New Astronomy 14 (2009) 37–39

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New Astronomy

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Members of the double pulsar system PSR J0737-3039: Neutron stars orstrange stars?

Manjari Bagchi a,*, Jishnu Dey b,1,2, Sushan Konar c, Gour Bhattacharya b, Mira Dey b,1,2

a Tata Institute of Fundamental Research, Astronomy and Astrophysics, Homi Bhaba Road, Colaba, Mumbai, Maharastra 400005, Indiab Department of Physics, Presidency College, Kolkata 700073, Indiac CTS Physics, Indian Institute of Technology, Kharagpur, India

a r t i c l e i n f o a b s t r a c t

Article history:Received 16 February 2008Received in revised form 23 April 2008Accepted 28 April 2008Available online 6 May 2008

Communicated by E.P.J. van den Heuvel

PACS:21.65.Qr21.65.Mn26.60.Kp97.60.Gb97.60.Jd

Keywords:Dense matterEquation of state(Stars:) pulsars: individual (PSR J0737-3039)

1384-1076/$ - see front matter � 2008 Elsevier B.V. Adoi:10.1016/j.newast.2008.04.006

* Corresponding author. Fax: +91 22 2280 4610.E-mail address: manjari@tifr.res.in (M. Bagchi).

1 Associate, IUCAA, Pune, India.2 Supported by DST Ramanna grant, Govt. of India.

One interesting method of constraining the dense matter Equations of State is to measure the advance-ment of the periastron of the orbit of a binary radio pulsar (when it belongs to a double neutron star sys-tem). There is a great deal of interest on applicability of this procedure to the double pulsar system PSRJ0737-3039 (A/B). Although the above method can be applied to PSR A in future within some limitations,for PSR B this method cannot be applied. On the other hand, the study of genesis of PSR B might be usefulin this connection and its low mass might be an indication that it could be a strange star.

� 2008 Elsevier B.V. All rights reserved.

1. Introduction

It was argued by Witten (1984) that strange quark matter, com-posed of u, d and s quarks, is more bound than nuclei at zero pres-sure and is therefore the true ground state of matter. Ever since theadvent of this hypothesis the existence and the observational char-acteristics of the strange quark stars (Alcock et al., 1986; Haenselet al., 1986) are being debated.

Unfortunately, strange stars and neutron stars have a number ofalmost similar physical properties like the range of masses, stablerotation periods, cooling history and so on, but strange stars aremore compact than neutron stars. Because of this, quite a few com-pact objects were speculated to be strange stars but there has beenno conclusive evidence for the case or against it. For example, RXJ1856.5-3754 has been the subject of such a recent debate because

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of certain peculiarities of its thermal X-ray properties (Drake et al.,2002; Henderson and Page, 2007).

Understandably the most convincing proof for a strange starwould come from a direct indication of the equation of state andwe believe that the double neutron systems (DNS) might provideus with that answer. Precise measurements of a number of param-eters of DNS systems allow for the study of a variety of phenomenalike the effects of general relativity, the emission of gravitationalwaves or the intricacies of the binary evolution. In particular, inthe case of PSR J0737-3039, the only double pulsar system (Burgayet al., 2003; Lyne et al., 2004) detected so far, it is possible to mea-sure many more properties like the mass ratio of the two neutronstars directly obtainable from pulsar timing. The two pulsars arenamed as J0737-3039A and J0737-3039B. The values of spin periodand magnetic field of these two are P ¼ 22:7 ms, B ¼ 6:4� 109 Gfor pulsar A and P ¼ 2:77 s and B ¼ 1:6� 1012 G for pulsar B.Apparently A is a typical recycled pulsar and B is the one born sec-ond. The periods PA;B and their time derivatives provide upper lim-its for the lifetimes tA � 210 Myr and tB � 50 Myr. The estimatedseparation (sum of the semi major axes) was R � 1012 cm andthe eccentricity was e � 0:11 when pulsar B was born. The present

38 M. Bagchi et al. / New Astronomy 14 (2009) 37–39

values of separation and eccentricity are 8:8� 1011 cm and0.0877775(9). As the values of R and e does not change consider-ably with time, the analysis of the origin of PSR J0737-3039B isinsensitive to the exact age of the pulsar.

Formation models of PSR J0737-3039 were considered by vari-ous authors (Dewi and van den Heuvel, 2004; Podsiadlowski et al.,2005; Piran and Shaviv, 2005). Dewi and van den Heuvel (2004)proposed that J0737-3039 has originated from a close helium starplus neutron star (HeSNS) binary in which at the onset of theevolution the helium star had a mass in the range 4.0–6.5 M�and an orbital period in the range 0.1–0.2 day. In their model, akick velocity in the range 70–230 km/s must have been impartedto the second neutron star at its birth. Podsiadlowski et al.(2005) proposed an electron capture supernova scenario. Usingthe observational indications that the binary system will end upwithin 50 pc from the galactic plane with 0:088 < e > 0:14 andwith a transverse velocity less than 30 km/s, provided 50 Myrs inthe past the progenitor system had a circular orbit, Piran and Sha-viv (2005) estimated that it is most likely that the progenitor ofPSR J0737-3039B had a mass of 1:55� 0:2 M� with a low kickvelocity 30 km/s. The progenitor may well have been a NeOMgstar. Willems et al. (2006) used population synthesis method toestimate the most likely radial velocity of the binary. They favoredthe standard formation scenario with reasonably high kick veloci-ties (70–180 km/s) and pre-SN mass m2;i of at least 2M� which fitswith a Helium star progenitor, but acknowledged that for verysmall transverse velocities (�10 km/s) lower mass progenitorsare allowed or even favored.

2. The nature of the members of PSR J0737-3039

The system is rich in observational phenomena, including ashort radio eclipse of A by B and orbital modulation of the radioflux of B affected by A. Much radio pulse data from both pulsarshas already been accumulated. High energy observations couldalso be important to these studies since both stars also emit X-raysand they are now being detected recently.

2.1. Radio observations

The best answer to our question regarding the equation of statewould come from the measurement of the moment of inertia ofindividual stars in this system. The moment of inertia can be deter-mined by measuring the extra advancement of the periastron ofthe orbit above the standard post-Newtonian one due to thespin–orbit coupling (Damour and Shäfer, 1988) using timing anal-ysis of radio data. Periastron advance (which is the observablequantity) for a DNS system is given by:

_x ¼ 3b20n

1� e2 1þ f0b20 � ðgs1bs1b0 þ gs2bs2b0Þ

� �ð1Þ

where the first term inside the square bracket represents 1PN term,the second term term inside the third bracket represents 2PN term,and the third term inside the third bracket represents spin–orbitcoupling (SO). The parameters used in the above expression are de-fined as:

b0 ¼ðGMnÞ1=3

cð2Þ

bsa ¼cIaxa

Gm2a

ð3Þ

f0 ¼1

1� e2

394

x21 þ

274

x22 þ 15x1x2

� �� 13

4x2

1 þ14

x22 þ

133

x1x2

� �ð4Þ

gsa ¼xað4xa þ 3xaþ1Þ

6ð1� e2Þ1=2 sin2 i½ð3 sin2 i� 1Þk � sa þ cos iK0 � sa ð5Þ

where G is the gravitational constant, Ia is the moment of inertia ofath body (a ¼ 1;2), xa ¼ 2p=Pspin is its angular velocity of rotation(here aþ 1 means modulo 2, i:e: 2+1=1) and n ¼ 2p=Porb.x1 ¼ m1=M; x2 ¼ m2=M and M ¼ m1 þm2, k is the orbital angularmomentum vector, sa is the spin vector and K0 is the line of sightvector. Using (Eq. (1)), the moment of inertia can be estimated fromthe observed value of _x provided we know Pspin, e, Porb, m1 and m2

(which can be estimated from timing analysis of radio data) of thebinary components which is the case for J0737-3039 A and B.

On the other hand, the moment of inertia of a star of knownmass can be theoretically calculated using a particular EoS. Bejgeret al. (2005) calculated the moment of inertia for both PSR J0737-3039 A and B using 25 EoS of dense matter including an EoS forstrange quark matter. Bejger et al. (2005) found IA to lie between1:894� 1045 g cm2 and 0:726� 1045 gcm2. They also checked thatthe moment of inertia estimated using Hartle’s approximations (asdescribed in Kalogera and Psaltis (1999)) differs from the exact cal-culation with rotating axisymmetric stellar model by not morethan 1%. We re-performed the analysis and found IA to lie between0:67—0:74� 1045 g cm2. It is worthwhile to mention that the stif-fest EoS (MFT17) chosen by Bejger et al. strongly overestimate andthe softest EoS (BPAL12) strongly underestimate nuclear matterincompressibility. So from the view point of a theoretician, the va-lue of IA is likely to be somewhere in the middle region of fig. 1 ofBejger et al. (2005).

But the point to note here is that, in the expression of _x, themoments of inertia of both members of a DNS system are present(Eq. (1)) which means that we have one observable and two un-knowns which is impossible to solve. But we have checked thatthe bsa term is significant only for Pspin < 100 ms, so the term forJ0737-3039B can be neglected and only the contribution fromJ0737-3039A remains. So determining the moment of inertia ofPSR J0737-39B is impossible where measuring the same for PSRJ0737-39A is possible by neglecting the spin–orbit coupling termdue to PSR J0737-39B. This implies that this method of under-standing the form of the matter building the star from pulsartiming analysis can be used for PSR J0737-39A, but not for PSRJ0737-39B. So we cannot test the prediction of IB as claimed byBejger et al. (2005).

Even for PSR A, to measure the moment of inertia within 10% ofaccuracy, we need to improve the accuracy in the knowledge ofbinary parameters to a significant extent. This possibility was stud-ied recently by Iorio who concludes that ‘‘the possibility of reach-ing in a near future the required accuracy to effectively constrain IA

to 10% level should be, perhaps, considered with a certainskepticism”.

2.2. Genesis of PSR J0737-39B

One can consider an estimate of minimum progenitor mass forPSR J0737-39B, keeping in mind the recent comment by Stairs et al.(2006), that an important point usually neglected is the contribu-tion from gravitational binding energy which is defined as

Egrav ¼ MP �MG ð6Þ

where MG is the gravitational mass and MP is the proper mass. Theincrease in baryonic energy is given by

Ebar ¼Z R

0

DEðrÞnðrÞdr

1� 2GMðrÞr

h i1=2 ð7Þ

where DE is the increase in energy per baryon due to the conversionfrom ONeMg matter to strange quark matter, n is the number den-sity, G is the gravitational constant, M and R are the mass and radiusof the star. So the mass of the progenitor will be

M. Bagchi et al. / New Astronomy 14 (2009) 37–39 39

Mprogenitor ¼ Mpulsar þ Etot þ Dm ð8Þ

where

Etot ¼ Egrav þ Ebar ð9Þ

and Dm is the mass loss during the conversion process. PSR J0737-3039B, which has MG ¼ 1:249 M�, corresponds to MP ¼ 1:5187 inour SS model (Bagchi et al., 2006) and we found Egrav ¼ 0:2697 M�and Ebar ¼ 0:0708 M� giving Etot ¼ 0:3405 M�. So Mprogenitor ¼1:249þ 0:3405þ Dm ¼ 1:5895þ Dm. This value is close to thatestimated by Piran and Shaviv (2005) i:e:1:55� 0:2 M� with a lowkick velocity 30 km/s. On the other hand, if J0737-3039 is a neutronstar, we get using APR EoS (Akmal et al., 1998), MP ¼ 1:4357 givingEgrav ¼ 0:1867 and Ebar ¼ 0 giving Mprogenitor ¼ 1:249þ 0:1867þDm ¼ 1:4357þ Dm which is also not far from Piran and Shaviv’s.Remember, detailed simulation is needed to know the exact valueof Dm which we hope will be done in the future. So it is very diffi-cult to identify whether J0737-3039 B is a strange star or a neutronstar from these arguments.

Another interesting outcome is that, in our model (Bagchi et al.,2006), a strange star with MG ¼ 1:249 M� has 1:9058� 1057 bary-ons while a neutron star with MG ¼ 1:249 M� has 1:6390� 1057

while a normal NeOMg star of mass 1:59 M� has 1:9060� 1057

number of baryons. We have assumed, of course, that the gravita-tional mass is the same as its baryonic mass for a normal star – asthe general relativistic effects are very small. This estimate showsthat if J0737-3039 B is a strange star then the baryon loss isnegligible (0.01%) implying a small Dm. On the other hand, ifJ0737-3039 B is a neutron star then the baryon loss is larger(14%) implying larger values for Dm. Small baryon loss (as obtainedin the first case) supports Piran and Shaviv’s model with small kick.So this study would suggest PSR B to be a strange star.

3. Conclusions and summary

We have discussed how the double pulsar system can help usto constrain the dense matter EsoS. Radio observations (timinganalysis) may help us to constrain the EoS of PSR A in future and

may allow us to deduce whether it is a strange star or a neutronstar.

For PSR B, as this is not possible in the present situation, we canuse indirect methods, e:g: modeling its formation scenario from thepresent day observed parameters. The small mass of the star mightbe an indication that it is a strange star, since in the formation ofsuch a star, in addition to the gravitational binding energy loss,mass is also lost in the form of baryonic energy. Although this issuggestive, more modeling is required to support such aconclusion.

Acknowledgements

The authors thank Ignazio Bombaci and Alak Ray for excitingdiscussion, Bart Willems for helpful comments and Tomasz Bulikfor sending their moment of inertia results. MD thanks DST, Govt.of India, for Ramanna Fellowship. JD also thanks DST for the Ram-anna project for sustenance.

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