We discuss the "constant speed of sound" (CSS) parameterization of the equation of state of high density matter and its application to the Field Correlator Method (FCM) model of quark matter. We show how observational constraints on the maximum mass and typical radius of neutron stars are expressed as constraints on the CSS parameters. We find that the observation of a 2 M star already severely constrains the CSS parameters, and is particularly difficult to accommodate if the squared speed of sound in the high density phase is assumed to be around 1/3 or less.We show that the FCM equation of state can be accurately represented by the CSS parameterization, which assumes a sharp transition to a high-density phase with density-independent speed of sound. We display the mapping between the FCM and CSS parameters, and see that FCM only allows equations of state in a restricted subspace of the CSS parameters.

We calculate the effective masses of neutrons and protons in dense nuclear matter within the microscopic Brueckner-Hartree-Fock many-body theory and study the impact on the neutrino emissivity processes of neutron stars. We compare results based on different nucleon-nucleon potentials and nuclear three-body forces. Useful parametrizations of the numerical results are given. We find substantial in-medium suppression of the emissivities, strongly dependent on the interactions. 26.60.Kp, 97.10.Cv. Introduction.-With the commissioning of increasingly sophisticated instruments, more and more details of the very faint signals emitted by neutron stars (NS) can be quantitatively monitored. This will allow in the near future an ever increasing accuracy to constrain the theoretical ideas for the ultra-dense matter that composes these objects.One important tool of analysis is the temperature-vs.-age cooling diagram, in which currently a few observed NS are located. NS cooling is over a vast domain of time (10 −10 -10 5 yr) dominated by neutrino emission due to several microscopic processes [1]. The theoretical analysis of these reactions requires, apart from the elementary matrix elements, the knowledge of the density of states of the relevant reaction partners and thus the nucleon effective masses.The present report is focused on the problem of the theoretical determination of this important input information and reports nucleon effective masses in dense nuclear matter obtained within the Brueckner-Hartree-Fock (BHF) theoretical many-body approach. We study the dependence on the underlying basic two-nucleon and three-nucleon interactions and provide useful parametrizations of the numerical results. Finally some estimates of the related in-medium modification of the various neutrino emission rates in NS matter will be given. We begin with a short review of the BHF formalism and the relevant neutrino emission processes, before presenting our numerical results.The Brueckner-Hartree-Fock approach.-Empirical properties of infinite nuclear matter can be calculated using many different theoretical approaches. In this paper we concentrate on the non-relativistic BHF method, which is based on a linked-cluster expansion of the energy per nucleon of nuclear matter [2][3][4]. The basic ingredient in this many-body approach is the reaction matrix G, which is the solution of the Bethe-Goldstone equation

We compare a set of equations of state derived within microscopic many-body approaches, and study their predictions as far as phenomenological data on nuclei from heavy ion collisions, and astrophysical observations on neutron stars are concerned. We find that all the data, taken together, put strong constraints not easy to be fulfilled accurately. However, no major discrepancies are found among the selected equations of state and with respect to the data. The results provide an estimate of the uncertainty on the theoretical prediction at a microscopic level of the nuclear equation of state.

We model neutron star cooling, in particular the current rapid cooldown of the neutron star Cas A, with a microscopic nuclear equation of state featuring strong direct Urca processes and using compatible nuclear pairing gaps as well as effective masses. Several scenarios are possible to explain the features of Cas A, but only large and extended proton 1 S 0 gaps and small neutron 3 PF 2 gaps are able to accommodate also the major part of the complete current cooling data. We conclude that the possibility of strong direct Urca processes cannot be excluded from the cooling analysis.