Mon.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 Duchêne& 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-Giguère & 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, González Hernándezet 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 progenitor (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 observed, 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 luminosity, 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 Duchêne& 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%

Cas A and the Crab Were Not Stellar Binaries At Death

Similar Cas A and the Crab Were Not Stellar Binaries At Death