Cooling neutron star in the Cassiopeia~A supernova remnant: Evidence for superfluidity in the core

0.25 MB·English

by  Peter S. Shternin

Mon.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
neutronsshouldbeT ≈(7−9)×108K.Otherwisethesecond
cnmax Gnedin O. Y., Yakovlev D. G., Potekhin A. Y., 2001, MNRAS,
temperaturedropoccursearlierorlaterthanrequiredbyobserva-
324,725
tions.
GusakovM.E.,KaminkerA.D.,YakovlevD.G.,GnedinO.Y.,
• TheT (ρ)profileovertheNScoreshouldberatherwidefor
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).
HaenselP.,PotekhinA.Y.,YakovlevD.G.,2007,NeutronStars
• The neutrino emission of the star before the second temper-
1.EquationofStateandStructure.Springer,NewYork
ature drop should be 30–100 times lower than due to the mod-
HeinkeC.O.,HoW.C.G.,2010,ApJ,719,L167
ified Urca process (e.g., the modified Urca can be suppressed
HeiselbergH.,Hjorth-JensenM.,1999,ApJ,525,L45
bystrongprotonsuperfluidity).Otherwisethesecondtemperature
HoW.C.G.,HeinkeC.O.,2009,Nature,462,71
dropwouldnotbepronounced.
Kaminker A. D.,Haensel P.,Yakovlev D. G., 2001, A&A, 373,
Whenthesecriteriaaremet,wecanstilllocateT (ρ)profiles L17
cn
indifferentpartsoftheNScore.If,however,wewishtoexplainall Kaminker A. D., Potekhin A. Y., Yakovlev D. G., Chabrier G.,
currentobservationsofisolatedNSswithoneandthesameT (ρ)- 2009,MNRAS,395,2257
cn
profile, we will be forced to push this profile deeper in the core KolomeitsevE.E.,Voskresensky D.N.,2008,Phys.Rev.C,77,
(Fig.2).Alternatively,wecouldemploybroaderprofilesbutwith 065808
density-dependent factorq(whichcanincreasewithinthecoreas LattimerJ.M.,PrakashM.,2007,Phys.Rep.,442,109
forsinglet-statepairing,e.g.,Kolomeitsev&Voskresensky2008). LattimerJ.M.,vanRiperK.A.,PrakashM.,PrakashM.,1994,
Thiswould shift the efficiency of theCPF process to higher ρ in ApJ,425,802
superfluidmatter. LeinsonL.B.,2001,Nucl.Phys.,A687,489
WehavetakenoneEOSandfocusedon1.65M neutronstar LeinsonL.B.,2008,Phys.Rev.C,78,015502
⊙
modelbutourbasicconclusionswillnotchangeforalargevariety LeinsonL.B.,2010,Phys.Rev.C,81,025501
ofEOSsandmassesM.Forinstance,takingthesameEOSwehave LeinsonL.B.,Pe´rezA.,2006,Phys.Lett.B,683,114
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
cn
foranyMfromthisrange. PageD.,GeppertU.,WeberF.,2006,Nucl.Phys.A,777,497
Our calculations indicate that the second temperature drop PageD., LattimerJ. M., Prakash M., Steiner A. W.,2004, ApJ,
lasts for a few tens of years and Cas A NS is at its active CPF 155,623
neutrinoemissionstage.Thesemodelswouldbeinconsistentwith PageD., LattimerJ. M., Prakash M., Steiner A. W.,2009, ApJ,
asharpstopofthetemperaturedeclineinafewyears,whichcan 707,1131
beverifiedwithfutureobservations. PageD.,PrakashM.,LattimerJ.M.,SteinerA.W.,2010, PRL,
AfterthesecondtemperaturedroptheCasANSisexpected submitted,arXiv:1011.6142v1
tobecomearathercoldslowlycoolingNS. Patnaude D. J., Vink J., Laming J. M., Fesen R. A., 2010, ApJ
Lett.,submitted,arXiv:1012.0243
PavlovG.G.,LunaG.J.M.,2009,ApJ,703,910
PavlovG.G.,ZavlinV.E.,AschenbachB.,Tru¨mperJ.,SanwalD.,
ACKNOWLEDGEMENTS
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.,
2008, inBassaC.,WangZ.,Cumming A.,KaspiV.,eds., AIP
REFERENCES
Conf. Proc. V. 983. 40 Years of Pulsars: Millisecond Pulsars,
Akmal A., Pandharipande V. R., Ravenhall D. G., 1998, Phys. MagnetarsandMore.Am.Inst.Phys.,Melville,NY,p.379
Rev.C,58,1804 Yakovlev D. G, Ho W. C. G., Shternin P. S., Heinke
CaraveoP.A.,DeLucaA.,MarelliM.,BignamiG.F.,RayP.S., C. O., Potekhin A. Y., 2011, MNRAS, doi:10.1111/j.1365-
Saz-ParkinsonP.M.,KanbachG.,2010,ApJ,725,L6 2966.2010.17827.x,arXiv:1010.1154
(cid:13)c 2010RAS,MNRAS000,1–6
6 P.S. Shterninetal.
YakovlevD.G.,KaminkerA.D.,GnedinO.Y.,HaenselP.,2001,
Phys.Rep.,354,1
YakovlevD.G.,PethickC.J.,2004,ARA&A,42,169
(cid:13)c 2010RAS,MNRAS000,1–6