Proto-neutron star structure within an extended lowest-order constrained variational method at finite temperature

The lowest-order constrained variational approach at finite temperature is extended by adding a semiphenomenological three-body force to its formulation. The equation of state (EOS) of hot asymmetric nuclear matter is obtained within the framework of the extended model. The density and temperature dependence of the mentioned three-body force is also discussed. The EOS of the proto-neutron star as well as its mass-radius relation is studied for several values of constant entropy and lepton fraction. We find that the maximum gravitational mass of the proto-neutron star is slightly sensitive to the value of the entropy and lepton fraction.

Figure 1

The temperature dependence of $f_T\left(r\right)$ at ${\rho }_B=0.17{\mathrm{fm}}^{-3}$ for SNM.

Figure 2

(a) The density dependence of $f_T\left(r\right)$ at $T=10$ MeV for SNM. (b) Same as panel (a) but for ${\overline{V}}_{12}^{}(r,T)$.

Figure 3

The temperature dependence of the $V_{\sigma \tau }^{2\pi }$ component of the effective two-body interaction at ${\rho }_B=0.17{\mathrm{fm}}^{-3}$ for SNM.

Figure 4

Same as Fig. 3 but for the $V_t^{2\pi }$ component.

Figure 5

Same as Fig. 3 but for the $V_c^R$ component.

Figure 6

(a) Free energy per baryon of the symmetric nuclear matter as a function of density for different values of temperature with and without the TBF. (b) Same as panel (a) but for the pure neutron matter.

Figure 7

(a) The temperature of the PNS matter as a function of baryon density for different values of entropy per baryon obtained with and without the TBF for $Y_e=0.3$. (b) Same as panel (a) but for $Y_e=0.4$.

Figure 8

(a) Relative population of the constituents of the PNS core calculated by using AV18 potential and for $Y_e=0.3$ and $S/A=1$. (b) Same as panel (a) but for $S/A=2$.

Figure 9

(a) Relative population of the constituents of the PNS core calculated by using AV18 potential and for $Y_e=0.4$ and $S/A=1$. (b) Same as panel (a) but for $S/A=2$.

Figure 10

Relative population of the constituents of the PNS core calculated by using AV18 + TBF potential and for $Y_e=0.3$ and $S/A=1$. (b) Same as panel (a) but for $S/A=2$.

Figure 11

Relative population of the constituents of the PNS core calculated by using AV18 + TBF potential and for $Y_e=0.4$ and $S/A=1$. (b) Same as panel (a) but for $S/A=2$.

Figure 12

(a) The EOS of the proto-neutron star with $Y_e=0.3$ calculated with and without the TBF for some fixed values of the entropy per baryon. (b) Same as panel (a) but for $Y_e=0.4$.

Figure 13

(a) The mass-radius relation of the proto-neutron star with $Y_e=0.3$ calculated with and without the TBF for some fixed values of the entropy per baryon. (b) Same as panel (a) but for $Y_e=0.4$.