Two clocks in the PSR J0737--3039 binary system and their ...

B inary Radio Pulsars A SP C onference Series,Vol.T B D ,2004 eds. F.A .Rasio & I.H .Stairs

T w o clocks in the P SR J0737{3039 binary system and their im plications for the system ’s origin and evolution

arXiv:astro-ph/0404274v1 14 Apr 2004

D .R .Lorim er,1 M .B urgay,2 P.C .C .Freire,3 A .G .Lyne,1 M .K ram er,1 A .Possenti,4 M .A .M cLaughlin,1 F.C am ilo,5 R .N .M anchester,6 N .D ’A m ico,4 B .C .Joshi7 1U niversity

ofM anchester,JodrellB ank O bservatory,SK 11 9D L,U K degliStudidiB ologna,D ipartim ento diA stronom ia,Italy 3N A IC ,A recibo O bservatory,H C 3 B ox 53995,A recibo,PR 00612,U SA 4IN A F - O sservatorio A stronom ica diC agliari,09012 C apoterra, Italy 5C olum bia A strophysics Laboratory, 550 W 120th St,N Y 10027,U SA 6AT N F,C SIR O ,PO B ox 76,Epping,N SW 2121,A ustralia 7N C R A ,PO B ox B ag 3,G aneshkhind,Pune 411007, India 2U niversita

A bstract. A sdiscussed elsew here in these proceedings,the double pulsar system is a m agni cent laboratory for gravitational physics and for studying pulsar m agnetospheres. H ere we consider the uses of having two clocks in the system in the context ofits origin and evolution. W e nd that the \standard" evolutionary scenario involving spin-up of the rst-born neutron star in an X -ray binary phase is consistent w ith the observed param eters. Equality ofthe spin-dow n ages ofthe two pulsars requires that the post-accretion spin period of A m ost likely lies in the range 16 < P 0;A < 21 m s. T he likely age ofthe system is 30 70 M yr.

1. Introduction A n application of the standard binary pulsar evolutionary m odel (e.g. B hattacharya & van den H euvel1992) to the double pulsarsystem J0737{3039 identi es the 22.7-m s pulsar (hereafter A ) as the rst-born neutron star. Follow ing an initialphase w here A existed as a regular radio pulsar w ith a m ain-sequence com panion,the currently observed spin param eters ofA are the resultofa subsequent X -ray binary phase w here it acquired m atter and angular m om entum from the secondary star after the secondary evolved o the m ain sequence and over owed itsR oche lobe. B y processesthatarenotfully understood,thism asstransfer phase also resulted in a reduction of A ’s m agnetic eld (Shibazakiet al.1989). Follow ing the supernova explosion ofthe secondary,a second neutron star was form ed w hich we now observe as the 2.77-s pulsar (hereafter B ). W hile the spin periodsofboth these pulsars,and the low inferred m agnetic eld of A relative to B 1 are consistent w ith this m odel, a further test is to 1

D ue to the interaction ofA ’s w ind w hich penetrates deep into B ’s m agnetosphere,som e care should be taken w hen interpreting B ’s m agnetic eld strength. In spite ofthis disruption,B is observed to be spinning dow n due to a steady braking torque w hich w e m odelin Section 2.

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com pare the tim e since the spin-up phase ofA ended (TA ) w ith the tim e since B has been active as a radio pulsar (TB ). W e therefore expect TA = TB . T he sim plest m eans to test this prediction is to use the characteristic ages of A and B , w hich are based on the observed periods and period derivatives: _ _ 108 A = P A =(2P A ) and B = P B =(2P B ). Lyne et al. (2004) nd A = 2:1 8 yr and B = 0:5 10 yr. Possible explanations for this discrepancy are: (i) the standard evolutionary scenario does not apply; (ii) as observed in other pulsars (see e.g. K ram er et al.2003), characteristic ages are not reliable; (iii) both the m odeland the characteristic agesare w rong!G iven the aforem entioned circum stantialevidence in favour ofrecycling hypothesis,the sim plest solution is option (ii). W e now brie y investigate the im plications for this case. Further details w illbe given in a forthcom ing paper (Lorim er et al.in preparation). 2. M odeling the spin-dow n for A and B W e consider a generic pulsar spin-dow n m odelofthe form _= K

n

(1)

;

w here for a spin period P ,the angular frequency = 2 =P ,n is the braking index (for spin-dow n due to m agnetic dipole radiation,n = 3) and K depends on the braking torque applied to the star. In the sim plest case,both K and n are independent of tim e and equation (1) can be integrated directly. For the case n 6 = 1,we nd the \true age" ofthe pulsar "

ttrue =

2 (n

1)

1

#

P0 P

n 1

(2)

;

w here P 0 is the initial spin period and = P =2P_ is the characteristic age. A lternatively,ifK decays exponentially w ith 1=e tim e scale tdecay ,then treduced = tdecay ln(1 + ttrue=tdecay )

(3)

is the so-called \reduced age". W e now consider various applications of these solutions by sim ply equating the derived ages for the two pulsarsand determ ining their resulting initialspins and ages. In order to distinguish between both pulsars,we use \A " and \B " subscripts w here appropriate. C ase 0: spin-dow n due to a non-decaying m agnetic dipole. W e rst assum e thatboth pulsarsspin dow n due to m agnetic dipole radiation (i.e.nA = nB = 3), their braking torques do not decay (i.e. K A and K B are constant) and that the initialspin period ofB was m uch sm aller than currently observed (i.e.P 0;B P B ). R equiring that ttrue;A = ttrue;B , the initialspin period of A after the spin-up phase (P 0;A ) and the tim e since spin-up ceased (T ) are: q

P 0;A = P A

1

(B = A )’ 20m s; and T = TB =

B

’ 50M yr:

(4)

A sm entioned by Lyne etal.(2004),the value forP 0;A isconsistent w ith the period ofJ0737{3039A predicted by spin-up m odels(e.g.A rzoum anian etal.1999).

T wo clocks in the PSR J0737{3039 binary system

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Figure 1. Sim ulated distributions of the post-accretion spin period ofA (leftpanels)and the tim e since the end ofthe spin-up phase (right panels). In each case,the distributionsare calculated assum ing a range ofinitialspin periodsforB (solid curves)and a negligible initialperiod (dotted curves). T he thick verticalline show s A ’s current spin period.

C ase 1: no torque decay,nA = 3 and 1:4 < nB < 3:0. A m orerealistic m odel isto relax the assum ption ofdipolarspin-dow n forB and allow itsbraking index to vary in the range observed forothernon-recycled pulsars(1:4 < nB < 3:0;see e.g. K aspi& H elfand 2002 for a review ). For a at braking index distribution in this range, a sim ple M onte C arlo sim ulation to com pute ttrue;B for a large num ber of trials results in the distributions of P 0;A and T for the condition ttrue;A = ttrue;B show n in Fig. 1. In order to show the negligible e ect of B ’s

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unknow n initialspin period on the results,we perform ed allcalculations w ith a at distribution in the range 0 < P 0;B < P B (solid lines) and for P 0;B = 0 (dashed lines). In both cases,the resulting initialspin period distribution for A peak sharply justbelow 20 m s.T he age distribution peaksat 50 M yr(i.e. B ). C ase 2: no torque decay,variable braking indices for A and B .R elaxing the conditions on braking indices im posed in case 1,the centre panelofFig.1 show sthe resultsw hen nA and nB are draw n from atdistributionsin the range 0 < n < 5. R egardlessofB ’sinitialspin period,the peak oftheP 0;A distribution is increased over case 1;the age distribution favours sm aller ages than case 1. C ase 3: nA = nB = 3, exponential torque decay for B . T he above two casesassum eno decay ofthebraking torque.A n alternative solution to the spindow n m odelis the case ofan exponentially decaying braking torque resulting in equation (3)above. T hecauseoftorquedecay isuncertain and controversial,and thoughtto be due to eitherthe decay ofthe neutron star’sm agnetic eld and/or thealignm entofthespin and m agnetic axesw ith tim e(seee.g.Taurisand K onar 2001). Since torque decay is not thought to be signi cant for recycled pulsars (B hattacharya & van den H euvel1992),we considerhere the case in w hich only the torque on B decays. In Fig.1 we show the sim ulated distributions resulting from the equality ttrue;A = treduced;B assum ing pure m agnetic dipole braking (nA = nB = 3) and a torque decay on B w ith a tim escale td;B draw n from a at distribution between 10 and 100 M yr. T he e ect ofsuch a decay is to decrease the age signi cantly so that the distribution peaks at around 30-40 M yr. 3. C onclusions T he two clocks in the double pulsarsystem J0737{3039 provide a unique m eans to constrain the age and birth spin periods of the two pulsars. T hese sim ple case studies dem onstrate the use ofthe recycling m odelto place constraints on the post-accretion spin period ofA (P 0;A )and the age since spin-up ceased (T ). Forthe spin-dow n m odelsconsidered,we nd P 0;A to be in the range 16 21 m s and T to be in the range 30 70 M yr. T his is shorter than the age of100 M yr assum ed in the m ergerrate calculations by B urgay etal.(2003)and K alogera et al.(2004) and hence increases the overallneutron star m erger rate by 20{40% . R eferences A rzoum anian,Z.,C ordes,J.M .& W asserm an,I.,1999. A pJ,520,696. B hattacharya,D .& van den H euvel,E.P.J.,1991. Phys. Rep.,203,1. B urgay,M .et al.,2003,N ature,426,531. K alogera,V .et al.,2004,A pJ,601,L179. K aspi,V .M .& H elfand,D .J.,2002. In:N eutron Stars in Supernova Rem nants, 3,eds Slane,P.O .& G aensler,B .M .,A SP,San Francisco. K ram er,M .et al.,2003. A pJ,593,31. Lyne,A .G .et al.,2004. Science,303,1153. Shibazaki,N .et al.,1989. N ature,342,656. Tauris,T .M .& K onar,S.,2001. A & A ,376,543.