Modern compact star observations and the quark matter EoS

A hybrid equation of state for dense matter is presented that satisfies phenomenological constraints from modern compact star observations which indicate high maximum masses of about 2 M_sun and large radii of R> 12 km. The corresponding isospin symmetric equation of state is consistent with flow data analyses of heavy-ion collisions. The transition from nuclear to two-flavor color superconducting quark matter at n approximately 0.55 fm^{-3} is almost a crossover.Comment: 2 pages, 2 figures; Proceedings of the Erice School on 'Radioactive Beams, Nuclear Dynamics and Astrophysics' to be published in 'Prog. Part. Nucl. Phys.

Composition and thermodynamics of nuclear matter with light clusters

We investigate nuclear matter at finite temperature and density, including the formation of light clusters up to the alpha particle The novel feature of this work is to include the formation of clusters as well as their dissolution due to medium effects in a systematic way using two many-body theories: a microscopic quantum statistical (QS) approach and a generalized relativistic mean field (RMF) model. Nucleons and clusters are modified by medium effects. Both approaches reproduce the limiting cases of nuclear statistical equilibrium (NSE) at low densities and cluster-free nuclear matter at high densities. The treatment of the cluster dissociation is based on the Mott effect due to Pauli blocking, implemented in slightly different ways in the QS and the generalized RMF approaches. We compare the numerical results of these models for cluster abundances and thermodynamics in the region of medium excitation energies with temperatures T <= 20 MeV and baryon number densities from zero to a few times saturation density. The effect of cluster formation on the liquid-gas phase transition and on the density dependence of the symmetry energy is studied. Comparison is made with other theoretical approaches, in particular those, which are commonly used in astrophysical calculations. The results are relevant for heavy-ion collisions and astrophysical applications.Comment: 32 pages, 15 figures, minor corrections, accepted for publication in Physical Review

Structural Dynamics and Catalytic Mechanism of ATP13A2 (PARK9) from Simulations

ATP13A2 is a gene encoding a protein of the P5B subfamily of ATPases and is a PARK gene. Molecular defects of the gene are mainly associated with variations of Parkinson’s disease (PD). Despite the established importance of the protein in regulating neuronal integrity, the three-dimensional structure of the protein currently remains unresolved crystallographically. We have modeled the structure and reactivity of the full-length protein in its E1-ATP state. Using molecular dynamics (MD), quantum cluster, and quantum mechanical/molecular mechanical (QM/MM) methods, we aimed at describing the main catalytic reaction, leading to the phosphorylation of Asp513. Our MD simulations suggest that two positively charged Mg2+ cations are present at the active site during the catalytic reaction, stabilizing a specific triphosphate binding mode. Using QM/MM calculations, we subsequently calculated the reaction profiles for the phosphoryl transfer step in the presence of one and two Mg2+ cations. The calculated barrier heights in both cases are found to be ∼12.5 and 7.5 kcal mol–1, respectively. We elucidated details of the catalytically competent ATP conformation and the binding mode of the second Mg2+ cofactor. We also examined the role of the conserved Arg686 and Lys859 catalytic residues. We observed that by significantly lowering the barrier height of the ATP cleavage reaction, Arg686 had major effect on the reaction. The removal of Arg686 increased the barrier height for the ATP cleavage by more than 5.0 kcal mol–1 while the removal of key electrostatic interactions created by Lys859 to the γ-phosphate and Asp513 destabilizes the reactant state. When missense mutations occur in close proximity to an active site residue, they can interfere with the barrier height of the reaction, which can halt the normal enzymatic rate of the protein. We also found large binding pockets in the full-length structure, including a transmembrane domain pocket, which is likely where the ATP13A2 cargo binds

Baryon chemical potential and in-medium properties of BPS skyrmions

We continue the investigation of thermodynamical properties of the BPS Skyrme model. In particular, we analytically compute the baryon chemical potential both in the full field theory and in a mean-field approximation. In the full field theory case, we find that the baryon chemical potential is always exactly proportional to the baryon density, for arbitrary solutions. We further find that, in the mean-field approximation, the BPS Skyrme model approaches the Walecka model in the limit of high density - their thermodynamical functions as well as the equation of state agree in this limit. This fact allows to read off some properties of the $\omega$-meson from the BPS Skyrme action, even though the latter model is entirely based on the (pionic) $SU(2)$ Skyrme field. On the other hand, at low densities, at the order of the usual nuclear matter density, the equations of state of the two models are no longer universal, such that a comparison depends on some model details. Still, also the BPS Skyrme model gives rise to nuclear saturation in this regime, leading, in fact, to an exact balance between repulsive and attractive forces. The perfect fluid aspects of the BPS Skyrme model, which, together with its BPS properties, form the base of our results, are shown to be in close formal analogy with the Eulerian formulation of relativistic fluid dynamics. Within this analogy, the BPS Skyrme model, in general, corresponds to a non-barotropic perfect fluid.Comment: Latex, 28 pages, 3 figure

1-2-3-flavor color superconductivity in compact stars

We suggest a scenario where the three light quark flavors are sequentially deconfined under increasing pressure in cold asymmetric nuclear matter, e.g., as in neutron stars. The basis for our analysis is a chiral quark matter model of Nambu--Jona-Lasinio (NJL) type with diquark pairing in the spin-1 single flavor (CSL) and spin-0 two/three flavor (2SC/CFL) channels, and a Dirac-Brueckner Hartree-Fock (DBHF) approach in the nuclear matter sector. We find that nucleon dissociation sets in at about the saturation density, n_0, when the down-quark Fermi sea is populated (d-quark dripline) due to the flavor asymmetry imposed by beta-equilibrium and charge neutrality. At about 3n_0 u-quarks appear forming a two-flavor color superconducting (2SC) phase, while the s-quark Fermi sea is populated only at still higher baryon density. The hybrid star sequence has a maximum mass of 2.1 M_sun. Two- and three-flavor quark matter phases are found only in gravitationally unstable hybrid star solutions.Comment: 4 pages, 2 figures, to appear in the proceedings of Quark Matter 2008: 20th International Conference on Ultra-Relativistic Nucleus Nucleus Collisions (QM 2008), Jaipur, India, 4-10 Feb 200

Equation of state at high densities and modern compact star observations

Recently, observations of compact stars have provided new data of high accuracy which put strong constraints on the high-density behaviour of the equation of state of strongly interacting matter otherwise not accessible in terrestrial laboratories. The evidence for neutron stars with high mass (M =2.1 +/- 0.2 M_sun for PSR J0751+1807) and large radii (R > 12 km for RX J1856-3754) rules out soft equations of state and has provoked a debate whether the occurence of quark matter in compact stars can be excluded as well. In this contribution it is shown that modern quantum field theoretical approaches to quark matter including color superconductivity and a vector meanfield allow a microscopic description of hybrid stars which fulfill the new, strong constraints. The deconfinement transition in the resulting stiff hybrid equation of state is weakly first order so that signals of it have to be expected due to specific changes in transport properties governing the rotational and cooling evolution caused by the color superconductivity of quark matter. A similar conclusion holds for the investigation of quark deconfinement in future generations of nucleus-nucleus collision experiments at low temperatures and high baryon densities such as CBM @ FAIR.Comment: 6 pages, 2 figures, accepted for publication in J. Phys. G. (Special Issue

Quark matter in compact stars?

Ozel, in a recent reanalysis of EXO 0748-676 observational data (astro-ph/0605106), concluded that quark matter probably does not exist in the center of compact stars. We show that the data is actually consistent with the presence of quark matter in compact stars.Comment: 4 pages, LaTeX; New title and overall rewrite to reflect version published in Nature. Conclusions unchange

Core collapse supernovae in the QCD phase diagram

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 proto-neutron 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 2 solar mass pulsar and their implications for further studies of core collapse supernovae in the QCD phase diagram.Comment: 19 pages, 4 figures, CPOD2010 conference proceedin

Heavy Ion Collisions at Relativistic Energies: Testing a Nuclear Matter at High Baryon and Isospin Density

We show that the phenomenology of isospin effects on heavy ion reactions at intermediate energies (few AGeV range) is extremely rich and can allow a ``direct'' study of the covariant structure of the isovector interaction in the hadron medium. We work within a relativistic transport frame, beyond a cascade picture, consistently derived from effective Lagrangians, where isospin effects are accounted for in the mean field and collision terms. Rather sensitive observables are proposed from collective flows (``differential'' flows) and from pion/kaon production ($\pi^-/\pi^+$, $K^0/K^+$ yields). For the latter point relevant non-equilibrium effects are stressed. The possibility of the transition to a mixed hadron-quark phase, at high baryon and isospin density, is finally suggested. Some signatures could come from an expected ``neutron trapping'' effect.Comment: 8 pages, 4 figures, espcrc1 (latex) style. Conf. "Perspectives in Hadronic Physics", ICTP Trieste May 2006, Nucl.Phys. A, to appea