22
0 23 0 222320
−200 20 20.5
−1000
−400 21
21
−600PTF11fzz PTF11fzz −2000PTF12cxj PTF12cxj
21.5
−600 −400 −200 0 0 20 40 60 80 100 −800 −600 −400 −200 0 0 20 40 60 80 100
t−t [day]
rise
FIG.1.—ThelightcurvesoftenSNe(namesarelistedineachpanel). ForeachSNtwoplotsareshown(sidebysideinthefirstandsecondcolumnsand
inthethirdandfourthcolumns). ColumnstwoandfourshowthelightcurveaftertheSNexplosion,whilethepanelsincolumnsoneandthreegiveonlythe
coaddedfluxresidual(relativetothereferenceimage)priortotheSNexplosion(iftherearemorethanfiveobservationspertimebin).Thetwoverticaldashed
linesshowtheassumedexplosiondate(trise)androughmaximum-luminositydate(tpeak;listedinTable1). Timeismeasuredrelativetotrise. Theredcircles
representR-bandobservationswhilethebluesquaresshowg-banddata. AllofthemeasurementsareinthePTFmagnitudesystem(Ofeketal. 2012a;2012b).
Thezeropointofthefluxresiduals(firstandthirdcolumns)is27,withtheexceptionofPTF10aazn(27.895),PTF10bjb(27.14),andPTF10tel(27.442). The
tickmarksontheright-handaxesofthefirstandthirdcolumnsshowthefluxesthatcorrespondtoPTFmagnitudesof22and23. Inthefirstandthirdcolumns,
filledsymbolsshowthefluxmeasurements,in15-daysbins.Onlybinscontainingsixormoremeasurementsareused.Theplussignsrepresentthe5s upperand
lowerlimits,asestimatedfromthebootstraptechniqueineachbin(Efron1982).Ifplussignsarefoundinconsecutivebinstheyareconnectedbyasolidline.
4 Ofeketal.
TABLE1
SNSAMPLE
Name Type a (J2000) d (J2000) MR,peak z DM trise tpeak FAP
(deg) (deg) (mag) (mag) (day) (day)
SN2010jl IIn 145.722236 +09.495037 20.6 0.011 33.44 55474 55494 0.01
SN2010jj IIn 31.717743 +44.571558 −18.0: 0.016 34.22 55512 55525 0.02
PTF10achk IIn 46.489751 10.522491 −18.7 0.0327 35.77 55535 55550 0.00
PTF10bjb IIn? 192.424667 −10.800159 −< 16.4 0.026 35.27 55326 55434 ...
SN2010bq IIn 251.730659 −+34.159641 1−8.5 0.032 35.73 55296 55311 0.00
PTF10gvf IIn 168.438496 +53.629126 −18.8 0.081 37.82 55321 55339 0.00
SN2010mc IIn 260.377817 +48.129834 −18.5 0.035 35.93 55427 55447 0.00
PTF10weh IIn 261.710251 +58.852064 −20.7 0.138 39.06 55453 55504 0.02
PTF11fzz IIn 167.694502 +54.105220 −20.3 0.082 37.85 55721 55783 0.00
PTF12cxj IIn? 198.161181 +46.485090 −17.3 0.036 35.96 56033 56048 0.01
SN2011cc IIn 248.456000 +39.263528 −18.1: 0.0319 35.72 55624 55741 0.02
SN2011fx IIn 4.498167 +24.562778 −17.1: 0.0193 34.61 55780: 55803: 0.00
SN2011ht IIn 152.044083 +51.849194 −16.8 0.004 30.96 55830: 55880: 0.00
SN2011hw IIn/Ibn 336.560583 +34.216417 −19.1: 0.023 34.99 55860 55884: ...
SN2011iw IIn 353.700833 24.750444 −18.1: 0.023 34.99 55819 55894: 0.04
SN2012as IIn 231.285500 −+37.963722 −18.0: 0.0297 35.56 55968: 55976: 0.00
−
NOTE.—TheSNesample. TyperefertoSNtype,a (J2000)andd (J2000)aretheJ2000.0rightascensionanddeclination,respectively. MR,peakisthepeak
absoluteR-bandmagnitude,zistheSNredshift,DMisdistancemodulus,triseistheMJDoftheestimatedstartoftheSNrise,andtpeakistheMJDofthelight
curvepeak.Colonsignindicatesanuncertainvalue. ThetriseforSN2011iwisbasedonadetectionincoaddedPTFdataanditappearsasapartofthefastrise
followingthisdetection.FAPisthefalse-alarmprobabilitytodetectaprecursorbycoaddingimagesin15-daybinsasestimatedusingthebootstrapmethod(see
§4.2). Thevaluesarebasedon100bootstrapsimulationsandthereforetruncatedtotwofiguresafterthedecimalpoint. SNewithnodataarethoseinwhich
theprecursorisclearlydetectedinmanyindividualimages,andtherefore,thebootstrapanalysisonthecoaddeddataisineffective(see§4.2). SNebelowthe
horizontallinewerenotdetectedbyPTF,althoughPTFhavepre-explosionimagesoftheirlocations.
References:
SN2010jl:PTF10aaxf;Newtonetal.(2010);Stolletal.(2011);Smithetal.(2011);Chandraetal.(2012);Ofeketal.(2013a;2014a).
SN2010jj:PTF10aazn;Rich(2010);Silvermanetal.(2010).
PTF10achk:reportedhereforthefirsttime.
PTF10bjb:reportedhereforthefirsttime.
SN2010bq:PTF10fjh;Duszanowicz(2010);Challisetal.(2010);Ofeketal.(2013a).
PTF10gvf:reportedhereforthefirsttime.
PTF10tel:Ofek(2012);Ofeketal.(2013a;2013b).
PTF10weh:reportedhereforthefirsttime.
PTF11fzz:reportedhereforthefirsttime.
PTF12cxj:reportedhereforthefirsttime.
SN2011cc:Masonetal.(2011).
SN2011fx:Ciabattarietal.(2011).
SN2011ht:Bolesetal.(2011);Prietoetal.(2011);Romingetal(2012);Mauerhanetal.(2013b)
SN2011hw:Dintinjanaetal.(2011).
SN2011iw:Mahabaletal.(2011).
SN2012as:Jinetal.(2012).
TABLE2
SNOBSERVATIONS
Name Band MJD-trise MJD Mag MagErr LimMag Flux FluxErr
(day) (day) (mag) (mag) (mag) (counts) (counts)
PTF10aaxf R 232.84900 55241.15100 81.555 0.913 21.441 66.4 55.8
PTF10aaxf R −232.49900 55241.50100 82.323 −0.985 20.590 −134.7 122.2
PTF10aaxf R −229.61100 55244.38900 21.890 −0.392 21.802 −110.7 40.0
PTF10aaxf R −229.56800 55244.43200 82.112 0.653 21.247 110.9 66.7
PTF10aaxf R −223.68700 55250.31300 81.913 −1.045 20.936 − 92.3 88.8
− − −
NOTE. —PhotometricmeasurementsandfluxresidualsofthetheSNeinoursample. Magnitudearecalculatedinlaptitudes,andtheyhavemeaningonly
whensmallerthanthelimitingmagnitude. ThistableispublishedinitsentiretyintheelectronicversionofApJ.Aportionofthefulltableisshownherefor
guidanceregardingitsformandcontent.
Supernovaprecursors 5
16.5 150 19
1500
17 100 22
1000 19.1
500 17.5 50 23
0 222318 0 19.2
−500 18.5 −50
−1000 19.3
19 −100
−1500SN2011cc 19.5 SN2011cc −150SN2011fx 19.4 SN2011fx
−400 −300 −200 −100 0 0 20 40 60 80 100 −300 −200 −100 0 0 20 40 60 80 100
19 19.5
1000
e
d 19.2
Magnitu 5000 222319.4 5000 222320
x/ 19.6
Flu −500 19.8 −500
−1000SN2011ht SN2011ht SN2011hw SN2011hw
20 20.5
−300 −200 −100 0 0 20 40 60 80 100 −600 −400 −200 0 0 20 40 60 80 100
20.5 18.3
1000
100 22
20.6 18.4
50 2320.7 500 18.5
0 20.8 0 222318.6
20.9 18.7
−50 21 −500 18.8
21.1 18.9
−100
SN2011iw SN2011iw −1000SN2012as SN2012as
−400 −300 −200 −100 0 0 20 40 60 80 100 −400 −300 −200 −100 0 0 20 40 60 80 100
t−t [day]
rise
FIG.2.—LikeFigure1butforsixadditionalSNe.
1100
TABLE3
1000
LOGOFSPECTROSCOPICOBSERVATIONS
900
SNname MJD Telescope Instrument
800
(day) ns
bi 700
SN2010jl 55505 Keck-I LRIS
s1
SN2010jj 55505 Keck-I LRIS 0. 600
PTF10achk 5555554474 ULiHck883m SKNasItFS er in 500
b
PTF10bjb 55262 Keck-I LRIS m 400
u
SN2010bq 55300 Gemini-N GMOS N
300
PTF10gvf 55322 Keck-I LRIS
SN2010mc 55434 Gemini-N GMOS 200
55442 Lick3m Kast
55449 KPNO4m RCSpec 100
55455 Lick3m Kast
0
PTF10weh 55479 KPNO4m RCSpec −6 −4 −2 0 2 4 6
Residuals [s ]
55502 Lick3m Kast
55503 KPNO4m RCSpec FIG.3.—Thedistributionoffluxresidualsins units,atalltheepochsand
PTF11fzz 55736 Hale5m DBSP at16randompositionsaroundthepositionofPTF12cxj,onthesamehost
55873 WHT ISIS galaxy.
PTF12cxj 56035 Gemini-N GMOS
NOTE.—MJDistheobservationmodifiedJulianday. (coadding flux residuals in 15-day time bins), for each SN
werun100bootstrapsimulationsinwhichwemixedtheflux
is because the noise is not distributed normally (e.g., there residualsandtimes,andbinnedthedataagainin15-daybins
are outliers) owing to occasional subtraction artefacts, cos- with the same selection criteria. The probability to have a
mic rays, or asteroids in the field of view. For some SNe single detection, based on these simulations, is listed in col-
wehavehundredsofimages,andthereforetheprobabilityfor umn FAP (false-alarm probability) in Table 1. This proba-
a detection is on the order of a few percent per SN. There- bility may approach several percent for the entire sequence
fore,weconsiderasgoodcandidatesonlyeventswhichhave ofimages. However,afterpassingtheselectioncriteria,each
two consecutive detections (see 5). Figure 3 illustrates the candidate is tested using various binning schemes, and only
§
histogramof“random”-positionfluxresidualsinunitsofthe sourcesthatshowtwoconsecutiveindependentdetectionsare
flux-residualerrors(i.e., s )forthecaseofrandompositions consideredasgoodcandidates(see 5).
§
aroundPTF12cxj. It is apparentthat even thoughthere is a We also search for correlationsbetween the flux residuals
smallexcessaroundpositiveresiduals,theprobabilityofget- and airmass, and flux residuals and the amplitude of the ex-
tingresidualswhicharebiggerthan6s issmall. pected atmospheric refraction. Indeed, we find marginally
In order to test detections made using the second channel significant correlations between these properties; however,
6 Ofeketal.
theyaretoosmalltoaffectourresults. PTF observations detected the outburst in individual
To summarize, tests of our methodology suggest that the images, suggesting that the outburst was already active
false-alarmprobabilityforasingle-pointprecursordetection, 11monthspriortotheexplosion. AllofthePTFphotometric
inanentireSNdataset,is 5%perobject. Inordertoavoid measurementsarelistedinTable2. WenotethatPTFdidnot
∼
false detections, we consider as precursor candidates only observetheSNitself. Assumingtherewasasingleprecursor,
cases which show at least two detections clustered in time thepropertiesandenergeticsofthiseventarelistedinTable4.
(i.e.,assumingthenoiseisnotcorrelated).
5.3. PTF10bjb
5. CANDIDATEPRECURSOREVENTS PTF10bjb was discovered by PTF on 2010 Feb. 16, and
OursearchyieldedseveralSNewithcandidateprecursors. the onlyspectrumobtainedon 2010Mar. 7 resemblesthose
The precursors of PTF10bjb, SN2010mc, and SN2011ht ofluminousbluevariablesandSNe IIn. Close inspectionof
were clearly detected in individual images (first channel), thelightcurvesuggeststhattheSNwasdiscoveredwhileina
whilePTF12cxjandPTF10wehareweaklydetectedincoad- pre-explosionhighstate, andthatthespectrumwasobtained
ded images (second channel). Although these two weak priortotheexplosion. ThespectrumshowsBalmeremission
eventspassallourtestsandweconsiderthemtobereal,given lines, the broadercomponentof which has a velocity (s ) of
thelowsignal-to-noiseratioofthedetections,wealsodiscuss about 600kms 1. Also detected are emission lines of HeI
−
ourresultsassumingthesetwoeventsarenotreal. Imagesof andCaII.TheHeIl 5876lineshowsanarrowP-Cygnipro-
alltheprecursorsarepresentedinFigure4. filewithavelocityof 600kms 1,whiletheHa lineshows
−
aP-Cygniprofilewith∼avelocityof 300kms 1. Thespec-
−
5.1. PTF10tel trumofthiseventispresentedinFig∼ure6.
PTF10telisdiscussedindetailbyOfeketal. (2013b). For The light curve of PTF10bjb is shown in Figure 7. Be-
completeness,herewesummarizethemainpropertiesofthis tween 80daysupto0dayspriortotheassumedexplosion
∼
event. TheobservationsofPTF10telshowanoutburstabout time of this SN, which is based on the fast rise in the SN
40dayspriortotheprobableexplosion. Thisprecursorisde- light curve, we detect a significant excess in the flux resid-
tectedviaboththefirstandsecondchannels. Ourphotomet- uals. This excess had a peak absolute magnitude of 15.1
−
ric and spectroscopic observations suggest that this event is and it lasted for 110days. Two years after trise, the SN
∼
produced by an energetic outburst releasing 10 2M at is detected at a flux level which is a factor of 5 dimmer
− ∼
typical velocities12 of 2000kms 1, and powe∼red by at l⊙east than the pre-explosion outburst. Assuming zero bolometric
− correction,thepeakbolometricluminosityofthisoutburstis
6 1047ergofenergy.
×For completeness we show in Figure 5 the light curve of ∼3×1041ergs−1,anditsradiatedenergyis∼2.6×1048erg.
PTF10telfromOfeketal. (2013b). Thephysicalparameters
In addition, there is a possible detection of the progenitor
ofthisSNandprecursorarelistedinTable4.
at an absolute magnitudeof roughly 14 about a year prior
−
to the SN explosion. However, given that there is a single
5.2. SN2011ht
detection at this time, we do not consider this to be a good
SN2011ht was discovered by Boles (2011) on 2011 Sep. precursor candidate (see 4.2). The physical parameters of
29.2(UTCdatesareusedthroughoutthispaper),atapparent theSNandtheprecursora§relistedinTable4.
magnitude17.0. Basedonaspectrumobtainedon2011Sep.
30, Pastorello et al. (2011) suggested that it is a SN impos- 5.4. SN2011hw
tor sharing some similarities with the eruption of the lumi-
SN2011hw was discovered by Dintinjana et al. (2011)
nous blue variable UGC2773-OT (Smith et al. 2010). The
on 2011 Nov. 18.7, at apparent magnitude 15.7. Valenti et
spectrumshowsnarrowlinesofH,CaII(H&Kandthenear-
al. (2011) reported that a spectrum obtained on 2011 Nov.
infrared triplet, with P-Cyg profiles), and a forest of narrow
19.8 shows it to be similar to the transitional Type IIn/Ibn
FeIIabsorptionfeatures. Also, prominentNaI D, ScII,and
SN2005la (Pastorello et al. 2008). The spectrum is blue
BaIIfeaturesaredetectedinabsorption. Prietoetal. (2011)
and exhibits emission lines of H and HeI. The most promi-
obtainedafurtherspectrumon2011Nov.11.5.Theyreported
nent HeI lines compete in strength with Ha . The FWHM
substantialevolutionwithrespectto theinitialclassification,
velocity of Ha is 2700kms 1, while that of HeI l 5876 is
withstrongBalmerandweakerHeIandFeIIemissionlines −
superposedonabluecontinuum. Basedonthespectrumand 2000kms−1. We notethatthe apparentmagnitudeofthis
∼
the SN absolute magnitude,they suggestedthat it is likely a SNreportedbyDintinjana&Mikuz(2011)correspondstoan
SN IIn. Thisis supportedby Rominget al. (2012),who re- absolute magnitude of about 19.3. Our initial search sug-
−
portedontheSwift-UVOTobservationsofthisSN,detecting gestedthatthereisadetectionofanoutburst 3monthsprior
∼
a 7mag rise in the UVW2 band over 40days, peaking at a totheSNexplosion. However,sincethisisbasedonasingle
u-bandmagnitudeofabout 18. detection,wedonotconsiderthistobeagoodcandidate.
−
Fraseretal. (2013)reportedonanoutburstpeakingataz-
bandabsolutemagnitudeof 11.8detected 9monthsprior 5.5. PTF10weh
− ∼
totheexplosion,andwiththelastdetection 4monthsbefore PTF10weh was discovered by PTF on 2010 Sep. 22.14.
∼
theexplosion.TheeventwasdetectedbybothPanSTARRS-1 The SN brightened to a peak absolute magnitude of about
andthe CatalinaSkySurvey. Thedurationofthe outburstis 20.7over 40days. Aspectrumtakenon2010Oct. 10ex-
not well constrained, and it can be either a single event that −hibitsa blue∼continuumtogetherwithBalmer emissionlines
lastedformorethan4monthsormultipleshorterevents. as well as HeI and HeII. The widest componentof the Ha
linehasavelocity(s )of 1000kms 1. Thefirsttwospec-
−
12Thisisthelargers ofatwo-componentGaussianfit. traofthissourceareshow∼ninFigure8.
Supernovaprecursors 7
FIG.4.—Imagesoftheprecursors,SN,andnondetectionsfortheSNePTF10weh,PTF10tel,SN2011ht,PTF12cxj,andPTF10bjb(fromtoptobottom).In
eachrow,thefiveimagespresent(lefttoright)thereferenceimage,thepre-SNexplosionnondetection,thebrightestprecursorforeachobject(wheremorethan
onewasdetected),theSN,andapost-SNimage(ifavailable). Thecontoursfromthereferenceimagearealsooverplotted. Alloftheprecursorscanbeclearly
seen,exceptPTF10wehwhichismarginallydetected. AdetailedinspectionoftheimagesofPTF10wehinwhichtheprecursorisdetecteddonotrevealany
cosmeticproblems(e.g.,cosmicrays)neartheprecursorlocation,andthebalanceofevidenceisthatthisprecursorisreal(seediscussionregardingfalse-alarm
probabilityin§4.2).However,inFigure19wealsoshowthecorrelationsbetweentheSNandprecursorproperties,excludingPTF10weh.
ThelightcurveofthisSNandthecandidateprecursorevent zero bolometric correction, this correspondsto a luminosity
isshowninFigure9.Thereisapossibleprecursor 3months of 1.9 1042ergs 1.Thelowerlimitontheradiatedenergy
priortotheSNrise,lastingfor 40days.Aclose∼-upviewof of∼thepr×ecursoris −5 1048erg.Thephysicalparametersof
theprecursorlightcurveispres∼entedinFigure10. Figure11 theSNanditsoutb∼urst×arelistedinTable4.
givesanotherversionoftheprecursorlightcurve,showingall Inaddition,thepre-explosionlightcurveofthisSNreveals
ofitsindividualfluxmeasurements,alongwithfluxmeasure- additional possible detections 11–14months prior to the SN
mentsatrandompositionsinthehostgalaxyandothernearby explosion. However,giventhatthesedetectionsarenotcon-
galaxies. Inspectionofthedatarevealsthatthedetectionde- secutive in time, we do not regard them as good precursor
pendson the binningscheme. However,giventhatthere are candidates.
fourtemporallyadjacentpointsthatdeviatebymorethan5s ,
we consider this to be a good precursor candidate. The ab-
solute magnitude of this precursor is about 17. Assuming
5.6. PTF12cxj
−
8 Ofeketal.
TABLE4
PRECURSORPROPERTIES
Name D t d t LSN,peak ESN Lprec,peak Eprec Ha narrow Ha wide e−1MCSM
(day) (day) (ergs 1) (erg) (ergs 1) (erg) (kms 1) (kms 1) (M )
− − − −
⊙
SN2010mc 20 30 6.9 1042 2 1049 2.6 1041 6 1047 500 2000 0.015
PTF10bjb −85 110 >8× 1041 >×2.0 1049 3.3×1041 2.×4 1048 ∼300 ∼600 0.56
SN2011ht −205 210 1.5×1042 2.5 1×049 1.5×1040 2 ×1047 ∼260 ∼1800 0.06
PTF10weh −80 40 5.3×1043 7.2×1050 1.9×1042 5×1048 100 1000 0.5
PTF12cxj-A −10 7 2.3×1042 8 ×1048 2.2×1041 9×1046 ∼200 ∼1200 0.014
PTF12cxj-B −700 15 × × 4.3×1040 6×1046 ∼ ∼
SN2009ip −25 50 4.6 1042 3 1049 2 ×1041 8×1047 200 2000 0.02
−660 ... × × 1×1041 ...× ∼ ∼ ...
−710 60 1×1041 6 1047 0.02
−1060 60 2×1041 6×1047 0.02
− × ×
NOTE. —PropertiesoftheprecursorsandSNe. Ha narrowandHa widearethelinewidthofthenarrowandwidecomponentsoftheHa linesinunitsofthe
Gaussians (multiplyby2.35togetFWHM).D tistheaveragetimeoftheprecursor.Allofthevaluesareorder-of-magnitudeestimates.TheHa linewidthsfor
SN2011htareadoptedfromRomingetal.(2012).ThevalueslistedforSN2009ipareadoptedfromFoleyetal.(2011),Smithetal.(2010),Drakeetal.(2010),
Ofeketal.(2013c),andMarguttietal.(2014).SNelistedabovethehorizontallineareinoursampleandusedtoestimatetheprecursorrates.Eventsbelowthe
horizontallinearenotinoursample,butusedinthecorrelationanalysis(Figs.19and20).WenotethatSN2006jc(Pastorelloetal.2007;Foleyetal.2007)was
excludedfromthecorrelationanalysissincetheCSMinthisSNishydrogendeficient.
17
s s s s Hg Hb HeI Ha CaII
18 −18
19 −17 −1]
]gamR[ FTP2201 50LEddfor50M⊙star 0.1M⊙Ni56+Co56 −−1165]gam[ R .sbFTP ˚−−12scmA10−16
A g
22 −14 er
[
x
u
23 −13 Fl
24 −12
−60 −40 −20 0 20 40 60
JD − 2455428.722 [day]
FIG.5.—ThelightcurveofSN2010mc(PTF10tel)asobtainedwiththe 4000 5000 6000 7000 8000 9000
Palomar48-inchtelescope. Theredcirclesarebasedonindividualimages, ˚
Observedwavelength[A]
thesquaresarebasedoncoaddedimages,whiletheemptytrianglesrepresent
the3s upperlimitsderivedfromcoaddedimages. Theerrorbarsrepresent FIG.6.—ThespectrumofPTF10bjbasobtainedbyKeck-I/LRISon2010
the1s errors.TheobjectmagnitudesaregiveninthePTFmagnitudesystem. Mar.7.
Thedashedlineshowstheexpectedluminosityfromtheradioactivedecayof
anejected massof0.1M ofNi56, assumingthatatlate timestheoptical
depthissufficientlylarge⊙toconverttheradioactive energytoopticallumi-
nosity,butnotsolargethatitgoesintoPdV work. Thislinerepresentsan
upperlimitonthetotalamountofNi56 intheejecta; itwassettocoincide 18.5 s
withthelatestobservationoftheSNatJD 2,455,758.Thedottedlinerep- −16.5
resentsabolometricluminosityequalto50≈timestheEddingtonluminosity 19
fora50M star(anorderofmagnitudeestimateofthemassoftheprogenitor −16
assumingi⊙tisamassivestar). Therightedgesofthe“S”symbolsabovethe 19.5
lfirgohmtcOufrevkeeintdailc.a2t0e1t3hbe)e.pochsatwhichweobtainedspectra(Figureadopted B mag] 20 −−1155.5Mag
PTF12cxjwasdiscoveredbyPTFon2012Apr. 16.14.The R [APTF202.15 −14.5Abs.
SNrosetoanR-bandabsolutemagnitudeof 17.2overtwo
− −14
weeks. ThespectrumoftheSN,presentedinFigure12,was 21.5
obtained on 2012 Apr. 18 during the early rise of the SN. −13.5
ThespectrumhasBalmerandHeIlinesinemission. Fitting 22
a two Gaussian modelto the Ha line shows that, the widest −400 −200 0 200 400 600 −13
componenthasavelocitywidth(s )of1200kms 1. MJD−55326.0 [day]
−
ThisSNhasalargenumberofpre-explosionobservations, FIG.7.— Thelight curve of PTF10bjb exhibits a clear outburst lasting
and it shows a single detection 384 days prior to its t . for 4monthspriortotheexplosion(identifiedbythefastriseinthelight
∼ rise curv∼e). Anadditionalpossibledetectionisseen 400dayspriortotheex-
Closer inspection reveals that this detection depends on the plosion,butwedonotconsiderittobeagoodca∼ndidatesinceitisbasedon
binningscheme,andthatwithshorterbinsoffourdays,mul- asinglebinneddetection(seethediscussionaboutfalse-alarmprobabilityin
tiple detections at an absolute magnitude of about 13.5 §4.2).Theupperlimitscorrespondsto5s boundscalculatedin15-daybins.
−
are seen. Moreover, inspection of the g-band data shows a
Supernovaprecursors 9
Hg HeIIHb HeI Ha
2010 Nov 03
−1]
˚A
−2m 2010 Oct 10
c10−16
−1
s
g
r
e
[
x
u
Fl
FIG.11.— Thecounts-space light curve ofSNPTF10weh. Eachblack
circlerepresentsapoint-spreadfunction(PSF)fluxmeasurementonanindi-
vidualPTFexposureafterimagesubtraction. Theprecursorislabelled,and
4000 4500 5000 5500 6000 6500 7000 7500 8000
˚ themeanprecursorfluxisshownasagreenhorizontalline,withthehashed
Observedwavelength[A]
arearepresentingtheuncertainty.Thebluelineshowstheaverageofrandom
measurementsinothergalaxiesintheimage,illustratingthetypicalfluxun-
FIG.8.—SpectraofPTF10wehasobtainedusingtheKPNO4mtelescope
certaintyandresidualinthefluxmeasurementsafterimagesubtraction. The
equippedwiththeRCspectrograph.
redcirclesshowtheaverageofrandommeasurementsinthesamehostasthe
SN(wherethehostisextendedenoughtoallowthistest),trackingtheran-
domsubtractionnoisethatmayaffectthefluxmeasurements.Thehorizontal
redlinedenotesthemeanoftheredcircles,andisconsistentwithzeroflux
18 −21 asexpectedafterimagesubtraction. Theabsolutemagnitudescaleisshown
18.5 −20.5 ontheright-handaxisforreference,andtheabscissashowsthetimeindays
19 −20 relativetotheSNtrise.
19.5 −19.5
Hg Hb HeI Ha
g] 20 −19
B ma 20.5 −18.5Mag
R [APTF212.15 −−1187.5Abs. ˚−1A]1e−16
22 −17 −2
m
22.5 −16.5 c
23 −16 −1s
23−.5500 0 500 1000 erg
MJD−55453.0 [day] [
x
u
FIG.9.—ThePTFR-bandlightcurveofPTF10weh.Filledcirclesshowin- Fl
dividualmeasurements,whilefilledboxesmark3-daybinnedmeasurements
withatleasttwomeasurementsperbin.Theemptytrianglesdenote5s upper
limits. Thebinsizeis3dayspriortotheSNexplosionand15daysafterthe
SNexplosion.
1e−17
4000 5000 6000 7000 8000 9000
˚
Observedwavelength[A]
18 −21 FIG.12.—SpectrumofPTF12cxjasobtainedwiththeGemini-Ntelescope
18.5 −20.5 equippedwiththeGMOSspectrograph.
19 −20
19.5 −19.5 marginaldetectionaround 435dayspriortotrise. ThefullR-
−
g] 20 −19 bandlightcurveisillustratedinFigure13. Themostconvinc-
B ma 20.5 −18.5Mag ingprecursorcandidateeventsaredetectedabouttwoweeks
[ATF 21 −18 Abs. atinodns7o0f0tdhaisysSpNrifioerltdo,ttrhisee.liGghivtecnurthveelianrtgheisnpulmotbuertiolifzeodbs2e-rdvaay-
RP21.5 −17.5 binsand4s upperlimits. Aclose-upviewofthelightcurve
22 −17 ofthetwoprecursorsisshowninFigure14. TheR-bandpeak
22.5 −16.5 absolutemagnitudesofthesecandidateprecursorsare 14.8
−
23 −16 and 13. However,thecandidateprecursortwoweeksprior
−
23.5 to the explosionis veryclose in time to the SN fastrise and
−100 −50 0 50 100 150 200 250 300 350 400
MJD−55453.0 [day] thereforemayberegardedaspartoftheSN rise. Asseenin
FIG.10.— Close-up view ofthe PTF R-bandlight curve ofPTF10weh Figure14,thetwodetectionsarefollowedbyanondetection
aroundtheprecursorcandidatetime(seealsoFig.9).Filledcirclesdenotein- which is about a magnitude deeper than the possible detec-
dividualmeasurements,whilefilledboxesmark3-daybinnedmeasurements tionat 8dayspriortot . Furthermore,at2 extrapolation
withatleasttwomeasurementsperbin. Theemptytrianglesare5s upper − rise
to the SN rise flux suggests that the SN started its rise after
limits. Thebinsizeis3dayspriortotheSNexplosionand15daysafterthe
SNexplosion. this candidate precursor. We cannot rule out the possibility
thatthisprecursoris partof the SN lightcurve(e.g., similar
10 Ofeketal.
18
18.5 −17.5
19 −17
19.5 −16.5
g] 20 −16
B ma 20.5 −15.5Mag
[ATF 21 −15 Abs.
RP21.5 −14.5
22 −14
22.5 −13.5
23 −13
23.5 −12.5
−1000 −800 −600 −400 −200 0 200 400
MJD−56033.0 [day]
FIG.15.—LikeFigure11,butforPTF12cxj.
FIG.13.—ThePTFR-bandlightcurveofPTF12cxj.Filledcirclesdenote
individualmeasurements,whilefilledboxesmarkbinnedmeasurements.The
emptytrianglesshow4s upperlimits. Thebinsizeis2dayspriortotheSN 0.8
explosion.Theminimumnumberofmeasurementsineachbinis4.
0.7
0.6
18
18.5 −17.5 0.5
n
19 −17 o
ati 0.4
19.5 −16.5 el
mag] 202.05 −−1165.5Mag uto corr 00..23
[TF 21 −15 bs. A 0.1 3s
RP A
21.5 −14.5
0
22 −14
−0.1
22.5 −13.5
23 −13 −0.2 0 10 20 30 40 50 60 70 80
23.5 −12.5 Time lag [days]
−750 −700 −650 −20 −10 0 10 20 30 40 50
MJD−56033.0 [day] FIG.16.—Thediscreteautocorrelationfunction(Edelson&Krolik1988)
FIG.14.— The light curve of PTF12cxj shows two possible precursors ofthefluxresiduals ofPTF12cxj, taken beforetrise. Inordertocalculate
(based on multiple consecutive detections, where single detections are ig- theautocorrelation function weusetimebins of3days. Thedotted hori-
nored). Theupperlimitscorrespondsto4s boundscalculatedin2daybins. zontallines representthelowerandupper3s bounds, estimated assuming
Extrapolationofthelightcurve,basedonat2law(grayline),suggeststhat s 1/√N,whereNisthenumberofmeasurementsineachtimebin.
≈
thedetectionsvisibleataround 10daystookplacebeforetheSNexplosion
(seealsoFigure4).Furthermore−,thereisadeepnondetectionbetweenthese
signal is caused by the lunar synodic period (i.e., the limit-
detectionsandtheassumedtimeoftheSNexplosion.Wenotethatevenifwe
removethiseventfromoursample,therateofprecursorsdoesnotchanged ingmagnitudeisbetterduringdarktime). Nevertheless,this
bymuch,andthecorrelations(Fig.19)arestilldetected. means that the progenitor of PTF12cxj is likely detected in
several binned images, and that its absolute R-band magni-
tudeisabout 13,brightereventhanthepossibleprogenitor
toSN2011dh;Arcavietal. 2011).
−
of SN2010jl/PTF10aaxf(Smith et al. 2011). Given the de-
As before,Figure15 showsanotherversionofthe precur-
tectionofasignalintheautocorrelation,weconsiderthetwo
sorlightcurve,withalloftheindividualfluxmeasurements,
precursoreventsasreal,andtheirpropertiesarelistedinTa-
alongwithfluxmeasurementsinrandompositionsonnearby
ble4.
galaxiesandthesamehostgalaxy.
The second candidate precursor is detected 700days
∼ 6. CONTROLTIME
priortotheSNexplosion,anditisalsobasedontwomarginal
detectionsseparatedbyabouttwoweeks. Ifreal,thepeakab- InordertocalculatetherateofSNprecursors,weneedto
soluteR-bandmagnitudeofthisprecursorisabout 13. estimatethe“controltime” —thatis, forhowlongeachSN
−
ForalloftheSNeinoursample,wealsocalculatedtheau- locationwasobserved(priortoitsexplosion)toagivenlim-
tocorrelationfunctionof the flux residualsprior tot . The itingmagnitude. Table5lists,foreachSN,thetimebinwin-
rise
only SNe which exhibited significant (at the 3s level) auto- dows(of15days)priortotheSNexplosionandthe5s sensi-
correlation at lag one (i.e., corresponding to two successive tivitydepthateachwindowforbinswithmorethanfivemea-
measurements) are PTF12cxj (4.7s ) and PTF10tel (3.2s ). surements(secondchannel),orthemedian6s limitingmag-
Figure16presentsthediscreteautocorrelationfunction(Edel- nitude at windows with fewer than six measurements (first
son & Krolik 1988) of all the flux residuals of PTF12cxj, channel).
measured before t . The figure shows significant autocor- Tocalculatethecontroltimeasafunctionofabsolutemag-
rise
relation on time scales of a few days to ten days. This may nitude,wesumoveralltheSNe thenumberoftimebins(in
indicatethatthefluxresidualsarenotpureuncorrelatednoise, Table 5) in which the limiting absolute magnitude is deeper
butcontainafractionoftheprogenitorlight. Moreover,itis than the absolute magnitudeof interest, and multiply by the
possiblethattheprogenitorisvariableontimescalesofafew binsize(i.e.,15days).Figure17displaysthesamplecumula-
days. Analternativeexplanationtothevariabilityisthatthis tivecontroltimeasafunctionofabsoluteR-bandmagnitude.