Constraints on Skyrme equations of state from doubly magic nuclei, ab initio calculations of low-density neutron matter, and neutron stars

We use properties of doubly magic nuclei, ab initio calculations of low-density neutron matter and of neutron stars to constrain the parameters of the Skyrme energy-density functional. We find all of these properties can be reproduced within a constrained family of Skyrme parameters. The maximum mass of a neutron star is found to be sensitive to the neutron effective mass. A value of $[m_n^{*}/m]\left({\rho }_0\right)=0.60–0.65$ is required to obtain a maximum neutron-star mass of 2.0 to 2.1 solar masses. Using the constrained Skyrme functional with the aforementioned effective mass, the predicted radius for a neutron star of 1.4 solar masses is 12.4(1) km and tidal polarizability is $\mathrm{\Lambda }=423\left(40\right)$.

Figure 1

The EOS in the form of pressure versus density used in this Rapid Communication. The red band corresponds to 12 Skyrmes with $m_n^{*}/m=0.60–65$ (at ${\rho }_0$) whereas the blue band corresponds to 12 Skyrmes with $m_n^{*}/m=0.85$. All EoSs are connected to a common crustal EoS [11] with crust-core transition density calculated using the empirical relation of Ref. [35].

Figure 2

Mass-versus-radius relation predicted by the two groups of Skyrme EoSs described in the text. The horizontal gray line indicates a value of 1.4 solar mass, and the two vertical bands show the range of intersections between the gray line and EoSs from each group, which corresponds to the range of predicted 1.4 solar mass neutron-star radius.

Figure 3

Correlation between neutron-star tidal deformability and radii of the predicted 1.4 solar mass neutron star from two groups of Skyrmes (blue open square and red solid circle marker). The shaded aqua rectangular box in the background shows constraints from event GW170817 [10].