Strong correlations of neutron star radii with the slopes of nuclear matter incompressibility and symmetry energy at saturation

Abstract

We examine the correlations of neutron star radii with the nuclear matter incompressibility, symmetry energy, and their slopes, which are the key parameters of the equation of state (EoS) of asymmetric nuclear matter. The neutron star radii and the EoS parameters are evaluated using a representative set of 24 Skyrme-type effective forces and 18 relativistic mean field models, and two microscopic calculations, all describing 2M⊙ neutron stars. Unified EoSs for the inner-crust-core region have been built for all the phenomenological models, both relativistic and non-relativistic. Our investigation shows the existence of a strong correlation of the neutron star radii with the linear combination of the slopes of the nuclear matter incompressibility and the symmetry energy coefficients at the saturation density. Such correlations are found to be almost independent of the neutron star mass in the range 0.6-1.8M⊙. This correlation can be linked to the empirical relation existing between the star radius and the pressure at a nucleonic density between one and two times saturation density, and the dependence of the pressure on the nuclear matter incompressibility, its slope and the symmetry energy slope. The slopes of the nuclear matter incompressibility and the symmetry energy coefficients as estimated from the finite nuclei data yield the radius of a 1.4M⊙ neutron star in the range 11.09-12.86 km.PACS numbers: 21.65.+f, 21.30.Fe, 26.60.+c The bulk properties of neutron stars are mainly governed by the behaviour of the equation of state (EoS) of highly asymmetric dense matter. The correlations of the various EoS parameters of asymmetric nuclear matter with the different properties of neutron star, such as the crust-core transition density and pressure, radii, maximum mass and cooling rate, have been studied [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. The crust-core transition density is strongly correlated with the slope of the symmetry energy, L 0 , at saturation density (ρ 0 ∼ 0.16 fm −3 ) [5,6,11]. However, the transition pressure is found to be strongly correlated with a linear combination of the slope and curvature of the symmetry energy at the sub-saturation density (ρ = 0.1 fm −3 ) [7,11,12]. The simultaneous determination of mass and radius of low-mass neutron stars can better constrain the product of nuclear matter incompressibility and symmetry energy slope parameter [13].The correlations of the neutron star radii of different masses with the EoS parameters have been investigated extensively. The covariance analysis, based on a single model, suggests the existence of strong correlations of the radii of low-mass neutron stars (M NS ∼ 0.6-1.2M ⊙ ) with the symmetry energy slope parameter L 0 [10], the correlations becoming weaker with the increase of the neutron star mass. Similar analysis for the correlations of the radii with the symmetry energy slope over a wider range of densities was performed for two different models, having different behaviours on the density dependence of the symmetry energy, a...

Future prospects for constraining nuclear matter parameters with gravitational waves

“…Previous important analyses by Alam et al [29] found approximately universal relations between the NS radius at a given mass and the nuclear parameters mentioned above (similar work can be found in Refs. [30,31]).…”

“…[27] and followed up in Refs. [11,28,29,35], we offer a generic method to parameterize NS EoSs. This is done by first Taylor expanding the energy per nucleon e of asymmetric nuclear matter about δ = 0 (symmetric nuclear matter), where δ ≡ (n n − n p )/n is the isospin symmetry parameter for nuclear matter with n n neutron density, n p proton density, and total density n = n n + n p : e(n, δ) = e(n, 0) + S 2 (n)δ 2 + O(δ 4 ).…”

“…with y ≡ (n − n 0 )/3n 0 . The above coefficients, all evaluated at the nuclear saturation density, determine the NS EoS and are referred to in the literature [27,28] as the energy per particle e 0 ; incompressibility coefficient K 0 ; third derivative of symmetric matter Q 0 ; the slope of the incompressibility M 0 ≡ Q 0 + 12K 0 [11,29]; symmetry energy J 0 ; its slope L 0 ; and its curvature K sym,0 .…”

Empirical constraints on the high-density equation of state from multimessenger observables

“…Correlations between nuclear matter parameters and NS properties have been explored using several nuclear models [24][25][26][27][28][29][30][31][32]. These studies, however, show a considerable model dependence since different models with similar values of the nuclear matter parameters may result in different EoSs.…”

Evolution of a proto-neutron star with a nuclear many-body equation of state: Neutrino luminosity and gravitational wave frequencies

“…(10). In the literature, there is no generally accepted fitting formula for these functions [19,[26][27][28][29]. In order to perform our evolutionary numerical simulations, we need a fitting formula which is accurate in a wide density range, extending from n B ≲ 0.5 fm −3 to n B ≳ 0.001 fm −3 relevant for the core and the crust of the star, respectively.…”