Structure of hybrid protoneutron stars within the Nambu--Jona-Lasinio model

We investigate the structure of protoneutron stars (PNS) formed by hadronic and quark matter in $\beta$-equilibrium described by appropriate equations of state (EOS). For the hadronic matter, we use a finite temperature EOS based on the Brueckner-Bethe-Goldstone many-body theory, with realistic two- and three-body forces. For the quark sector, we employ the Nambu--Jona-Lasinio model. We find that the maximum allowed masses are comprised in a narrow range around 1.8 solar masses, with a slight dependence on the temperature. Metastable hybrid protoneutron stars are not found.Comment: 7 pages, 6 figures, revised version accepted for publication in Phys. Rev.

Hybrid neutron stars within the Nambu-Jona-Lasinio model and confinement

Recently, it has been shown that the standard Nambu-Jona-Lasinio (NJL) model is not able to reproduce the correct QCD behavior of the gap equation at large density, and therefore a different cutoff procedure at large momenta has ben proposed. We found that, even with this density dependent cutoff procedure, the pure quark phase in neutron stars (NS) interiors is unstable, and we argue that this could be related to the lack of confinement in the original NJL model.Comment: 2 pages, 1 figure, to be published in the proceedings of the conference EXOCT07, Catania, 11-15 June, 200

The Equation of State of Dense Matter : from Nuclear Collisions to Neutron Stars

The Equation of State (EoS) of dense matter represents a central issue in the study of compact astrophysical objects and heavy ion reactions at intermediate and relativistic energies. We have derived a nuclear EoS with nucleons and hyperons within the Brueckner-Hartree-Fock approach, and joined it with quark matter EoS. For that, we have employed the MIT bag model, as well as the Nambu--Jona-Lasinio (NJL) and the Color Dielectric (CD) models, and found that the NS maximum masses are not larger than 1.7 solar masses. A comparison with available data supports the idea that dense matter EoS should be soft at low density and quite stiff at high density.Comment: 8 pages, 5 figures, invited talk given at NPA3, Dresden, March 200

Astrophysical constraints on the confining models : the Field Correlator Method

We explore the relevance of confinement in quark matter models for the possible quark core of neutron stars. For the quark phase, we adopt the equation of state (EoS) derived with the Field Correlator Method, extended to the zero temperature limit. For the hadronic phase, we use the microscopic Brueckner-Hartree-Fock many-body theory. We find that the currently adopted value of the gluon condensate $G_2 \simeq 0.006-0.007 \rm {GeV^4}$, which gives a critical temperature $T_c \simeq 170 \rm MeV$, produces maximum masses which are only marginally consistent with the observational limit, while larger masses are possible if the gluon condensate is increased.Comment: 7 pages, 5 figure

Relativistic Approach to Superfluidity in Nuclear Matter

Pairing correlations in symmetric nuclear matter are studied within a relativistic mean-field approximation based on a field theory of nucleons coupled to neutral ($\sigma$ and $\omega$) and to charged ($\varrho$) mesons. The Hartree-Fock and the pairing fields are calculated in a self-consistent way. The energy gap is the result of a strong cancellation between the scalar and vector components of the pairing field. We find that the pair amplitude vanishes beyond a certain value of momentum of the paired nucleons. This fact determines an effective cutoff in the gap equation. The value of this cutoff gives an energy gap in agreement with the estimates of non relativistic calculations.Comment: 21 pages, REVTEX, 8 ps-figures, to appear in Phys.Rev.C. e-mail: [email protected]

Elementary excitations in homogeneous superfluid neutron star matter: Role of the proton component

The thermal evolution of neuron stars depends on the elementary excitations affecting the stellar matter. In particular, the low-energy excitations, whose energy is proportional to the transfered momentum, can play a major role in the emission and propagation of neutrinos. In this paper, we focus on the density modes associated with the proton component in the homogeneous matter of the outer core of neutron stars (at density between one and three times the nuclear saturation density, where the baryonic constituants are expected to be neutrons and protons). In this region, it is predicted that the protons are superconductor. We study the respective roles of the proton pairing and Coulomb interaction in determining the properties of the modes associated with the proton component. This study is performed in the framework of the Random Phase Approximation, generalized in order to describe the response of a superfluid system.The formalism we use ensures that the Generalized Ward's Identities are satisfied. An important conclusion of this work is the presence of a pseudo-Goldstone mode associated with the proton superconductor in neutron-star matter. Indeed, the Goldstone mode, which characterizes a pure superfluid, is suppressed in usual superconductors due to the long-range Coulomb interaction, which only allows a plasmon mode. However, for the proton component of stellar matter, the Coulomb field is screened by the electrons and a pseudo-Goldstone mode occurs, with a velocity increased by the Coulomb interaction.Comment: Submitted for publicatio

Critical Enhancement of the In-medium Nucleon-Nucleon Cross Section at low Temperatures

The in-medium nucleon-nucleon cross section is calculated starting from the thermodynamic T-matrix at finite temperatures. The corresponding Bethe-Salpeter-equation is solved using a separable representation of the Paris nucleon-nucleon-potential. The energy-dependent in-medium N-N cross section at a given density shows a strong temperature dependence. Especially at low temperatures and low total momenta, the in-medium cross section is strongly modified by in-medium effects. In particular, with decreasing temperature an enhancement near the Fermi energy is observed. This enhancement can be discussed as a precursor of the superfluid phase transition in nuclear matter.Comment: 10 pages with 4 figures (available on request from the authors), MPG-VT-UR 34/94 accepted for publication in Phys. Rev.

Elementary excitations in homogeneous neutron star matter

We study the collective density modes which can affect neutron-star thermodynamics in the baryonic density range between nuclear saturation ($\rho_0$) and $3\rho_0$. In this region, the expected constituents of neutron-star matter are mainly neutrons, protons and electrons ($npe$ matter), under the constraint of beta equilibrium. The elementary excitations of this $npe$ medium are studied in the RPA framework. We emphasize the effect of Coulomb interaction, in particular the electron screening of the proton plasmon mode. For the treatment of the nuclear interaction, we compare two modern Skyrme forces and a microscopic approach. The importance of the nucleon effective mass is observed.Comment: misprint corrected in Eq. (1