Constraints on the high-density nuclear equation of state from the phenomenology of compact stars and heavy-ion collisions

A new scheme for testing nuclear matter equations of state (EsoS) at high densities using constraints from neutron star phenomenology and a flow data analysis of heavy-ion collisions is suggested. An acceptable EoS shall not allow the direct Urca process to occur in neutron stars with masses below $1.5~M_{\odot}$, and also shall not contradict flow and kaon production data of heavy-ion collisions. Compact star constraints include the mass measurements of 2.1 +/- 0.2 M_sun (1 sigma level) for PSR J0751+1807, of 2.0 +/- 0.1 M_sun from the innermost stable circular orbit for 4U 1636-536, the baryon mass - gravitational mass relationships from Pulsar B in J0737-3039 and the mass-radius relationships from quasiperiodic brightness oscillations in 4U 0614+09 and from the thermal emission of RX J1856-3754. This scheme is applied to a set of relativistic EsoS constrained otherwise from nuclear matter saturation properties with the result that no EoS can satisfy all constraints simultaneously, but those with density-dependent masses and coupling constants appear most promising.Comment: 15 pages, 8 figures, 5 table

Isospin Dynamics in Heavy Ion Collisions: from Coulomb Barrier to Quark Gluon Plasma

Heavy Ion Collisions (HIC) represent a unique tool to probe the in-medium nuclear interaction in regions away from saturation. In this report we present a selection of new reaction observables in dissipative collisions particularly sensitive to the symmetry term of the nuclear Equation of State (Iso-EoS). We will first discuss the Isospin Equilibration Dynamics. At low energies this manifests via the recently observed Dynamical Dipole Radiation, due to a collective neutron-proton oscillation with the symmetry term acting as a restoring force. At higher beam energies Iso-EoS effects will be seen in Imbalance Ratio Measurements, in particular from the correlations with the total kinetic energy loss. For fragmentation reactions in central events we suggest to look at the coupling between isospin distillation and radial flow. In Neck Fragmentation reactions important $Iso-EoS$ information can be obtained from the correlation between isospin content and alignement. The high density symmetry term can be probed from isospin effects on heavy ion reactions at relativistic energies (few AGeV range). Rather isospin sensitive observables are proposed from nucleon/cluster emissions, collective flows and meson production. The possibility to shed light on the controversial neutron/proton effective mass splitting in asymmetric matter is also suggested. A large symmetry repulsion at high baryon density will also lead to an "earlier" hadron-deconfinement transition in n-rich matter. A suitable treatment of the isovector interaction in the partonic EoS appears very relevant.Comment: 18 pages, 12 figures, lecture at the 2008 Erice School on Nuclear Physics, to appear in Progress in Particle and Nuclear Physic

Determination of the neutron star mass-radii relation using narrow-band gravitational wave detector

The direct detection of gravitational waves will provide valuable astrophysical information about many celestial objects. The most promising sources of gravitational waves are neutron stars and black holes. These objects emit waves in a very wide spectrum of frequencies determined by their quasi-normal modes oscillations. In this work we are concerned with the information we can extract from f and p$_I$-modes when a candidate leaves its signature in the resonant mass detectors ALLEGRO, EXPLORER, NAUTILUS, MiniGrail and SCHENBERG. Using the empirical equations, that relate the gravitational wave frequency and damping time with the mass and radii of the source, we have calculated the radii of the stars for a given interval of masses $M$ in the range of frequencies that include the bandwidth of all resonant mass detectors. With these values we obtain diagrams of mass-radii for different frequencies that allowed to determine the better candidates to future detection taking in account the compactness of the source. Finally, to determine which are the models of compact stars that emit gravitational waves in the frequency band of the mass resonant detectors, we compare the mass-radii diagrams obtained by different neutron stars sequences from several relativistic hadronic equations of state (GM1, GM3, TM1, NL3) and quark matter equations of state (NJL, MTI bag model). We verify that quark stars obtained from MIT bag model with bag constant equal to 170 MeV and quark of matter in color-superconductivity phase are the best candidates for mass resonant detectors.Comment: 10 pages and 3 figure

Constraining the Symmetry Energy: A Journey in the Isospin Physics from Coulomb Barrier to Deconfinement

Heavy Ion Collisions (HIC) represent a unique tool to probe the in-medium nuclear interaction in regions away from saturation. In this work we present a selection of reaction observables in dissipative collisions particularly sensitive to the isovector part of the interaction, i.e. to the symmetry term of the nuclear Equation of State (EoS). At low energies the behavior of the symmetry energy around saturation influences dissipation and fragment production mechanisms. We will first discuss the recently observed Dynamical Dipole Radiation, due to a collective neutron-proton oscillation during the charge equilibration in fusion and deep-inelastic collisions. Important Iso-EOS effects are stressed. Reactions induced by unstable 132Sn beams appear to be very promising tools to test the sub-saturation Isovector EoS. New Isospin sensitive observables are also presented for deep-inelastic, fragmentation collisions and Isospin equilibration measurements (Imbalance Ratios). The high density symmetry term can be derived from isospin effects on heavy ion reactions at relativistic energies (few AGeV range), that can even allow a ``direct'' study of the covariant structure of the isovector interaction in the hadron medium. Rather sensitive observables are proposed from collective flows and from pion/kaon production. 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. The importance of studying violent collisions with radioactive beams from low to relativistic energies is finally stressed.Comment: 15 pages, 5 figures, Int.Workshop on Nuclear Dynamics in Heavy Ion Reactions and Neutron Stars, Beijing Normal Univ. July 07, to appear in Int.Journ.Modern Physics E (2008

Probing the nuclear equation of state by K+K^+ production in heavy ion collisions

The dependence of $K^+$ production on the nuclear equation of state is investigated in heavy ion collisions. An increase of the excitation function of $K^+$ multiplicities obtained in heavy ($Au+Au$) over light ($C+C$) systems when going far below threshold which has been observed by the KaoS Collaboration strongly favours a soft equation of state. This observation holds despite of the influence of an in-medium kaon potential predicted by effective chiral models which is necessary to reproduce the experimental $K^+$ yields.Comment: 4 pages Revtex, 4 PS figures, to appear in Phys. Rev. Let

Phase transitions of hadronic to quark matter at finite T and \mu_B

The phase transition of hadronic to quark matter and the boundaries of the mixed hadron-quark coexistence phase are studied within the two Equation of State (EoS) model. The relativistic effective mean field approach with constant and density dependent meson-nucleon couplings is used to describe hadronic matter, and the MIT Bag model is adopted to describe quark matter. The boundaries of the mixed phase for different Bag constants are obtained solving the Gibbs equations. We notice that the dependence on the Bag parameter of the critical temperatures (at zero chemical potential) can be well reproduced by a fermion ultrarelativistic quark gas model, without contribution from the hadron part. At variance the critical chemical potentials (at zero temperature) are very sensitive to the EoS of the hadron sector. Hence the study of the hadronic EoS is much more relevant for the determination of the transition to the quark-gluon-plasma at finite baryon density and low-T. Moreover in the low temperature and finite chemical potential region no solutions of the Gibbs conditions are existing for small Bag constant values, B < (135 MeV)^4. Isospin effects in asymmetric matter appear relevant in the high chemical potential regions at lower temperatures, of interest for the inner core properties of neutron stars and for heavy ion collisions at intermediate energies.Comment: 24 pages and 16 figures (revtex4

Rapidity distribution as a probe for elliptical flow at intermediate energies

Interplay between the spectator and participant matter in heavy-ion collisions is investigated within isospin dependent quantum molecular dynamics (IQMD) model in term of rapidity distribution of light charged particles. The effect of different types and size rapidity distributions is studied in elliptical flow. The elliptical flow patterns show important role of the nearby spectator matter on the participant zone. This role is further explained on the basis of passing time of the spectator and expansion time of the participant zone. The transition from the in-plane to out-of-plane is observed only when the mid-rapidity region is included in the rapidity bin, otherwise no transition occurs. The transition energy is found to be highly sensitive towards the size of the rapidity bin, while weakly on the type of the rapidity distribution. The theoretical results are also compared with the experimental findings and are found in good agreement.Comment: 8 figure

Sodium bicarbonate ingestion and individual variability in time to peak pH

The aim of this study was to determine the individual variability in time to peak pH after the consumption of a 300mg.kg-1 dose of sodium bicarbonate (NaHCO3). Seventeen active males volunteered to participate in the study (mean ± SD: age 21.38 ± 1.5y; mass 75.8 ± 5.8kg; height 176.8 ± 7.6cm). Participants reported to the laboratory where a resting capillary blood sample was taken aseptically from the fingertip. After this, 300 mg.kg-1 of NaHCO3 in 400ml of water with 50ml of flavoured cordial was ingested. Participants then rested for 90 min during which repeated blood samples were procured at 10 minute intervals for 60 mins and then every 5 min until 90 min. Blood pH concentrations were measured using a blood gas analyser. Results suggested that time to peak pH (64.41±18.78 min) was highly variable with a range of 10-85 min and a coefficient of variation of 29.16%. A bi-modal distribution occurred, at 65 and 75 min. In conclusion, researchers and athletes, when using NaHCO3 as an ergogenic aid, should determine, in advance their time to peak pH to best utilise the added buffering capacity this substance allows