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Advances in Space Research 38 (2006) 2915–2916

Superbursts and long bursts as surface phenomenon of compact objects

Monika Sinha a,*, Mira Dey a, Subharthi Ray b, Jishnu Dey a,c

a Department of Physics, Presidency College, 86/1 College Street, Calcutta 700 073, Indiab Inter University Centre for Astronomy and Astrophysics, Post bag 4, Ganeshkhind, Pune 411 007, India

c Azad Physics Centre, Department of Physics, Maulana Azad College, Calcutta 700 013, India

Received 23 September 2005; received in revised form 16 January 2006; accepted 16 January 2006

Abstract

We suggest that superbursts from some low mass X-ray binaries may be due to breaking and re-formation of diquark pairs, on thesurface of realistic strange stars. Diquarks are expected to break up due to the explosion and shock of the thermonuclear process. After aprolonged accretion when almost all pairs get broken, the subsequent production of copious diquarks may produce sufficient energy toproduce the superbursts.� 2006 Published by Elsevier Ltd on behalf of COSPAR.

Keywords: Dense matter; Elementary particles; Diquarks; Stars; Superburst

1. Introduction

Recently some type-I X-ray bursters show bursts 1000times longer in duration and 1000 times more energeticthan typical type-I X-ray bursts. That is why they areknown as superbursts. Till date superbursts have beenobserved from eight different sources. Two of them showedrepeated superbursts.

There are models of superbursts for neutron stars interms of unstable carbon burning (Cumming and Bildsten,2001; Strohmayer and Brown, 2002). But there is disparitybetween the superburst energies and recurrence timeobserved and the energies and recurrence time predictedby theoretical models.

We have employed the realistic strange star (ReSS)model (Dey et al., 1998) to get a good estimate of the ener-gy liberated in a superbursts. We suggest that diquarkspresent on the ReSS surface are expected to break up dueto the explosion and shock of the thermonuclear processes.The subsequent production of copious diquarks mayaccount for superburst.

0273-1177/$30 � 2006 Published by Elsevier Ltd on behalf of COSPAR.

doi:10.1016/j.asr.2006.01.027

* Corresponding author.E-mail address: monika2003@vsnl.net (M. Sinha).

2. The spin–spin potential and interaction energy

The quark–quark interaction has a spin dependent com-ponent. This spin dependent potential is a delta functionwhich gets changed to a smeared one when one introducesthe idea of a finite glueball mass or a ‘secondary chargecloud screening’ as in electron-physics as explained byBhaduri et al. (1980).

The form of the potential is given below:

Hij ¼ �2asr3

3mimjp1=2ðki � kjÞðSi � SjÞe�r2r2

ij : ð1Þ

The factor r3/p1/2 normalizes the potential. In this equa-tion as is the strong coupling constant, and the subscriptedm, k and S are the constituent masses, colour matrices andspin matrices for the respective quarks. Inverse of r is theeffective range of the potential.

For this spin dependent part of quark–quark interactiontwo quarks will form a diquark, in which their spins areeither parallel or antiparallel, whenever they come closer.That is two quarks will be spin aligned to form a diquark.

This spin dependent part of the quark–quark potential isresponsible for the mass difference between nucleons and Disobars which is known as N � D mass difference. Dey and

Table 2The correlation energy for u–d pairs for spin singlet (colour �3) states inMeV. For spin triplet (colour 6) state the energies will be six times less

Sets 1 2 3 4 5 6

Eud �23.578 �23.287 �41.025 �38.225 �52.814 �46.636

Table 1Parameters of the Gaussian potential

Sets 1 2 3 4 5 6

as 0.5 0.5 0.87 0.87 1.12 1.12r(fm�1) 6.0 4.56 0.87 2.61 6.0 2.03

2916 M. Sinha et al. / Advances in Space Research 38 (2006) 2915–2916

Dey (1984) found that this gives r varying from 6 to2.03 fm�1 for a set of as 0.5–1.12 can reproduce observedN � D mass difference. As nucleons and D isobars consistof only u and d quarks, from the observable like N � Dmass difference one can get the potential parameters onlyfor u � d interaction. The parameters we have used are giv-en in Table 1.

Anti-symmetry of flavour symmetric diquark wave func-tion requires that while space part is symmetric, diquarkmust be either in spin singlet and colour symmetric (6)state, or in spin triplet and colour anti-symmetric (�3) state.In both cases spin–spin force is repulsive1 and formation ofpair is inhibited.

For flavour anti-symmetric diquarks, however, the situ-ation is the opposite. Colour symmetric (6) configurationis associated with the spin triplet so that (ki Æ kj)(Si Æ Sj)1/3 and colour anti-symmetric state (�3) goes with the spinsinglet which gives (ki Æ kj)(Si Æ Sj) = 2. These channels pro-duce attraction. Hence there is a probability for exampleof u, d quarks to pair up predominantly in spin singletstate. The effect of this can be found easily in our modelsince we know the distribution of the u and d quarks inthe momentum space and their Fermi momenta areuniquely determined from precise and lengthy calculationssatisfying beta stability and charge neutrality (Dey et al.,1998).

The potential (Eq. (1)) is evaluated in the momentumspace. Thus on average the correlation energy of a paircan be found as:

Eud ¼ �1

2ðki � kjÞðSi � SjÞ

2asr2p3mimj

nu þ nd

nund

6� 2

ð2pÞ4I ; ð2Þ

where nu and nd are number density of u and d quarks,respectively, at the star surface. Here

I ¼Z kfu

0

Z kfd

0

Z 1

�1

f ðku; kd ; hÞk2d dkdk2

u dku dðcos hdÞ ð3Þ

1 Private communication, R.K. Bhaduri.

and

f ðki; kj; hÞ ¼

1� exp �k2

i þk2j

4� kikj cosðhijÞ

2

r2

0@

1A

k2i þ k2

j

4� kikj cosðhijÞ

2

; ð4Þ

where subscripted ks are momenta of interacting quarksand kfis are Fermi momenta for ith species of quark at starsurface.

These correlation energies for different sets of parame-ters (see Table 1) are given in Table 2.

3. Conclusions

The overall effect of producing a diquark is lowering ofenergy of two single quarks by a few MeV. Once the pairsare misaligned during normal bursts the recombination ofall broken pairs may provide bursts with energy releaseestimated to be large. The estimated total energy liberated,1042 erg, can be explained in our model with the calculatedpair density �0.27 fm�3 and a surface thickness of only amicron, if the entire surface is involved.

References

Bhaduri, R.K., Cohler, L.E., Nogami, Y. Quark–quark interaction andthe nonrelativistic quark model. Phys. Rev. Lett. 44, 1369–1372,1980.

Cumming, A., Bildsten, L. Carbon flashes in the heavy-element ocean onaccreting neutron stars. Astrophys. J. 559, L127–L130, 2001.

Dey, J., Dey, M. Effect of quark–quark tensor and spin–spin force on theradiative decay of D-isobar. Phys. Lett. B 138, 200–204, 1984.

Dey, M., Bombaci, I., Dey, J., Ray, S., Samanta, B.C. Strange stars withrealistic quark vector interaction and phenomenological density-dependent scalar potential. Phys. Lett. B 438, 123–128. Addendum1999, 447, 352–353; Erratum 1999, 467, 303–305, 1998.

Strohmayer, T.E., Brown, E.F. A remarkable 3 hour thermonuclear burstfrom 4U 1820-30. Astrophys. J. 566, 1045–1059, 2002.