Study of measured pulsar masses and their possible conclusions

0.22 MB·English

by  C. M. Zhang

Astronomy&Astrophysicsmanuscriptno.
(willbeinsertedbyhandlater)
Study of measured pulsar masses and their possible conclusions
C.M.Zhang1,J.Wang1,Y.H.Zhao1,H.X.Yin2,L.M.Song3,D.P.Menezes4
D.T.Wickramasinghe5,L.Ferrario5,andP.Chardonnet6
1 1 NationalAstronomicalObservatories,ChineseAcademyofSciences,Beijing100012,China,
1 e-mail:[email protected]
0 2 SchoolofSpaceScienceandPhysics,ShandongUniversityatWeihai,Weihai264209,China
2
3 AstronomicalInstitute,InstituteofHighEnergyPhysics,ChineseAcademyofSciences,Beijing100039,China
n
a
J 4 DepartmentdeF´ısica,CFM,UniversidadeFederaldeSantaCatarinaFloriano´polis,SC,CP.476,CEP88.040-900,Brazil

9
2 5 MathematicalSciencesInstitute,TheAustralianNationalUniversity,CanberraACT0200,Australia

] 6 Lapth-Lapp,UniversitdeSavoie,B.P.110,74941-Annecy-le-VieuxCedex,France
E
H
thedateofreceiptandacceptanceshouldbeinsertedlater
.
h
p Abstract. Westudythestatisticsof61measuredmassesofneutronstars(NSs)inbinarypulsarsystems,including18double
- NS (DNS) systems, 26 radio pulsars (10 in our Galaxy) with white dwarf (WD) companions, 3 NSs with main-sequence
o companions,13NSsinX-raybinaries,andoneundeterminedsystem.Wederiveameanvalueof M =1.46±0.30M⊙.When
r
t the46NSswithmeasuredspinperiodsaredividedintotwogroupsat20milliseconds,i.e.,themillisecondpulsar(MSP)group
as andothers,wefindthattheirmassaveragesare,respectively,M=1.57±0.35M⊙andM=1.37±0.23M⊙.Intheframeworkof
[ thepulsarrecyclinghypothesis,thissuggeststhatanaccretionofapproximately∼0.2M⊙issufficienttospinupaneutronstar
andplaceitinthemillisecondpulsargroup.Basedontheseestimates,anapproximateempiricalrelationbetweentheaccreting

4 mass(∆M)ofrecycledpulsaranditsspinperiodisproposedas∆M = 0.43(M⊙)(P/1ms)−2/3.IfwefocusonlyontheDNS,
v the mass average of all 18 DNSs is 1.32±0.14M⊙, and the mass averages of the recycled DNSsand the non-recycled NS
9
2 companionsare,respectively,1.38±0.12M⊙and1.25±0.13M⊙.Thisisconsistentwiththehypothesisthatthemassesofboth
4 NSsinDNSsystemhavebeenaffectedbyaccretion.ThemassaverageofMSPsishigherthantheChandrasekharlimit1.44M⊙,
whichmayimplythatmostofbinaryMSPsformviathestandardscenariobyaccretionrecycling.Ifweweretoassumethatthe
5
. massofaMSPformedbytheaccretioninducedcollapse(AIC)ofawhitedwarfmustbelessthan1.35M⊙,thentheportionof
0
thebinaryMSPsinvolvedintheAICswouldnotbehigherthan20%,whichimposesaconstraintontheAICoriginofMSPs.
1
Withaccretingmassfromthecompanion,thenuclearmattercompositionofMSPmayexperienceatransitionfromthe’soft’
0
equationofstate(EOS)toa’stiff’EOSorevenneutrontoquarkmatter.
1
:
v Keywords.stars:binaries:close–stars:pulsars:general–stars:fundamentalparameters–stars:neutron
i
X
r
a 1. Introduction nuclearfuel,astarundergoesasupernova(SN)explosion,and
the central region of the star collapses under gravity to form
Massisoneoftheimportantparametersofaneutronstar(NS),
a NS in the central supernova remnant (SNR) (Haensel et al.
from which we can infer the stellar evolution of its progeni-
2007). Hence, the NS mass statistics help the astronomers to
tor, the nuclear matter composition of a compact object (e.g.
infer the properties of its progenitor star, and its links to SN
Haenseletal.2007)oritsequationofstate(EOS),andstrength
and SNR. However,unlike the otherNS parameters,e.g. spin
ofgravitationalfieldiftheNSradiusisknown.Inotherwords,
period and magnetic field, NS mass is only measured in the
theprecisemassmeasurementscanprovidesignificanttestsof
binarysystem(e.g.Freire2008;Lorimer2008;Lyne&Smith
studiesofstellarevolution,nuclearphysicsofsuperdensemat-
2005).Therefore,thestatisticsofthemeasuredNSmassesmay
ter,andEinstein’sgeneralrelativityinthestronggravityregime
provide information about the NS accretion history in the bi-
(Lattimer & Prakash 2004, 2007; Kramer & Stairs 2008), as
naryphases(e.g.Stairs2004;Manchester2004;Bhattacharya
wellasinsightintobinaryevolutionsinceNSmassesaremea-
&vandenHeuvel1991).
suredinbinarysystems.
A NS is one of the possible ends for a massive star with An accurate measurement of a NS mass in a pulsar bi-
massgreaterthan∼4-8M⊙.Afterhavingfinishedburningthe nary system needs five relativistic post-Keplerian parameters,
2 C.M.Zhangetal.:Studyofmeasuredpulsarmassesandtheirpossibleconclusions
e.g., the periastron advance, time dilation, orbital shrinking
rate,and Shapirodelays,whichcan in principlebe measured.
AlloftheserelativisticparametersplaceconstraintsontheNS
masses, andwhenthree aremeasured,anaccuratedetermina-
XRB(13)
t2pi0roe0nc4ios,fe2lNy0S0i8nmaadbso,sue2bs0l0be9enc).eoumTtrheosenp-NostsSasribm(lDeasN(seeS.sg).hsLyaosvrteiemmbeser,e2ns0u0mc8he;aaFssruertiherdee 4SCLVH42XC SHVUMUAMeTaeeyE3gl1xE nr1TCaC91 8 8X EJ X5 5XJ X2X21X- C3-2-1J20-28-3-811A4 -1-0 1-332 R 5897032./01 -42 00 -S53.1086-9 5228415C5630
firstdiscoveredpulsarPSRB1913+16(Hulse&Taylor1975; DNS (18) JJ11581181+-14793064
Taylor&Weisberg1982)anddoublepulsarsystemPSRJ0737- J1829+2456
B1534+12
3039 (Burgay et al. 2004; Lyne et al. 2004; Kramer & Stairs B1913+16
B2127+11
2008), because the eccentric orbits of both systems provide J0737-3039
J1756-2251
well-measuredrelativisticparameters.UnlikeDNSs,massesof J1906+0746
mtthhiealitlrinsbeoicrnomanradylloyprubnlisotasrssaurffi(eMcsoiSePncsitr)creaulrlaeatrinv(oiostrtieocafsesyffuectcohtsldoecwtaenremcbcieenneut,sreiscdinitcytoe) NSWD(16) JJJJJJJBJBJJBJJJ0001111112011112467001789040788332514410013230507112513499738253-+++--+--+-++-++446234011502000475577770837403961041410004233 5958452777583
provideextraequationstosolvethemasses(Freire2000;Freire
emteaals.u2r0e0d4w).itThhlearrgefeoerrer,otrhse,smucahssaessPoSfRMJS0P51s4yCst4e0m0s2Aare(Forfetierne GCNS(10) BBBJJJJJJJ1110111001988577700510214442211244888116---------+522422277091400002225250222IH B8422111 ACABIJ((T Teerr 5 5 I )J)
etal.2004),exceptincasesofhigheccentricity.Theobserva- MSNS(3) JJ01074450--75331490
tions of relativistic parameters in pulsar binary systems have uncertain(1) JJ11970533+-20234207
presented the first application of general relativity and pro-
videdthemostwidelyavailablelaboratoriesfortestingtheories 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2
of gravitation (e.g. Hulse & Taylor 1975; Taylor & Weisberg List of 61 Neutron Star Masses (M )
1982;Weisberg& Taylor 2003;Thorsettetal. 1993;Stairs et
al.2002).
Fig.1.Listof61measuredNSmassesinthedifferenttypesof
Mass measurements are also possible in X-ray binaries,
NSbinarysystems.Theirdetailsandreferencescanbeseenin
where a neutron star X-ray pulsar and an optical companion
Table 1-3.Verticalline M=1.4M⊙ delineatesthe mass mean
reside.CarefulmonitoringofthecyclicalDopplershiftsofthe
valueinferredfromGaussianfitting.
pulse periodandDopplershifts of the spectralfeaturesof the
opticalcompanioncanbeusedtodeterminetheorbitalperiod
as well as the radial velocity, which provide/infer the mass
function of the system. Both masses are known when the in-
25
clinationangleofaneclipsingbinarysystemcanbemeasured
(e.g. van Kerkwijket al. 1995;Jonker et al. 2003).The accu-
20
racy of this method is not so high as that of measuring DNS
mass, usually being affected by an error of about ∼ 10% or
more(seeTable1). er15
b
Thorsett and Chakrabarty (TC99) presented the results of um
a statistical study of 19 NS binary systems, and obtained a N10
Gaussian distributionof massaround1.35M⊙, with a narrow
deviation of 0.04 M⊙. The sample has increased significantly 5
since then. There are now about61 NSs with measured (esti-
mated)massesinvarioustypesofbinarysystems. 0
0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8
Inthispaper,wepresentastatisticalanalysisofthemasses M(M )
ofNSsinbinariesusingthecurrentdataset,andinvestigatein
particular the pulsar recycling hypothesis.We present a com- Fig.2.Histogramof61measuredNSmasses. A Gaussianfit-
pilationofallNSmassobservationsin Sect.2. InSect. 3,we tingcurveissuperimposedonthehistogramplot,withthemass
studytherelationbetweentheNSmassanditsspinperiod.Our meanvalue1.40M⊙ andstandarddeviation0.18M⊙.
conclusionsaregiveninSect.4.
Table 2, we first list the 18 DNSs that have masses with high
2. Statisticsofpulsarmasses accuracies, then 16 radio pulsars with WD companions,3 ra-
dio pulsars with the main-sequence star companionsand one
2.1.NSmassdistribution
uncertainsystem.InTable3,wealsolistthe10Galacticradio
In Tables 1-3, we list all known NSs with measuredand esti- pulsarswithWDcompanions.
mated masses, including their binary parameters when avail-
able.InTable1,welistthe13systemsconsistingofX-rayNSs To illustrate all NS mass distributions, a histogram of NS
withloworhighmasspost-main-sequencestarcompanions.In massesisplottedinFig.2,whereafittedGaussiandistribution
C.M.Zhangetal.:Studyofmeasuredpulsarmassesandtheirpossibleconclusions 3
functionis shownwith a mean mass of 1.40M⊙ and a small
uncertainty of 0.19 M⊙, that is slightly higher than the previ-
3.4
ous statistical mean value of 1.35± 0.04M⊙by TC99. About 3.2
∼67%(∼90%)ofallNSsarewithintherangeof1.2M⊙–1.6M⊙ 3.0 HMXB/XB
2.8
(1.0M⊙– 1.8M⊙). The NSs with masses over 1.8M⊙ repre- 2.6 LMXB
sentabout∼10%ofallsamples.Themaximumandminimum 2.4 DNS
v2a0l2u1eBs)oafnNdS0.m97as±se0s.2a4reM, r⊙e(s2pAec1ti8v2e2ly-3,721.7)4. ± 0.2 M⊙(J1748- M(M) 122...802 NNGSSCWMNSSD
ItisinterestingtoinvestigatewhythepresentNSmassav- 1.6
erage is higher than that measured ten years ago. The data of 1.4
1.2
NS masses by TC99 are based on the DNSs, which are gen-
1.0
erally less than the canonical value of 1.4 M⊙. The present 0.8
NSmassdataincludesalltypesofbinarysystemswithdiffer- 0.6 MSP
0.4
entevolutionaryhistories.Inparticular,therearemanyNSWD 1 10 100 1000 10000 100000
systems,whichhavesignificantlyhighNSmassesasshownin Ps(ms)
Table1-3.
ItisgenerallyassumedthatMSPsareformedfromthespin- Fig.3. Diagram of mass versus spin period for 39 NSs. The
up of a magneticneutronstar caused by accretionin a binary horizontallineM=1M⊙(3.2M⊙)standsforthemeasuredmin-
system(e.g.Alparetal.1982;Bhattacharya&vandenHeuvel imummass(theoreticalmaximummass,seeRhoades&Ruffini
1991;vandenHeuvel2004).Iftheneutronstarswerebornwith 1974).Theverticallineat20msseparatesthesamplesintotwo
thestandardpulsartypefields∼ 1012 G, ithastobe assumed groups,MSP(< 20ms)andlessrecycledNS(> 20ms).Itis
that the field decays to ∼ 108−9 G by accretion as well. The found that the mass averages of two groups are, respectively,
MSPs are understood to be evolutionarily linked to the long- 1.57±0.35M⊙ and1.37±0.23M⊙.Thesolidcurvestandsfor
lived LMXBs (e.g. van den Heuvel 2004). The evidence of a therelationbetweenaccretionmassandspinperiodofrecycled
MSPthatislinkedtoanLMXBwasfoundwiththediscovery pulsarasdescribedinEq.(1)and(2),M =1.40+0.43(Ps)−2/3
ms
ofthefirstaccretion-poweredX-raypulsarSAXJ1808.4-3658 (M⊙).
(spin frequency of 401 Hz, Wijnands & van der Klis 1998).
A consequence of the re-cycling hypothesis for the origin of byB∼∆M−7/4,whichinfersarelationas∆M ∼ P−3/2.Onthe
s
MSPs is that the mass of a MSP should be higher than that
basisoftheaboveestimatesandarguments,weproposeanem-
of non-recycled pulsar. It has long been believed that a MSP
pirical relation between the accreting mass (∆M) of recycled
should possess a higher mass than the canonical value of 1.4
pulsaranditsspinperiodas
M⊙, e.g. ∼ 1.8M⊙, because of the significant amount of ac-
cretion(e.g.vandenHeuvel&Bitzaraki1995ab;Burderietal. ∆M = M (P/ms)−2/3 , (1)
a
1999;Stella&Vietri1999).Thus,ifthisrelationbetweenMSP
where M is a characteristic accretion mass when a pulsar is
massandaccretionexists,wemayexpecttoseeitinNSmass a
spun-up to one millisecond. The mass of recycled pulsar (M)
statisticstakenoverdifferentspinperiodranges.
increaseswithaccretionandisroughlyexpressedas,
WefirstdividedallNSsamplesintotwogroups,thosewith
spin periods longer than and equal to or shorter than 20 ms.
M = M +∆M , (2)
0
The20msdividinglinewastakensomewhatarbitrarilyasthe
periodbelowwhichapulsarwouldbeclassifiedasaMSP.We whereM isthemassofNSatbirthwhileNSspinperiodisas
0
findthatthemassaveragesofMSPsandlessrecycledNSsare longasthoseofHMXBs.
1.57±0.35M⊙and1.37±0.23M⊙,respectively.Theexpected ExploitingEq.(1)and(2)tofittheNSmassandspinperiod
trendisthereforeclearlyseeninthedata.Theabovetrendcan data as shown in Fig.3, we find that M0 = 1.40 ± 0.07 M⊙
alsobeseeninFig.3.Themasssystematicallydecreaseswith and Ma = 0.43± 0.23 M⊙. Because of the broadness of the
the spin period,or alternatively,spin-up is associated with an initial NS mass distribution and the large errors in measuring
increaseinmassofNS. NSmass,thefittingCODisaslowas0.07.
By dividing the pulsars into three groups, the mass av-
erages are, respectively, M=1.57 ±0.35 M⊙(P < 20 ms), 2.2.SpecialDNSmassspectrum
M=1.38±0.23M⊙(20ms < P < 1000ms),and M=1.36±0.24
M⊙(P > 1000 ms). Here, we note that the average mass of The mass average of all eighteen DNSs in nine systems is
the recycled pulsar increases with the stellar spin-up. In gen- 1.32±0.14M⊙, whichissystematicallylowerthanthatofthe
eral,the spinperiodsandmagneticfields(B)of recycledpul- less recycled NS (M=1.37±0.23 M⊙). The mass averages of
sarsarejustbelowthespin-uplineinB-P diagramofpulsars the nine recycled and non-recycled DNSs are, respectively,
s
(e.g. Bhattacharya & van den Heuvel 1991; Lorimer 2008), 1.38±0.12M⊙and1.25±0.13M⊙,wherethemassofrecycled
where the B-P correlation is given by P ∼ B6/7 from the NS is generally higher than that of non-recycled one, which
s s
accretion-inducedmagneticevolutionmodelforrecycledpul- maybetheindicationthateithertheaccretioninducesthemass
sars(Zhang&Kojima2006),themagneticfieldandaccretion increasefortherecycledNSortheevolutionofDNSprogen-
mass correlation for recycled pulsars is given approximately itors makes the mass of non-recycled NS low. However, we
4 C.M.Zhangetal.:Studyofmeasuredpulsarmassesandtheirpossibleconclusions
nificantphasesofaccretion.Nevertheless,theAICsystemsare
2.0
likelyonaveragetohaveaccretedlessmass.
DNS mass ratio - Orbit period
1.8
In Fig.3, four of twenty-two BMSPs have masses of less
1.6 than 1.35 M⊙, which are less than Chandrasekhar mass limit
1.4 1.44 M⊙, that may be candidate AIC MSPs. Of course, for a
1.2 NS with initial mass of 1.1 M⊙, a recycled process will also
BM workbyaccreting0.25M⊙ fromitscompanion.Ifweassume
AM/1.0 the four MSPs to be the candidate AICs, then a constrainton
0.8 the productionof AIC can be derivedthat no more than 20%
0.6 (∼4/22)ofBMSPsareinvolvedintheAICprocesses.
0.4
0.2 2.4.Pulsar:neutronstarorquarkstar?
0.0
0.1 1 10 From the updated measured pulsar masses, we have insuffi-
Porb(day) cient informationto clearly infer the nuclearmatter composi-
Fig.4. Mass ratio versusorbitalperioddiagramfor 9 pairs of tionsinsidethecentralcompactobjects,sincewerequiremea-
DNSs,wheretheverticalaxisMA/MBrepresentsthemassratio surements of the stellar radii to determine the nuclear matter
oftherecycledNStonon-recycledone. properties given in Fig.5, a mass-radius plot of compact ob-
ject.Theoretically,pulsarsmayconsistofhadronicmatteronly
(Menezes & Provideˆncia 2004a), hadronic and quark matter
cannot derive how much mass is accreted into these systems,
(hybrid stars) either bearing or not a mixed phase (Menezes
sincefortwosystems(J1811-1736andJ1518+4904)bothNS
& Provideˆncia 2004b; Panda, Menezes & Provideˆncia 2004;
pairmasseshavelargedifferenceswithlargeerrors,e.g.,PSR
J1811-1736with1.5−+00..142M⊙ and1.06+−00..415M⊙(seeTable2). T(Matesunmezie,sY,aPsruohviirdaeˆ&nciVao&skrMeseelnrosskey22000063a);oIrvqaunaorvkemtaalt.te2r0o0n5l)y.
ThemassratiosofsevenDNSsareclosetounityandthose
All calculations dependon choosing of appropriateequations
of the other two with longer orbital periods are higher than
of state based on nuclear physics and thermodynamics re-
unity, as shown in Fig.4. It is too early to draw conclusions
quirements,whichenterasinputtotheTolman-Oppenheimer-
aboutanyratio gap,separatedby the orbitalperiodat 2 days,
Volkoff equations. The output are a family of stars, for in-
sincefewerDNSsamplesarenotsufficienttoinferawarranty
stance, with certain gravitational and baryonic masses, radii,
statistical result. The cause of the systematically lower mass
and central energy. The maximum gravitational mass and the
values of DNS systems than the typical 1.4 M⊙ remains un-
associatedradiusareimportantconstraintsontheequationsof
known.WeproposethattheevolutionoftheDNSprogenitors
state.Generallyspeaking,thehadronicmatterequationofstate
mayinfluenceorinteracteachother,whichmayberesponsible
(EOS) produces maximum masses higher than hybrid stars,
fortheparticularmassspectrumdistributionsshownabove.
which in turn, give slightly higher masses than quark stars.
Radii are usually smaller for quark stars. However, these re-
sultsareverymodeldependentascaneasilybeseenfromthe
2.3.OnAICmechanismforMSPformation referencesmentionedabove.
Therefore, based on the present results we cannot deter-
Although we have focussed on the standard formation model
minereliablywhetherthepulsarisaNSoraquarkstar(QS)in
(recycled NS) of MSPs which involves accretion, associated
thispaper.However,wenotethattheusageoftheterminology
fielddecayandspinup,othermodelsarepossible(e.g.Kiziltan
NS to denote the central object of a pulsar is traditional and
& Thorsett 2009abc). These include the often discussed pos-
doesnotimplyanydetailofitsnuclearmattercomposition.
sibility of the accretion induced collapse (AIC) of a white
dwarfontoa neutronstar (e.g.vandenHeuvel1994;Verbunt Theoretically,theNSmaximummasslimitof3.2M⊙ was
1990; Fryer et al. 1999; van Paradijs et al. 1997; Ferrario & proposed by Rhoades & Ruffini (1974).The measured pulsar
Wickramasinghe2007).In this model,a white dwarf of mass massesarethenfarbelowthislimit,whichwouldexcludemany
>1.2M⊙ consistingO,Ne,andMg(e.g.Nomoto&Yamaoka knownEOSmodelsforthebehaviorofmatteratsupra-nuclear
1992)collapsesontoawhitedwarfbecauseoftheaccretionof densities.ThepossibleexistenceofhighmassNSobservations
matterduringthecourseofbinaryevolution,whereaNSisas- favors a stiff EOS (e.g. Ozel 2006; on the NS stiffness see
sumedtobebornasweaklymagneticandrapidlyspinningas Stergioulas2003).The”soft”EOSmodelspredictlowerpres-
thoseobservedMSPs. suresforagivendensity,correspondingtoalessmassivestar,
Hurley et al. (2010) presented a comparative study of the e.g.<1.5M⊙.RecycledNSsinbinarysystemsshouldfindthat
expected propertiesof binary MSPs (BMSPs) born by means thestiffnessincreases,andthatthephasetransitionofnuclear
ofNSrecyclingandAIC.Theyconcludedthatbothprocesses mattermayoccur(e.g.Glendenning&Weber 2001;Menezes
produce significant populations of BMSPs that could poten- etal.2006b).
tially beidentifiedwithBMSPs. Furthermore,priortothe de- ThefractionofNSswithmassesoutsiderange1.2M⊙-1.8
tachedBMSPphaseattheendofbinaryevolution,boththeNS M⊙ islessthan20%,whichwouldprovideusefulinformation
recyclingand AIC binary systems may have experiencedsig- abouttheirprogenitorpropertiesinmostcases.
C.M.Zhangetal.:Studyofmeasuredpulsarmassesandtheirpossibleconclusions 5
Table1.ParametersofneutronstarsinX-raybinaries
System M(M⊙) Mc(M⊙) Porb(d) Pspin(ms) eccentricity type Refs
4U1538-52 1.06+0.41 16.4+5.2 3.73 5.28×105 0.08 HMXB X1
−0.34 −4.0
SMCX-1 1.05±0.09 15.5±1.5 3.89 708 <4×10−5 HMXB X2
CenX-3 1.24±0.24 19.7±4.3 2.09 4814 <8×10−4 HMXB X3
LMCX-4 1.31±0.14 15.6±1.8 1.41 1.35×104 <0.01 HMXB X2
VelaX-1 1.88±0.13 23.1±0.2 8.96 2.83×105 0.09 HMXB X4
1.86±0.16 23.8±0.2 8.96 2.83×105 0.09 HMXB X4
4U1700−37∗ 2.44±0.27 58±11 3.41 No 0.2 HMXB X5
HerX-1 1.5±0.3 2.3±0.3 1.70 1240 <3×10−4 XB X6
4U1820-30 1.29+0.19 ≤0.106 0.08 6.9×105 No XB X7
−0.07
2A1822-371 0.97±0.24 0.33±0.05 0.23 590 <0.03 LMXB X8
XTEJ2123-058 1.46+0.30 0.53+0.28 0.25 3.9 No LMXB X9
−0.39 −0.39
CygX-2 1.78±0.23 0.60±0.13 9.84 No 0.0 LMXB X10
1.5±0.3 0.63±0.16 9.84 No 0.0 LMXB X10
V395CAR/2S0921C630 1.44±0.10 0.35±0.03 9.02 No No LMXB X11
SaxJ1808.4-3658 <1.4 <0.06 0.08 2.49 <0.0005 LMXB X12
HETEJ1900.1-2455 <2.4 <0.085 0.06 2.65 <0.005 LMXB X13
*Thecompactobjectmaybeablackhole(Lattimer&Prakash2007).LMXB—Low-massX-raybinary,HMXB—High-massX-raybinary.
X1—vanKerkwijketal.1995(M, M ,P ,eccentricity);Robbaetal.2001(P ).X2—vanKerkwijketal.1995(P ,eccentricity);van
c orb s orb
derMeeretal.2005(M, M );vanderMeeretal.2007(P ).X3—vanKerkwijketal.1995;Ashetal.1999(P ,eccentricity);vander
c s orb
Meeretal.2005(M,Mc);vanderMeeretal.2007(Ps).X4—Quaintrelletal.2003(M=2.27,1.88M⊙,Mc,Porb,eccentricity,Ps);Barzivet
al.2001(M=1.86M⊙).X5—Clarketal.2002(M, Mc);Hammerschlag-Hensbergeetal.2003(Porb,eccentricity).X6—Chengetal.1995
(P ,eccentricity);Reynoldsetal.1997(M,M );Martinetal.2001(P );vanderMeeretal.(2007)(P ).X7—Wangetal.2010(M,M ,
orb c s s c
eccentricity,P );Shaposhnikovetal.2004(M,P );Dibetal.2004(P ).X8—Jonker&vanderKlis2001(P ,eccentricity,P );Jonker
s orb orb orb s
etal.2003(M,M ).X9—Tomsicketal.1999(P );Tomsicketal.2002(M,M ,P ,eccentricity).X10—Cowley,Crampton&Hutchings
c s c orb
1979(P );Orosz&Kuulkers1999(M, M , P ,eccentricity);Elebert,Callanan&Torres,etal.2009a. X11—Steeghs&Jonker 1996;
s c orb
2007(1.44M⊙);Shahbaz,&Watson2007(1.370.13M⊙).X12—Elebertetal.2009b;Chakrabarty&Morgan1998;Jain,Dutta&Paul
(P ).X13—Elebertetal.2008;Kaaret,Morgan&Vanderspeketal.2006(P ).
orb orb
3. Summaryandconclusions
3.5
m=3.2
)mass3.0 Rs Casuality siWnugerehcmoavennectlssutsuoidfoinpesdulatshnaedrsmitmaatpsislsiteciscaatiilnodnbissintarairrbeyuotsbiyotsantisenmoefdst:,haenudptdhaetefdolmloewa--
s (solar 22..05 UU M Stiff EOS mas(s1a)vFeorarg6e1orfeMlia=b1ly.4m6±ea0s.3urMed⊙(iesstoimbtaatiende)d,pwulhsiacrhmisashsiegsh,ear
Mas thanfound(1.35M⊙)in1999byTC99.
al 1.5 (2)Ourstatisticsindicatethatthemassaverageofthemore
n Soft EOS
vitatio1.0 hraigphidelrythraontatthinagtoMftShPesle(sMsr=ec1y.5c7le±d0o.3n5esM(M⊙=f1o.r37P±s<02.203mMs⊙)foisr
Gra0.5 SS1 Ps> 20 ms). This implies that the NS masses increase in the
AFO
FPS accretingspin-upbinarysystems,whileaMSPaccretingabout
0.0 ∼0.2 M⊙ fromits companionappearsto be present. The rela-
0 5 10 15 20 25 30
tion between the accretion mass (∆M) of recycled pulsar and
Fig.5.NSmassversusraRdaiudisups l(okmt.)TheEOScurvesandstraight itsspinperiodisproposedtobe∆M =0.43(M⊙)(P/1ms)−2/3.
(3)Thestatisticsof18DNSsindicatethattheirmassaver-
linesfollowthesamemeaningsasthoseofLattimer&Prakash
(2004,2007) and Miller (2002), where SS1 and AFO stand age M=1.32±0.14M⊙is systematically lower than the typical
mass value of the less recycled PSRs, which seems to imply
for EOSs of the quark matters. For most NSs with measured
that the mass formation or evolution history of DNS should
masses of 1.0-2.0 M⊙, their nuclear matter compositions are
differfromthoseoftheotherbinarysystems.
difficult to distinguish as those of either neutrons or quarks,
(4)Apartfromthestandardrecycledprocessesforthefor-
since NS radii cannotbe precisely measured in general using
mation of MSPs, the mechanism by AIC of accreting white
present-dayobservations(e.g.Truemperetal.2004).
dwarfsisinvestigatedbytheMSPmassdistribution,sinceAIC
needsthemassofMSPtobelessthantheChandrasehkarmass
limit1.44M⊙.IftheAICexplodesafteraccreting∼0.1M⊙ of
crust,thenfewerthan20%ofBMSPsareinferredtobeinthe
AIC processes,whichprovidea quantitativeconstraintonthe
formationratesofAICMSPs.
6 C.M.Zhangetal.:Studyofmeasuredpulsarmassesandtheirpossibleconclusions
Table2.Parametersofradiobinarypulsars
System M(M⊙) Mc(M⊙) Porb(d) Pspin(ms) eccentricity type Refs
J1518+4904 1.56+0.20 1.05+1.21 8.63 40.9 0.249 DNS R1
−1.20 −0.14
J1811-1736 1.5+0.12 1.06+0.45 18.8 104.2 0.828 DNS R2
−0.4 −0.1
J1829+2456 1.15+0.1 1.35+0.46 1.176 41.0 0.139 DNS R3
−0.25 −0.15
B1534+12 1.33±0.0020 1.35±0.0020 0.421 37.9 0.274 DNS R4
B1913+16 1.44±0.0006 1.39±0.0006 0.323 59.0 0.617 DNS R5
B2127+11C 1.35±0.080 1.36±0.080 0.335 30.5 0.681 DNS R6
J0737-3039A(B) 1.34±0.010 1.25±0.010 0.102 22.7(2773) 0.088 DNS R7
J1756-2251 1.40+0.04 1.18+0.06 0.320 28.5 0.181 DNS R8
−0.06 −0.04
J1906+0746@ 1.25 1.37 0.166 144 0.085 DNS R9
J0437-4715 1.58±0.18 0.24±0.017 5.74 5.76 1.9×10−5 NSWD R10
J0621+1002 1.70+0.59(+0.32) 0.97+0.43(+0.27) 8.32 28.9 0.003 NSWD R11
−0.63 −0.29 −0.24 −0.15
J0751+1807 1.26±0.14 0.19±0.03 0.263 3.48 3×10−6 NSWD R12
2.1+0.4(corrected) 0.19±0.03 0.263 3.48 3×10−6 NSWD R12
−0.5
J1012+5307 1.7±1.0 0.16±0.02 0.605 5.26 <10−6 NSWD R13
1.64±0.22 0.16±0.02 0.605 5.26 <10−6 NSWD R13
J1045-4509 <1.48 0.13 4.08 7.47 <10−5 NSWD R14
J1141-6545 1.27±0.01 1.02±0.01 0.198 394 0.172 NSWD R15
1.3±0.02 0.986±0.02 0.198 394 0.172 NSWD R15
J1713+0747 1.53+0.08(1.6±0.24) 0.33±0.04 67.83 4.75 7.5×10−5 NSWD R16
−0.06
B1802-07 1.26+0.15 0.36+0.67 2.62 23.1 0.212 NSWD R17
−0.67 −0.15
J1804-2718 <1.73 0.2 11.1 9.34 4×10−5 NSWD R18
B1855+09 1.58+0.10 0.27+0.010 12.33 5.36 2.2×10−5 NSWD R19
−0.13 −0.014
J1909-3744 1.44±0.024 0.20±0.0022 1.53 2.95 10−7 NSWD R20
J2019+2425 <1.51 0.32−0.35 76.5 3.93 1.1×10−4 NSWD R21
B2303+46 1.34±0.10 1.3±0.10 12.34 1066 0.658 NSWD R22
J0437-4715 1.76±0.20 0.25±0.018 5.74 5.76 1.918×10−5 NSWD R23
J1023+0038 1.0-3.0 0.14-0.42 0.198 1.69 ≤2×10−5 NSWD R24
J1738+0333 1.6±0.2 0.2 0.354 5.85 1.1×10−6 NSWD R26
J0045-7319 1.58±0.34 8.8±1.8 51.17 926 0.808 NSMS R27
J1740-5340 1.53±0.19 >0.18 1.35 3.65 <10−4 NSMS R28
J1903+0327 1.67±0.01 1.05 95.17 2.15 0.437 NSMS R29
J1753-2240 ∼1.25 ∼1.25 13.64 95.1 0.304 uncertain U
DNS—doubleneutronstar;NSWD—pulsar-whitedwarfbinary; NSMS—neutronstar/main-sequence binary; @ TherecycledNSshouldbe
thecompanionbecauseofthestrongmagneticfieldofPSRJ1906+0746∼1012G.R1—Niceetal.1995(P ,P ,eccentricity);TC99(M,M );
orb s c
Janssenetal.2008(mp < 1.17andmc > 1.55M⊙).R2—Lyneetal.2001(Porb,Ps,eccentricity);Lorimeretal.2008(M,Mc);Breton,2009
(M,M ). R3—Champion et al. 2004 (P ,P , eccentricity); Lorimer et al. 2008 (M,M ); Breton et al. 2009 (M,M ). R4—Wolszczan 1991
c orb s c c
(P ,P ,eccentricity);Stairsetal.2002(M,M ).R5—Hulse&Taylor1975 (P ,P ,eccentricity); Weisberg&Taylor2003(M,M ).R6—
orb s c orb s c
Andersonetal.1990(P ,P ,eccentricity);Jacoby,Cameron&Jenetetal.2006;TC99(M,M ).R7—Burgayetal.2003(P ,P ,eccentricity);
orb s c orb s
Lyneetal.2004(M,M ).R8—Manchesteretal.2001(P ,P ,eccentricity);Faulkneretal.2005(M,M ).R9—Lorimer&Stairs2006(P ,
c orb s c orb
P ,eccentricity);Kasianetal.2007;Lorimeretal.2008(M,M );Bretonetal.2009(M,M ).R10—Johnstonetal.1993(P ,P ,eccentricity);
s c c orb s
vanStratenetal.2001(M,M ).R11—Camiloetal.1996(P ,P ,eccentricity);Splaveretal.2002(M,M ).R12—Lundgrenetal.1995(P ,
c orb s c orb
P ,eccentricity);Niceetal.2004(M,M );Niceetal.2005,Niceetal.2008(M,M ).R13—Nicastroetal.1995(P ,P ,eccentricity);van
s c c orb s
Kerkwijketal.1996,2005;Callananetal.1998;TC99(M,M ).R14—Bailesetal.1994(P ,P ,eccentricity);TC99(M,M ).R15—Kaspi
c orb s c
etal.2000(P ,P ,eccentricity);Burgayetal.2003(M,M );Bailesetal.2003;Bhat&Bailes,2008(M,M ).R16—Fosteretal.1993(P ,
orb s c c orb
P ,eccentricity);Splaveretal.2005(M,M ).R17—DAmicoetal.1993(P ,P ,eccentricity);TC99(M,M );Lorimeretal.2008(M,M );
s c orb s c c
Bretonetal.2009(M,M );Freire2000.R18—Lorimeretal.1996(P ,P ,eccentricity);TC99(M,M );Bretonetal.2009(M,M ).R19—
c orb s c c
Segelsteinetal.1986(P , P ,eccentricity);Nice,Splaver&Stairs2003(M,M ).R20—Jacobyetal.2003(P , P ,eccentricity);Jacoby
orb s c orb s
etal.2005(M,M ).R21—Niceetal.1993(P ,P ,eccentricity);Niceetal.2001(M,M ).R22—Deweyetal.1985(P ,P ,eccentricity);
c orb s c orb s
Kerkwijk&Kulkarni1999(M,M ).R23—Johnstonetal.1993(P ,P ,eccentricity);vanBeverenetal.2008(M,M ).R24—Archibaldetal.
c orb s c
2009(P ,P ,eccentricity,M,M ).R26—Jacoby,PhDthesis,(2004);FreirePhDthesis,2000.R27—Bell&Besselletal.1995(M,M );Kaspi,
orb s c c
Bailes&Manchesteretal.1996(P ,P ,eccentricity).R28—Kaluznyetal.2003(P ,M);D”Amicoetal.2001(P ,eccentricity,M ).R29—
orb s orb s c
TC99(P ,P ,eccentricity,M ).R29—Championetal.2008(P ,P ,eccentricity,M,M );Freireetal.2009.U—uncertaincompaniontype,
orb s c orb s c
Keithetal.2009ab(P ,P ,eccentricity,M,M ).
orb s c
(5) The nuclear matter compositions of the less massive maybepossible(Menezes2006b),whichwouldprovideclas-
DNSs and heavier MSPs may be different. During accretion, sificationsofthenuclearmatterinsideDNSsandMSPs.
thematterphasetransitionfromthe’soft’EOSto’stiff’EOS,
or even the matter transition between the neutron and quark Moreover, the newly measured mass 1.97± 0.04 M⊙of a
MSPPSRJ1614C2230withaspinperiodof3.15milliseconds
C.M.Zhangetal.:Studyofmeasuredpulsarmassesandtheirpossibleconclusions 7
Table3.ParametersofGalacticclusterpulsars
System M(M⊙) Mc(M⊙) Porb(d) Pspin(ms) eccentricity type Refs
J0024-7204I(B0021-72I) 1.44 0.15 0.23 3.49 6.3×10−5 GC G1
J0024-7204H(B0021-72H) 1.41+0.04 0.18+0.086 2.380 3.21 0.071 GC G1
−0.08 −0.016
J1518+0204B(B1516+02B) 2.08±0.19 >0.13 6.860 7.95 0.14 GC G2
J1911-5958A 1.40+0.16 0.18 0.837 3.48 <10−5 GC G2
−0.10
J1802-2124 1.21±0.1 >0.81 0.699 12.65 3.2×10−6 GC G3
J1824-2452C <1.367 >0.26 8.078 4.158 0.847 GC G4
J0514-4002A <1.52 >0.96 18.79 4.99 0.888 GC G5
J1748-2021B 2.74±0.2 >0.11 20.55 16.76 0.57 GC G6
J1748-2021I(Ter5I) 1.3±0.02 0.24 1.328 9.57 0.428 GC G7
J1748-2021J(Ter5J) 1.88+0.02 0.38 1.102 80.34 0.35 GC G7
−0.08
GC—Globularclusterpulsars.G1—Manchesteretal.1991;Freireetal.2003;Lorimeretal.2008.G2—Wolszczanetal.1989;Bassaet
al.2006;Cocozzaetal.2006;Freireetal.2007;Lorimeretal.2008;Freireetal.2008b.G3—Lorimeretal.2008;Lorimeretal.2008;
Faulkner et al. 2004; Ferdman etal. 2010 (1.24±0.11M⊙).G4—Ransom and Freire,2009. G5—Freire&Ransom 2007. G6—Freire&
Ransom,2008;Freireetal.2008a;Freire2009.G7—Ransometal.2005.
seemstohintthateitherMSPaccretesmoremassfromitscom- J. M., Camilo F., Kalogera V., Kim C., LorimerD. R. 2003,
panionor a highmass of pulsaris broughtin born(Demorest Nature,426,531
etal.2010). CamiloF.,NiceD.J.,ShraunerJ.A.,TaylorJ.H.1996,ApJ,
469,819
ChakrabartyD.&MorganE.H.1998,Nature,393,346
Acknowledgements
ChakrabartyD.,MorganE.H.,MunoM.P.,GallowayD.K.,
Wijnands R., van der Klis M., & Markwardt C. B. 2003,
This research has been supported by NSFC (10773017),
Nature,424,42
NBRPC (2009CB824800),and CNPq/Brazil. Thanks are due
Champion D. J., Lorimer D. R., McLaughlin M. A., et al.
tothediscussionswithP.C.Freire.Theauthorsareverygrate-
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