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

We study relativistic mean-field (RMF) models including nucleons interacting with scalar, vector, and isovector 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 $n\gtrsim n_{*}>n_0$, where $n_0$ 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 $n\lesssim n_0$. 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 $1.72M_{\odot }$ to $M\ge 2.01M_{\odot }$.

Figure 1

Left panel: the scalar-field potential $U\left(f\right)$ in the NLW model and $\tilde{U}\left(f\right)$ in the NLWcut model for various values $c_{\sigma }$, as functions of the scalar field parameter $f$. The symbols indicate the values of $[f\left(n\right);U(f\left(n\right)),\tilde{U}(f\left(n\right))]$ for the density $n$ of the ISM varying from $n_0$ to $10n_0$ with the $1n_0$ step. Right panel: the nucleon effective mass in the ISM as a function of the nucleon density for the same models.

Figure 2

Left panel: Total pressure $P$ for the NLW and NLWcut models as a function of the nucleon density in the ISM for various values $c_{\sigma }$; the insertion demonstrates the binding energy per nucleon. Two shadowed areas show the constraints on the pressure from the particle flow and the kaon production data in HIC extracted in [21, 22]. Bold dots show the extrapolation of the pressure consistent with GMR [22]. Right panel: The NS mass and radius as functions of the central density for our models. The hatched band denotes the uncertainty in the value of the maximum measured NS mass of $(2.01\pm 0.04)M_{\odot }$.

Figure 3

Contour plot of the maximum NS mass as a function of $m_N^{*}\left(n_0\right)$ and $K\left(n_0\right)$ for the NLWcut models with $c_{\sigma }=1$, simulating the case of the original NLW model (left panel) and $c_{\sigma }=0.3$ (right panel). Contour lines are shown with the mass step $0.05M_{\odot }$.

Figure 4

Same as Fig. 2, but for the FSUGold model.