Table Of ContentMon.Not.R.Astron.Soc.000,1–6(2010) Printed16March2011 (MNLATEXstylefilev2.2)
Cooling neutron star in the Cassiopeia A supernova remnant:
Evidence for superfluidity in the core
Peter S. Shternin1,2⋆, Dmitry G. Yakovlev1, Craig O. Heinke3,
Wynn C. G. Ho4†, Daniel J. Patnaude5
1IoffePhysicalTechnicalInstitute,Politekhnicheskaya26,194021St.Petersburg,Russia
2St.PetersburgStatePolytechnicalUniversity,Politechnicheskaya29,195251,St.Petersburg,Russia
1 3DepartmentofPhysics,UniversityofAlberta,Room238CEB,11322-89Avenue,Edmonton,AB,T6G2G7,Canada
1 4SchoolofMathematics,UniversityofSouthampton,Southampton,SO171BJ,UnitedKingdom
0 5SmithsonianAstrophysicalObservatory,Cambridge,MA02138,USA
2
n
Accepted.Received;inoriginalform
a
J
1
2 ABSTRACT
According to recent results of Ho&Heinke (2009) and Heinke&Ho (2010), the Cas-
] siopeia A supernovaremnantcontainsa young(≈ 330 yr old) neutron star (NS) which has
R carbonatmosphereandshowsnoticeabledeclineoftheeffectivesurfacetemperature.Were-
S port a new (November 2010) Chandra observation which confirms the previously reported
. decline rate. The decline is naturallyexplainedif neutronshave recently becomesuperfluid
h
(intriplet-state)inthe NScore,producinga splashof neutrinoemissiondueto Cooperpair
p
- formation(CPF) process that currently accelerates the cooling.This scenario puts stringent
o constraintsonpoorlyknownpropertiesofNScores:ondensitydependenceofthetemperature
r T (ρ)fortheonsetofneutronsuperfluidity[T (ρ)shouldhaveawidepeakwithmaximum
t cn cn
s ≈ (7−9)×108 K], on the reductionfactor q of CPF processby collectiveeffectsin super-
a
fluidmatter(q > 0.4),andontheintensityofneutrinoemissionbeforetheonsetofneutron
[
superfluidity(30–100timesweakerthanthestandardmodifiedUrcaprocess).Thisisserious
2 evidencefornucleonsuperfluidityinNScoresthatcomesfromobservationsofcoolingNSs.
v
5 Key words: dense matter – equation of state – neutrinos – stars: neutron – supernovae:
4 individual(CassiopeiaA)–X-rays:stars–superfluidity
0
0
.
2
1
1 INTRODUCTION on NS surface although no pulsations have been observed, e.g.,
0
Pavlov&Luna2009).
1 It is well known that NS cores contain superdense
RecentlyHo&Heinke (2009) haveshown that theobserved
: matter whose properties are still uncertain (see, e.g.,
v spectrumissuccessfully fittedtakingacarbon atmospheremodel
Haensel,Potekhin&Yakovlev 2007; Lattimer&Prakash 2007).
i withalowmagneticfield(B.1011 G).Thegravitationalmassof
X One can explore these properties by studying the cooling of
the object, as inferred from the fits, is M ≈ 1.3−2M , circum-
r isolated NSs (see, e.g., Pethick 1992; Yakovlev&Pethick 2004; ⊙
ferential radius R ≈ 8−15 km, and the non-redshifted effective
a Page,Geppert&Weber2006;Pageetal.2009,forreview).
surfacetemperatureT ∼ 2×106 K(Yakovlevetal.2011).These
We analyse observations of the NS in the supernova rem- s
parametersindicatethatthecompactsourceisanNSwiththecar-
nant Cassiopeia A (Cas A). The distance to the remnant is d =
bonatmosphere.Itemitsthermalradiationfromtheentiresurface
3.4+0.3 kpc(Reedetal.1995).TheCasAageisreliablyestimated
−0.1 andhasthesurfacetemperaturetypicalforanisolatedNS.Itisthe
as t ≈ 330 ± 20 yr from observations of the remnant expan-
youngestinthefamilyofobservedcoolingNSs.
sion (Fesenetal. 2006). The compact central source was identi-
Yakovlevetal. (2011) compared these observations withthe
fied in first-light Chandra X-ray observations (Tananbaum 1999)
NScoolingtheory.TheauthorsconcludedthattheCasANShas
and studied by Pavlovetal. (2000); Chakrabartyetal. (2001);
alreadyreachedthestageofinternalthermalrelaxation.Itcoolsvia
Pavlov&Luna(2009)butitsnaturehasbeenuncertain.Thefitsof
neutrinoemissionfromthestellarcore; itsneutrinoluminosityis
theobservedX-rayspectrumwithmagnetizedornon-magnetized
notverydifferentfromthatprovidedbythemodifiedUrcaprocess.
hydrogen atmosphere models or with black-body spectrum re-
Following Ho&Heinke (2009), Heinke&Ho (2010) anal-
vealed too small size of the emission region (could be hot spots
ysedChandraobservations of theCasANSduring10yearsand
foundasteadydeclineofT byabout4%.Theyinterpretitasdi-
s
⋆ E-mail:[email protected] rectobservationof CasANScooling,thephenomenonwhichhas
† E-mail:[email protected] neverbeenobservedbeforeforanyisolatedNS.Theseresultsare
(cid:13)c 2010RAS
2 P.S. Shterninetal.
confirmedbynewobservationswereportbelow.Weinterpretthem
Table 1. Carbon atmosphere spectral fits, using the best spectral fit (M,
asamanifestationofneutronsuperfluidityintheCasANS. R,NH)ofHeinke&Ho(2010)andYakovlevetal.(2011),withtheaddi-
When thispaper wasnearly completed webecame awareof tionof2010data.Epochdatesareforthemidpointsoftheobservations,or
thepaper byPageetal.(2010)who proposed similarexplanation weightedmidpointsofmergeddatasets.Temperatureerrorsare1σconfi-
oftheCasANSobservations.Howeverthetwopapersarediffer- denceforasingleparameter.
entindetails,andcanberegardedascomplementary.Inparticular,
Epoch Exposure logTs ObsID(s)
wediscussthedependenceofcoolingcurvesonthepoorlyknown (Year) ks K
efficiencyofneutrinoemissionduetoCPFprocessandthepossi-
bilitytointerpretobservationsofallcoolingstarsbyonemodelof 2000.08 50.56 6.3258+0.0019 114
−0.0019
superdensematter.Itisimportantthatwereportthenewobserva- 2002.10 50.3 6.3237−+00..00001188 1952
tion. 2004.11 50.16 6.3156−+00..00001199 5196
2007.93 50.35 6.3108+0.0019 9117,9773
−0.0019
2009.84 46.26 6.3087+0.0018 10935,12020
−0.0018
2010.83 49.49 6.3060+0.0019 10936,13177
−0.0018
2 NEWCHANDRAOBSERVATIONS
We use the Chandra data on the Cas A NS, discussed and fitted shorterrelaxation,lastingtypically. 100yr.Weproposeanother
byHeinke&Ho(2010),andaddonenew datapoint. Briefly,the interpretationbasedontheeffectsofsuperfluidityinNScores,in
analyseddataincludetheChandraACIS-SobservationsofCasA linewiththeworkofGusakovetal.(2004).
longer than 5 ks. In order to ensure that all considered data are Neutrons,protons(andotherbaryonsifpresent)inNSinteri-
directlycomparable,wetakeonlythe‘directlycomparabledata’of orscanbesuperfluid(duetoCooperpairing).Freeneutronsinthe
Heinke&Ho(2010).WeexcludethesubarrayobservationofCas innercrustandprotonsinthecoreundergoCooperpairinginspin-
A(Pavlov&Luna2009),sincethepileupproperties(Davis2001) singletstate,whileneutronsinthecorecanpairinspin-tripletstate.
of thisspectrum differ fromthe others, and thoseobservations in Critical temperatures of superfluidity onset T (ρ) are very model
c
which the Cas A NS dithered over bad pixels (most of the 2004 dependent(asreviewed,e.g.,byPageetal.2004).
observations). Ourideaisthattheinitialcrust-corerelaxationinCasANSis
The new data point is produced from two ACIS-S observa- over,leavingthestarsufficientlywarm.Weassumefurtherthatnot
tionsofCasA(Patnaudeetal.2010:ObsIDs10936,13177)taken too strong triplet-state neutron superfluidity appeared in the core
on 2010 October 31 and 2010 November 2for 33 and 17 ks (re- sometimeago.ItinitiatesasplashofneutrinoemissionduetoCPF
spectively) and telemetered in GRADED mode (as done for pre- processproducingthesecondT dropthatmimicsthesecond(de-
s
viousCasAobservations).WeusedCIAO4.2andCALDB4.2.1to layed)thermalrelaxation.Theseconddropismainlyregulatedby
reprocess thedataand produce response functions, correctingfor (i)thedensitydependenceT =T (ρ)ofthecriticaltemperature
cn cn
thetime-dependentACISquantumefficiencydegradationandgain for the neutron pairing in the NS core, (ii) the reduction factor q
changes,butnotforthecharge-transferinefficiency(asthiscannot of CPFprocess bycollective effectsinsuperfluid matterand (iii)
bemodeledwithGRADEDdata).Weextractedsourcespectrawith theneutrinoluminositypriortotheonsetofneutronsuperfluidity.
a4pixel(2.37”)radiusregion,andbackgroundspectrafromanan- Thesepropertiesareverymodeldependentandpoorlyknownbut
nulusof5to8pixels,asinHeinke&Ho(2010).Wecombinedthe canbeconstrainedfromtheCasANSobservations.
twonew observations intoone setof spectraand responses (with The CPF process was first predicted by
aneffectivedateof2010November1),andgroupedthespectrum Flowers,Ruderman&Sutherland (1976) for singlet-state
by200counts/bin. pairing neglecting collective superfluid effects. Collec-
We fitted these spectra simultaneously, forcing the NS mass tive effects can suppress the process (q < 1) as was
and radius, along withthe distance and NH, to be the same as in first noticed by Leinson (2001) and calculated later by
thebestfitofHeinke&Ho(2010)andYakovlevetal.(2011),and Leinson&Pe´rez (2006); Sedrakian,Mu¨ther&Schuck (2007);
findingthe1σerrorsonthesurfacetemperatureateachepoch.This Kolomeitsev&Voskresensky (2008); Steiner&Reddy (2009);
fittingisdesignedtocleanlydefinetherelativevariationinthetem- Leinson (2010); some discussion is also given by Pageetal.
perature,separatingthisquestionfromtheabsoluteuncertaintyin (2009); the results are controversial. The main attention has
thetemperature (described indetailinYakovlevetal.2011).The been paidtoCPFprocess due tosinglet-statepairing of neutrons
fittedvaluesofthenon-redshiftedeffectivesurfacetemperatureTs whichhasbeenfoundtobestronglysuppressed(q ≪ 1).Weare
(Table1)areslightlydifferentfromthosereportedbyHeinke&Ho interested in triplet-state pairing in which case the suppression
(2010) for the2004–2009 observations, but withinthe1σ errors. isthought tobe lessdramatic. If the latterCPFprocess were not
Thekeyresultisthatthenewobservationconfirmsandextendsthe affected by collective effects, then 24% of neutrino emissivity
coolingtrendseeninHeinke&Ho(2010). would go through the vector weak interaction channel, while the
rest (76%) would go through the axial-vector channel. Collective
effects suppress the vector channel almost completely but the
axial-vector channel survives. Exact value of q is debatable (the
3 SECONDTEMPERATUREDROP
lowest estimate q ≈ 0.19 is given by Leinson 2010). Instead of
The observed surface temperature decline is too steep and can- relyingonanyspecificmodel,weconsiderqasafreeparameter.
notbedescribedbythetheorydiscussedbyYakovlevetal.(2011) We illustrate this idea by cooling simulations of NSs
(whodidnotanalysethedeclineitself).Heinke&Ho(2010)sug- with nucleon cores. We take the Akmal-Pandharipande-
gested that Cas A NS undergoes the last years of the internal Ravenhall (APR) equation of state (EOS) in the core
crust-core relaxation accompanied by a pronounced surface tem- (Akmal,Pandharipande&Ravenhall1998).ByAPRwemeanthe
perature drop. However, the theory predicts (e.g., Lattimeretal. parametrization of APR results by Heiselberg&Hjorth-Jensen
1994;Gnedin,Yakovlev&Potekhin2001;Yakovlevetal.2011)a (1999)–theversionAPRIproposedbyGusakovetal.(2005).The
(cid:13)c 2010RAS,MNRAS000,1–6
CoolingCas A NeutronStar 3
10
M M q M M
T 868cn [10 K] c1.0 b a 1.65 1.5T 5s b[MK] c =0.76 T12..255s [MK] =1.65 pNSF
1.5 1 2 t a 3
T 10 10
4 [yr]
int (330 yr) M
1.75 M
2
1.65
1.45
4 8 12 16 a320 a 340
t
14 -3
Figure1.(Coloronline)Left:Models(a),(b)and(c)forcriticaltemperatureoftriplet-stateneutronpairinginNScore.Verticaldottedlinesshowcentral
densitiesofNSswithM=1and1.65M⊙(forAPR [E1O0S) g.T chmins]olidlineisthetemperatureprofileinthe1.65M⊙ s[tyarr]ofage330yrwithneutronsuperfluidity
(a).Right:Lines(a),(b)or(c)showcoolingofthe1.65M⊙starwithstrongprotonsuperfluidityandmoderateneutronsuperfluidity(a),(b)or(c)inthecore
(q=0.76)comparedwithobservationsofCasANScooling.Thedottedlineisthesameforthe1.75M⊙starandneutronsuperfluidity(a).Theline(a)for
M=1.65M⊙isalsoshownintheinsetoverlongertimespan.LinespSFandNintheinsetarecalculatedforM=1.65M⊙neglecting,respectively,neutron
superfluidityandentirenucleonsuperfluidityinthecore.
maximummassofastableNSforthisEOSis M = 1.929M ; 1.65M star of nearly Cas A NS age with T (ρ) models (a)–(c)
max ⊙ ⊙ cn
the powerful direct Urca process of neutrino emission is open in fromtheleftpanelandwithq = 0.76(axialvectorchannelisnot
stars with M > M = 1.829M . Let the direct Urca process suppressed). The curves are compared with the Cas A NS data.
DU ⊙
and even less efficient modified Urca process be either not All three superfluidity models agree with these data. Taking su-
allowed or strongly suppressed in the Cas A NS. Otherwise the perfluidity (a) and increasing the stellar mass to 1.75M makes
⊙
star would be too cold after the initial crust-core relaxation; we the CPF process more important and starts the second tempera-
would beunable tosignificantlyspeed upitscoolingby theCPF turedropearlier(thedottedcurve),indisagreementwiththedata.
process. To suppress Urca processes we assume the presence of However, we could easily readjust (slightly decrease) T (ρ) and
cn
strong proton superfluidity in the core, with critical temperature explaintheCasANSdatawiththe1.75M model.Therefore,we
⊙
T (ρ) & (2−3)×109 K;exactvalues ofT areunimportant. It cansuccessfullyfitthedataforarangeofNSmassesandtakethe
cp cp
occurswithinafewdaysafterthestarformation.TheprotonCPF 1.65M starasanexample.Theinsetshowsthecoolingcurve(a)
⊙
neutrinoemissiondoesnotinfluencethecoolingevenifthisemis- (M = 1.65M ) over longer time scale. The second temperature
⊙
sion were not affected by collective effects (e.g., Yakovlevetal. dropatt ∼ 250yrisclearlypronounced here.Also,weshowthe
2001). As long as neutrons are non-superfluid, the neutrino coolingofnon-superfluidstar(curveN)andthestarwithprotonsu-
emission is mainly generated in neutron-neutron bremsstrahlung perfluidityalone(curvepSF).WithouttheCPFprocess,theslopes
process.ItisweakandleavestheCasANSsufficientlywarmbe- ofbothcurvesaremuchsmallerthanrequired.
forethesecondtemperaturedrop.Unlessthecontraryisindicated, In Fig. 2 we test two neutron superfluidity models, (a) and
we consider NSs with ordinary (non-accretted, non-magnetized) (c),againstobservationsofotherisolatedNSs.Observationaldata
heat blanketing envelopes (e.g., Potekhin,Chabrier&Yakovlev are taken from references cited in Yakovlevetal. (2008) and
1997; Potekhinetal. 2003) and neglect superfluid effects in the Kaminkeretal. (2009) with the exception of PSR J0007+7303.
stellar crust (which weakly affect the cooling after the crust-core ThedataonthelattersourcearetakenfromCaraveoetal.(2010)
relaxation; e.g.,Yakovlevetal.2001).Note,thatasplashof CPF andLinetal.(2010).Notethatinsimilarfig.5ofYakovlevetal.
neutrinosmakesthestarslightlynon-isothermal,withthecooling (2011)sourcelabels12,13and14shouldrefertoRXJ1856–3754,
slightlydependentonthethermalconductivityinthecore,butthe GemingaandPSRB1055–52,respectively.
isothermalstateissoonrestored. WemakeareasonableassumptionthatallNSshavedifferent
Illustrative results are shown in Figs. 1, 2 and 3. The left masses but the same physics of matter in their cores. Wepresent
panel of Fig. 1 gives three models of T (ρ). We do not rely on coolingcurves(solidlines)foranumberofmasses(fromtoptobot-
cn
any specific theoretical model but consider three phenomenolog- tom),from1M to M .Recall,thatweusethemodelofstrong
⊙ max
ical curves (a), (b) and (c) (locating neutron superfluidity at pro- proton superfluidity intheentirecore that switchesoff Urcapro-
gressivelylowerdensities).Inour casethemaximumofT (ρ)is cessesinallstars.Withthisassumption, neutronsuperfluidity(a)
cn
strictlyconstrainedtoT ≈ (7−9)×108 K.Higherorlower allows us to explain almost all sources, except for warmest and
cnmax
T (ρ)peakswouldstartthesecondtemperaturedropintheCasA coolest ones (for their ages). However, neutron superfluidity (c)
cn
NSearlierorlaterthanrequiredbytheobservations(orevencom- producestoostrongCPFneutrinoemissioninlow-massstarsand
pletelywashoutthisdropinaveryyoungoroldstar).TheT (ρ) cannotexplainthemajorityofwarmerstars,althoughitagreeswith
cn
profilesshouldnotbetoonarrowandthereductionfactorqshould theCasANSdata.
notbetoosmall(otherwisethesecondtemperaturedropwouldbe Furthermore, we can rise the cooling curves of low-mass,
weak). Other plotsgivetheoretical cooling curvesT∞(t) (i.e.,the not too old NSs assuming they have more heat transparent heat-
s
redshiftedsurfacetemperatureversust). blanketing envelopes of light elements . For example, the dashed
The right panel of Fig. 1 gives three cooling curves for the curvesinFig.2arecalculatedfor M = 1M NSwiththecarbon
⊙
(cid:13)c 2010RAS,MNRAS000,1–6
4 P.S. Shterninetal.
3
1 1
2.5 4 4 12 Geminga
K] a 13 PSR B1055-52c
2[M 3 3 1145 RPSXR J 1J2805463-3+7257440
T 1.5s Cas A Cas A 16 RX J0720.4-3125
2 9 2 9
8 11 13 8 11 13
1
5 5
6 7 16 6 7 16
1 Crab 12 12
10 10
2 3C 58
14 14
3 PSR J1119-6127
0.5 4 RX J0822-43 15 8 PSR B1706-44 15
5 PSR J1357-6429 9 PSR J0538+2817
6 RX J0007.0+7303 10 PSR B2334+61
7 Vela 11 PSR 0656+14
2 t 4 6 2 t 4 6
Figure2.(Coloronline)Sequ1encesof(solid1)0coolingcurve1s0forNSsofm1as0ses1from1M⊙ to1M0max (through100.1M⊙)withst1ro0ngprotonsuperfluidityand
moderateneutronsuperfluidity(a)(left)or(c)(right)in[ythre]core(q=0.76)comparedwithobservations o[fyirs]olatedNSs.Dashedlinesrefertowarmeststars
ofthesetypes–1M⊙starswiththecarbonsurfacelayerofmass10−8M⊙.Dash-and-dottedlinesrefertocoolestMmaxstarswithoutprotonsuperfluidityin
theinnercore.
envelopeofmass10−8M .Wecanalsolowerthecoolingcurvesof
⊙
massive(M )stars:thedash-dottedlinesarecomputedbytaking
max K]
more realistic models for proton superfluidity, with T (ρ) going M
down at high densities. Thisopens direct Urca processcpinthe in- T2.5s [
nercoreandgivescoldestpossibleNSs.Therefore,wecanreally 1.55 K] 2
explainallthedatawithsuperfluidity(a),butnotwithsuperfluid- M
[
ity(c). T s 1.5 0.7
ThesecondtemperaturedropisknownintheNScoolingthe- 0.4
0.19
ory (e.g., Kaminker,Haensel&Yakovlev 2001). Cooling models
1 2 t 3
like (a) and (c) in Fig. 2 have been analysed by Gusakovetal.
10 10
(2004) withthesame conclusion that models like(a)can explain 1.5 [yr]
M M
observations of allisolated NSs.Similarmodels of NSswithnu-
cleoncores,wheredirectUrcaisforbiddenbutCPFoperates,were =1.65
usedasthebasisoftheminimalcoolingtheory(Pageetal.2004,
q
2006,2009)although thattheoryemploys selectedT (ρ)profiles,
c
mostfavorablebythetheoryofnucleonsuperfluidity.Nowwesee =0.7 0.4 0.19
t
thatthemodelofGusakovetal.(2004)isalsosuitabletoexplain 1.45
theCasANSdata. Figure3.(Coloro3n2li0ne)Sameasontherigh3t4p0anelofFig.1butforcon-
stant Tcn over the core at three [vyarlu]es q = 0.19(Tcn = 7.55×108 K),
Finally,Fig.3demonstratestheeffectofsuppressionofCPF 0.4(7.2×108 K)and0.7(7×108 K).Theinsetshowsthesamecooling
neutrino emission in the axial-vector channel. To maximize the curves but over larger range ofages, together with the dashed curve for
CPFemissionwetakeconstantTcnoverthecore.Itproducesespe- non-superfluidstarandthedash-and-dotcurveforthestarwithoutproton
ciallystrongsplashofCPFneutrinoswhenthesecondtemperature superfluiditybutwithneutronsuperfluidityatTcn=4.3×108K.
dropstarts.Threesolidlinesarethecoolingcurvesforthe1.65M
⊙
starcalculatedatq=0.7,0.4and0.19.Otherwisetheconditionsare
thesameasintherightpanelofFig.1.WithourconstantTcn,CPF layerofmass∼10−12M⊙,wecouldraisethelattercurvetotheCas
neutrinoemissionatq=0.7istoostrong;itgivesfasterCasANS A NS level but would be unable to reproduce the cooling slope.
coolingthanrequiredbyobservations.Thecaseq=0.4nowagrees Ourcalculationsshow thatthemodifiedUrcaemissionshouldbe
withtheobservations. Smallerq = 0.19givesslowercoolingthat suppressed at least by a factor of 30 (for the most efficient CPF
cannotexplainthedata.NoticethattheTcn=constmodelishardly emissionwithq=0.76andconstantTcn)togettherequiredslope.
realistic.FormorerealisticTcn(ρ)profileswecanreconciletheory TakingsmallerqornarrowerTcn(ρ)-profilewouldrequirestronger
withtheCasANSdataatq > 0.4.Thisgivesausefulrestriction suppressionofthemodifiedUrcaprocess.
ontheuncertaintheoreticalparameterq.
IntheinsetofFig.3weshowthesamethreecoolingcurves
overlargerrangeofages.Inaddition,weplotthesamedashedline
4 CONCLUSIONS
fornon-superfluidstarasintherightpanelofFig.1,andanother
dot-and-dashed line for the star with neutron superfluidity alone We report a new (November, 2010) Chandra observation of the
withT =4.3×108 Kandq=0.76.Thelattersuperfluiditytrig- youngCasANSthatconfirmstheobserved(Heinke&Ho2010)
cn
gers asplash of CPFneutrinos, but the mainmodified Urca neu- steadydeclineofthesurfacetemperatureT (by4%over10years).
s
trinoemissionistoostrongandthesplashcannotproduceasteep Weproposeanaturalexplanationoftheobserveddecline.Weas-
T decline requiredby theobservations. Adding acarbon surface sume that the Cas A NS underwent the traditional internal crust-
s
(cid:13)c 2010RAS,MNRAS000,1–6
CoolingCas A NeutronStar 5
core relaxation some time ago and now demonstrates the second Chakrabarty D., Pivovaroff M. J., Hernquist L. E., Heyl J. S.,
temperaturedropduetotheonsetoftriplet-stateneutronsuperflu- NarayanR.,2001,ApJ,548,800
idityinitscoreandassociatedneutrinoemission.Wecanexplain DavisJ.E.,2001,ApJ,562,575
theCasANSobservationsunderthefollowingconditions: FesenR.A.etal.,2006,ApJ,645,283
FlowersE.G.,RudermanM.,SutherlandP.G.,1976, ApJ,205,
• Themaximumcriticaltemperaturefortriplet-statepairingof
541
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cn 2004,A&A,423,1063
theCPFneutrinoemissiontogainenoughstrength.
GusakovM.E.,KaminkerA.D.,YakovlevD.G.,GnedinO.Y.,
• For the same reason the suppression of the CPF process by
2005,MNRAS,363,555
collectiveeffectscannotbetoostrong(q>0.4).
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• The neutrino emission of the star before the second temper-
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⊙
modelbutourbasicconclusionswillnotchangeforalargevariety LeinsonL.B.,2010,Phys.Rev.C,81,025501
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consideredtheCasANSmodelswith M from1.4M to1.9M . Lin L. C. G., Huang R. H. H., Takata J., Hwang C. Y., Kong
⊙ ⊙
ByslightlychangingT (ρ)profilesweareabletoexplainthedata A.K.H.,HuiC.Y.,2010,ApJ,accepted,arXiv:1010.1354
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2000,ApJ,531,L53
We are grateful to A. Y. Potekhin for critical remarks. PSS PethickC.J.,1992,Rev.Mod.Phys.,64,1133
and DGY acknowledge support from Rosnauka (grant NSh Potekhin A. Y., Chabrier G., Yakovlev D. G., 1997, A&A, 323,
3769.2010.2) and Ministry of Education and Science of Russian 415
Federation (contract 11.G34.31.0001 with SPbSPU and Leading PotekhinA.Y.,YakovlevD.G.,ChabrierG.,GnedinO.Y.,2003,
Scientist G. G. Pavlov). WCGH acknowledges support from the ApJ,594,404
Science and Technology FacilitiesCouncil (STFC)in the United Reed J.E.,Hester J. J.,Fabian A.C.,Winkler P.F.,1995, ApJ,
KingdomthroughgrantnumberPP/E001025/1.PSSacknowledges 440,706
support of the Dynasty Foundation and RF Presidential Program Sedrakian A., Mu¨ther H., Schuck P., 2007, Phys. Rev. C, 76,
MK-5857.2010.2. COH acknowledges support from the Natural 055805
SciencesandEngineeringResearchCouncil(NSERC)ofCanada. SteinerA.W.,ReddyS.,2009,Phys.Rev.C,79,015802
TananbaumH.,1999,IAUCirc.No.7246
YakovlevD.G.,GnedinO.Y.,KaminkerA.D.,PotekhinA.Y.,
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