Clusterized nuclear matter in the (proto-)neutron star crust and the symmetry energy

Though generally agreed that the symmetry energy plays a dramatic role in determining the structure of neutron stars and the evolution of core-collapsing supernovae, little is known in what concerns its value away from normal nuclear matter density and, even more important, the correct definition of this quantity in the case of unhomogeneous matter. Indeed, nuclear matter traditionally addressed by mean-field models is uniform while clusters are known to exist in the dilute baryonic matter which constitutes the main component of compact objects outer shells. In the present work we investigate the meaning of symmetry energy in the case of clusterized systems and the sensitivity of the proto-neutron star composition and equation of state to the effective interaction. To this aim an improved Nuclear Statistical Equilibrium (NSE) model is developed, where the same effective interaction is consistently used to determine the clusters and unbound particles energy functionals in the self-consistent mean-field approximation. In the same framework, in-medium modifications to the cluster energies due to the presence of the nuclear gas are evaluated. We show that the excluded volume effect does not exhaust the in-medium effects and an extra isospin and density dependent energy shift has to be considered to consistently determine the composition of subsaturation stellar matter. The symmetry energy of diluted matter is seen to depend on the isovector properties of the effective interaction, but its behavior with density and its quantitative value are strongly modified by clusterization.Comment: A contribution to the upcoming EPJA Special Volume on Nuclear Symmetry Energ

Light clusters in nuclear matter: Excluded volume versus quantum many-body approaches

The formation of clusters in nuclear matter is investigated, which occurs e.g. in low energy heavy ion collisions or core-collapse supernovae. In astrophysical applications, the excluded volume concept is commonly used for the description of light clusters. Here we compare a phenomenological excluded volume approach to two quantum many-body models, the quantum statistical model and the generalized relativistic mean field model. All three models contain bound states of nuclei with mass number A <= 4. It is explored to which extent the complex medium effects can be mimicked by the simpler excluded volume model, regarding the chemical composition and thermodynamic variables. Furthermore, the role of heavy nuclei and excited states is investigated by use of the excluded volume model. At temperatures of a few MeV the excluded volume model gives a poor description of the medium effects on the light clusters, but there the composition is actually dominated by heavy nuclei. At larger temperatures there is a rather good agreement, whereas some smaller differences and model dependencies remain.Comment: 12 pages, 6 figures, published version, minor change

Statistical Model for a Complete Supernova Equation of State

A statistical model for the equation of state (EOS) and the composition of supernova matter is presented with focus on the liquid-gas phase transition of nuclear matter. It consists of an ensemble of nuclei and interacting nucleons in nuclear statistical equilibrium. A relativistic mean field model is applied for the nucleons. The masses of the nuclei are taken from nuclear structure calculations which are based on the same nuclear Lagrangian. For known nuclei experimental data is used directly. Excluded volume effects are implemented in a thermodynamic consistent way so that the transition to uniform nuclear matter at large densities can be described. Thus the model can be applied at all densities relevant for supernova simulations, i.e. rho=10^5 - 10^15 g/cm^3, and it is possible to calculate a complete supernova EOS table. The model allows to investigate the role of shell effects, which lead to narrow-peaked distributions around the neutron magic numbers for low temperatures. At larger temperatures the distributions become broad. The significance of the statistical treatment and the nuclear distributions for the composition is shown. We find that the contribution of light clusters is very important and is only poorly represented by alpha-particles alone. The results for the EOS are systematically compared to two commonly used models for supernova matter which are based on the single nucleus approximation. Apart from the composition, in general only small differences of the different EOSs are found. The differences are most pronounced around the (low-density) liquid-gas phase transition line where the distribution of light and intermediate clusters has an important effect. Possible extensions and improvements of the model are discussed.Comment: 33 pages, 22 page

A statistical study of the mass and density structure of Infrared Dark Clouds

How and when the mass distribution of stars in the Galaxy is set is one of the main issues of modern astronomy. Here we present a statistical study of mass and density distributions of infrared dark clouds (IRDCs) and fragments within them. These regions are pristine molecular gas structures and progenitors of stars and so provide insights into the initial conditions of star formation. This study makes use of a IRDC catalogue (Peretto & Fuller 2009), the largest sample of IRDC column density maps to date, containing a total of ~11,000 IRDCs with column densities exceeding N_{H2} = 1 X10^{22} cm^{-2} and over 50,000 single peaked IRDC fragments. The large number of objects constitutes an important strength of this study, allowing detailed analysis of the completeness of the sample and so statistically robust conclusions. Using a statistical approach to assigning distances to clouds, the mass and density distributions of the clouds and the fragments within them are constructed. The mass distributions show a steepening of the slope when switching from IRDCs to fragments, in agreement with previous results of similar structures. IRDCs and fragments are divided into unbound/bound objects by assuming Larson's relation and calculating their virial parameter. IRDCs are mostly gravitationally bound, while a significant fraction of the fragments are not. The density distribution of gravitationally unbound fragments shows a steep characteristic slope. (see paper for full Abstract).Comment: 15 pages, accepted for publication in Ap

Superfluid Properties of the Inner Crust of Neutron Stars

Superfluid properties of the inner crust matter of neutron stars, formed by nuclear clusters immersed in a dilute neutron gas, are analysed in a self- consistent HFB approach. The calculations are performed with two pairing forces, fixed so as to obtain in infinite nuclear matter the pairing gaps provided by the Gogny force or by induced interactions. It is shown that the nuclear clusters can either suppress or enhance the pairing correlations inside the inner crust matter, depending on the density of the surrounding neutrons. The profile of the pairing field in the inner crust is rather similar for both pairing forces, but the values of the pairing gaps are drastically reduced for the force which simulates the polarisation effects in infinite neutron matter.Comment: 13 pages, 6 figures. Corrected typos and new format. To appear in Phys. Rev.

Strange hadron matter and SU(3) symmetry

We calculate saturation curves for strange hadron matter using recently constructed baryon-baryon potentials which are constrained by SU(3) symmetry. All possible interaction channels within the baryon octet (consisting of $N$, $\Lambda$, $\Sigma$, and $\Xi$) are considered. It is found that a small $\Lambda$ fraction in nuclear matter slightly increases binding, but that larger fractions ($>10$) rapidly cause a decrease. Charge-neutral ${N,\Lambda,\Xi}$ systems, with equal densities for nucleons and cascades, are only very weakly bound. The dependence of the binding energies on the strangeness per baryon, $f_s$, is predicted for various ${N,\Lambda,\Xi}$ and ${N,\Lambda,\Sigma,\Xi}$ systems. The implications of our results in relativistic heavy-ion collisions and the core of a dense star are discussed. We also discuss the differences between our results and previous hadron matter calculations.Comment: 14 pages RevTeX, 7 postscript figure