ЯДЕРНАЯ ФИЗИКА, 2012, том 75, № 5, с. 656-663
ЭЛЕМЕНТАРНЫЕ ЧАСТИЦЫ И ПОЛЯ
CORE COLLAPSE SUPERNOVAE IN THE QCD PHASE DIAGRAM
© 2012 T. Fischer1)'2)*, D. Blaschke3)'4), M. Hempel5), T. Klahn3), R. Lastowiecki3), M. Liebendorfer5), G. Martinez-Pinedo1), G. Pagliara6), I. Sagert6), F. Sandin7)'8), J. Schaffner-Bielich6), S. Typel1)'9)
Received March 31, 2011
We compare two classes of hybrid equations of state with a hadron-to-quark matter phase transition in their application to core collapse supernova simulations. The first one uses the quark bag model and describes the transition to three-flavor quark matter at low critical densities. The second one employs a Polyakov-loop extended Nambu—Jona-Lasinio (PNJL) model with parameters describing a phase transition to two-flavor quark matter at higher critical densities. These models possess a distinctly different temperature dependence of their transition densities which turns out to be crucial for the possible appearance of quark matter in supernova cores. During the early post-bounce accretion phase quark matter is found only if the phase transition takes place at sufficiently low densities as in the study based on the bag model. The increase critical density with increasing temperature, as obtained for our PNJL parametrization, prevents the formation of quark matter. The further evolution of the core collapse supernova as obtained applying the quark bag model leads to a structural reconfiguration of the central protoneutron star where, in addition to a massive pure quark matter core, a strong hydrodynamic shock wave forms and a second neutrino burst is released during the shock propagation across the neutrinospheres. We discuss the severe constraints in the freedom of choice of quark matter models and their parametrization due to the recently observed 2M0 pulsar and their implications for further studies of core collapse supernovae in the QCD phase diagram.
1. INTRODUCTION
Stars more massive than 8M© explode as core collapse supernovae, with kinetic explosion energies of the ejected material on the order of 1051 erg. The remnants, the protoneutron stars (PNSs), are initially hot and lepton-rich and cool via deleptonization during the first 30 seconds after the onset of the explosion. Above a certain progenitor mass threshold on the order of 40M©, which is an active subject of research, stars will no longer explode. Such models will collapse and from black holes. The critical mass for a PNS to collapse and from a black hole is given
!)GSI, Helmholtzzentrum für SchwerionenforschungGmbH, Darmstadt, Germany.
2)Technische Universitat Darmstadt, Germany.
3)Institute for Theoretical Physics, University of Wroclaw, Poland.
4)Bogoliubov Laboratory of Theoretical Physics, JINR, Dubna, Russia.
5)Department of Physics, University of Basel, Switzerland.
6)Institut für Theoretische Physik, Ruprecht-Karls-Universitat, Heidelberg, Germany.
7)Department of Computer Science and Electrical Engineering, EISLAB, Lulea Tekniska Universitet, Sweden.
8)Departement AGO-IFPA, Universite Liege, Belgium.
9)Excellence Cluster Universe, Technische Universität Munchen, Germany.
E-mail: t.fischer@gsi.de
by the equation of state (EoS). The commonly used EoS in core collapse supernova simulations are based on pure hadronic descriptions, e.g., the compressible liquid-drop model with surface effects [1] and relativistic mean field theory including the Thomas-Fermi approximation for heavy nuclei [2]. The conditions that are obtained in PNS interiors during the simulation, are several times nuclear matter density, temperatures on the order of several tens of MeV and a low proton-to-baryon ratio given by the electron fraction of Ye = Yp < 0.310). Under such conditions, the quark-hadron phase transition is not unlikely to take place and the assumption of pure hadronic matter becomes questionable. Ab initio calculations of the phase diagram and EoS of quantum chro-modynamics (QCD) as the fundamental theory of strongly interacting matter come from simulations of this gauge theory on the lattice but are still restricted to low baryon densities (chemical potentials). In this region of the phase diagram they predict a crossover transition with a pseudocritical temperature for chiral symmetry restoration and deconfinement at Tc ~ ~ 150-170 MeV [3, 4]. A critical endpoint for firstorder transitions is conjectured but lies, if it exists at all, outside the region presently accessible by
10)The proton-to-baryon ratio, Yp = up/ub, is equal to the electron fraction, Ye := Ye- — Ye+, in the absence of muons.
lattice QCD. An interesting conjecture supported by a statistical model analysis of hadron production in heavy-ion collisions and by the large-Nc limit of QCD suggests the existence of a triple point in the phase diagram [5] due to a third, "quarkyonic" phase at temperatures T <Tc and high baryon densities [6]. This state of matter might become accessible in experiments at the planned third generation of heavy-ion collision facilities FAIR in Darmstadt (Germany) and NICA in Dubna (Russia) [7] which thus allow systematic laboratory studies of conditions like in supernova collapse and protoneutron star evolution [8].
In order to investigate the appearance of quark matter in core collapse supernova models, the implementation of a quark—hadron hybrid EoS is required. It must be valid for a large range of densities nB, temperatures T and proton-to-baryon ratios. At large baryon densities, where lattice QCD cannot be applied due to current conceptional limitations, phenomenological models are commonly used. In the present study we will discuss hybrid EoS which employ quark matter models that are representative examples from two wide classes: bag models and Nambu—Jona-Lasinio-type (NJL) models. The popular and simple thermodynamical bag model is inspired by the success of the vacuum MIT bag model for the hadron spectrum [9]. It describes quarks as non-interacting fermions of a constant mass confined by an external "bag" pressure B. NJL-type models are constructed to obey basic symmetries of the QCD Lagrangian like the chiral symmetry of light quarks, and to describe its dynamical breaking which results in medium-dependent masses (see [10] and references therein). The inclusion of diquark interaction channels leads to a rich phase structure at low temperatures and high densities with color superconductivity (diquark condensation) in two-flavor (2SC) and three-flavor (CFL) quark matter (see, e.g., [11] for the phase structure and [12] for the relevance to protoneutron stars; detailed information concerning color superconductivity is found in review articles [10, 13]). These models have no confining interaction and would therefore lead to the unphysical dominance of thermal quark excitations already at temperatures well below Tc. Their coupling to the Polyakov loop potential is essential to suppress the unphysical degrees of freedom and it can be adjusted to fit the behavior of lattice QCD thermodynamics at low densities [14]. Extending this effective model to high densities leads to the class of Polyakov-loop extended Nambu—Jona-Lasinio (PNJL) models of which we apply one for this study.
Different assumptions made for the description of quark matter lead to different critical conditions for the onset of deconfinement, which are given in terms of a critical density that depends on the
temperature and the proton-to-baryon ratio. The resulting different phase diagrams may lead to a different evolutionary behavior for core collapse supernovae. The central supernova conditions start from low densities (6 x 10-6 fm-3/1010 g cm-3) and temperatures (0.6 MeV), where pure hadronic matter dominates, and approach densities above nuclear saturation density (0.16 fm-1/2.7 x 1014 g cm-3) at temperatures on the order to tens of MeV and Yp ~ 0.2—0.3. The nature of the QCD transition is not precisely understood on a microscopic level. Therefore, one usually splices independent nuclear and quark matter EoS by constructing the phase transition using more or less appropriate conditions for the phase equilibrium. Popular examples are the Maxwell, Gibbs, or Glendenning [15] constructions, whereby usually the Maxwell construction leads to the smallest region between critical densities for the onset and the end of the mixed phase. We will disregard finite size effects (pasta structures) and also non-equilibrium effects due to the nucleation of the new phase with the justification that weak processes establishing the chemical equilibrium are fast compared to the typical timescales encountered in supernova simulations [16]. We will compare the evolution of a representative core collapse supernova simulation in the two different phase diagrams based on the bag model and the PNJL model. The core collapse supernova model is based on general relativistic radiation hydrodynamics and three flavor Boltzmann neutrino transport [17—22].
The manuscript is organized as follows: in Section 2 we introduce the standard core collapse supernova phenomenology. In Section 3 we briefly introduce the two quark—hadron hybrid EoS, the quark bag model and the PNJL model. The evolution of a representative 15M© core collapse supernova model in the phase diagram is illustrated in Section 4 by comparing the quark bag and PNJL models. We close with a summary in Section 5.
2. THE STANDARD SCENARIO OF CORE COLLAPSE SUPERNOVAE
Si-burning produces Fe-cores at the final phase of stellar evolution of massive stars. These Fe-cores start to contract due to the photodisintegration of heavy elements and electron captures. The latter reduces the dominant pressure of the degenerate electron gas. During the collapse, density and temperature rise and hence electron captures, which deleptonize the central core, increase. The collapse accelerates until neutrino trapping densities, on the order of p ~ 1011—1013 g/cm3, are obtained after which the collapse proceeds
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