Long-term evolution of anomalous X-ray pulsars and soft gamma repeaters

0.69 MB·

by  Onur Benli

Mon.Not.R.Astron.Soc.000,000–000(0000) Printed29January2016 (MNLATEXstylefilev2.2)
Long-term evolution of anomalous X-ray pulsars and soft
gamma repeaters
O. Benli(cid:63) & U¨. Ertan
Sabancı University, 34956, Orhanlı Tuzla, I˙stanbul, Turkey
6
1 2016January28
0
2
ABSTRACT
n
a
J We have investigated the long-term evolution of individual anomalous X-ray pul-
sars (AXPs) and soft gamma repeaters (SGRs) with relatively well constrained X-ray
8
luminosity and rotational properties. In the frame of the fallback disc model, we have
2
obtained the ranges of disc mass and dipole field strength that can produce the ob-

] servedsourceproperties.Wehavecomparedourresultswiththoseobtainedearlierfor
E dim isolated neutron stars (XDINs). Our results show that (1) the X-ray luminosity,
H period and period derivative of the individual AXP/SGR sources can be produced
. self-consistently in the fallback disc model with very similar basic disc parameters to
h
those used earlier in the same model to explain the long-term evolution of XDINs,
p
(2) except two sources, AXP/SGRs are evolving in the accretion phase; these two
-
o exceptional sources, like XDINs, completed their accretion phase in the past and are
r now evolvinginthe finalpropellerphase andstillslowing downwith thedisc torques,
t
s (3) the dipole field strength (at the poles) of XDINs are in the 1011−1012 G range,
a while AXP/SGRs have relatively strong dipole fields between 1−6×1012 G, and (4)
[
the source properties can be obtained with large ranges of disc masses which do not

1 allowacleartestofcorrelationbetweendiscmassesandthemagneticdipolefieldsfor
v the whole AXP/SGRs and XDIN population.
6
4 Key words: accretion, accretion discs – stars: neutron, magnetars – pulsars: indi-
8 vidual (AXPs, SGRs) – X-rays: individual
7
0
.
1
0 1 INTRODUCTION period and the period derivative of the star. The surface
6
emissionispoweredbytheintrinsiccoolingofthestar(Page,
1 Young isolated neutron stars manifest themselves as mem-
Geppert & Weber 2006). The cooling curves of the sources
: bers of different populations, namely anomalous X-ray pul-
v arefoundtobesimilarforcrustalfieldslessthan∼1014 G,
sars (AXPs), soft gamma repeaters (SGRs), dim isolated
i while for stronger fields the field decay becomes important,
X neutron stars (XDINs), rotating radio transients (RRATs),
and significantly modify both the X-ray luminosity and the
r central compact objects (CCOs) and the so-called ‘high-
rotational evolution of the sources (Vigano` et al. 2013). In
a magnetic-field’ radio pulsars. The reason for these single
recent years, the magnetar model which was originally pro-
neutron stars to emerge as different classes is likely to be
posedtoexplainthepropertiesofAXP/SGRs(seeOlausen
thedifferencesintheirinitialconditions,whilesomeofthese
& Kaspi 2014 for a recent catalogue of AXP/SGRs1) was
sources could be evolving in different phases of similar evo-
developedtoexplainthelong-termrotationalandX-raylu-
lutionary tracks.
minosityevolutionoftheyoungneutronstarpopulationsin
The initial condition of an isolated neutron star evolv-
general. In this model, the dipole field strength on the star
inginvacuumcouldbedefinedbyitsinitialperiod,P ,and
0 inferred from the dipole formula is greater than 1014 G for
the magnetic moment µ = B R3/2 where R is the radius
0 most AXP/SGRs, and in the ∼ 1013–1014 G range for the
of the star, and B is the magnetic dipole field strength
0 XDINs.Intheeffortstoexplainthepropertiesofyoungneu-
on the pole of the star. The rotational evolution of these
tronstarsystemsinasinglepicture,themagnetarmodelhas
sources are governed by the magnetic dipole torques. Us-
some difficulties in producing the X-ray luminosity, period
ing the dipole torque formula, B could be estimated as
0 and period derivatives of the individual sources simultane-
B (cid:39)6.2×1019 (PP˙)1/2 where P and P˙ are the rotational
0
(cid:63) E-mail:[email protected] 1 http://www.physics.mcgill.ca/pulsar/magnetar/main.html
(cid:13)c 0000RAS
¨
2 O. Benli & U. Ertan
ously (Vigano` et al. 2013, see Mereghetti, Pons & Melatos our results with those obtained for XDINs by Ertan et al.
2015 for a recent review). (2014).
The rotational powers of AXP/SGRs are much lower
The properties and likely evolutionary paths of a neu-
than the observed X-ray luminosities (∼ 1033–1036 erg
tron star that evolves with a fallback disc are very differ-
s−1) for most sources. They show short super-Eddington
ent from those of the sources evolving in vacuum described
((cid:54)1 s) soft gamma-ray bursts. Among young neutron star
above. In the fallback disc model (Chatterjee, Hernquist &
groups,thesesourceshaverelativelyhighperiodderivatives
Narayan 2000; Alpar 2001), the rotational history of a neu-
(∼ 10−13 to ∼ 10−10 s s−1) and long periods, clustered
tron star is determined mainly by the disc torques that are
in the 2–12 s range, like XDIN periods. AXP/SGRs are
muchstrongerthanthedipoletorquesinmostcases.TheX-
themostvariableX-raysourcesamongtheisolatedneutron
rayluminosityisproducedbymassaccretionontothestar
stars.ManysourcesweredetectedinthehardX-rays(>10
fromthedisc,orbyintrinsiccoolingofthestarwhenaccre-
keV) with luminosities comparable to the soft X-ray lumi-
tion is not possible. It was suggested by Alpar (2001) that
nosities(Kuiper,Hermsen&Mendez2004;denHartogetal.
thepropertiesofdifferentneutronstarpopulationscouldbe
2006; Kuiper et al. 2006). In the fallback disc model, hard
explained if the properties of fallback discs are included in
X-ray spectrum and the energy dependent pulse properties
the initial conditions in addition to B and P . This model
0
can be explained by the bulk motion and thermal Comp-
was developed to include the effects of inactivation of the
tonization of the accreting matter in the accretion column
disc at low temperatures and the X-ray irradiation of the
(Tru¨mperetal.2010,2013;Kylafis,Tru¨mper&Ertan2014,
disc, with the contribution of the cooling luminosity, on
Zezas,Tru¨mper&Kylafis2015),withthepropertiesconsis-
the long-term evolution of the sources (Ertan et al. 2009;
tent with the results of the long-term evolutionary models.
C¸alı¸skan et al. 2013; Ertan et al. 2014). The evolutionary
These sources have also been observed in optical, near and
curves obtained from this model are significantly different
mid infrared (IR) bands with spectra that can be well fit-
from those given by the analytical fallback disc solutions
ted by the emission spectrum of viscously active irradiated
which cannot take dynamical outer disc radius and irradia-
fallback discs (Ertan & C¸alı¸skan 2006; Ertan et al. 2007).
tion effects into account.
Among these sources, AXP 4U 0142+61 was detected in a
ThismodelthatcanexplainthegeneralX-rayluminos- broad band from optical to mid–IR (Wang, Chakrabarty &
ity,Lx,androtationalpropertiesofAXP/SGRs(Ertanetal. Kaplan2006).Themodelfitstothisdataprovidesanupper
2009) with conventional dipole fields (∼ 1012 G) was also limit to B which is less than 1013 G, also consistent with
0
extendedtoexplainthelong-termevolutionoftheso-called the fields estimated from the long-term evolution of these
‘high-Bradiopulsar’PSRJ1734–333withverylowbraking sources in the fallback disc model.
index (n = 0.9±0.2) (C¸alı¸skan et al. 2013) and recently We briefly describe the model in Section 2.1. In Sec-
discovered ‘low-B magnetars’ SGR 0418+5729 and Swift tion2.2,weillustratetheeffectoftheinitialconditions(disc
J1822.3–1606 (Alpar, Ertan & C¸alı¸skan 2011; Benli et al. mass, magnetic dipole field and initial period) on the long-
2013).Weshouldnoteherethatthebrakingindicessmaller termevolutionoftheneutronstars.InSection3,wesumma-
thann=3couldalsobeachievedbyisolatedneutronstars. rize the observational properties of AXP/SGRs studied in
This requires that the magnetic dipole field of the neutron the present work. Our results fortwelveAXP/SGRs with a
starisburiedintotheinnercrustbyapost-supernovaaccre- comparisontoXDINpropertiesobtainedbythesamemodel
tionofmatterwithtotalmass10−3−10−4M(cid:12).Subsequent are given in Section 4. We discuss and summarize our con-
re-emergence of the field leads the neutron star to a rota- clusions in Section 5.
tional evolution with a growing dipole field on a time-scale
of∼1−100kyr.Duringthisgrowingfieldphase,thebrak-
ing index of the star could be significantly smaller than the
conventional value, n = 3, which is expected for the stars 2 MODEL
thatspindownbythedipoletorquesofaconstantmagnetic
dipole fields (see e.g. Geppert, Page & Zannias 1999, Pons, 2.1 Description of the model
Vigano` & Geppert 2012).
WeemploythefallbackdiscmodeldevelopedbyErtanetal.
The number of sources with average and seemingly ex- (2009). We solve the disc diffusion equation with an initial
tremepropertiesareincreasingwiththenewdetectionslike surface density profile of a steady thin disc using the α–
the recently measured rapid and persistent change in the prescriptionofthekinematicviscosity(Shakura&Sunyaev
brakingindexofPSRJ1846−0258.Limitationsofthemod- 1973). At a given radial distance r from the star, the effec-
els could be understood through source-by-source analyses tivetemperatureofthediscisTeff ∼=σ1/4(D+Firr)1/4where
ofeachpopulation.Thissystematicapproachcouldalsohelp D istheviscousdissipationrateandF =(CM˙c2)/(4πr2)
irr
todeterminethedifferencesintheinitialconditionsofdiffer- is the irradiation flux, where c is the speed of light, C is
ent populations together with their likely evolutionary con- theirradiationparameterwhichdependsonthealbedoand
nections.Recently,weperformedadetailedstudyforXDINs geometry of the disc. The dynamical outer radius, r , of
out
in the fallback disc model (Ertan et al. 2014), and showed the viscously active disc corresponds to the current radial
that the X-ray luminosity, period and period derivative of positionofacriticalminimumtemperature,T ,forthedisc
p
eachXDINsourcecouldbeacquiredsimultaneouslybyneu- togenerateviscosityandbeabletotransportmassandan-
tron stars with fallback discs for certain ranges of the disc- gularmomentumthatis,r =r(T =T ).Inthelong-term
out p
mass and the dipole field strength. In the present work, we evolution,r propagatesinwardwithdecreasingX-raylu-
out
perform the same analysis for AXP/SGR sources with rel- minosity, L , leaving inactive matter beyond r . Results
x out
atively well-known quiescent state properties, and compare of earlier work on the long-term evolution of AXP/SGRs
(cid:13)c 0000RAS,MNRAS000,000–000
Long-term evolution of anomalous X-ray pulsars and soft gamma repeaters 3
and XDINs indicate that T ∼100 K, for a plausible range neglect losses through the propeller effect. This assumption
p
of irradiation efficiencies. In the simulations, we start with does not affect our results qualitatively.
an initial rout ∼1014 at which the effective temperature of In the accretion phase, there is also a spin-up torque
the disc is ∼ Tp with the initial X-ray luminosity. The re- associated with the mass accretion on to the star from the
sults obtained by Inutsuka & Sano (2005) imply that the co-rotation radius, ∼ M˙ (GMr )1/2. When ω2 (cid:29) 1, this
co ∗
turbulentviscositymechanisminthediscremainsactivefor torqueisnegligibleincomparisonwiththespin-downtorque
temperaturesaslowas∼300K,whichisinagreementwith giveninequation1.Nevertheless,someofthesources,espe-
the critical temperatures we obtained from the model fits. ciallythosewithrelativelylargediscmasses,couldapproach
In the fallback disc model, the main X-ray source of the rotational equilibrium for a certain epoch of the evolu-
accreting AXP/SGRs is the accretion on to the poles of tion with decreasing efficiency of the net spin-down torque
the star, which can be written as Lacc = GMM˙/R where (Section 1). In general, we can write down the total torque
G is gravitational constant, M and R is the mass and ra- acting on the star as the sum of the spin-down and spin-up
dius of the star, M˙ is the mass flow rate on to the star. torques,Ntot =Nsd+NsuwhereNsu ∼=M˙ (GMrco)1/2.The
Intrinsic cooling luminosity, Lcool, powers the star in the magneticdipoleradiationalsocontributestothespin-down
propeller phase or when the accretion luminosity decreases torque, while the disc torque is usually the dominant spin-
belowLcool inthelatephasesofevolution.Weusethetheo- down mechanism. When Nsu is negligible, the total torque
reticalcoolingluminositycurvecalculatedbyPage,Geppert becomesequaltothespin-downtorquegivenbyequation1.
& Weber (2006) for neutron stars with conventional dipole In Section 4, we will show that most AXP/SGRs are in the
fields. When the accretion is not allowed, we calculate the accretion phase with ω2 (cid:29) 1. We estimate that only two
∗
totalcoolingluminosityconsideringalsotheenergydissipa- AXPs,namely1E2259+5864U0142+61,areevolvingclose
tionduetomagneticanddisctorquesassuggestedbyAlpar to rotational equilibrium at present.
(2007). In the fallback disc model, starting from the earlier Inourcalculations,weneglectthemagneticfielddecay
works (e.g. Chatterjee, Hernquist & Narayan 2000; Alpar whichcouldaffecttheevolutionofAXP/SGRsintheaccre-
2001), it is assumed that part of the inflowing disc mat- tionphase.Fromthemagneticfielddecaymodels(e.g.Gep-
teris accretedonto thesurfaceof thestar inthespin-down pert,Page&Zannias1999,Konar&Bhattacharya1999),we
phase.Therearetheoreticalworks(e.g.Rappaport,Fregeau estimate that this effect is not significant for most of these
& Spruit 2004 and D’Angelo & Spruit 2012), and strong sources which have ages between 103 and a few 104 yr and
observationalevidencessupportingthisassumption.Forin- dipolefieldsstrengths∼1−4×1012 G(onthepole).Initial
stance, for the recently discovered transitional millisecond magnetic dipole fields of these sources could be a few times
pulsars,itisestimatedthattheaccretion–propellertransi- strongerthantheirfieldatpresent.Thefieldcouldhavede-
tiontakesplaceataccretionratesthatareordersofmagni- cayedbyarelativelylargefactorforthetwoAXPs,namely
tudelowerthantheratecorrespondingtothespinup-down 1E 2259+586 and 4U 0142+61, which seem to evolve with
transition (Archibald et al. 2014, Papitto et al. 2015). The relativelyhighdiscmasses.Oursimplificationputsanuncer-
criticalconditionfortheaccretion–propellertransitionisnot tainty on the ages of the model sources. The ages indicated
wellknown.Inourmodel,weassumethatthemass-flowonto by our model calculations could be taken as an upper limit
the star is allowed when the light cylinder radius, rLC, is totheactualagesofthesources.Nevertheless,incorporating
greaterthantheAlfve´nradiusrA =(GM)−1/7 µ4/7 M˙i−n2/7, a detailed field decay model in our calculations would not
where µ is the magnetic dipole moment of the neutron star change the current field strengths of the sources estimated
and M˙in is the rate of mass-flow arriving the inner disc ra- in the present work. After we complete our study on differ-
dius, rin. ent neutron star systems with our current simple model, a
Thetorqueactingontheneutronstarcanbefoundby detailed population analysis of the young neutron star sys-
integrating the magnetic torque from rA to the corotation tems in the fallback disc model, considering also the effects
radius,rco =(GM/Ω2∗)1/3 (seeErtan&Erkut2008andEr- of the field decay on the model curves, will be presented in
tanetal.2009fordetailsofthetorquemodel).Thisassumes an independent work.
awideboundarylayerbetweenrAandrco,neverthelessmost For AXP/SGRs and XDINs, our results are not sensi-
ofthecontributiontothespin-downtorquecomesfromthe tivetotheinitialperiodP (seee.g.Ertanetal.2009).With
0
radiiclosetorco.Therefore,themagnetictorquesintegrated differentP0values,modelcurvesconvergetothesamesource
fromrA torco,oracrossanarrowboundarylayer,sayfrom propertiesinthelong-term,providedthatthesourcesenter
2rcotorco,givesimilarresults.Thisisduetotheverysharp the accretion phase in the early phases of their evolution.
radialdependenceofthemagneticpressure(∝r−6).Theto- The minimum temperature of the viscously active disc, T ,
p
talspin-downtorqueintegratedfromrA torco canbewrit- is a basic disc property that is expected to be the same for
ten as, all the fallback discs around young neutron star systems,
even if the disc composition is not well-known. Following,
1
Nsd =I Ω˙∗ = 2M˙in (GMrA)1/2 (1−ω∗2) (1) Ertan et al. (2009), we keep Tp in the ∼ 50−150 K range
in the models of all different sources like low–B magnetars,
where I is the moment of inertia, Ω˙ is the rate of change ‘high-Bradiopulsars’,andXDINstoremainselfconsistent.
∗
of the angular velocity of the star, ω = Ω /Ω (r ) is the Similarly, we fixed the other main disc parameters, namely
∗ ∗ K A
fastness parameter, Ω is the rotational angular frequency the irradiation strength C =1×10−4 and the viscosity pa-
∗
of the neutron star and Ω (r ) is the Keplerian angular rameterα=0.045followingtheresultsofErtan&C¸alı¸skan
K A
velocityofthediscattheAlfve´nradius.Accretionfromthe (2006) and C¸alı¸skan & Ertan (2012). The actual disc mass,
innerdiscontotheneutronstarisallowedwhenr <r < M , and the magnetic field strength, B , at the pole of the
co A d 0
r . In this phase, we assume that M˙ = M˙, that is, we starcoulddifferfromsourcetosource.Werepeatthesimu-
LC in
(cid:13)c 0000RAS,MNRAS000,000–000
¨
4 O. Benli & U. Ertan
lationsmanytimes,tracingthevaluesofM andB ,tofind
d 0
therangesofthesequantitiesthatcanreproducethesource
11003377
properties. The disc mass, Md, is estimated by integrating LLttoott
theinitialsurfacedensityprofilefromtheinnertotheinitial 11003366 LLccooooll
outer disc radius (∼5×1014 cm).
-1-1g s)g s)11003355
erer
2.2 LStoanrg-wteitrhmaEFvaolllubtaicoknadrisycPhases of a Neutron L(L(totaltotal11003344
11003333
In our model summarized in Section 2.1, there are four ba-
sicparametersthatdeterminetheevolutionarycurvesofthe 11003322
modelsources:magneticdipolefieldstrengthonthepoleof 110000
the star, B , the initial disc mass, M , the initial period
0 d
of the star, P , and the minimum critical temperature, T ,
0 p
1100
below which the disc becomes passive. The critical temper-
ature Tp is degenerate with the irradiation parameter C, P (s)P (s)
which is constrained to ∼1–7×10−4 range with the results 11
obtained by Ertan & C¸alı¸skan (2006).
Dependingontheinitialparameters,themodelsources
00..11
could follow rather different evolutionary paths. The X-ray
luminosity and rotational evolution of a source could pass
through three basic evolutionary phases, namely the initial Initia(Rl apdroiop eplhlears peh)ase Accretion phase Finalp phraospeeller
propellerphase,accretionphaseandfinalpropellerphaseas
5sLe×xe,n1e0iv2noylFurtiigsio.dn1u.eofTtothhpeeetnsoeopturrpacateino.enTlohsfhetohawebsrinutnhpeetrrXdisi-sercaiyinnltuLomxthianetolsitgith(cid:39)yt, -1-1P/dt (s s)P/dt (s s) 1100--1111
dd
cylinderandtheonsetofaccretionphase.Thismighthappen
at different times of evolution for different sources. Some
sources may never enter the initial propeller phase, while 1100--1122
some others remain always in this phase as radio pulsars 110011 110022 110033 110044 110055 110066
depending on the initial conditions. The dashed line in the TTiimmee ((yyeeaarrss))
top panel represents the cooling history of a neutron star
with a dipole field strength of 1012 G on the surface of the
star. It is seen that L dominates L when accretion is Figure 1. A sample model curve that shows three basic evolu-
cool acc
not allowed or in the late phase of the accretion episode. tionary episodes of a neutron star-fallback disc system. For this
Theevolutioniseasiertofollowfromtheperiodderivative, illustrative model, B0 = 2×1012 G, Md = 5.7×10−4 M(cid:12) g
P˙, curve. The torque acting on the star is most efficient in cm−2,P0=75msandTp=150K.Durationsofinitialpropeller
phase(blueregion),accretionphase(whiteregion)andfinalpro-
the accretion phase. When the positive term is negligible,
pellerphases(green region)depend onthe initialconditions.To
that is, when r is not very close to r , P˙ is found to be
A co reach the long periods of several seconds, a source should pass
independent of both M˙ and P. This constant P˙ behaviour
through the accretion phase. The initial propeller phase, which
oftheillustrativemodelsourceintheaccretionphaseisseen couldbeexperiencedbyafractionofthesources,hasnotasignif-
in the bottom panel of Fig. 1. icant effect on the properties achieved in the accretion and final
WithdecreasingM˙ ,r movesoutwardfasterthanthe propellerphases(seethetextfordetails).
in A
lightcylinderradius,r .Inthemodel,accretionisswitched
LC
off when r is found to be greater than r . For the illus-
A LC
trative model in Fig. 1 this correspond to t (cid:39) 3×104 yr. (B =1013−1014G)inferredfromtheirobservedP andP˙.In
From this point on, P˙ decreases with decreasing M˙ . In thefallbackdiscmodel,XDINpropertiescouldbeachieved
in
this final propeller phase, the sources do not accrete but with B (cid:39) 1012 G (Ertan et al. 2014) which together with
still spin-down by the disc torques. It is seen in the middle longperiods,placethesesourcesunderthepulsardeath–line
panelofFig.1thatP remainsalmostconstantinthisphase in the B−P diagram.
because of decreasing torque efficiency after termination of
the accretion episode.
In the initial and final propeller phases, there is no
accretion on to the star, and the pulsed radio emission is 3 SOURCE PROPERTIES
allowed. Nevertheless, we expect that sources could show
SGR 0526–66:
pulsed radio emission only in the initial propeller phase,
since in the final propeller stage, the sources with conven- For SGR 0526–66, P (cid:39) 8.1 s and P˙ (cid:39) 3.8×10−11 s s−1
tionaldipolefieldsandlongperiodsareusuallynotcapable (Tiengo et al. 2009). The 0.5–10 keV unabsorbed flux was
of producing pulsed radio emission; they are already below reported as ∼10−12 erg s−1 cm−2 and for a distance of 50
the pulsar death–line. Note that known and non-detected kpc, which corresponds to LMC region, the bolometric X-
XDINs, and their progenitors would be expected to be ra- rayluminosityofthesourceis∼5×1035ergs−1(Parketal.
dio pulsars as well if they had indeed strong dipole fields 2012).
(cid:13)c 0000RAS,MNRAS000,000–000
Long-term evolution of anomalous X-ray pulsars and soft gamma repeaters 5
SGR 0501+4516: analysis of the radio pulses, Levin et al. (2012) measured a
factorof2decreaseintheP˙ ofthesourcesinceitsdiscovery
For SGR 0501+4516, P = 5.76 (Go¨gˇu¨¸s, Woods & Kouve- in radio. In the present work, we assume a P˙ range from
liotou 2008), P˙ (cid:39) 5.8×10−12 s s−1 (Go¨gˇu¨¸s et al. 2010).
1 to 2 ×10−11 s s−1. Single BB fits to the X-ray spectra
Based on a likely association of the source with the super-
of PSR J1622–4950, extracted from Chandra and XMM-
novaremnantHB9,Aptekaretal.(2009)estimatedthemin-
Newtonobservations,atfourdifferentdates(Andersonetal.
imum distance to the source as 1.5 kpc. We have converted
2012), give an unabsorbed flux ∼1.1×10−13 erg s−1 cm−2
the observed X-ray flux into a bolometric X-ray luminos-
in 0.3–10 keV. From the dispersion measure, Levin et al.
ity range assuming that the source lies at a distance in the
(2010)givesadistance∼9kpc.Weestimatethebolometric
1.5–5 kpc range. A black body + power-law model fit well
X-ray luminosity ∼9.2×1032 erg s−1 for d=9 kpc.
to the quiescent soft X-ray spectrum of SGR 0501+4516
(Camero et al. 2014). The best-fitting parameters are kT
= 0.52±0.02 keV with a blackbody radius of 0.39±0.05
SGR 1900+14:
km, N = 0.85(3) × 1022 cm2 and the power law index
H
Γ = 3.84 ± 0.06. This corresponds to an L range from SGR 1900+14 has a period P = 5.2 s (Hurley et al. 1999;
x
4.7×1033 to 5.2×1034 erg s−1 for distances from 1.5 to Kouveliotou et al. 1999). The most resent timing analy-
5 kpc. sis indicated a spin-sown rate, P˙ = 9.2(4)×10−11 s s−1
(Mereghettietal.2006).Thedistanceofthesourceis12–15
kpc (Vrba et al. 1996). We use the spectral fit parameters
XTE J1810–197:
obtained by Mereghetti et al. (2006). For a hydrogen col-
XTEJ1810–197hasP =5.5sandP˙ ∼4−10×10−12 ss−1 umn density, NH = 2.12×1022 cm2, converting the 2–10
(Camilo et al. 2007a). The source showed transient pulsed keV unabsorbed flux into 0.1–10 keV unabsorbed flux by
radio emission during an X-ray outburst phase (Halpern using WebPIMMS. we estimate the bolometric luminosity
et al. 2005). It was the first pulsed radio detection from ofthesourceLx ∼3×1035 ergs−1 ford=12.5kpc(Davies
an AXP/SGR source. For a distance d = 3.5 kpc (Bernar- et al. 2009).
dinietal.2009;Minteretal.2008),convertingtheabsorbed
0.6–10 keV data of Bernardini et al. (2009) into 0.1-10 keV
unabsorbed X-ray flux using the same spectral fit parame- CXOU J010043.1–721134:
ters, we estimate L ∼1.6×1034 erg s−1.
x The period and period derivative of CXOU J010043.1–
721134 are P = 8 s and P˙ = 1.9×10−11 s s−1 (McGarry
1E 1841–045: etal.2005).ThesourceislocatedinSmallMagellanicCloud
(SMC), dwarf satellite of our galaxy, with d∼60 kpc. The
1E 1841–045 was discovered by Einstein HRI (Kriss et al. X-rayspectraofthissourcecanbefitbya2BBmodelwith
1985) and is the first source identified as an AXP with an theparameters,R ∼12.1km,R ∼1.7km,kT ∼0.3
BB1 BB2 1
X-ray pulse period of 11.8 s by Vasisht & Gotthelf (1997). keV, kT ∼0.7 keV (Tiengo, Esposito & Mereghetti 2008).
2
ThissourceislocatedinthesupernovaremnantKes73with With N = 5.9×1020 cm2 (Dickey & Lockman 1990) we
H
a distance of 8.5 kpc (Tian & Leahy 2008). This source obtain L ∼6.5×1034 erg s−1.
x
has the longest period in the currently known AXP/SGR
population. A recent temporal analysis of the source gives
P˙ (cid:39)4.1×10−11 ss−1 (Dib&Kaspi2014).Fromtheparam- 1RXS J170849.0–400910:
eters of 0.5–10 keV spectrum in the quiescent state that is
welldescribedbyblackbody+power-lowwithΓ=1.9±0.2 ThissourcehasP =11s,andP˙ =1.9×10−11 ss−1 (Dib&
and kT =0.43±0.003 keV (Kumar & Safi-Harb 2010), we Kaspi2014),andadistanceof3.8kpc(Durant&vanKerk-
estimate L ∼5×1035 with d=8.5 kpc. wijk 2006). From the unabsorbed 0.5–10 keV flux reported
x
by Rea et al. (2007) we estimate L =1.5×1035 erg s−1.
x
1E 1048.1–5937:
1E 1547.0–5408:
A detailed temporal analysis of 1E 1048.1–5937 data, that
weretakenbyRXTE between1996July3and2008January Thisactivetransientsource,alsoknownasSGRJ1550–5418,
9givesP (cid:39)6.5sandP˙ ∼2.25×10−11 ss−1 (Dib,Kaspi& was discovered in 1980 by Einstein satellite in the X-ray
Gavriil 2009). The source showed fluctuations and anoma- band.Later,thesourcewasalsoobservedintheradioband
liesduringitstemporalevolutionformorethandecades.We with a pulsation period, P = 2.1 s and P˙ = 2.3×10−11
adopt P and P˙ values measured by Dib, Kaspi & Gavriil s s−1 (Camilo et al. 2007b). From the analysis of more re-
(2009) in our analysis. Based on the X-ray spectral param- sent X-ray observations with RXTE and Swift, its average
etersobtainedbyTametal.(2008),weestimateLx as1035 period derivative was estimated as P˙ (cid:39) 4.8×10−11 s s−1
ergs−1 foradistanceofd∼9kpc(Durant&vanKerkwijk aftertheburst(Dibetal.2012).WeadopttheP˙ valuemea-
2006). sured by Camilo et al. (2007b) in the quiescent state. The
unabsorbed flux in 0.5–10 keV band is 5.4×10−12 erg s−1
cm−2 (Bernardinietal.2011).TheX-rayluminosityisesti-
PSR J1622–4950:
matedtobe1.3×1034 and5.2×1034 ergs−1 fordistances,
ThePSRJ1622–4950wasdiscoveredintheradiobandwith d=4.5kpc(fromthedustmodelbyTiengoetal.2010)and
a spin period of 4.3 s (Levin et al. 2010). From the timing d=9 kpc (derived from the dispersion measure by Camilo
(cid:13)c 0000RAS,MNRAS000,000–000
¨
6 O. Benli & U. Ertan
1036 CSX1GEOR 1U 81 4J90101-0-0+0014.4.5. 1036 1SEG R15 04570.01-+-54450186
1035 1E 1048.1--5937
-1erg s)1034 S1RGXRS 0 5J12760--86.6.. -1erg s)1035
L (total1033 L (total11003334
1032 1032
100 100
10 10
P (s) P (s)
1 BBB0=00==4.252.. 56 M MMd=dd==1276...086 1 BB0=0=12.4.2 M Md=d=130..27
0.1 BBB00==0=322..86.8 MM Mdd==d=11622...000 0.1 BB0=0=1.24. 8 M Md=d=151..06
10-10 10-10
-1dt (s s) 10-11 -1dt (s s) 10-11
P/ P/
d d 10-12
PSR J1622--4950
10-12 10-13 XTE J1810--197
102 103 104 105 106 102 103 104 105 106
Time (years) Time (years)
Figure 2. The long-term evolutionary model curves of six Figure 3. The illustrative model curves representing the long-
AXP/SGRs.ForalltheseAXP/SGRs,bothMd andB0 arecon- termevolutionsofthefourAXP/SGRswhichhaveuncertainties
strained to very narrow ranges with central values given in the ineitherLx orP˙ measurements.Theerrorbarsshowtheuncer-
middle panel. The names of the sources are shown in the top taintiesinmeasurements.Forthesesources,unlikethesixsources
panel.Forthesemodels,Tp=100KandC =1×10−4.B0 and giveninFig.2,ourmodelcannotwellconstraintheMd andB0
Md valuesaregiveninunitsof1012 Gand10−6 M(cid:12).Forthese values.B0 andMd valuesaregiveninunitsof1012 Gand10−6
sources accretion goes on till t ∼ 5×105 yr. But, the accretion M(cid:12). The model parameters are given in Table 1. The constant
luminosityremainbelowthecoolingluminosityatt∼afew104 P˙ epochs correspond to accretion phases. 1E 1547.0–5408 and
yr. XTEJ1810–197entertheaccretionphaseattimes∼3×102and
5×103 yrrespectively.
et al. 2007b). We adopt this X-ray luminosity range for 1E
1547.0–5408 in our model calculations. the quiescent state. For d = 3.2 kpc (Kothes, Uyaniker &
Yar 2002), the bolometric X-ray luminosity (including the
hardx-rayemission)isassumedas∼2×1035 ergs−1 inthe
4U 0142+61: quiescent state (see Table 3 of Vigano` et al. 2013).
4U0142+61isoneofthemostextensivelystudiedAXPsin
different energy bands from optical to hard X-rays. It has
P = 8.7 s and P˙ = 2×10−12 s s−1 (Dib & Kaspi 2014). 4 RESULTS
The soft(< 10 keV) and the hard X-ray luminosity of the We could reproduce the observed source properties (P, P˙
source are ∼3.2×1035 and 1.4×1035 erg s−1 respectively
and L ) of 12 AXP/SGRs in the frame of the fallback disc
x
(denHartogetal.2008).Inthequiescentstate,0.8–160keV
model (Figs. 2, 3, 4 and 5) using similar basic disc parame-
luminosityofthesourceis∼4.6×1035ergs−1foradistance ters(α=0.045,C =1×10−4,T ∼100K).Wehavechosen
p
d=3.6 kpc (Durant & van Kerkwijk 2006).
AXP/SGRswithrelativelywell-knownquiescent-stateprop-
ertiesforaninvestigationofthediscmassandmagneticfield
correlation. Our results indicate that the 12 AXP/SGRs
1E 2259+586:
that we have studied here are evolving in the accretion
This source has P = 7 s and P˙ = 4.8×10−13 s s−1 (Dib phase.Twosources,namely4U0142+61and1E2259+586,
& Kaspi 2014; Morini et al. 1988). The unabsorbed flux of seemtobetheonlyAXP/SGRsthatarecurrentlyevolving
the source in 1–10 keV band is 5×10−11 erg s−1 cm−2 in close to rotational equilibrium (see Figs 4 and 5). We have
(cid:13)c 0000RAS,MNRAS000,000–000
Long-term evolution of anomalous X-ray pulsars and soft gamma repeaters 7
Table 1.Theinitialdiscmass(Md),dipolemagneticfieldstrengthatthepoleofthestar(B0),minimumactivedisctemperature(Tp)
andthecurrentageofthesourcesfoundfromthemodelswiththeevolutionarycurvesgiveninFig4.,andtheobservedpropertiesLx,
P andP˙ ofthesources.WetaketheirradiationparameterC=10−4 andtheviscosityparameterα=0.045forallofthesources.
Name Md B0 Tp age Lx P P˙
(10−6 M(cid:12)) (1012 G) (K) (yr) (1033 ergs−1) (s) (10−13 ss−1)
SGR0526–66 12.0 3.8 100 6×103 500 8 380
XTEJ1810–197 6.0–24.0 1.2–1.8 100 2–4×104 16 5.5 40–100
1E1841–045 12.0 4.2 100 7×103 ∼500 11.8 410
1E1048.1–5937 6.0 2.8 100 8×103 100 6.5 225
PSRJ1622–4950 0.7–1.2 1.8–2.2 100 ∼1×104 0.9 4.3 100–200
SGR1900+14 6.6 5.6 100 1.6×103 300 5.2 920
SGR0501+4516 12.0–18.0 1.4 100 3×104 4.7–52 5.76 58
CXOUJ0100... 7.8 2.5 100 1.3×104 65 8 190
1RXSJ1708... 12.0 2.6 100 1.4×104 150 11 190
1E1547.0-5408 1.0-2.1 4.0 100 2×103 13–52 2 230
4U0142+61 47.5–570.0 2.4–2.6 54 ∼0.3–2×105 460 8.7 20
1E2259+586 28.5–570.0 1.2 30 ∼1–4×105 ∼200 7 4.8
Table 2.ObservedpropertiesofthesixXDINs(seeErtanetal.2014andreferencesthereinfordetails).
P (s) P˙ (10−14 ss−1) Lx (1031 ergs−1)
RXJ0720.4–3125 8.39 ∼7 ∼16
RXJ1856.5–3754 7.06 2.97(7) 9.5
RXJ2143.0+0654 9.43 4.1(18) 11
RXJ1308.6+2127 10.31 11.2 7.9
RXJ0806.4–4123 11.37 5.5(30) 2.5
RXJ0420.0–5022 3.45 2.8(3) 2.6
obtainedthemodelcurvesthatcanfittheindividualsource luminosity.Inthefinalpropellerphase,weobtaintheprop-
properties with the model parameters given in Table 1. In erties of XDINs with a large range of M . Nevertheless, B
d 0
the model, the dipole field strength, B , is well constrained values of these sources are well constrained despite the un-
0
fortheaccretingsources.EstimatedB andM rangesgiven certaintyintheirinitialdiscmasses.InFig.6,weplottheB
0 d 0
in Table 1 corresponds to the uncertainties in measured P˙ and M values of both AXP/SGRs and XDINs, estimated
d
values (PSR J1622–4950, XTE J1810–197) and distances from the model results. It is seen in Fig. 6 that the magni-
(SGR 0501+4516, 1E 1547.0-5408). Our earlier results in- tude of the dipole field on the pole of the star, B , ranges
0
dicate that SGR 0418+5729 completed its evolution in the from∼3×1011 Gto∼6×1012 GforthetotalAXP/SGR
accretion phase, and is now evolving in the final propeller andXDINsources.Inaddition,itisclearlyseenthattheB
0
phase (Alpar, Ertan & C¸alı¸skan 2011), Swift J1822.3–1606 valuesofXDINs(∼3×1011–1×1012 G)remainssystemat-
could be in either accretion or in the final propeller phase icallybelowthoseofAXP/SGRs(∼1×1012−6×1012 G).
depending on its actual X-ray luminosity in the quiescent Due to large uncertainties in M , we could not determine
d
state(Benlietal.2013)andSGR0501+4516isfoundtobe whether there is a correlation between the disc mass and
accreting from the fallback disc at present (Benli, C¸alı¸skan the dipole field strength of these sources.
& Ertan 2015).
Recently, Ertan et al. (2014) analysed the individual
5 DISCUSSION AND CONCLUSIONS
source properties of six XDINs using the same model as
we employ in the present work. With almost the same ba- Wehaveinvestigatedthelikelylong-termevolutionarypaths
sicdiscparameters,currentX-rayluminosityandrotational ofindividualAXP/SGRsourceswithrelativelysmalluncer-
properties of XDINs can also be produced by this model. tainties in distances and period derivatives in the quiescent
ForcomparisonwithAXP/SGRsproperties,wealsopresent state.OurresultsshowthattheobservedP,P˙ andL values
x
theresultsobtainedbyErtanetal.(2014)forXDINsinTa- of 14 sources, including the two low-B magnetars analyzed
ble 3. The properties of the six XDINs could be achieved earlier (Alpar, Ertan & C¸alı¸skan 2011; Benli et al. 2013),
by the sources in the final propeller phase, unlike most of could be achieved by neutron stars evolving with fallback
theAXP/SGRswhichseemtobestillaccretingmatterfrom discs and conventional dipole fields. Comparing Tables 1
thedisc(Figs.2and3).Inthepropellerphases,thesurface and 3, it is seen that the basic disc parameters, namely the
emission of the sources are powered mainly by the cooling irradiationstrength,C,thetransitiontemperaturebetween
(cid:13)c 0000RAS,MNRAS000,000–000
¨
8 O. Benli & U. Ertan
Table 3. The disc parameters and the corresponding ages for the six XDINs. The viscosity parameter α = 0.045 for all the model
sources.(TakenfromErtanetal.2014).
B0 (1012 G) Md (10−6 M(cid:12)) Tp (K) C (10−4) age(105 y)
RXJ0720.4–3125 1.1–1.3 0.8–12.0 106 1 1.45
RXJ1856.5–3754 0.9–1.1 0.8–18.0 100 1 1.85
RXJ2143.0+0654 1.0–1.2 1.0–11.6 100 1 1.9
RXJ1308.6+2127 0.9–1.0 0.8–18.0 100 1.5 2.1
RXJ0806.4–4123 0.8–0.9 0.5–18.0 100 2.3 3.1
RXJ0420.0–5022 0.35–0.38 4.8–18.0 82 7 3.2
1038
1038
1037 1037
-1g s)1036 -1g s)1036
L (ertotal1035 Md = 47.5 L (ertotal11003345
1034 MMdd == 111940..00 1033
1033 Md = 570.0
100 100 Md =28.5
Md=500
Md=190.0
10 10 Md=570.0
P (s) P (s)
1 1
0.1 0.1
10-10 10-11
-1dt (s s) 10-11 -1dt (s s) 10-12
P/ P/
d 10-12 d
10-13 10-13
102 103 104 105 106 103 104 105 106
Time (years) Time (years)
Figure4.Illustrativemodelcurvesthatcouldrepresentthelong- Figure5.ThesameasFig.7,butfor1E2259+586.Forallthese
termevolutionof4U0142+61.Reasonablemodelfitscouldbeob- modelcurves,B0=1.2×1012 G,Tp=30KandC=1×10−4.
tainedwithalargerangeofdiscmass,anarrowB0rangearound Md valuesaregiveninunitsof10−6 M(cid:12).Reasonablemodelfits
2.6×1012 G, and Tp ∼ 50−60 K. These models are obtained forthissourcecouldbeobtainedwithTp∼30–40Kattheages
withTp =54KandMd values(inunitsof10−6 M(cid:12))shownin t∼1–4×105yr(betweenthedashedverticallines).Thesemodel
thetoppanel.Themodelsourcescanacquirethesourceproper- sources, like those in Fig 4, remain in the accretion phase their
ties at the ages in the range limited by the vertical dashed lines birthstothepresentages.
showninthefigure(∼3×104–2×105 y).Thehorizontaldashed
linesshowtheobservedpropertiesofthesource.Forthesemodel
curves,accretionremainsasthedominantsourceofluminosity. OurresultsindicatethatmostAXP/SGRsarecurrently
in the accretion phase. The two relatively old low-B mag-
netarsseemtohavecompletedtheaccretionepoch,andare
the active and passive disc state, T , and the α parameter currently spinning down by the disc torques without accre-
p
ofthekinematicviscosityareallalmostthesameasthepa- tion on to the star, in the final propeller phase. Most of
rameters used for XDINs in Ertan et al. (2014). The model theaccretingsourcesarenotclosetorotationalequilibrium,
can produce the individual source properties (P, P˙, L ) si- with the exceptions 4U 0142+61 and 1E 2259+586 which
x
multaneously for each of AXP/SGR and XDIN sources. seem to have initial disc masses greater than those of other
(cid:13)c 0000RAS,MNRAS000,000–000
Long-term evolution of anomalous X-ray pulsars and soft gamma repeaters 9
AXP/SGR sources. We have obtained plausible model fits
CXOU J010043.1--721134
forthesesourceswithrelativelylowT values(seeTable1), SGR 1900+14
p SGR 0526--66
which might be due to unknown details of the disc-field in- 1013 1E 11E04 188.14-1--5-903475
teraction geometry and efficiency when the Alfve´n radius 11REX 1S5 J4177.00-854490.8..
SGR 0501+4516
approaches the co-rotation radius. XTE J1810--197
PSR J1622--4950
The birth rate of XDINs are estimated to be compa- XDINs
rable to the radio pulsar birth rate and about an order of
G)
magnitudegreaterthanthatofAXP/SGRs(seee.g.Popov, B (0
Turolla&Possenti2006).Inotherwords,thenumberofcur-
rently known AXP/SGRs is not sufficient for these sources 1012
to be the only progenitors of XDINs. Furthermore, our re-
sultsimplythatafractionofAXP/SGRshaveevolutionary
paths not converging into the XDIN properties. In partic-
ular, some of AXP/SGRs could reach periods longer than
the longest presently observed XDIN period, ∼12 s, but at 1 10 100
Md (10-6 MO• )
late phases with very low luminosities. One basic difference
between these populations seems to be the relatively weak Figure 6. The B0 versus Md distribution of some AXP/SGRs
dipole fields (∼ 1011–1012 G) of XDINs (see Tables 1 and (presentwork)andthesixXDINs(fromErtanetal.2014).The
3o)f.XFDorINthsisisBli0kerlayntgoe,bteheduoebsteorvpehdysuipcaplercolinmstirtafionrtspreartiohdesr seorruorrcebsaarscqruepirreestehnetotbhseerBv0edansdouMrcde prarnopgeesrtfioesr wPh,iPc˙hatnhde mLxodsei-l
multaneously.
than the selection effects (see Fig. 3 of Ertan et al. 2014).
Because, for given basic disc parameters, the dominant fac-
tor that determines the maximum period is the strength of
cated in the upper tails of both B and M distributions
0 d
the dipole field, rather than the disc mass. With the rela-
are likely to be the sources that are observed as X-ray lu-
tively weak dipole fields of XDINs, indicated by the model, minousAXP/SGRs.Inourmodel,P˙ ∝B2 intheaccretion
0
thelongestattainableperiodsarealreadyclosetotheupper
episode, and therefore among the accreting sources those
bound of observed periods. This result for the period up- withrelativelyhighP˙ valueshavealsostrongerdipolefields.
per limits needs more detailed investigation and should be
This conclusion cannot be generalized to the stars that are
takenwithsomecautionduetooursimplifiedconditionfor
closetotherotationalequilibrium,like4U0142+61and1E
the transition between the accretion and propeller phases.
2259+586orthesourcesinthepropellerphase,likeXDINs.
The relation between B and the period upper limit will
0 As a final note, in our model, the sources in the first
be investigated in detail in an independent paper. In our
propeller phase could be observed as high-B radio pulsars.
model, the disc torque acting on the star is most efficient This is because the efficient disc torques increase P˙ signifi-
in the accretion epochs, and the increasing periods of the
cantlybeyondthelevelthatcanbeachievedbythemagnetic
sources level off with termination of the accretion epoch.
dipoletorqueswiththesamefieldstrength.Adetailedpop-
The results obtained by Ertan et al. (2014) imply that, un-
ulationsynthesisofthesesources,whichisbeyondthescope
like most AXP/SGRs, for the six XDIN sources2 accretion
of the present work, will be studied in a separate paper.
phase terminated long ago, and they are slowing down in
the final propeller phase at present.
Since the model results do not well constrain the disc
ACKNOWLEDGMENTS
masses for XDINs, we are not able to determine whether
thereisasystematicrelationbetweentheactualdiscmasses We acknowledge research support from Sabancı University,
andthedipolefieldsofthecombinedXDINandAXP/SGR and from TU¨BI˙TAK (The Scientific and Technological Re-
populations (see Fig. 6). Nevertheless, we estimate that searchCouncilofTurkey)throughgrant113F166.Wethank
XDINs are likely to be close to the lower bounds on their M. A. Alpar for useful discussions and comments on the
allowed disc masses seen in Fig. 6, since evolution with low manuscriptwhoisamemberoftheScienceAcademy–Bilim
discmassesleavesmostoftheyoungXDINsbelowthecur- Akademisi, Istanbul, Turkey.
rentdetectionlimits.Thispictureisconsistentwiththelack
of detections of many young XDINs in X-rays at the ages
of AXP/SGRs. This might also imply that the disc masses
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