Neutron-star deformation due to anisotropic momentum distribution of neutron-star matter

Herein, we present a theoretical study of how Fermi-surface distortion affects symmetric nuclear matter, pure neutron matter, and neutron-star matter. The results indicate that, for the binding energy of symmetric nuclear matter, the generally accepted value extracted from the Bethe-Weizäcker mass formula for nuclei can constrain the degree of anisotropy because of Fermi-surface deformation $\delta \lesssim 0.05$. The value of $\delta$ starts to affect the stiffness of the equation of state for symmetric nuclear matter and pure neutron matter when $\delta \gtrsim 0.01$. Moreover, if the Fermi surface is distorted, the results indicate that neutron stars can be deformed into an oblate shape. This deformation depends on two factors: the stiffness of the corresponding equation of state and value of $\delta$. The corresponding deformation near the maximum neutron-star mass comes from the anisotropic pressure within these stars, which is caused by the distortion of Fermi surface predicted by the equation of state of the models.

Figure 1

Illustration of adjusting the coordinates of NS pressures (a) original coordinates and (b) coordinates after rotation.

Figure 2

(a) Pressure as a function of the ratio of nucleon-to-nuclear saturation densities. (b) Energy per particle as a function of the density around the saturation density for SNM with different $\delta$ values obtained from TM1 parameter set. The dashed curves correspond to various numbers $\delta$ deformation, respectively.

Figure 3

Similar to Fig. 2 but for the case predicted by the NL3 parameter set.

Figure 4

Similar to Fig. 2 but for the case predicted by the G2 parameter set.

Figure 5

Similar to Fig. 2 PNM predicted by the TM1 parameter set.

Figure 6

Similar to Fig. 3 PNM predicted by the NL3 parameter set.

Figure 7

Similar to Fig. 4 but for the case PNM predicted by the G2 parameter set.

Figure 8

NS mass $M$ as a function of NS radius $R$ for EOSs using the (a) G2 and (b) NL3 parameter sets. Here we use $\delta =0.01,0.05$, and 0.005.

Figure 9

Relation between eccentricity $e$ for EOSs using the G2 and NL3 parameter sets with (a) the energy density at the NS center $\left({\epsilon }_c\right)$ and (b) $M$ from a NS. Here we use $\delta =0.05$ and 0.005.

Figure 10

NS mass $M$ as a function of NS radius $R$ ($R, R_e$, and $R_p$) relations using EOSs predicted by using the G2 parameter set with (a) $\delta =0.05$ and (b) $\delta =0.005$.

Figure 11

NS mass $M$ as a function of NS radius $R$ ($R, R_e$, and $R_p$) when using EOSs predicted by NL3 parameter set with (a) $\delta =0.05$ and (b) $\delta =0.005$.

Figure 12

NS shape for the EOS predicted by parameter set G2 with $\delta =0.05$ for $M=1.95M_{\odot }$ and with $\delta =0.005$ for $M=1.92M_{\odot }$; NL3 with $\delta =0.05$ for $M=2.54M_{\odot }$, and with $\delta =0.005$ for $M=2.53M_{\odot }$.

Figure 13

Spherical radius $R$ as a function of energy density at NS center ${\epsilon }_c$ and for (a) G2 with $\delta =0.05$, (b) G2 with $\delta =0.005$, (c) NL3 with $\delta =0.05$, and (b) NL3 with $\delta =0.005$.

Figure 14

Mass as a function of ${\epsilon }_c$ for G2 and NL3 parameter sets with $\delta =0.005$ and $\delta =0.05$.

Figure 15

Anisotropic factor ${\sigma }_c$ at the NS center as a function of NS star radius (a) $R_e$ and (b) $R_p$ obtained by using the EOSs predicted by using the G2 and NL3 parameter sets with $\delta =0.05$ and $\delta =0.005$.