Higher-order symmetry energy of nuclear matter and the inner edge of neutron star crusts

Abstract

The parabolic approximation to the equation of state of the isospin asymmetric nuclear matter (ANM) is widely used in the literature to make predictions for the nuclear structure and the neutron star properties. Based on the realistic M3Y-Paris and M3Y-Reid nucleon-nucleon interactions, we investigate the effects of the higher-order symmetry energy on the proton fraction in neutron stars and the location of the inner edge of their crusts and their core-crust transition density and pressure, thermodynamically. Analytical expressions for different-order symmetry energy coefficients of ANM are derived using the realistic interactions mentioned above. It is found that the higher-order terms of the symmetry energy coefficients up to its eighth-order ( ) contributes substantially to the proton fraction in stable neutron star matter at different nuclear matter densities, the core-crust transition density and pressure. Even by considering the symmetry energy coefficients up to , we obtain a significant change of about 40% in the transition pressure value from the one based on the exact equation of state. Using equations of state based on both Paris and Reid effective interactions which provide saturation incompressibility of symmetric nuclear matter in the range of 220 ≤ 0 ≤ 270 , we estimate the ranges 0.090 −3 ≤ ≤ 0.095 −3 and 0.49 −3 ≤ ≤ 0.59 −3 for the liquid coresolid crust transition density and pressure, respectively. The corresponding range of the proton fraction at this transition density range is found to be 0.029 ≤ ( ) ≤ 0.032.

Stability ofβ-equilibrated dense matter and core-crust transition in neutron stars

“…The density, the pressure and the proton fraction at the inner edge separating the liquid core from the solid crust of the neutron stars determined to be ρ t = 0.0938 fm −3 , P t = 0.5006 MeV fm −3 and x p(t) = 0.0308, respectively, are also in close agreement with other theoretical calculations [54] corresponding to high nuclear incompressibility and with those obtained using SLy4 interaction [58].…”

“…The proton fraction obtained using nuclear symmetry energy does not affect seriously the results of exact calculation. Since the higher-order symmetry-energy coefficients are needed to describe reasonably well the proton fraction of the β-stable (npe) matter at high nuclear densities and the core-crust transition density [54], exact calculations are performed using the density dependent M3Y effective nucleon-nucleon interaction for investigating the proton fraction in neutron stars and the location of the inner edge of their crusts and their core-crust transition density and pressure.…”

Towards understanding astrophysical effects of nuclear symmetry energy

“…The main features discussed above are in general agreement with those found in other recent studies, see, e.g., refs. [201,202,203,204,205,206,208,209,214,215,216,217,218,219,220,221,223], while quantitatively, the predicted core-crust transition densities and pressures are still model and interactions dependent for the reasons we mentioned above. Among all the available studies in the literature, it is very instructive to mention the rather systematic work in refs.…”

Core-crust transition in neutron stars with finite-range interactions: The dynamical method

“…The boundary between the outer and inner crust is determined by nuclear masses, and corresponds to the neutron drip out density around 4 × 10 11 g cm −3 [3,4]. However, * cgonzalezboquera@ub.edu † mariocentelles@ub.edu ‡ xavier@fqa.ub.edu § trr1@rediffmail.com the transition density from the crust to the core is much more uncertain and strongly model dependent [5][6][7][8][9][10][11][12][13][14][15][16].…”