Gamma Ray Bursts from delayed quark-deconfinement phase transition in neutron stars

PROCEEDINGS SUPPLEMENTS

Nuclear Physics B (Proc. Suppl.) 113 (2002) 268-274

ELSEVIER

phase transition

Gamma Ray Bursts from delayed quark-deconfinement in neutron stars Z. Berezhiani “Dipartimento

a, I. Bombaci di Fisica,

b, A. Drago ‘, F. Frontera

Universita

di L’Aquila

d and A. Lavagno

and INFN

Sezione

e

de1 Gran Sasso,

I-67010

Coppito,

Italy b Dipartimento

‘Dipartimento ‘TESRE,

di Fisica,

di Fisica,

Universita

Universit&

CNR, I-40129 Bologna,

eDipartimento

di Fisica,

Politecnico

di Pisa and INFN di Ferrara

Sezione di Pisa, I-56127 Pisa, Italy

and INFN Sezione di Ferrara,

I-44100 Ferrara,

Italy

Italy di Torino

and INFN Sezione di Torino,

I-10129 Torino,

Italy

There have been recently strong observational indications [l] about the possibility that some Gamma-Ray Bursts (GRBs) can take place years after a supernova (SN) explosion due to some mechanism involving the compact star left by the stellar collapse associated to the supernova. In the present work, we propose a model to explain this possible “delayed” GRB-SN association. Our model is based on the conversion of a pure hadronic star (neutron star) into a star made at least in part of deconfined quark matter. The conversion process can be delayed if the surface tension of the interface between the hadronic and deconfined quark matter phases is taken into account. The nucleation time (i.e. the time to form a critical-size drop of quark matter) can be extremely long if the mass of the star is small. Via mass accretion the nucleation time can be dramatically reduced and the star is finally converted from the metastable into the stable configuration. A huge amount of energy, of the order of 1O52-1O53 erg, is released during the conversion process and can produce a powerful gamma ray burst. The delay between the supernova explosion generating the metastable neutron star and the stellar conversion can explain the delay observed in GRB990705 [I] and in GRBOll211 [2].

1. INTRODUCTION The recent discovery of redshifted Fe K-lines in the X-ray afterglow of some Gamma Ray Bursts (GRBs) [l-5] g’Ives a very strong indication in favour of an association

between

GRBs

and Su-

pernova (SN) explosions. Particularly, in the case of the gamma ray burst of July 5, 1999 (GRB990705) and in the case of GRB011211, it has been possible to estimate the time delay between the two events. For GRB990705 the supernova explosion is evaluated to have occurred about 10 years before the GRB [l], while for GRB011211 about four days before the burst [2]. The scenario which emerges from these findings is the following two-stage scenario: (i) the first event is the supernova explosion which forms a compact stellar remnant, i.e. a neutron star (NS); 0920-5632/02/$ - see front matter0 2002 Elsevier Science B.V PI1 SO920-5632(02)01851-O

(ii) the second catastrophic event is associated with the NS and it is the energy source for the observed GRB. These new observational data, and the scenario outlined above, poses severe problems for most of the current theoretical models for the central energy source (the so called “central engine”) of GRBs. The main difficulty of all these models is to give an answer to the following questions: what is the origin of the second “explosion”? How to explain the long time delay between the two events? In the so called supranowa model [6] for GRBs the second catastrophic event is the collapse to a black hole of a supramassive neutron star, i.e. a fast rotating NS with a baryonic mass MB above the maximum baryonic mass for non-rotating All rights reserved.

Z. Berezhiani et al. /Nuclear

Physics B (Proc. Suppl.) 113 (2002) 268-274

configurations. In this model, the time delay between the SN explosion and the GRB is equal to the time needed by the fast rotating newly formed neutron star to get rid of angular momentum and to reach the limit for instability against quasiradial modes where the collapse to a black hole occurs (see e.g. [7]). Questions concerning both the duration of the burst and its energy have been raised by several authors [8,9], suggesting that in the supranova model the burst would turn out to be too short and too weak. In the present work we propose an alternative model to explain the GRB-SN association and in particular the long time delay inferred for GRB990705 and GRB011211. In our model the second explosion is related to the conversion from a metastable, purely hadronic star (neutron star) into a more compact star in which deconfined quark matter (QM) is present. This possibility has already been discussed in the literature [lo-121. The new and crucial idea we introduce here, is the metastability of the purely hadronic star due to the existence of a non-vanishing surface tension at the interface separating hadronic matter from quark matter. The mean-life time of the metastable NS can then be connected to the delay between the supernova explosion and the GRB. As we shall see, in our model we can easily obtain a burst lasting a few tens of seconds, in agreement with the observations. The order of magnitude of the energy released is also the appropriate one to power a GRB. 2. COMPACT

269

where a decor&red quark phase of matter could be found. Various possibilities have been discussed in the literature, concerning the theoretical picture of the internal structure of the compact stars usually called “neutron stars”. Depending on the microscopic properties of ultradense matter, and particularly on the possibility to have deconfined quark matter in the star, it is possible to have three different classes of compact stars: (a) purely Hadronic Stars (HS), in which below the usual neutron star crust one has a layer of neutron-rich nuclear matter in beta-equilibrium with electrons and muons, and possibly an inner core containing hyperons or a condensate of negative kaons in addition to the particles mentioned above. In these compact stars no fraction of quark matter is present; (b) Hybrid Stars (HyS), which possess a “quark core” either as a mixed phase of deconfined quarks and hadrons or as a pure quark matter phase; (c) Quark Stars (QS), which can be realized as pure u,d,s strange quark matter stars (the so called Strange Stars) satisfying the Bodmer-Witten hypothesis [14,15], or as stars which above a strange quark matter core possess a mantle of mixed quark-hadron phase [16]. Compact stars of each of the three classes could be endowed with strong magnetic fields and could manifest their presence in the universe as pulsars or as compact X-ray sources in binary systems. A sizeable amount of observational data collected by the new generations of X-ray satellites, is providing a growing body of evidence for the existence of quark stars [17-221.

STARS

Quantum Chromodynamics (QCD), as the fundamental theory of strong interactions, predict the transition to a deconfined quark phase to occur at a density of a few times nuclear matter saturation density (ps N 2.8 x 1014g/cm3). The search of this new phase of matter is one of the main goal in heavy ion physics [13]. Experiments at Brookhaven National Lab’s Relativistic Heavy Ion Collider (RHIC) and at CERN’s Large Hadron Collider (LHC), will hopefully clarify this issue in the near future. The core of a neutron star is one of the best candidate in the universe

3. QUANTUM QUARK STARS

NUCLEATION OF MATTER IN HADRONIC

In our scenario, we consider a purely hadronic star whose central density (pressure) is increasing due to spin-down or due to mass accretion (from a companion star or from the interstellar medium). As the central density approaches the quark deconfinement critical density, a virtual drop of quark matter can be formed in the central region of the star. The quantum fluctuations of a spherical droplet of quark matter having a radius

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270

R are regulated

by a potential

energy of the form

PI M/M,

U(R) = $xR3nq(p,

- ph) + 47r0R2

(1)

where nq is the quark baryon density, ph and pp are the hadronic and quark chemical potentials at, a fixed pressure P and ~7 is the surface tension for the surface separating the quark phase from the hadronic phase. For the sake of simplicity and to make our present discussion more transparent, in the previous expression we neglect the so called curvature energy [24] and the terms connected with the Coulomb energy [25,26]. The inclusion of these terms will not modify the general physical picture of our model and the conclusion of the present study [27]. The value of the surface tension g is poorly known, and typical values used in the literature range within lo-50 MeV/fm” [25,26]. The process of formation of a bubble having a critical radius, can be computed using a semiclassical approximation. The procedure is rather straightforward. First one computes using the well known Wentzel-Kramers-Brillouin (WKB) approximation the ground state energy Eo and t,he oscillation frequency vo of the virtual QM drop in the potential well U(R). Then it is possible to calculate in a relativistic framework the probability of tunneling as [26] PO =

4Eo) exp [ -~ Tl

I

where A is the action

under

A(E) = ; J,“+ {[2M(R)c2

the potential

barrier

+ E - U(R)]x (3)

[U(R) - El}“” Here R,t are the classical M(R)

= hph (I-

dR. turning

points

and

z)2R3

is the droplet effective mass, Ph being the hadronic mass density. nh and nq are the baryonic number densities at a same and given pressure in the hadronic and quark phase, respectively. The nucleation time is then equal to 7 =

(VoPoNJl,

(5)

I 8

10

12

14

R[bl

Figure 1. The mass-radius relation for different types of compact stars. The curve labelled GM3 is relative to a pure hadronic star described by the GM3 EOS with hyperons. The curve labelled 170 is relative to an hybrid star in which the quark matter sector is described by the MIT bag model with B1i4 = 170 MeV and m, = 150 MeV. Finally the curve labelled 155 is a pure quark star. Stellar masses are plotted in unit of the solar mass.

where N, is the number of virtual centers of droplet formation in the star. N, is of the order of 104’ [26]. In our analysis we have adopted rather common models for describing both the hadronic and the quark phase of dense matter. For the hadronic phase we used models which are based on a relativistic lagrangian of hadrons interacting via the exchange of pion, sigma, rho and omega mesons. The parameters adopted are the standard ones [30]. Hereafter we refer to this model as the GM equation of state (EOS). For the quark phase we have adopted a phenomenological EOS [31] which is based on the MIT bag model for hadrons. The parameters here are: the mass m, of the strange quark, the so-called pressure of the vacuum B (bag constant) and the QCD structure constant.

Z. Berezhiani

et al. /Nuclear

Physics B (Proc. Suppl.)

M/MO

Figure 2. Quark matter nucleation time as a function of the gravitational mass of the hadronic star for 0 = 30 MeV/fm”. Each curve refer to a different value of B114 (MeV). The strange quark mass is taken equal to 150 MeV. The hadronic sector is described by the GM3 EOS with hyperons.

4. RESULTS We show in Fig. 1 the typical mass-radius relations for the three possible types of compact stars. As it appears, stars having a deconfined quark content (HyS or QS) are more compact than purely hadronic stars (HS). In our scenario a metastable HS having, e.g., a mass of 1.3 Ma and a radius of - 13 km can collapse into an HyS having a radius of - 9.5 km or into a QS with radius - 8.5 km. The nature of the stable configuration reached after the stellar conversion (i.e. an HyS or a QS) will depend on the parameters of the quark phase EOS. The nucleation time, i.e. the time needed to form a critical droplet of deconfined quark matter can be calculated for different values of the stellar central pressure PC which enters in the expression of the energy barrier in eq. (1). The nucleation time can be plotted as a function of the gravitational mass MHS of the HS corresponding to the given value of the central pressure. The result of our calculations for a specific EOS of dense matter are reported in Fig. 2, where each curve refer

113 (2002) 268-274

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to a different value of the bag constant. As we can see, from the results in Fig. 2, an hadronic star can have a mean-life time many orders of magnitude larger than the age of the universe (TUniv = lo-20 x log yr = 3.1-6.3 x1017 s). As the star accretes a small amount of mass, the consequential increase of the central pressure lead to a huge reduction of the nucleation time and, as a result, to a dramatic reduction of the HS meanlife time. Once a critical-size droplet of quark matter is formed, it is possible to calculate its rate of growth [10,32]. The QM front absorbs hadrons liberating the constituent quarks. As the “chemical” equilibrium is re-established by the weakinteraction processes of the type u + e- + s + I/, , a large amount of neutrinos and antineutrinos are produced in the stellar core. Whether the conversion process occurs in a deflagration regime (either laminar or turbolent) or in a detonation regime (thus driving an explosive transient) has been debated in the literature [10,32], but detailed studies are still lacking. Available studies [10,32] indicate that the stellar conversion process occurs in a very short time, in the range of 10P2lo2 s, depending on the speed of the “burning front” of hadronic matter into quark matter. Next we consider the total energy EC”“” released in the conversion from a metastable hadronic star to an hybrid star or a quark star (the final state of such transition depends on the details of the quark matter EOS and in particular on the value of the bag parameter). The energy gain is calculated as a difference of the gravitational mass between the hadronic and hybridquark star at the same baryonic number [la]. In Table 1 we report Econv(~) and the corresponding “critical mass” M,,(T) of the metastable hadronic star, (taking r = 1 yr) when an hybrid star is formed in the conversion process. EConv is a few 1O52 erg. An energy of the order of 1O53 erg is liberated when a quark star is formed [12]. Thus the total energy liberated in the stellar conversion process is in the range 1052-1053 erg. This tremendous amount of energy, mainly originates from the energy liberated in the deconfinement phase transition [la]. To generate a strong GRB, an efficient mech-

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Table 1 Critical mass MC, of the metastable hadronic star (in unit of the mass of the sun AJa = 1.989 x 1O33 g) and energy released E conuin the conversion to hybrid star assuming the hadronic star mean life time r equal to 1 year. Results are reported for various choices of the surface tension c and of the bag constant B. The strange quark mass is taken equal to 150 MeV. For the hadronic matter EOS the GM3 model with hyperons has been used. B’/”

(MeV)

0 (MeV/fm2)

MC, IMa

EC”“” ( 105rerg)

170

20

1.25

170

30

1.33

33.5

170

40

1.39

38.0

165

30

1.15

38.6

160

30

0.91

45.7

anism to transfer the energy released in the stellar conversion into an electron-photon plasma is needed. In earlier work it was this difficulty that hampered the possibility to connect GRBs and the hadronic-quark matter phase transition in compact stars. Only more recently it was noticed [33] that near the surface of a compact stellar object, due to general relativity effects, the efficiency of the neutrino-antineutrino annihilation into e+e- pairs is strongly enhanced with respect to the Newtonian case. The efficiency of the neutrino pair annihilation into e+e- pairs could be as high as 10% [33]. The total energy deposited into the electron-photon plasma can therefore be of the order of 1051-1052 erg. We must also mention that a more effective way to generate photons and/or e+e- pairs have been proposed in the literature, based on the decay of axion-like particles [34]. This mechanism, would have an extremely large efficiency and would transfer into the GRB most of the energy released in the stellar conversion. It is also important to stress tha.t in our scenario the duration of the burst is related both to the speed of the “burning front” of hadronic matter to quark matter, discussed above, and to the time during which neutrinos are trapped in the dense stellar material. This neutrino trapping time is of the order of a few tens of seconds [35]. Therefore the duration of the burst turns out to be of the order of a few tens of seconds in a very natural way, in agreement with observations for

30.0

“long” (~GRB > 10 s) GRBs. The strong magnetic field of the compact star will affect the motion of the electrons and positrons, and in turn could generate a moderate anisotropy in the GRB. Moreover, it has been recently shown [36] that the stellar magnetic field could influence the velocity of the “burning front” of hadronic matter into quark matter. This results in a strong geometrical asymmetry of the forming quark matter core along the direction of the stellar magnetic axis, thus providing a suitable mechanism to produce a collimated GRB [36]. Other anisotropies in the GRB could be generated by the rotation of the star. 5. DISCUSSION

AND

CONCLUSIONS

The nature of the compact star at birth (i.e. HS or HyS/QS) will depend on the value of its initial mass Mi,, with respect to the value of the critical mass MC, for the stellar conversion. While the value of MC, is set by the fundamental theory of strong interactions (EOS, QM-HM surface tension), the value of Mi, is determined by stellar evolution and is related to the value of the mass of the progenitor star. Due to many uncertainties in the stellar evolution modelling, the so called neutron star initial mass function (i.e. the number of neutron stars as a function of their mass at birth) is not known with high accuracy. For those stars that explode as Type II supernovae, the models give [37] Mi, in the range 1.2 - 1.8 Al, (stellar

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Physics

remnants in the upper part of this range could directly form a black hole). If Mi, > IM,, then the quark deconfinement phase transition will occur during the stellar core bounce in the presupernova collapse, or within a few seconds after the core bounce. In this case the energy liberated during the quark deconfinement phase transition will help the supernova to explode [38]. An hybrid star or a quark star is formed directly in the supernova event. If Mi, < McT the compact remnant left by the supernova explosion is a pure HS. This star can live in a metastable state with a mean-life time which depends on the value of its central density. Eventually, as discussed in the present work, the star will be converted to a quark star or to an hybrid star and could originate a GRB. In conclusion, we propose the following origin for (at least some of) the GRBs having a duration of tens of seconds. They can be associated with the conversion from a metastable pure hadronic star to a more compact hybrid star or quark star. The time delay between the supernova explosion originating the hadronic star and the GRB is regulated by those processes which increase the central pressure of the star (matter accretion and/or spin-down of the HS). There are various specific signatures and interesting astrophysical consequences of the mechanism we are proposing. First of all, two different families of compact stars exist in nature: pure hadronic stars (metastable) which have radii in the range of 12 - 20 km (as in the case [39] of the compact star 1E 1207.4-5209, assuming M = 1.4 Ma), and hybrid or quark stars with radii in the range of 6 - 8 km (see ref.s [17,19,20,22]). In other words, the existence of quark stars (or hybrid stars) does not conflict with the existence of pure hadronic stars. Second, all the GRBs generated by the present mechanism should have the same energy. REFERENCES 1. 2. 3. 4.

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