ULXs: Neutron Stars vs Black Holes

0.13 MB·

by  Andrew King

Mon.Not.R.Astron.Soc.000,1–4(2014) Printed18January2016 (MNLATEXstylefilev2.2)
ULXs: Neutron Stars vs Black Holes
Andrew King1,2 and Jean–Pierre Lasota3,4
1 Theoretical Astrophysics Group, Department of Physics & Astronomy, University of Leicester, LeicesterLE1 7RH, UK
6 2 Astronomical Institute Anton Pannekoek, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, Netherlands
1 3 Institut d’Astrophysique de Paris, CNRSet Sorbonne Universit´es, UPMC Paris 06, UMR 7095, 98bis Bd Arago, 75014 Paris, France
0 4 Nicolaus Copernicus Astronomical Center, Bartycka18, 00-716 Warsaw, Poland
2

n
a 18January2016
J

4
1 ABSTRACT
We consider ultraluminous X–ray sources (ULXs) where the accretor is a neutron

] star rather than a black hole. We show that the recently–discovered example (M82
E
X–2) fits naturally into the simple picture of ULXs as beamed X–ray sources fed at
H super–Eddington rates, provided that its magnetic field is weaker (≃ 1011G) than a
. new–born X–ray pulsar, as expected if there has been mass gain. Continuing accre-
h
p tion is likely to weakenthe field to the point that pulsing stops,and makethe system
- indistinguishable from a ULX containing a black hole. Accordingly we suggest that a
o
significantfractionofallULXsmayactuallycontainneutronstaraccretorsratherthan
r
t blackholes,reflectingtheneutron–starfractionamongtheirX–raybinaryprogenitors.
s Weemphasizethatneutron–starULXs arelikelytohavehigher apparentluminosities
a
[ than black hole ULXs for a given mass transfer rate, as their tighter beaming out-
weighstheirlowerEddingtonluminosities.Thisfurtherincreasesthelikelyproportion

1 of neutron–star accretors among all ULXs. Cygnus X–2 is probably a typical descen-
v
dantof neutron–starULXs, which may thereforeultimately end as millisecondpulsar
8
binaries with massive white dwarf companions.
3
7 Key words: accretion, accretion discs – binaries: close – X-rays: binaries – black
3
hole physics – neutron stars – pulsars: general
0
.
1
0
6
1 INTRODUCTION nosities which exceed the usual Eddington limit by factors
1
: (νB/ν)2. The effect is greatest for the strongest fields,
v Ultraluminous X–ray sources (ULXs) have apparent lumi- ∼as found in magnetars. In this picture M82 X–2 would evi-
i
X nositiesLabovetheEddingtonlimit forastandardstellar– dentlybecompletelydifferentfromallotherULXsfoundso
mass accretor (often taken as L & 1039ergs−1), but are far.
r
a notinthenucleioftheirhostgalaxies. Thesedefiningprop- In this paper we adopt a very different viewpoint, and
erties initially led to suggestions that their accretors were try to see if M82 X–2 instead fits naturally into a unified
black holes with masses higher than stellar, but below su- pictureapplyingtoall ULXs.Thisispromising, sincethere
permassive – called intermediate–mass black holes (IMBH: is a lot of evidence that the basic cause of the unusual be-
Colbert & Mushotzky 1999). It is now widely accepted in- haviourofULXsisasuper–Eddingtonmasssupply,andthis
steadthatmost–orperhapsall–ULXsarestandardX–ray isevidentlyperfectlypossibleforaneutronstaraccretor(see
binariesinunusualandshortlivedphases(Kinget al.2001). below). So we assume that for reasons discussed below, the
Perhaps because the required breach of the Eddington binarysuppliesmasstothevicinityoftheaccretorinULXs
limit is then minimised, many authors have assumed that (including M82 X–2) at a rate significantly above thevalue
theaccretorinULXsisalwaysablackhole.Butinastriking M˙Edd that would produce the Eddington luminosity LEdd
recent paper Bachetti et al. (2014) find a ULX (M82 X–2) if all of it could be accreted. Much of this mass is instead
withL 1.8 1040ergs−1(about100timesEddington)and driven off by radiation pressure, producing geometrical col-
a coher≃ent p×eriodicity P = 1.37 s, which they interpret as limation or beaming of most of the emission (see Section 2
thespinperiodofanaccretingmagneticneutronstar(X–ray below). As a result we generally detect only ULXs beamed
pulsar).Onelineofexplanationofthisresult(cfTong2015; towards us. Multiplying their fluxes by 4πD2, where D is
Ek¸si et al.2015;Dall’Osso et al.2015)usesthefactthatthe the source distance, then overestimates the intrinsic source
electron–scatteringcross–sectionissignificantlyreduced(by luminosity by a factor 1/b 1, where b=Ω/4π 1 is the
≫ ≪
afactor( (ν/ν )2)forfrequenciesν belowcyclotron(ν )) beaming factor (Ω is thetrue solid angle of emission).
B B
∼
for certain polarizations and field directions, allowing lumi- In this picture ULX behaviour requires only that the
(cid:13)c 2014RAS
2 Andrew King and Jean–Pierre Lasota
mcraetsosrsudpefipnlyinrgatMe˙Eisdd≫.IMt˙fEodlldo,wwsh(aKtienvgeretthael.n2a0t0u1r)etohfatthUeLacX- Rsph ≃ 247m˙0Rg (1)
accretors canbeneutronstarsorwhitedwarfsprovidedonly (Shakura& Sunyaev 1973), where the local energy release
that thesupply rate exceeds 10−8M⊙yr−1 or 10−5M⊙yr−1 isclose tothelocal Eddington valueandtheremust besig-
respectively. In line with this prediction Fabbiano et al. nificant outflow (here R = GM/c2 = 2.1km is the grav-
g
(2003) suggested that one of the ULXs in the Antennae itational radius of the neutron star, of mass M 1.4M⊙,
∼
probablyhasawhitedwarfaccretor.Similarly,themagnetic andm˙0 istheEddingtonfactorfarfromtheaccretor,sofor
neutronstarinM82X–2canappearasaULXprovidedthat thermal–timescale systems m˙0 = M˙tr/M˙Edd). We will find
mass is supplied at a rate ≫10−8M⊙yr−1. that for M82 X–2, Rsph is larger than the magnetospheric
Our aim here then is to see how pulsed systems like radiusR (seeeqn15below)wheremagneticeffectsbecome
M
M82X–2fitintoageneralpictureofULXsasbinarieswith important.
super–Eddington mass supply rates and beamed emission. We expect outflow from disc radii inside Rsph also. To
Theinterestingaspectisthatthehighobservedspinuprate keep each disc radius close to its local Eddington limit, the
ofM82X–2givesinformation aboutthemagneticaccretion outflowmustensurethattheaccretionrateatdiscradiusR
process. Klu´zniak & Lasota (2015, hereafter KL) make this decreases as
point: they investigated M82 X–2 as a system containing a
R
weak–field pulsar, but theirmodel does not explain the ob- M˙(R) M˙Edd (2)
≃ Rin
served super–Eddington apparent luminosity. We will find
that to make the observed spinup rate consistent with the where Rin RM is the innermost disc radius. Integrating
∼
beaming needed to produce the apparent luminosity deter- the local disc emission shows (cf Shakura& Sunyaev 1973)
minesthemagneticmoment oftheneutronstar.Theresult that thetotal accretion luminosity is
implies that the beaming process works at accretion disc
L LEdd[1+lnm˙0]. (3)
radialscaleswhicharelargerthanthosewheremagneticef- ≃
fectsbecomeimportant.M82X–2istheneffectivelyafairly The main constraint on m˙0 for M82 X–2 comes from
normal accreting magnetic neutron star inside a collimat- the beaming factor b, which has to account for most of the
ing disc structure arising from the super–Eddington mass difference between its apparent luminosity 1040ergs−1
supply. and the Eddington luminosity LEdd 2 ≃1038ergs−1 of
≃ ×
a 1.4M⊙ neutron star. King (2009) gives an approximate
formula
73
2 ULX ACCRETION b (4)
≃ m˙2
0
There are (at least) two classes of ULXs, corresponding
to super–Eddington mass supply in two distinct situations valid for m˙0 & √73 ≃ 8.5. This form ensures that soft
X–ray components in ULX spectra (cf Kajava & Poutanen
(King, 2002):
2009) obey an inverse luminosity–temperature correlation
(a) thermal–timescale mass transfer in high–mass X–
ray binaries (HMXBs), which is the natural sequel to the Lsoft ∼ T−4, as observed. The b ∝ m˙−02 scaling (but not
its normalization) also follows quite independently by not-
usual HMXB wind–capture phase once the companion fills
ing(cfthediscussionbeforeeqn(3)above)thatthevertical
its Rochelobe, and
(b) long-lasting transient accretion disc outbursts in size of the disc structure near Rsph must scale with m˙01,
while all thecentral accretors essentially gain mass at their
low–mass X-ray binaries.
Eddingtonrate(m˙ =1)andsoareself–similar.Thisformof
M82 X–2 is clearly in the first group (cf KL) as it is
beamingisfoundtoreproducethelocalluminosityfunction
known(Bachettiet al.2014) tohaveastellar companion of
of ULXsvery well (Mainieri et al. 2010).
massM2 &5.2M⊙ andradiusR2 &7M⊙.Thisstarmustbe
Combining(3,4)togivetheapparent(spherical)lumi-
fillingitsRochelobe,giventhebinaryperiodof2.5d.Since
M2 is significantly larger than thelikely neutronstar mass, nosity Lsph =L/b we find
thebinaryandthecompanion’sRochelobemustbeshrink- m1 4500 (5)
ing because mass is transferred to the neutron star orbit, L40 ≃ m˙20(1+lnm˙0)
further from the binary’s centre of mass. Mass transfer on
thecompanion’sthermaltimescaleresults(cfKing& Ritter (King 2009) where m1 is the accretor mass in M⊙ and L40
is theapparent luminosity in unitsof 1040ergs−1. For M82
1999; King & Begelman 1999; King, Taam, & Begelman
2000;Podsiadlowski & Rappaport2000),andcangiverates X–2 we takem1 =1.4,L40 =1.8, which gives
aiosnhmighassasaMn˙dtrit∼s 1d0e−gr5eMe⊙oyfrl−o1bed–efiplleinndg.inWg oenwtihlleficnodmpthanat- m˙0≃36 (6)
M82 X–2 probably has a more modest (but still strongly fixingthemass transfer rate in thebinary as
super–Eddington) transfer rate M˙tr ∼ 1.2×10−6M⊙yr−1, M˙0 1.2 10−6M⊙yr−1. (7)
suggestingthatitisfairlynearthebeginningofthethermal– ≃ ×
timescale phase (cf King & Ritter 1999) characterizing its
ULXstage.Wewillseethatthisisprobablythereasonthat
1 In black–hole accretion the innermost part of a super–
this system pulses at all.
Eddingtonflowisadvectiondominatedandtheheightoftheac-
Givenasuper–Eddingtonmasssupply,theresultingac- cretionflowisindependent oftheaccretionrate(Sadowskietal.
cretion discis stableat large disc radii,down tothe‘spher- 2016;Lasotaetal.2016);itisnotclearwhathappensinaccretion
ization radius’ ontoaneutronstar.
(cid:13)c 2014RAS,MNRAS000,1–4
ULXs: Neutron Stars vs Black Holes 3
We will see in thenext Section that mass accretes near the of even a relatively small mass severely reduces the sur-
magnetosphereataratesignificantlysmallerthanthis,self– face fields of neutron stars – this is central to the con-
consistently implying from (2) that the magnetospheric ra- cept of pulsar recycling, which is implicated in the pro-
diusR (eqn10) is smaller than thespherization radius ductionofmillisecondpulsars(Radhakrishnan & Srinivasan
M
1982; Alparet al. 1982; Taam & van den Heuvel 1986;
Rsph ≃5×107cm, (8) Bhattacharya & van den Heuvel1991).Itisunclearwhether
definingtheULX beaming. M82 X–2 or systems like it will end by producing millisec-
ondpulsarsornotwhenaccretionstops:givenitsspinperiod
anddeducedmagneticfield,theneutronstarinM82X–2is
3 SPIN AND SPINUP OF M82 X–2 currently below the pulsar‘death line’
Magnetic accretors are characterized observationally by BP−2 1.7 1011Gs−2 (16)
≃ ×
their spin period P and spinup rate ν˙ = d(2π/P)/dt. For
(Ruderman& Sutherland1975),so resurrection asa pulsar
M82 X–2 we have P =1.37 s, and an unusually high value
will require spinup to beat field decay. We can expect M82
ν˙ = 2 10−10s−2. This gives a very short spinup (period
× X–2 to transfer several M⊙ towards its neutron–star com-
halving) timescale
panion. But since the surface accretion rate is limited to
tspin 2π 360yr. (9) M˙Edd or even less (perhaps M˙Edd multiplied by the frac-
≃ Pν˙ ≃ tional surface area of the accreting polecaps) the neutron–
Physically, the magnetic accretion process is characterized starmassgrowsmuchless.AclearexampleofthisisCygX–
bythemagnetospheric(‘Alfv´en’)radiusR wherethemat- 2, where a prolonged super–Eddington phase has nonethe-
M
ter stresses in the accretion disc are comparable with those less left behind a fairly normal (but not strongly magnetic)
ofthemagneticfieldofdipolemomentµ=1030µ30Gcm−3, neutronstar,whichmayyetliveagainasaradiopulsaronce
i.e. accretion stops (King& Ritter 1999).
R =2.9 108M˙−2/7m1/7µ4/7cm, (10)
M × 17 1 30
where M˙17 is the accretion rate at the magnetosphere in 5 CONCLUSION
unitsof 1017gs−1 (cf e.g.Frank et al. 2002).Discaccretion
is assumed to give way to flow along fieldlines within R , We have seen that M82 X–2 fits into the simple picture
M
so the disc angular momentum arriving at R predicts a of ULXs as beamed X–ray sources fed at super–Eddington
M
theoretical spinup rate rates. Its magnetic field has apparently been weakened by
accretion,andwecanexpectthatitsfieldwillshortlybeun-
ν˙ =2.7 10−12M˙6/7m−3/7R6/7µ2/7I−1Hzs−1 (11)
× 17 1 6 30 45 abletochanneltheflow(formallyRM <R∗)sothatpulsing
where R6 is the neutron star radius in units of 106cm, and will stop. The system will then be indistinguishable from a
I45 its moment of inertia in units of 1045gcm2 (see e.g. ULX containing a black hole. The mass transfer rate from
Frank et al. 2002). thecompanionwillincreasesubstantially(seeKing & Ritter
Usingtheobservedvalueof ν˙ inthisequationandtak- 1999) so the current ULX might become a HLX (hyperlu-
ing m1 = 1.4, R6 = I45 = 1 gives the current value of the minous X-raysource).
local accretion rate at R=R as Onthisbasiswesuggestthatasignificantfractionofall
M
ULXs might actually contain neutron star accretors rather
M˙(RM)≃2.8×10−7µ−301/3M⊙yr−1. (12) than black holes. This is already plausible because a large
Forself–consistency wemustnowimposethescaling (2),in fractionofthehigh–massX–raybinaryprogenitorsofULXs
theform have such accretors, and in principle dynamical mass mea-
surements might offer a way of checking this idea. Perhaps
Rsph = M˙tr , (13) surprisingly,neutron–starULXsactuallyhavehigherappar-
RM M˙(RM) entluminositiesthanblack–holeULXsforagivenmasssup-
which gives plyrateM˙supp (cfKing,2006). Usingm˙0 =M˙supp/M˙Edd
∝
1/m1 we can rewrite (5) as
µ30 0.1. (14)
≃ C lnm1
The magnetospheric radius is then L − , (17)
∝ m1
RM 2.0 107cm, (15) withC aconstant.Inotherwordsforaloweraccretormass,
≃ ×
the tighter beaming resulting from a higher Eddington ac-
and the accretion rate at the magnetospheric radius
M˙(RM) 2 10−7M⊙yr−1. cretion ratiooutweighsthedecreaseintheEddingtonlumi-
≃ × nosity.Inmostcases–certainlythethermal–timescalemass
transferdiscussed here–M˙supp isindependentofm1.Then
4 EVOLUTION weexpectneutron–starULXstohavehigherapparentlumi-
nosities than black–hole ones and so to be relatively easier
Since µ = BR3 we see from (14) that the magnetic to find, further increasing the number of neutron–star ac-
∗
field of the neutron star in M82 X–2 must be signifi- cretors among detected ULXs. A constraint on the relative
cantly lower than is usual for a new–born neutron star, number of neutron–star versus black–hole ULXs produced
i.e. B 1011G, rather than 1012G. This is rea- bythis‘early massiveCaseBevolution’comesfromthede-
≃ ≃
sonable, since it has long been suspected that accretion layeddynamicalinstability(Webbink1977;Hjellming1989),
(cid:13)c 2014RAS,MNRAS000,1–4
4 Andrew King and Jean–Pierre Lasota
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Yong& Li2015). L25
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ACKNOWLEDGMENTS
JPL acknowledges support from the French Space Agency ThispaperhasbeentypesetfromaTEX/LATEXfileprepared
CNESandPolishNCNgrantsUMO-2013/08/A/ST9/00795 bythe author.
and DEC-2012/04/A/ST9/00083. ARKthankstheInstitut
d’Astrophysique, Paris, for hospitality during a visit where
this work was performed. Theoretical astrophysics research
attheUniversityofLeicesterissupportedbyanSTFCCon-
solidated Grant.
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