Making a soft relativistic mean-field equation of state stiffer at high density

Abstract

We study relativistic mean-field (RMF) models including nucleons interacting with scalar, vector and iso-vector mean fields and mean-field self-and cross-interaction terms. Usually, in such models the magnitude of the scalar field increases monotonically with the nucleon density, and the nucleon effective mass decreases. We demonstrate that the latter quantity stops decreasing and the equation of state stiffens, provided the mean-field self-interaction potential rises sharply in a narrow vicinity of the values of mean fields corresponding to nucleon densities n > ∼ n * > n0, where n0 is the nuclear saturation density. As a result the limiting neutron star mass increases. This procedure offers a simple way to stiffen the equation of state at densities above n * without altering it at densities n < ∼ n0. The developed scheme allows a neutron star application of the RMF models, which are well fitted to finite nuclei but do not fulfill the experimental constraint on the limiting neutron star mass. The exemplary application of the method to the well-known FSUGold model allows us to increase the limiting neutron star mass from 1.72 M⊙ to M ≥ 2.01 M⊙. A relativistic mean-field (RMF) model proposed and advertised in [1-3] is a convenient vehicle for construction of the equation of state (EoS) of baryon matter, which preserves causality. Various RMF models are successfully used to describe neutron stars (NS) and heavy-ion collisions, see [4][5][6]. The models prove to be also applicable to atomic nuclei, where a high precision in the description of gross properties of finite nuclei close to the valley of stability can be achieved [7,8]. An accurately calibrated parametrization of the RMF model was introduced in [9], known as the FSUgold model, which allows one to compute the ground state properties of finite nuclei and neutron rich matter.In order to describe finite nuclei well, one includes the self-and cross-interaction terms of meson fields [9][10][11] and/or nonlinear derivative couplings [12]. However these models yield a rather soft EoS and cannot describe the heavy NSs with masses of (2.01 ± 0.04)M ⊙ , where M ⊙ is the mass of the Sun, which were recently unambiguously identified experimentally [13,14]. Additional complication arises if hyperons are included in the consideration, since in their presence the EoS softens even more, cf. [15]. To reconcile the appropriate description of the properties of atomic nuclei and the NS mass constraints, one exploits density-dependent coupling constants [16]. Similarly, one could use mean-field-dependent coupling constants, cf. [17,18].In this Rapid Communication, we will demonstrate that, if the mean-field self-interaction potential rises sharply in a narrow vicinity of the values of mean fields corresponding to nucleon densities n > ∼ n * > n 0 , where n 0 is the nuclear saturation density, the nucleon effective mass saturates and the EoS stiffens. As a result the limiting NS mass may increase above the value (2.01 ± 0.04)M ⊙ . This procedure offers a simple way to stiffen ...

Vlasov formalism for extended relativistic mean field models: The crust-core transition and the stellar matter equation of state

“…[50]. This extra term does not change the model properties at saturation density and below, but hardens the EoS above saturation density, allowing the description of 2M , but, at the same time, not satisfying the KaoS restrictions.…”

“…f 0 and α have the same values as in Ref. [50], 0.2 and (4.822 × 10 −4 )m 4 N , respectively. The stellar matter EoS were built using the BPS outer crust EoS, the most adequate NL3ωρ or NL3σρ inner crust EoS, and the homogeneous matter core EoS.…”

“…We note that the Z271σρ5-6 models fail this last constraint; however, by using the procedure of Ref. [50], we are able to get parametrizations Z271σρ5 * -6 * that describe 2M stars. Models NL3ωρ6, NL3σρ6, and Z271σρ5 * -6 * fail the flow and KaoS experiments.…”

“…This problem can be solved by introducing an extra effective potential, dependent on the σ meson, that hinders the effective nucleon mass to stop decreasing at a density above the saturation density, as suggested in Ref. [50]. In Figure 10, we show, in the top panel, the nucleon effective mass as a function of the density for the Z271 model, with and without the σ cut potential, U f , Eq.…”

“…Since the Z271 family does not satisfy the latter constraint, we implement the mechanism proposed in Ref. [50]; adding an extra nonlinear σ function that hardens the EoS above saturation.…”