Table Of ContentMon.Not.R.Astron.Soc.000,000–000 (0000) Printed13January2017 (MNLATEXstylefilev2.2)
Cas A and the Crab Were Not Stellar Binaries At Death
C. S. Kochanek1,2,
1 Department of Astronomy, The Ohio State University, 140 West 18th Avenue, Columbus OH 43210
2 Centerfor Cosmology and AstroParticle Physics, The Ohio State University,191 W. Woodruff Avenue, Columbus OH 43210
7 13January2017
1
0
2 ABSTRACT
n The majority of massive stars are in binaries, which implies that many core collapse
a supernovae(ccSNe)shouldbebinariesatthetimeoftheexplosion.Hereweshowthat
J the three most recent, local (visual) SNe (the Crab, Cas A and SN 1987A) were not
1 binaries, with limits on the initial mass ratios of q = M2/M1 <∼ 0.1. No quantitative
1 limits have previously been set for Cas A and the Crab, while for SN 1987A we
merely updated existing limits in view of new estimates of the dust content. The lack
] of stellar companions to these three ccSNe implies a 90% confidence upper limit on
R
the q >∼ 0.1 binary fraction at death of fb < 44%. In a passively evolving binary
S
model (meaning no binary interactions), with a flat mass ratio distribution and a
.
h Salpeter IMF, the resulting 90% confidence upper limit on the initial binary fraction
p ofF <63%isinconsiderabletensionwithobservedmassivebinarystatistics.Allowing
- a significant fraction fM ≃25% of stellar binaries to merge reduces the tension, with
o F < 63(1−fM)−1% ≃ 81%, but allowing for the significant fraction in higher order
r
t systems (triples, etc.) reintroduces the tension. That Cas A was not a stellar binary
s
at death also shows that a massive binary companion is not necessary for producing
a
[ a Type IIb SNe. Much larger surveys for binary companions to Galactic SNe will
become feasible with the releaseof the full Gaiaproper motionandparallaxcatalogs,
1
providing a powerful probe of the statistics of such binaries and their role in massive
v
star evolution, neutron star velocity distributions and runaway stars.
9
0 Key words: stars: massive – supernovae: general – supernovae: individual: Cas A,
1
Crab, SN 1987A
3
0
.
1
0
7 1 INTRODUCTION 2008, Smith et al. 2011, Eldridge et al. 2013). There are
1 many theoretical studies exploring the stripped Type IIb,
: A large fraction of massive stars appear to be in bi- Ib and Ic SNe in the context of binary evolution models
v
naries (see the reviews by Duchˆene& Kraus 2013 and (e.g., Yoon et al.2010,Yoon et al. 2012,Claeys et al.2011,
i
X Moe & Di Stefano 2016). Kobulnicky et al. (2014) estimate Dessart et al. 2012, Benvenutoet al. 2013, Kim et al. 2015,
that 55% are in binaries with P < 5000 days and mass ra- Yoon et al.2017),aswellasmodelsfortheeffectsofbinary
r
a tios of 0.2 < q < 1, while Sana et al. (2012) estimate that evolution on electron capture SNe(e.g., Moriya & Eldridge
69%areinbinariesandthattwo-thirdsofthesewillundergo 2016).
someformofinteraction.Moe & Di Stefano(2016)findthat
Discussions of the binary companions to local core
only16±8%ofthe9-16M⊙ starsthatwilldominatetheSN collapse SNe have largely focused on understanding run-
rate are single, and that they have an average multiplicity
away B stars (e.g., Blaauw 1961, Gies & Bolton 1986,
(companions per primary) of 1.6±0.2.
Hoogerwerf et al. 2001, Tetzlaff et al. 2011) and the contri-
Mass transfer, mass loss and mergers then signifi- butionofbinarydisruptiontothevelocitiesofneutronstars
cantly modify thesubsequent evolution of the system (e.g., (NS) (e.g., Gunn& Ostriker 1970, Iben & Tutukov 1996,
Eldridge et al. 2008, Sanaet al. 2012). This will, in turn, Cordes & Chernoff 1998, Faucher-Gigu`ere & Kaspi 2006).
modifythepropertiesofanyresultingsupernovae(SNe)over van den Bergh(1980)seemstohavebeenthefirsttosearch
theexpectationsforisolatedstars.Forexample,thenumbers supernova remnants (SNRs) for runaway stars by looking
of stripped Type Ibc SNe and the limits on their progeni- for a statistical excess of O stars close to the centers of 17
tor stars both suggest that many are stripped through bi- SNRsandfindingnone.Guseinov et al.(2005)examined48
narymasstransferratherthansimplywind(orother)mass SNRs for O or B stars using simple color, magnitude and
loss (e.g., De Donder& Vanbeveren 1998, Eldridge et al. propermotion selection cutstoproducealist of candidates
(cid:13)c 0000RAS
2 C. S. Kochanek et al.
5
10
#4 #2
center #N3S/#5
#1
#6
15
20
-0.5 0 0.5 1 1.5 2
Figure 1. Coadded grizy PS1image of the Crab.The position Figure2. Ther/r−iCMDofthestarswithin60′.′0ofthecenter
of the geometric center of the remnant (“center”) and the neu- of the Crab SNR or NS. The solid curve shows the PARSEC
tron star are indicated by 3′.′0 radius green circles. The larger (Bressanetal.2012)isochroneforSolarmetallicitystarswithan
green circle shows the region within 60′.′0 of the center. The 30 age of 107.3 years at a distance of 2 kpc and with an extinction
starswithin60′.′0ofeither thecenter ortheNSaremarked,and of E(B−V) = 0.4 mag. The dashed curves show the effect of
the six closest to the center are numbered in order of their dis- reducing(raising)theextinctiontoE(B−V)=0mag(0.9mag).
tance from the center. The NS is star #5. The arrows show the Uncertainties in the distance modulus are much less important,
predicted positions of sources with proper motions at the time corresponding to vertical shifts of ±0.5 mag. Red filled squares
of the SN. As expected, the predicted position of the pulsar is ontheisochronesmarkstarswithmassesof1,2,5and10M⊙.
closeto the center of the SNR. Seven stars have proper motions
in NOMAD with uncertainties in their back-projected positions
ofapproximately 12′.′0asshown bythe circleat thehead of one
2005, Li et al. 2006), and SN 2008bk (Mattila et al. 2008).
ofthepropermotionvectors.Atadistanceof2.0kpc,astarwill
have moved 10′.′1(v/100 km/s) since the SN, so the 60′.′0 search AlloftheselimitsassumethattheSNemadelittledust,an
issuewediscussfurtherinKochanek(2017)andconsiderin
radiuscorrespondstoavelocityofroughly600km/s.
more detail for SN 1987A below.
Kochanek(2009)examinedthestatisticalpropertiesex-
pected for surviving binary companions to SNe assuming
based on the USNO A2 catalog (Monet et al. 1998). None
passively evolving systems (i.e. no binary interactions). As
of these systems havebeen investigated in any quantitative
already noted, the companions are generally significantly
detail. Din¸celet al. (2015) identify a good candidate in the
∼ 3×104 year old SNR S147 containing PSR J0538+2817 fainter than the exploding star, although this is frequently
notthecaseforstrippedSNprogenitors–forTypeIbcSNe,
and argue that it was also likely to have been an interact-
itshouldnotbesurprisingtofindthatthebinarycompanion
ing binary. Considerably more effort has been devoted to
ismorevisuallyluminousthantheSNprogenitor.Thispoint
searching for single degenerate companions to Type Ia SN
isofconsiderableimportancefortheonecandidateTypeIb
(e.g., Schweizer & Middleditch 1980 Ruiz-Lapuenteet al.
progenitor iPTF13bvn (Cao et al. 2013, Groh et al. 2013,
2004, Ihara et al. 2007, Gonz´alez Hern´andezet al. 2012,
Bersten et al. 2014, Fremling et al. 2014, Eldridge et al.
Schaefer & Pagnotta 2012).
2015, Eldridge & Maund 2016, Folatelli et al. 2016). If the
Searches for binary companions to core-collapse SNe
initial binary fraction is F, then the fraction of passively
in external galaxies are more challenging because the com-
evolving binaries that are in stellar binaries at death is
panion is generally significantly fainter than the progeni-
tor (see Kochanek 2009). The Type IIb SN 1993J is prob- F qmax
f = where f = qx−1P(q)dq, (1)
awbhliylethtehebeesxtistceansece(Mofauandcoetmapla.n2io0n04,toFotxheet aTly.p2e01I4I)b, b 1+Ffq q Zqmin
SN 2011dh is debated, with Folatelli et al. (2014) arguing x ≃ 2.35 is the slope of the initial mass function (IMF),
for a detection and Maund et al. (2015) arguing that the q ≤ q = M /M ≤ q ≤ 1 is the mass ratio and
min 2 1 max
flux may be dominated by late time emission from the P(q) with dqP(q) ≡ 1 is the distribution of mass ratios.
SN. There is some evidence of a blue companion for the For a SalpeRter IMF and a flat P(q) distribution extending
Type IIb SNe 2001ig (Ryderet al. 2006) and SN 2008ax over0≤q≤1,f =0.426 andthefractionofSNeinstellar
q
(Crockett et al. (2008). There are limits on the existence binariesatdeathis23%,41%,57%and70%forinitialbinary
companionstotheTypeIcSNe1994I(Van Dyket al.2016) fractions of F = 25%, 50%, 75% and 100%, respectively.
and SN 2002ap (Crockett et al. 2007) and the Type IIP Essentially, only theexplosions of primaries occur in stellar
SNe 1987A (Graves et al. 2005), SN 2005cs (Maund et al. binaries,sothefractionofSNeinstellarbinariesislessthan
(cid:13)c 0000RAS,MNRAS000,000–000
Cas A and the Crab Were Not Binaries 3
15
10 #3 #5
#2 #6
#1 #7
center
#4
NS
#11 #8
#9
#12 #10
#13
5
0.1 1 10 100
Figure 4. Coadded grizyPS1 image of Cas A. The positionof
Figure 3. The luminosities and temperatures of the stars if at the geometric center of the remnant (“center”) and the neutron
thedistanceoftheCrabandconstrainedbytheextinctionprior. starareindicatedby3′.′0radiuscircles.Thelargercircleshowsthe
Filledblacksquaresmarkthestarsthatcouldbeatthedistance region within 30′.′0 of the center. The 13 PS1 stars lying within
of the Crab (χ2 < χ2+4) and an association is not ruled out 30′.′0ofeitherthegeometriccenterortheneutronstararemarked
2 0
bytheavailablepropermotions.Openredtrianglesareforstars and labeled in order of their distance from the center. None of
that either cannot lieat the distance of the Crab(χ2 >χ2+4) the stars have proper motion measurements in NOMAD. Stars
2 0
or have a proper motion inconsistent with an association. The #4, #9 and #13 have proper motions in HSOY but the shift
pulsar,fitasastar,isindicatedbythefilled,cyanpentagon.The in position to the time of the SN is too small to display. At a
solidlinesshowisochroneswithagesof106,106.5,107,107.5 and distanceof3.4kpc,astarwillhavemoved2′.′1(v/100km/s)since
108 yearswhilethedashedlinesshowthetracksfor0.5,1.0,1.5, the SN, so the 30′.′0 search radius corresponds to a velocity of
2.0and3.0M⊙ starsoverthisrangeoftimes. roughly1500km/s
the initial fraction of binaries because some of the SNe are L1 = 104.7L4.7L⊙ are chosen to match the end point of a
theexplosionsofsecondaries.Binaryevolution,particularly 107.4 year PARSEC (Bressan et al. 2012) stellar isochrone.
stellarmergers,thenaddsfurthercomplications,asdoesthe The scaling with mass and luminosity is very weak1, so
prevalence of triples and otherhigher order systems.
the only important variable is the temperature of the pri-
For a supernova of a given age, we need an estimate
mary. For thetypical red supergiant progenitors of Type II
of the radius inside the SNR that needs to be searched.
SNe (see Smartt 2009), we expect very low velocities, v <
Guseinov et al. (2005) simply used a fixed 1/6 of the di-
50km/s.IntherarecaseslikeSN1987Awheretheprimary
ameter of the remnant as cataloged by Green (2014) (for
is a bluesupergiant at thetimeof explosion, themaximum
themostrecentversion).Observedrunawaystarshavetyp- companion velocity is still v<∼300 km/s.
ical velocities of 50 km/s or less (e.g., Tetzlaff et al. 2011)
Companionstostripped,TypeIbcSNecanhavehigher
and theoretical studies find that it is difficult for binaries
velocitiesbecauseoftheveryhighprogenitortemperatures.
to produce velocities of more than a few 100 km/s (e.g.,
For these systems, the finite size of the secondary is im-
Cordes & Chernoff 1998, Eldridge et al. 2011). This has a
portant because the radius of the primary is ∼ R⊙, and
simple explanation in termsof stellar structurebecause the the companion velocities can in theory reach ∼ 103 km/s.
maximum (circular) orbital velocity of a secondary star is
Thisisonlytrueifthesystemwasaninteractingbinarybe-
limited by
cause the orbit of the secondary must also shrink to be far
GM 4πσT4 1/2 L 1/2 T2 −1 smaller than even the initial size the primary. Such tightly
v22 < 1+q1 (cid:20) L1 1(cid:21) (cid:20)1+(cid:16)L12(cid:17) T122(cid:21) (2) bproiumnadrybimnaarsiseshaarsetloesshalvikeelbyeetno bgereadtislyrupretdeducbedecabuysemtahses
where the mass ratio q = M2/M1 could be > 1 here, the loss and the orbital binding energy is larger than typical
semi-major axis is set to the sum of the two stellar radii, NS kick velocities (e.g., Cordes & Chernoff 1998). Theoret-
and we have expressed the radii in terms of the stellar lu- ically, Eldridge et al. (2011), using binary population syn-
minosities and effective temperatures. The highest possible thesis models that included such evolutionary paths, found
companion velocity is achieved for a low mass (q →0) and that velocities above 300 km/swere veryrare.
low luminosity L /L →0companion. This allows thesim-
2 1
ple upperlimit on thecompanion’s velocity of
v<50M1/2T L−1/4 km/s (3) 1 For L ∝ Mx, the velocity limit scales with primary mass as
10 3.5 4.7 v1 ∝ M1/2−x/4. For x = 3 (x = 2), this becomes v1 ∝ M1−1/4
wherethescalingsofM1 =10M10M⊙,T1 =103.5T3.5Kand (v1∝M10).
(cid:13)c 0000RAS,MNRAS000,000–000
4 C. S. Kochanek et al.
15
10
10
15
5
20
-0.5 0 0.5 1 1.5 0.1 1 10 100
Figure5. Thez/i−zCMDofthestarswithin30′.′0ofthecenter Figure 6. The luminosities and temperatures of the stars if at
oftheCasASNRortheNS.ThesolidcurveshowsthePARSEC thedistanceoftheCasAandconstrainedbytheextinctionprior.
(Bressanetal.2012)isochroneforSolarmetallicitystarswithan Filledblacksquaresmarkthestarsthatcouldbeatthedistance
ageof107.3 yearsatadistanceof3.4kpcandwithanextinction of Cas A (χ2 < χ2+4) and not ruled out by proper motions.
2 0
of E(B−V) = 1.6 mag (AV = 5.0). The dashed curves show Open red triangles mark stars that cannot be at the distance of
the effect of reducingthe extinction to AV =3.4or raisingitto the Crab (χ22 > χ20 +4) or an association is ruled out by the
6.5 or 8.0 mag. Uncertainties in the distance modulus are much proper motions. In practice, the only star which is inconsistent
lessimportant,correspondingtoverticalshiftsof±0.2mag.Red with the distance (#13) is also ruled out by its proper motion.
filledsquaresontheisochronesmarkstarswithmassesof1,2,5 Thesolidlinesshowisochroneswithagesof106,106.5,107,107.5
and10M⊙. and108 yearswhilethedashedlinesshowthetracksfor0.5,1.0,
1.5,2.0and3.0M⊙ starsoverthisrangeoftimes.
Here we consider the three most recent visually ob-
served, Local Group, core collapse SNe: the Crab, Cas A presence of significant amounts of hydrogen. However, the
and SN 1987A. For Galactic SN, the Crab and Cas A have SNR appears to contain too little mass or energy for it to
several advantages. Their youth means that the search ar- havebeenanormalTypeIISN,suggestingitmayhavebeen
eas are small, and the fact that they were visible by eye an electron capture SN (see the review by Hester (2008) or
means that they have modest extinctions and, by exten- the recent discussion by Smith (2013)). The binary models
sion, lie in regions with relatively low stellar densities for of Moriya & Eldridge (2016) would be one way of having
the Galaxy. We were unable to find any quantitative dis- such a low ejecta mass. Cas A is known to be a Type IIb
cussions of searches for binary companions to these two thankstospectraoflightechoesfromtheSN(Krause et al.
systems, but Guseinov et al. (2005) report no candidates 2008, Rest et al. 2008, Rest et al. 2011, Finn et al. 2016).
in their qualitative survey of 48 SNRs. The Crab pul- Single star evolution models generally have difficulty pro-
sar is observed in the optical/near-IR, but it is emission ducing Type IIb SNe (e.g., Younget al. 2006 for Cas A in
due to the pulsar and not from a surviving binary (e.g., particular, Podsiadlowski et al. 1993, Woosley et al. 1994,
Sandberg& Sollerman 2009, Scott et al. 2003). There have Claeys et al. 2011, Dessart et al. 2012, Benvenutoet al.
beenaseriesofunsuccessfulsearchesforanoptical/near-IR 2013, more generally). While SN 1987A was a Type II SN,
counterpart to the NS in Cas A which rule out any bound theprogenitor was also a bluerather than a red supergiant
system even at the level of a M2 ≃ 0.1M⊙ dwarf com- (see the review by Arnettet al. 1989). Several models have
panion (e.g., van den Bergh & Pritchet 1986, Kaplan et al. invokedbinaryinteractions,possiblywithafinalmerger,to
2001,Ryan et al.2001,Fesen et al.2006).Thesestudiesalso explain either the structure of the star or the surrounding
implicitly set strong limits on any unbound system, but winds(e.g.,Podsiadlowski & Joss1989,Podsiadlowski1992,
the topic is never discussed in these papers. Graves et al. Blondin & Lundqvist1993, Morris & Podsiadlowski 2009).
(2005) set very strong limits on the existence of a binary Here we take advantage of the recently released PS1
companion to SN 1987A but assumed there was very lit- survey data (PS1, hereafter, Chambers et al. 2016) along
tledustobscuration createdbytheSN.Morerecentstudies with their associated three-dimensional maps of dust in
have shown that SN 1987A formed far more dust than as- the Galaxy (Green et al. 2015) to examine stars near the
sumed by Graves et al. (2005) and that it is concentrated centers of the Crab and Cas A quantitatively. For consis-
towards the center of the remnant (Matsuura et al. 2011, tencywiththedustmaps,weusetheextinctioncoefficients
Indebetouwet al. 2014, Matsuura et al. 2015), making it A from Schlafly & Finkbeiner (2011). We also use, where
λ
necessary to revisit these limits. available, the NOMAD (Zacharias et al. 2005) or HSOY
TheCrabwasalmostcertainlyaTypeIISNeduetothe (Altmann et al. 2017) propermotions. Wefit the photome-
(cid:13)c 0000RAS,MNRAS000,000–000
Cas A and the Crab Were Not Binaries 5
tryofstarsnearthecenteroftheSNRusingSolarmetallic- theNSasstar#5. Table1providesthepositions andgrizy
itystarsdrawnfromthePARSECisochrones(Bressan et al. aperture magnitudes of these 30 stars along with their dis-
2012). For the coarse luminosity estimates we require, the tances from the centerof theSNRand theNS.
effectsofmetallicityonstellarcolorsshouldnotbeveryim- There are, in fact, no sources closer than 12′.′0 to the
portant.ForSN1987Awesimplyexaminetheconsequences center of the SNR. Since there is so little ambiguity in the
ofthenewdustobservations.Insections§2-4wediscussthe centergivenitsclose(arcsecond)agreementwiththeproper
Crab, Cas A and SN 1987A in turn, and we discuss the motion of the pulsar, and even a 10′.′0 search radius is al-
implications of theresults in §5. ready generous for the companion of a Type II SN, we can
immediately rule out the existence of a binary companion
withM2 >∼M⊙ simplyfromthestructureoftheCMD.This
could be strengthened further using the still deeper HST
2 THE CRAB (SN 1054) data. There are six sources between 12′.′0 and 15′.′0, where
Figure 1 shows the co-added grizy PS1 image of a roughly the pulsar is source #5, and then the next source is 21′.′7
2 arcmin region around the center of the Crab SNR. We from the center. We number the sources by their distance
adopt an age of 960 years and, following Kaplan et al. from the center of the SNR and have labeled only the six
(2008), a distance of 2.0±0.5 kpc or µ=11.51±0.54 as a closest sources in Figure 1.
distancemodulus.UsingtheGreen et al.(2015)dustdistri- Figure 2 shows the r/r−i color magnitude diagram
bution for the line of sight towards the center of the SNR, (CMD) of these sources. Superposed are the PARSEC
theextinctionis roughly E(B−V)≃0.4 mag. Green et al. isochrones for Solar metallicity stars with an age of
(2015) estimate that the dust distribution is well-defined 107.3 years, roughly corresponding to the epoch at which
out to a distance modulus of 14.2 which is well beyond the 12M⊙ starswoulddie,alongwiththeeffectsofchangingthe
distance to the Crab. This extinction estimate agrees well extinction estimates to E(B−V)=0 or 0.9 mag. The dis-
withotherdeterminations(e.g.,Wu1981,Blair et al.1992). tanceuncertaintiesaremuchlessimportant,sincetheyonly
We define the (J2000) center of the SNR as (05:34:32.84, correspondtoshiftingtheisochroneverticallyby±0.5mag.
22:00:48.0) from Nugent(1998)andtheposition ofthepul- LikeGuseinov et al.(2005),wefindnoplausiblecandidates
sar as (05:34:31.9, 22:00:52.1). Kaplan et al. (2008) mea- for a former binary companion.
sured the proper motion of the pulsar, and its estimated Seven of the stars (#1, 4, 13, 20, 21, 22 and 28) have
position at the time of the SN agrees very closely with the propermotionsintheNOMADcatalog,andtheirpredicted
estimatedcenteroftheSNR.ThecenteroftheSNRandthe positionsatthetimeoftheSNareindicatedbythearrowsin
position of the NS at present and in 1054 are both marked Figure 1. The uncertainties in thepropermotions lead to a
in Figure 1. position uncertainty of approximately 12′.′0 after 960 years,
For a distance of 2.0 kpc and an age of 960 years, a as indicated by the circle at the end of one of the proper
star with velocity v = 100v km/s has moved 10′.′1v . We motionvectors.Onlythedistantstar#22hasapropermo-
2 2
selected stars within 1 arcmin of either the center of the tionconsistentwiththepositionoftheSN,butitwouldalso
SNRortheNS,correspondingtoavelocitylimitofapprox- havetobemovingatalmost600km/s.Thetwocloserstars
imately 600 km/s. Since the proper motion of the NS only with proper motions, #1 and #4, are moving in the wrong
corresponds to v ≃ 100 km/s and the Crab is believed to direction to beassociated with theSN.
have been a Type II SN (even if peculiar) for which Equa- Toformalizethequalitativeimpression,wedrewasam-
tion3applies,onlysourceswithinroughly10′.′0ofthecenter ple of roughly 105 stars from the PARSEC isochrones, uni-
can plausibly besurvivingsecondaries. formlysamplinginagefrom106 to1010 yearsinincrements
The PS1 catalog for these 1 arcmin regions contains of 0.01 dex. We fit the PARSEC estimates of the absolute
171 sources, most of which are spurious detections created PS1magnitudestoallthecandidatesourcestoestimatethe
bythebright nebularemission orfaint sourcesin thewings distance and extinction. We considered four fits to each of
ofthebrighterpointsources.Whenwewenttofitmodelsto the candidate sources for each of the ∼ 105 stellar models.
thespectralenergydistributions(SEDs)oftheactualstars, First,wefitfortheextinctionE(B−V)anddistancemod-
we frequently found no good fits (χ2 > 100) for any stellar ulusµ with noconstraints on eithervariable. Given magni-
modeleventhoughwewereusingthePS1PSFmagnitudes. tudesmi with uncertainties σi and a model starwith abso-
Thisisverydifferentfrom thecaseofCas A(nextsection), lutemagnitudes Mi, thefit statistic is
where we almost always found very good model fits. Pre-
χ2 = (m −M −µ−R E(B−V))2σ−2. (4)
sumably this is because the PS1 photometry pipeline was 0 i i i i
never intended for photometry of stars in a nebular emis- Xi
sion region like the center of the Crab nebula. To remedy Second, we repeated the fits constrained by the estimated
this issue, we used Sextractor (Bertin & Arnouts 1996) to distance modulus µ ±σ to the Crab, χ2 = χ2 + (µ−
0 µ 1 0
identify sources on the roughly 2 arcmin square co-added µ )2/σ2.Forthelast fit,weaddedapriorontheextinction
0 µ
PS1 image and then used IRAF aperture photometry with based on the Green et al. (2015) estimates of the extinc-
a 3 pixel (0′.′75) aperture radius and a 6 pixel to 10 pixel tionasafunctionofdistancemodulustothefitconstrained
radiusskyaperture.Thislarger 2′ areaincludesmanystars by the distance modulus. We used the variance of their 20
beyondthebrightestnebularregions. Wethenmatchedthe alternate extinction realizations as an estimate of the un-
aperture results to the PS1 photometry and computed the certainty in the extinction at any given distance to give
necessaryphotometricoffsetsasthemedianoffsetafterclip- E(µ)±σ .Wesimplyaddedthispriortotheresultsofthe
E(µ)
pingoutliers.Intheendwehad30starstoconsider,labeled previousfitstogetχ2 =χ2+(E(B−V)−E(µ))2/σ2 .We
2 1 E(µ)
in order of distance from the center of the SNR, including did not repeat the fits with the (non-linear) constraint on
(cid:13)c 0000RAS,MNRAS000,000–000
6 C. S. Kochanek et al.
the extinction as a function of distance – the broad range 3 CASSIOPEIA A
of the input models and the simplicity of the conclusions
Figure 4 shows the co-added grizy PS1 image of a roughly
makes this complication unnecessary. We assumed uncer-
2 arcmin region centered on Cas A. The emission lines
tainties that arethelarger of thephotometric uncertainties
present in some of the bands show an outline of the rem-
and0.05mag.Theminimumuncertaintyisincludedtocom-
nant,andwehavemarkedthegeometriccenter(23:23:27.82,
pensate for modest systematic errors (e.g., extinction law,
58:48:49.4)oftheremnant(Thorstensen et al.2001)andthe
photometric systems, calibrations, metallicity).
These fits are carried out for each of the ∼ 105 stellar position of the neutron star (23:23:27.93, 58:48:42.5). We
adopt a distance of 3.4±0.3 kpc(Reed et al. 1995) and an
models, and the best fits are reported in Table 2. The ta-
age of 330 years. For this distance, a source with velocity
ble contains the goodness of fit for the best stellar model
with no priors (χ2), with a prior on the distance (χ2), and 100v2 km/s will have moved 2′.′0v2 in the 330 years since
withaprioronbo0ththedistanceandtheextinction(1χ2).In the SN. The 7′.′0 distance of the NS from the center of the
2 SNRcorresponds toa velocity of approximately 340 km/s.
practice,therearereasonablefitsforarangeofstellarmod-
The PS1 extinction estimate at the distance of Cas A
els,whichwecancharacterizewithquasi-Bayesianaverages
is E(B−V)≃1.2 (A =3.7) but it lies close to a sudden
such as V
jumpintheextinctiontoE(B−V)≃1.5 (A =4.7).This
V
hlogLi= e−χ′2/2logL e−χ′2/2 −1 (5) bisymSoearerleco(n1s9i7s1te)natnwdiltohweearrtlyhaensttihmeaetsetsimofatAesVof≃A4.3≃m5a.g3
V
hX ihX i to 6.2 mag by Hurford & Fesen (1996) and A = 6.2 ±
V
fortheluminosity.Intheseaverages,χ′2meansthatwehave 0.6magbyEriksen et al.(2009).Theseestimates arebased
renormalized theχ2 valuesso that thebest fithas aχ2 per on using predicted and observed SNR emission line ratios
degree of freedom of unity if the raw χ2 is larger than the to determine the extinction. The distances used in the PS1
extinction estimates are only reliable out to Cas A.
numberofdegreesoffreedom.Thishastheeffectofbroaden-
ing theuncertaintiesfor sources which are less well fit.The Weusedagenerousselectionradiusof30′.′0fromeither
same average is carried out for logT. The allowed spreads the center of the SNR or the NS, which corresponds to a
of the luminosity and temperatures about the averages are velocityofalmost 1500km/s.Theseregionscontain15PS1
estimated by the probability weighted dispersion of the so- sourcesofwhichtwoareartifacts.Thisleavesthirteenstars,
lutions about theaverages, which we haveagain labeled in orderof theirdistance from
thecenteroftheSNRasshowninFigure4andreportedin
σl2ogL= e−χ′2/2(logL−hlogLi)2 e−χ′2/2 −1.(6) TNaObMleA3D. Naonndetohfretehe(#st4a,r#s h9aavnedp#ro1p3e)rhmavoetiopnroepsetrimmaotteisonins
hX ihX i inHSOY.Thepredictedpositionsofthesethreestarsatthe
Table2reportstheseestimatesoftheluminositiesandtem- time of the SN are within a few arcseconds of their present
peraturesforthemodelswithaprioronthedistancebutnot positions and are too small to display in Figure 4. They
on the extinction (χ2) and the model with priors on both cannot have been associated with the SN.
1
theextinction and thedistance (χ2). The closest star (#1) lies 11′.′5 from the center of the
2
Asistypicaloftryingtoestimatestellardistancesusing SNR and 16′.′7 from the NS, corresponding to velocities of
onlyphotometry,itisnearlyimpossibletodosowithoutad- 560 and 820 km/s that are not physical for the companion
ditional constraints. Very few of the stars cannot be placed ofaTypeII(IIb)SN.TheNS,whileanX-raysource,isnot
atthedistanceoftheCrabifthereisnoconstraintontheex- detected to very deep optical/near-IR limits (>∼ 28 mag at
tinction(5of30haveχ2 >χ2+4).Withtheadditionofthe Rband,Fesen et al.2006).WeagainreplacedthePS1mag-
1 0
constraint ontheextinction atanygiven distanceincluded, nitudeswiththeresultsofaperturephotometry.Herenebu-
many fewer have solutions consistent with the distance (15 losityisnotanissueandthePS1PSFphotometryproduces
of 30 have χ2 > χ2 +4), but that still leaves many that goodfits.However,replacingthePS1PSFphotometrywith
2 0
are consistent with both priors. Curiously, the non-thermal forced aperture aperture photometry allowed us to include
emission of the NS (#5) can be well-modeled by a stellar photometry in more bands than PS1 reports due to limits
SED. on signal-to-noise ratios.
Figure 3 shows the luminosities and temperatures the Figure 5 shows the z/i−z CMD of the stars. The
stars would have at the distance of the Crab and with the brighter and closer (to the center) stars are labeled. Stars
extinction prior (χ22). The distribution looks similar with- such as #4, #6 and #9 which could have M >M⊙ at the
out the extinction prior, but the uncertainties, particularly distance of Cas A (and assuming more extinction than the
thetemperatureuncertainties, become larger (see Table 2). PS1model)areatleast 24′.′0from thecenterortheNSand
If any of these stars are at the distance of the Crab, none would require v>∼1200 km/sto beassociated with theSN.
of them are either luminous or massive. Moreover, many Threeofthefourbrighteststars(#4,#9and#13)arealso
of the more luminous stars are also the ones with proper ruledoutbytheirHSOYpropermotions.Thereisnoproper
motions, almost all of which are inconsistent with an asso- motioninformationfor#6.ThetwoclosestPS1starswould
ciationtoSN1054.Moreimportantly,anactualcompanion havetobeM <∼M⊙ andstill requireunreasonablyhighve-
to the Crab SN would have to be closer to the center of locities.
theSNRwherenostarsofsimilarmagnitudesareobserved. Table 4 presents the results of fitting stellar models to
ThisimpliesthattheCrabhadnostellarcompaniontoeven the SEDs. Most of the stars can be well-fit, with star #5
stricter limits of L<∼L⊙ and M <∼M⊙ even if we are very as theworst case. Weagain findthat roughly half thestars
conservative. have properties consistent with the distance and extinction
(cid:13)c 0000RAS,MNRAS000,000–000
Cas A and the Crab Were Not Binaries 7
ofCasA.Figure6showstheluminositiesandtemperatures As a result, it is really only the mid-IR dust emis-
of the stars including the extinction prior. As suggested by sion which constrains the luminosity of any central source.
the CMD, stars #4, #6 and #9 can have the highest lu- Matsuura et al. (2015) find a total central dust luminos-
minosities, with #4potentially being a ≃3M⊙ Bstar with ity in 2012 of 230L⊙. This luminosity is due to a combi-
L≃102.0L⊙.However, #4 and #9also haveHSOYproper nation of radioactive decay, absorption of radiation from
motions inconsistent with any association. The rest of the the expanding shocks, and any contribution from a central
stars would be low mass (M < M⊙) dwarfs. As with the source. Matsuura et al. (2015) estimate that the available
Crab, even these low mass stars are absent at distances heating from decay of 44Ti is ≃400L⊙, extrapolating from
from the center corresponding to reasonable velocities, so Jerkstrand et al. (2011), and that a further ∼50L⊙ can be
it is clear that any binary companion to Cas A at death heating from the shocks exterior to the dusty region. They
would haveto haveM <∼M⊙. donotdiscussanyadditionalcontributions,butthetwore-
quired heating sources already exceed the observed lumi-
nosity, which suggests that only a modest fraction of the
observed 230L⊙ could be due to a binary companion. A
4 SN 1987A reasonable upper limit is probably 10% of the total lumi-
Graves et al. (2005) obtained very tight limits on the pres- nosity, which corresponds to M <∼2.5M⊙ (see Figure 6). A
ence of an optical point source at the center of SN 1987A, 3M⊙ companion would already represent half the observed
luminosity.
withlimitsofνLν <0.26,0.33,0.15,0.30and0.28L⊙ inthe
F330W,F435W,F555W,F625W andF814W filters.Toac-
count for dustabsorption in theirestimates, theynote that
the fraction of the bolometric luminosity emerging in the
5 DISCUSSION
infrared on day 2172 was 97% (Bouchet & Danziger 1993)
implying an effective optical depth of τ ≃ 3.5. The effec- Examining the PS1 sources near the Crab and Cas A, it
tiveoptical depthat thetimetheirobservations (day6110) is clear that these SN had no binary companion at death
would then be τ = 0.45 because of the 1/t2 dilution of the with a mass M >∼M⊙. Graves et al. (2005) found a similar
opticaldepthduetoexpansion.Thisthenimpliesthatthere limit for SN 1987A, but the higher present day estimates
cannotbeabinarycompanion (orotherpointsource) more of the dust content imply a weaker limit of M <∼ 2.5M⊙
luminous than roughly L<2L⊙. from the observed dust luminosity. In terms of mass ratios,
Graves et al.(2005)discussscenariosinwhichthedust there are no companions to these three ccSNe with initial
mightbeclumped,butthesescenarioswerebasedonclumpy mass ratios above q >∼ 0.1. If the binary fraction at death
dust distributions in a foreground screen rather than a cir- is fb, the probability of finding no binaries companions in
cumstellarmedium.Foraclumpymediumcloselysurround- three systems is (1−fb)3, implying that fb < 0.44 at 90%
ingthesource,theextraabsorptionfromaclumpthathap- confidence.
pens to be along our line of sight will be partially balanced The stellar binary fraction of stars at death is generi-
bythe contribution from photons scattered ontoour line of cally lower than that at birth. Even for passively evolving
sightbyotherclumps(seethediscussioninKochanek et al. binarieswithnointeractions,onlytheexplosionsofthepri-
2012). This would essentially eliminate the worst case sce- mary are in a stellar binary. When the secondary explodes,
nariotheyconsider,wheretherewouldbenodilutionofthe theprimaryisacompactobjectwhichislikelybothdifficult
optical depth by expansion and the luminosity constraint todetectandneednolongerbeboundtothesecondary.Fol-
would be∼30 times weaker. lowing Equation 1 and again assuming a Salpeter IMF and
A more important issue is that Herschel and ALMA aflat P(q)distribution,thefactorfq =0.47 ifwedetectall
observations imply the existence of Md ∼ 0.5-1.0M⊙ of binaries with q > 0.1. This implies that the initial binary
dust in SN 1987A (Matsuura et al. 2011, Indebetouwet al. fraction is F <0.61 at 90% confidence.
2014, Matsuura et al. 2015), far more than the amount in- There is no simple way to estimate the initial binary
ferred at early times as used by Graves et al. (2005). The fraction includingbinaryinteractions short of afull simula-
characteristic visual optical depthscale for an SNRat time tionofbinaryevolution,whichisbeyondourpresentscope.
t=10t years is For example, the stars can merge, which would reduce the
10
numbersof binariesat death.Alternatively,aprimary with
15κM M
τ = d e ≃30κ M M E−1t−2. (7) too little mass to explode can accrete enough mass from
0 64πEt2 4 d0.1 e10 51 100
the secondary to explode, which would tend to increase
where a typical dust visual opacity is κ = 104κ cm2/g, the numbers of binaries at death. For example, if fraction
4
the dust mass is Md =0.1Md0.1M⊙, the total ejected mass fM of binaries merge prior to the explosion of the primary,
is Me = 10Me10M⊙ and the explosion energy is E = then we really havethelimit F(1−fM)<0.61. Sana et al.
1051E erg (see Kochanek 2017). At t = 16.7 years (6110 (2012) argue that f ≃ 0.25, which would shift the limit
51 M
days), the optical depth implied by the presently observed upwardstoF <∼0.81. Intheirreviewofbinarypopulations,
dust would havebeen τ ∼10κ M M E−1 rather than Duchˆene& Kraus(2013)citeamultiplicityfrequency(frac-
0 4 d0.1 e10 51
theτ ≃0.5assumedbyGraves et al.(2005).Eventoday,the tionofmultiplesystems)withq>0.1of>60%and80%for
optical depth would beof orderτ0 ∼3κ4Md0.1Me10E5−11. In 8-16M⊙ and>16M⊙,respectively,whileMoe & Di Stefano
short,giventheamountofdustseenbyHerschelandALMA, (2016)findthatonly16±9%(6±6)%of9-16M⊙ (>16M⊙)
theGraves et al.(2005)observationsprovidenousefullimit primaries are single. Thus, if there are only singles or bina-
on the luminosity of a binary companion (or emission from ries, the binary fractions can be reconciled by a having a
any stellar remnant). significant merger fraction.
(cid:13)c 0000RAS,MNRAS000,000–000
8 C. S. Kochanek et al.
However, many massive stars are in higher order sys- six systems and no detection f < 28% at 90% confidence.
b
tems (triples, etc.), and this reintroduces the tension. The The three systems we consider here are a peculiar if well-
fraction of massive stars in higher order systems is high – defined sample, and it is not clear how to incorporate the
Moe & Di Stefano (2016) find that (52±13)% (73±16%) possible detection in SNR S147 (Din¸cel et al. 2015). If we
of9-16M⊙ (>16M⊙) primariesare inhigherordersystems simply treat it likeasample of four objects with one detec-
with q > 0.1. Let f ≃ 62% be the fraction of non-single tion,thanf ≃31%withasymmetric90%confidencerange
H b
stars in higher order systems (i.e. 32% are in binaries and of 8%<f <66% that leaves much of tension intact.
b
52% are in higher order systems, and 62 = 52/(52+32)) . The Crab and Cas A are the easiest Galactic sys-
Thefractionofexplodingprimariesisstillf =F/(1+Ff ) tems to examine due to their youth and low extinction
p q
whereF isnowthefractionofnon-singlestarsatbirth.The and stellar densities. Searches to binary companions of cc-
fraction of these with a stellar secondary and no additional SNe are intrinsically easier than those for Type Ia be-
companionis(1−f )(1−f )whereweallowfractionf of cause there is no immediate need to rule out the exis-
H M M
binariestomerge.Thefraction wherethereisanadditional tenceoffaint,dwarfcompanions.Thesearchesshouldprob-
companion,sothatthereisastellarcompanionindependent ably not be limited to O/B stars (as in Guseinov et al.
of whether the primary and secondary have merged, is f . 2005). For passively evolving binaries, companions will
H
Thus,thefractionofexplodingprimarieswithastellarcom- be dominated by main sequence stars (Kochanek 2009),
panion(notnecessarilytheoriginalsecondary)isreducedby but binary evolution and mass transfer greatly broadens
(1−f )(1−f )+f ≃ 91% rather than 1−f ≃ 75% the spectrum of possible secondaries. It is necessary to
H M H M
forf =62%andamergerfractionoff =25%.Account- separate the ccSNe from the Type Ia’s using the pres-
H M
ing for these higher order systems, the limit on the initial ence of a NS, the composition/structure of the SNR (e.g.,
fraction of non-single stars is F(1−f +f f ) < 0.61), Lopez et al. 2009, Yamaguchi et al. 2014), or, as done for
M H M
leading to a limit of F <∼ 0.67 that is again in significant Cas A, light echo spectra. Modern, multiband photometry
tension with estimates of stellar multiplicities. such as the PS1 data used here, is an important improve-
This ignoresanycontribution from secondaries explod- ment, but studying large numbers of additional Galactic
ing in higher order systems which survive the explosion of SNRswill only become relatively straight forward with the
the primary. The fraction of exploding secondaries in this release of the full Gaia proper motion and parallax cata-
passive evolution model is f = Ff /(1+Ff ) ≃ 26% for logs (e.g., Gaia Collaboration et al. 2016). Searching SNRs
s q q
f =0.47 and F =0.75. In theabsence of higher order sys- in the Magellanic Clouds is also feasible starting from cat-
q
tems,noneofthesewould havestellarcompanionsat death alogslikeHarris & Zaritsky(2004)orNideveret al.(2017).
since the primary becomes a compact object independent Whilepropermotionswillbelacking,thefixeddistanceand
of whether the binary survives. With higher order systems, modest extinctions otherwise simplify theproblem.
fractionf oftheexplosionsofsecondariescouldalsohavea IdentifyingthesebinarycompanionstoccSNeisimpor-
H
stellar companion at death,although probably only asmall tant.Notonlyaretheyakeyobservationalconstraintonthe
fraction ofthesesystemsremainboundfollowing theexplo- role of binaries in ccSNe, but they also provide important
sion of theprimary. constraints on the formation of runaway stars and the ori-
AsecondinterestingpointisthatCasAwasaTypeIIb ginsofNSvelocities.Forexample,havingthevelocityofthe
SN (Krause et al. 2008, Rest et al. 2008) and yet it cannot formerbinarycompanionwouldgreatlyhelptoseparatethe
have been a binary at death unless the companion was a contributionsofbinarydisruptionandexplosivekickstothe
dwarf star or a compact object. Many models for Type IIb velocitiesofNS.Itwouldalsobeinterestingtoidentifysuch
SN invoke binary evolution and a massive companion, as systemstoobservetheconsequencesoftheSNexplosionfor
was originally suggested byPodsiadlowski et al. (1993) and the secondary. This has primarily been considered for stel-
Woosley et al. (1994) to explain SN 1993J. Searches for an lar companions to Type Ia SN (e.g., Marietta et al. 2000,
optical counterpart to the Cas A NS noted that any bound Shappeeet al. 2013, Pan et al. 2014), butthere should also
binary companion would have to be very low mass (e.g., belong term effects on close companions to ccSNe.
Chakrabarty et al. 2001, Fesen et al. 2006), but we could
findno quantitativediscussion of limits on unboundbinary
companions. Cas A is one of the SNR without candidate
O/BstarcompanionsinGuseinov et al.(2005)andtheissue ACKNOWLEDGMENTS
ismentionedinpassingbyClaeys et al.(2011).Intheirsur-
CSK thanks K. Auchettl,C. Badenes, S. deMink, J. J. El-
veyofpossiblebinarymodelsforTypeIIbSNe,Claeys et al.
dridge, T. Holland-Ashford, L. Lopez, K. Stanek, M. Pin-
(2011) essentially always were left with a companion that
sonneault,andT.Thompsonfordiscussionsandcomments.
should have been easily visible. This suggests that caution
CSK is supported by NSF grants AST-1515876 and AST-
should be exercised about invoking this theoretical moti-
1515927.
vation in searches for companions to other Type IIb SNe
like SN 1993J (e.g., Maund et al. 2004, Fox et al. 2014) or
SN 2011dh (e.g., Folatelli et al. 2014, Maund et al. 2015).
That the absence of binary companions in only three
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Cas A and the Crab Were Not Binaries 9
Table 1.StarsNeartheCrab
# dc dNS RA Dec g r i z y
1 12′.′1 10′.′8 83.633751 22.011540 17.875±0.007 16.749±0.005 16.508±0.005 16.232±0.005 16.098±0.005
2 12′.′2 5′.′6 83.634080 22.015580 16.406±0.005 15.429±0.004 15.102±0.004 14.941±0.003 14.875±0.004
3 13′.′2 5′.′6 83.632910 22.012900 20.213±0.041 18.479±0.018 17.886±0.017 17.490±0.009 17.114±0.011
4 13′.′2 22′.′0 83.639220 22.016270 17.145±0.005 16.076±0.004 15.767±0.003 15.870±0.005 15.513±0.004
5 13′.′4 0′.′5 83.633031 22.014530 17.207±0.009 16.304±0.009 16.088±0.009 15.821±0.007 15.687±0.009
6 14′.′2 12′.′4 83.633381 22.011031 18.836±0.011 17.822±0.011 17.578±0.009 17.343±0.009 17.163±0.011
7 21′.′6 32′.′2 83.642270 22.016590 21.955±0.330 20.354±0.110 18.801±0.029 18.147±0.021 17.785±0.025
8 28′.′0 41′.′3 83.643901 22.009151 21.057±0.118 19.822±0.053 19.412±0.050 19.336±0.057 19.104±0.099
9 29′.′1 31′.′3 83.633680 22.005790 22.833±0.327 20.526±0.067 19.380±0.044 19.003±0.030 18.544±0.035
10 30′.′3 43′.′4 83.644091 22.008290 19.849±0.030 18.572±0.026 18.195±0.013 18.019±0.013 17.729±0.022
11 31′.′3 24′.′3 83.632790 22.021190 18.055±0.009 16.971±0.005 16.813±0.009 16.396±0.005 16.398±0.007
12 32′.′9 24′.′8 83.627980 22.009300 20.487±0.066 19.226±0.026 18.745±0.019 18.357±0.018 18.355±0.059
13 40′.′1 53′.′7 83.648400 22.010360 15.976±0.004 14.929±0.003 14.580±0.003 14.377±0.002 14.258±0.003
14 42′.′1 45′.′7 83.634560 22.001831 21.708±0.131 20.549±0.103 21.173±0.168 21.441±0.346 20.392±0.264
15 43′.′8 57′.′1 83.649970 22.013350 19.691±0.019 18.806±0.025 18.246±0.011 18.137±0.015 17.996±0.030
16 44′.′3 56′.′2 83.645360 22.003920 19.306±0.025 17.970±0.018 17.516±0.009 17.264±0.013 17.008±0.018
17 44′.′5 31′.′4 83.623531 22.014000 21.403±0.155 19.944±0.095 19.034±0.046 18.747±0.054 18.441±0.064
18 46′.′3 36′.′4 83.623841 22.008830 19.301±0.043 18.178±0.028 17.915±0.022 17.711±0.013 17.572±0.028
19 52′.′5 47′.′0 83.633171 22.027510 21.674±0.130 19.710±0.029 18.614±0.024 18.098±0.017 17.837±0.021
20 53′.′9 67′.′1 83.652970 22.013090 18.549±0.013 17.471±0.011 16.953±0.009 16.819±0.009 16.612±0.013
21 54′.′1 63′.′6 83.642910 21.999390 17.840±0.011 16.788±0.011 16.540±0.007 16.369±0.005 16.098±0.009
22 56′.′5 62′.′2 83.637380 21.997660 16.915±0.005 15.841±0.004 15.490±0.005 15.354±0.004 15.119±0.005
23 56′.′7 45′.′2 83.625051 22.024660 21.395±0.129 20.314±0.137 19.727±0.071 19.585±0.075 19.326±0.088
24 58′.′8 72′.′4 83.653070 22.007001 19.107±0.013 17.892±0.007 17.595±0.009 17.162±0.007 17.182±0.015
25 59′.′3 72′.′2 83.650590 22.002890 20.473±0.041 19.430±0.040 19.089±0.036 18.953±0.036 18.766±0.054
26 60′.′6 53′.′2 83.621881 22.003800 19.146±0.015 18.085±0.009 17.933±0.009 17.620±0.009 17.480±0.013
27 63′.′8 50′.′2 83.618310 22.017740 19.334±0.018 18.261±0.026 17.996±0.015 17.825±0.015 17.564±0.021
28 66′.′5 55′.′4 83.617581 22.008580 17.723±0.007 16.672±0.005 16.724±0.007 16.229±0.005 16.051±0.007
29 68′.′1 55′.′2 83.620091 22.024130 21.746±0.236 19.173±0.086 18.695±0.018 18.258±0.015 17.765±0.030
30 68′.′3 55′.′9 83.616450 22.011591 18.793±0.017 18.011±0.018 17.899±0.011 17.694±0.009 17.448±0.017
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10 C. S. Kochanek et al.
Table 2.FitstoStarsNeartheCrab
# χ20 χ21 χ22 logL1/L⊙ logT1 logL2/L⊙ logT2
1 5.5 6.0 8.1 0.06±0.25 3.672±0.030 0.17±0.30 3.711±0.004
2 0.1 0.9 3.9 0.44±0.24 3.681±0.024 0.67±0.20 3.736±0.004
3 9.8 10.3 26.6 −0.11±0.33 3.676±0.037 −0.65±0.47 3.602±0.005
4 21.9 23.6 30.7 0.28±0.48 3.716±0.074 0.27±0.49 3.740±0.009
5 3.6 5.6 5.7 0.40±0.32 3.764±0.067 0.35±0.26 3.745±0.004
6 24.9 30.9 31.0 0.04±0.55 3.748±0.077 −0.17±0.28 3.730±0.008
7 0.1 0.5 0.7 −0.57±0.23 3.545±0.021 −0.67±0.19 3.533±0.003
8 5.1 9.5 16.7 −0.71±0.17 3.659±0.021 −0.37±0.12 3.716±0.008
9 13.5 14.3 17.8 −0.41±0.47 3.686±0.069 −0.97±0.35 3.566±0.004
10 17.8 19.2 19.9 −0.41±0.37 3.688±0.046 −0.50±0.24 3.681±0.005
11 12.7 15.0 16.8 0.04±0.39 3.709±0.057 −0.04±0.38 3.721±0.006
12 8.2 10.1 10.5 −0.62±0.30 3.666±0.040 −0.61±0.16 3.668±0.003
13 0.5 1.8 2.5 0.81±0.23 3.703±0.020 0.82±0.18 3.712±0.003
14 26.1 54.1 79.9 −0.29±0.42 3.714±0.052 0.05±0.22 3.762±0.016
15 8.7 10.0 11.5 −0.37±0.32 3.706±0.045 −0.36±0.11 3.715±0.004
16 3.6 3.8 3.9 −0.25±0.23 3.667±0.025 −0.23±0.24 3.662±0.002
17 6.9 7.1 7.4 −0.71±0.38 3.650±0.055 −0.93±0.14 3.610±0.002
18 15.6 18.0 21.1 −0.40±0.35 3.691±0.043 −0.29±0.19 3.719±0.006
19 23.6 27.6 32.8 0.04±0.64 3.736±0.096 −0.83±0.40 3.564±0.006
20 1.9 1.9 2.1 −0.11±0.25 3.685±0.051 −0.06±0.23 3.691±0.003
21 9.1 9.5 10.9 0.12±0.35 3.716±0.063 0.05±0.36 3.722±0.005
22 3.7 4.3 5.7 0.39±0.23 3.682±0.027 0.56±0.21 3.710±0.003
23 2.0 4.9 8.4 −0.89±0.19 3.629±0.024 −0.63±0.08 3.676±0.003
24 8.2 11.9 12.6 −0.29±0.34 3.686±0.044 −0.32±0.31 3.689±0.005
25 3.2 6.0 12.4 −0.70±0.16 3.662±0.019 −0.29±0.11 3.726±0.007
26 22.3 26.1 27.4 −0.18±0.46 3.720±0.059 −0.20±0.22 3.731±0.007
27 17.7 20.3 21.6 −0.29±0.40 3.709±0.051 −0.28±0.20 3.721±0.007
28 37.2 46.4 46.9 0.70±0.78 3.828±0.135 0.15±0.50 3.736±0.012
29 28.3 28.6 45.2 0.04±0.59 3.737±0.088 −0.87±0.42 3.592±0.004
30 18.1 27.5 29.9 0.07±0.54 3.765±0.071 0.22±0.20 3.785±0.011
TheIDnumbersarethesameasinTable1.Thegoodnesses offitχ2,χ2,andχ2 are
0 1 2
forfitswithnoprior,apriorforthedistancetotheSN,andaprioronboththe
distanceandtheextinction. Theprobabilityweightedmeanluminositiesand
temperatures arereportedforthelattertwomodels.
Table 3.StarsNearCasA
# dc dNS RA Dec g r i z y
1 11′.′7 16′.′9 350.869920 58.816130 26.968±6.896 22.959±0.243 21.610±0.085 21.066±0.096 20.460±0.127
2 16′.′6 21′.′9 350.871040 58.817400 24.223±0.478 22.431±0.153 21.512±0.089 20.907±0.093 20.540±0.143
3 19′.′8 26′.′7 350.862510 58.818970 −− 23.087±0.241 21.694±0.102 20.755±0.072 20.069±0.086
4 23′.′8 25′.′3 350.853010 58.813060 16.802±0.003 15.775±0.003 15.306±0.003 14.939±0.003 14.712±0.003
5 25′.′3 32′.′2 350.861801 58.820450 23.675±0.290 22.005±0.119 20.701±0.051 20.375±0.051 19.764±0.066
6 28′.′0 32′.′9 350.852650 58.817580 19.784±0.009 18.349±0.007 17.633±0.005 17.278±0.007 17.003±0.009
7 28′.′3 24′.′7 350.855350 58.807990 26.995±4.898 23.297±0.335 22.169±0.126 21.046±0.096 20.221±0.110
8 28′.′5 32′.′6 350.851430 58.816520 24.604±0.551 22.601±0.194 21.244±0.066 20.224±0.050 19.396±0.046
9 28′.′5 22′.′0 350.863360 58.805910 18.290±0.004 17.258±0.004 16.596±0.003 16.304±0.004 16.072±0.004
10 29′.′6 23′.′1 350.873351 58.806511 23.511±0.237 21.663±0.069 20.273±0.026 19.595±0.018 19.317±0.038
11 32′.′4 27′.′1 350.878290 58.807510 24.849±0.694 22.528±0.179 21.322±0.074 20.694±0.062 20.674±0.186
12 34′.′9 29′.′4 350.878871 58.806840 23.770±0.284 22.723±0.270 20.867±0.043 20.308±0.042 19.909±0.076
13 35′.′5 29′.′2 350.861641 58.804091 20.880±0.018 19.655±0.011 18.956±0.007 18.598±0.011 18.278±0.015
Thestarsarenumberedinorderoftheirdistancefromthecenter oftheSNR(dc)andthedistancefromtheNS(dNS)isalsogiven.
Themagnitudes areaperturemagnitudesfoundfromthePS1imagesandanentryof−−indicatesnodetection.
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Gies, D. R., & Bolton, C. T. 1986, ApJS, 61, 419 Green,G.M.,Schlafly,E.F.,Finkbeiner,D.P.,etal.2015,
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(cid:13)c 0000RAS,MNRAS000,000–000
