Relativistic parameterizations of neutron matter and implications for neutron stars

We construct parameter sets of the relativistic mean-field model fitted to the recent constraints on the asymmetry energy $J$ and the slope parameter $L$ for pure neutron matter. We find cases of unphysical behavior, i.e., the appearance of negative pressures, for stiff parameter sets with low values of the effective mass $m^{*}/m$. In some cases the equation of state of pure neutron matter turns out to be outside the allowed band given by chiral effective field theory. The mass-radius relations of neutron stars for all acceptable parameter sets shows a maximum mass in excess of $2M_{\odot }$ being compatible with pulsar mass measurements. Given the constraints on the model in the low-density regime coming from chiral effective theory, we find that the radius of a $1.4M_{\odot }$ neutron star is nearly independent of the value of $L$. This is in contrast to some previous claims for a strong connection of the slope parameter with the radius of a neutron star. In fact, the mass-radius relation turns out to depend only on the isoscalar parameters of symmetric matter. The constraints of GW170817 on the tidal deformability and on the radius are also discussed.

Figure 1

EoS for neutron matter as a function of $n/n_0$ at $J=30$ MeV for different values of the nucleon effective mass $m^{*}/m$ and slope parameter $L$. The top panel display solutions within the $\chi \mathrm{EFT}$ allowed band that present no instabilities, while the bottom panel collects some solutions for the neutron matter EoS that are outside the $\chi \mathrm{EFT}$ band and/or present instabilities.

Figure 2

The same as Fig. 2 but for $J=32$.

Figure 3

Scatter plot of the slope parameter $L$ and of the nucleon effective mass $m^{*}/m$ for $J=30$ MeV, where the unphysical solutions for neutron matter EoS (marked with a red plus sign), the solutions for neutron matter EoS outside the $\chi \mathrm{EFT}$ band (blue cross) and the physical solutions inside the $\chi \mathrm{EFT}$ region (green star) are indicated.

Figure 4

The same as Fig. 3 but for $J=32$ MeV.

Figure 5

Mass-radius relation for neutron stars for $J=32$ and a fixed value of the effective mass $m^{*}/m=0.60$, but for different values of the slope parameter, $50\le L\le 60$.

Figure 6

Mass-radius relation for neutron stars for $J=32$ MeV and $L=60$ MeV for different values of $m^{*}/m$.

Figure 7

Radius of $1.4M_{\odot }$ neutron star as a function of the slope parameter $L$ for different effective nucleon masses for $J=32$ MeV. At the right side of the figure, we show the upper limits on the radius of a $1.4M_{\odot }$ neutron star extracted from GW170817 by different groups [25, 26, 28, 73].