Gamma Ray Bursts and Delayed Quark-Deconfinement

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Gamma Ray Bursts and Delayed Quark-Deconfinement GAMMA RAY BURSTS AND DELAYED QUARK-DECONFINEMENT Ignazio Bombaci, Irene Parenti, and Isaac Vida˜na Dipartimento di Fisica “E. Fermi”, Universita‘ di Pisa & INFN, Sezione di Pisa, via Buonarroti, 2, I-56127, Pisa, Italy Abstract We describe a new model, proposed by Berezhiani et al. (2003), which is able to explain how a gamma-ray burst (GRB) can take place days or years after a supernova explosion. We show that above a threshold value of the gravitational mass a pure hadronic star (“neutron star”) is metastable to the conversion into a quark star (hybrid star or strange star), i.e. a star made at least in part of decon- fined quark matter. The stellar conversion process can be delayed if finite size effects at the interface between hadronic and deconfined quark matter phases are taken into account. A huge amount of energy, on the order of 1052 – 1053 ergs, 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 new collapse can explain the delay inferred in GRB 990705 and in GRB 011211. Next, we explore the consequences of the metastability of “massive” neutron stars and of the existence of stable compact quark stars on the concept of limiting mass of compact stars. Finally, we discuss the implica- tions of the present scenario on the interpretation of the stellar mass and radius extracted from the spectra of several X-ray compact sources. Keywords: Gamma rays: Gamma Ray Burst. Stars: Neutron Stars, Strange Stars. Dense Matter: equation of state, quark matter. 1. Introduction Gamma Ray Bursts (GRBs) are one of the most violent and mysterious phe- nomena in the universe which have challenged astrophysicists for decades (see e.g. (Piran 1999; Dermer 2001; Zhang & Meszaros 2003) for a general intro- duction on this subject). During the last ten years a large amount of new obser- vational data, collected by a variety of instruments on board of various satel- lites, has revolutionized our understanding of GRBs. The Burst And Transient Source Experiment (BATSE) on board of the Compton Gamma Ray Observa- tory (CGRO) has demonstrated that GRBs originate at cosmological distances. The BeppoSAX satellite discovered the X-ray “afterglow”. This has permitted 353 D. Blaschke and D. Sedrakian (eds.), Superdense QCD Matter and Compact Stars, 353–375. C 2006 Springer. Printed in the Netherlands. 354 SUPERDENSE QCD MATTER AND COMPACT STARS to determine the position of some GRBs, to identify the host galaxy and, in a number of cases, to measure the red-shift. Accurate determination of the GRB distance from the measured red-shifts, permitted, for the first time, to derive the energy Eγ emitted by the GRB. The measured fluency of the bursts implies an energy of the order of 1053 erg in the case of isotropic emission. There is now, however, compelling evidence that the γ-ray emission is not isotropic, but displays a jet-like geometry. For these bursts, the geometrically corrected gamma-ray energy is about 1051 erg (Frayl et al. 2001). The time duration Tγ of GRBs appears to have a bimodal distribution. Thus, according to their time duration, GRBs are classified as “short” GRBs when Tγ < 2 seconds, and “long” GRBs when Tγ > 2 s. Long GRBs represent about 75% of the total GRB population. It is believed that the two types of GRBs may have different progenitors. Many cosmological models for the energy source (the so-called central en- gine) of GRBs have been proposed. Presently some of the most popular mod- els are: the collapsar (hypernova) model, the merging of two neutron stars (or a neutron star and a black hole) in a binary system, the strong-magnetized millisecond pulsar model, the supranova model. Here, we will not discuss the various merits and drawbacks of the many theoretical models for the GRB cen- tral engine, and we refer the reader to recent review papers on this subject (e.g. Piran 1999; Dermer 2001; Zhang & Meszaros 2003)). In the following, we will report some recent research (Berezhiani et al. 2003; Bombaci et al. 2003) which try to make a connection between GRBs and quark-deconfinement phase transition. 1.1 The delayed Supernova–GRB connection A mounting number of observational data suggest a clear connection be- tween supernova (SN) explosions and GRBs (Bloom et al. 1999; Amati et al. 2000; Antonelli et al. 2000: Piro et al. 2000; Reeves et al. 2002; Hjorth et al. 2003; Butler et al. 2003). The detection of X-ray spectral features in the X-ray afterglow of several GRBs, has given evidence for a possible time delay between the SN explosion and the associated GRB. 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 a few years before the GRB (Amati et al. 2000; Lazzati et al. 2001), while for GRB011211 about four days before the burst (Reeves et al. 2002). The scenario which emerges from these findings is the following two-step scenario. The first event is the supernova explosion which forms a compact stellar remnant, i.e. a neutron star (NS); the second catastrophic event is as- sociated with the NS and it is the energy source for the observed GRB. These Gamma Ray Bursts and delayed Quark-deconfinement 355 new observational data, and the two-step scenario outlined above, poses se- vere problems for most of the current theoretical models for the central energy source of GRBs. The main difficulty of all these models is to understand the origin of the second “explosion”, and to explain the long time delay between the two events. In the so-called supranova model (Vietri & Stella 1998) for GRBs the sec- ond catastrophic event is the collapse to a black hole of a supramassive neu- tron star, i.e. a fast rotating NS with a baryonic mass MB above the maximum baryonic mass MB,max for non-rotating 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 quasi-radial modes where the collapse to a black hole occurs (Datta et al. 1998). The supranova model needs a fine tuning in the initial spin period Pin and baryonic stellar mass MB,in to pro- duce a supramassive neutron star that can be stabilized by rotation up to a few years. For example, if Pin ≥ 1.5 ms, then the newborn supramassive neutron star must be formed within ∼ 0.03M above MB,max (Datta et al. 1998). 1.2 The nature of Neutron Stars: Hadronic Stars or Quark Stars? One of the most fascinating enigma in modern astrophysics concerns the true nature of the ultra-dense compact objects called neutron stars. Different models for the EOS of dense matter predict a neutron star maximum mass (Mmax) in the range of 1.4 – 2.2 M, and a corresponding central density in 14 3 range of 4 – 8 times the saturation density (ρ0 ∼ 2.8 × 10 g/cm ) of nuclear matter (e.g. Shapiro & Teukolsky 1983; Haensel 2003). In the case of a star with M ∼ 1.4 M, different EOS models predict a radius in the range of 7 – 16 km (Shapiro & Teukolsky 1983; Haensel 2003; Dey et al. 1998). In a simplistic and conservative picture the core of a neutron star is modeled as a uniform fluid of neutron rich nuclear matter in equilibrium with respect to the weak interaction (β-stable nuclear matter). However, due to the large value of the stellar central density and to the rapid increase of the nucleon chemical potentials with density, hyperons (Λ, Σ−, Σ0, Σ+, Ξ− and Ξ0 particles) are expected to appear in the inner core of the star. Other exotic phases of hadronic matter such as a Bose-Einstein condensate of negative pion (π−)ornegative kaon (K−) could be present in the inner part of the star. According to Quantum Chromodynamics (QCD) a phase transition from hadronic matter to a deconfined quark phase should occur at a density of a few times nuclear matter saturation density. Consequently, the core of the more massive neutron stars is one of the best candidates in the Universe where such deconfined phase of quark matter (QM) could be found. Since β-stable hadronic matter posses two conserved “charges” (i.e., electric charge and baryon 356 SUPERDENSE QCD MATTER AND COMPACT STARS number) the quark-deconfinement phase transition proceeds through a mixed phase over a finite range of pressures and densities according to the Gibbs’ criterion for phase equilibrium (Glendenning 1992). At the onset of the mixed phase, quark matter droplets form a Coulomb lattice embedded in a sea of hadrons and in a roughly uniform sea of electrons and muons. As the pressure increases various geometrical shapes (rods, plates) of the less abundant phase immersed in the dominant one are expected. Finally the system turns into uni- form quark matter at the highest pressure of the mixed phase (Heiselberg et al. 1993; Voskresensky et al. 2003). Compact stars which possess a “quark matter core” either as a mixed phase of deconfined quarks and hadrons or as a pure quark matter phase are called Hybrid Neutron Stars or shortly Hybrid Stars (HyS) (Glendenning 1996). In the following of this paper, the more con- ventional neutron stars in which no fraction of quark matter is present, will be referred to as pure Hadronic Stars (HS).
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