The accurate determination of the maximum mass of the neutron stars is one of the most important tasks in astrophysics. It is directly related to the identification of the black holes in the universe, the production of neutron stars from the supernovae explosion, and the equation of state (EoS) of dense matter. However, not only the EoS is directly connected with neutron star masses, but also the speed of sound in dense matter is a crucial quantity which characterizes the stiffness of the EoS. The upper bound of the speed of sound imposes strong constraints on the maximum mass of neutron stars. However, this upper bound remains still an open issue. Recent observations, of binary neutron star systems, offer the possibility of measuring with high accuracy both the mass and the tidal polarizability of the stars. We study possible effects of the upper bound of the speed of sound on the upper bound of the mass and the tidal polarizability. We conclude that these kinds of measurements, combined with recent observations of neutron stars with masses close to $2 M_{\odot}$, will provide robust constraints on the equation of state of hadronic matter at high densities.Comment: 17 pages, 11 figure

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We systematically study the symmetry energy effects of the transition density nt and the transition pressure Pt around the crust-core interface of a neutron star in the framework of the dynamical and the thermodynamical method respectively. We employ both the parabolic approximation and the full expansion, for the definition of the symmetry energy. We use various theoretical nuclear models, which are suitable for reproducing the bulk properties of nuclear matter at low densities, close to saturation density as well as the maximum observational neutron star mass. Firstly we derive and present an approximation for the transition pressure Pt and crustal mass Mcrust. Moreover, we derive a model-independent correlation between Pt and the slope parameter L for a fixed value of the symmetry energy at the saturation density. Secondly, we explore the effects of the Equation of State (EoS) on a few astrophysical applications which are sensitive to the values of nt and Pt including neutron star oscillation frequencies, thermal relaxation of the crust, crustal fraction of the moment of inertia and the r-mode instability window of a rotating neutron star. In particular, we employ the Tolman VII solution of the TOV equations to derive analytical expressions for the critical frequencies and the relative time scales, for the r-mode instability, in comparison with the numerical predictions. In the majority of the applications, we found that the above quantities are sensitive mainly to the applied approximation for the symmetry energy (confirming previous results). There is also a dependence on the used method (dynamical or thermodynamical). The above findings lead us to claim that the determination of nt and Pt must be reliable and accurate before they are used to constrain relevant neutron star properties.PACS number(s): 26.60.Kp, 21.65.Ef, 26.60.Cj It was found that the transition density is related to some finite nuclei properties including neutron-skin, dipole polarizability e.t.c [15,16,17].The baryon transition density n t at the inner edge is uncertain due to our insufficient knowledge of the EoS of neutron-rich nuclear matter. In addition, the determination of the transition density n t itself is a very complicated problem because the inner crust may have an intricate structure. A well established approach is to find the density at which the uniform liquid first becomes unstable against small-amplitude density fluctuations, indicating the formation of nuclear clusters. This approach includes the dynamical method [18,19,20,21,22,23,24], the thermodynamical one [25,26,27,28] and the random phase approximation (RPA) [17,29]. Recently, a method to determine the transition density in the framework of the unified equation of state, has been presented in Ref. [30].The structure of the crust as well as some dynamical processes are affected appreciably by the location of the crust-core interface. Firstly, if the transition density n t is sufficiently high, it is possible for nonspherical phases, with rod-or plate-like nuclei, ...

The observation of maximally-rotating neutron stars (in comparison with non-rotating ones) may provide more information on the behavior of nuclear matter at high densities. In the present work we provide a theoretical treatment concerning the effects of the upper bound of the sound speed in dense matter on the bulk properties of maximally-rotating (at mass-shedding limit) neutron stars. In particular, we consider two upper bounds for the speed of sound, vs = c and vs = c/ √ 3, and the one provided by the relativistic kinetic theory. We investigate to what extent the possible predicted (from various theories and conjectures) upper bounds on the speed of sound constrain the ones of various key quantities, including the maximum mass and the corresponding radius, Keplerian frequency, Kerr parameter and moment of inertia. We mainly focus on the lower proposed limit, vs = c/ √ 3, and we explore in which mass region a rotating neutron star collapses to a black hole. In any case, useful relations of the mentioned bulk properties with the transition density are derived and compared with the corresponding non-rotating cases. We concluded that the proposed limit vs = c/ √ 3 leads to dramatic decrease on the values of the maximum mass, Kerr parameter and moment of inertia preventing a neutron star to reach values which derived with the consideration of realistic equations of state or from other constraints. Possible measurements of the Kerr parameter and moment of inertia would shed light on these issues and help to reveal the speed of sound bound in dense matter.

The nuclear symmetry energy plays an important role in the description of the properties of finite nuclei as well as neutron stars. Especially, for low values of baryon density, the accurate description of the crust-core interface strongly depends on the symmetry energy. Usually, the well known parabolic approximation is employed for the definition of the symmetry energy without avoiding some drawbacks. In the present work, a class of nuclear models, suitable for the description of the inner and outer core of neutron stars, is applied in studying the effect of higher orders of the expansion of the energy on the location of the crust-core transition. The thermodynamical and dynamical methods are used for the determination of the transition density nt and pressure Pt. The corresponding energy density functional is applied for the study of some relevant properties of both non-rotating and slow rotating neutron stars. We found that the larger the value of the slope parameter L, the slower the convergence of the expansion. In addition, a universal relation is presented between nt and L, by employing the full expression and dynamical approach. The crustal moment of inertia is very sensitive on the location of the transition while the effects are moderated concerning the critical angular velocity of the r-mode instability and minimum mass configuration. The effect on the tidal deformability is less but not negligible. In any case, the use of the parabolic approximation leads to the overestimation of nt and Pt and consequently, on inaccurate predictions.