Theoretical constraints on the properties of low-mass neutron stars from the equation of state of nuclear matter in the inner crust

By employing four typical equation of states (EOSs) of nuclear matter in the inner crust, the properties of low-mass neutron stars are investigated theoretically. Based on the well-known fact that there is a big gap between the neutron stars and white dwarfs in the mass-radius sequence of compact stars, according to the mass-radius relations of the four adopted EOSs, we conclude that there is a rough forbidden region for the central density and stellar radius to form a compact star; that is, there is no compact star in nature having central density in the region from about ${10}^{12}{\mathrm{kgm}}^{-3}$ to ${10}^{17}{\mathrm{kgm}}^{-3}$, and there is also no compact star having a radius in the region from about 400 km to 2000 km. Moreover, the properties of the low-mass neutron stars are also explored. It is shown that for a stable neutron star near the minimum mass point, the stellar size (with radius $>200$ km) is much larger than that of normal neutron stars, and there is a compact “core” concentrated at about 95% of the stellar mass in the inner core with a radius of about 13 km and density higher than the neutron-drip point $(4.3\times {10}^{14}{\mathrm{kgm}}^{-3})$. This property totally differs from that of normal neutron stars and white dwarfs. Furthermore, the Keplerian period, the moment of inertia, and the surface gravitational redshift of the star near the minimum-mass point are also investigated.

Figure 1

The EOSs of the nuclear matter in the inner crust.

Figure 2

The EOSs of the matter in the inner core, where the inset describes the EOSs of the matter in the outer crust.

Figure 3

The stellar masses as a function of the central densities for the four adopted EOSs, where the central densities range from ${10}^9{\mathrm{kgm}}^{-3}$ to $4\times {10}^{18}{\mathrm{kgm}}^{-3}$ and the star sequence covers from white dwarfs to neutron stars.

Figure 4

The mass-radius relations for the four adopted EOSs. For comparison, the mass-radius relations for the “soft” and “stiff” EOSs of Ref. [38] are also plotted.

Figure 5

The adiabatic indices in the density range from $3\times {10}^{11}{\mathrm{kgm}}^{-3}$ to $3\times {10}^{18}{\mathrm{kgm}}^{-3}$ as a function of the density for the four adopted EOSs.

Figure 6

The mass-radius relations for the low-mass neutron stars, where the inset is the masses as a function of the central densities, and the small square on the line denotes the $M_{\min }$ point.

Figure 7

The mass profile for the neutron star with minimum mass, where the stars mark the points with density at neutron-drip point and the circles mark the points at density ${10}^{12}{\mathrm{kgm}}^{-3}$. The inset is the corresponding density profile.

Figure 8

The mass profile for the neutron star at central density $1.66\times {10}^{17}{\mathrm{kgm}}^{-3}$, where the stars mark the points with density at neutron-drip point and the circles mark the points at density ${10}^{12}{\mathrm{kgm}}^{-3}$. The inset is the density profile for the inner core with density $>4\times {10}^{14}{\mathrm{kgm}}^{-3}$.

Figure 9

The Keplerian period ($P_K$) as a function of the central density ${\rho }_c$, where $P_K$ denotes the period of a star rotating at Keplerian frequency. The inset shows the $P_K\text{−}M$ relations.

Figure 10

The moment of inertia $I$ as a function of the central density ${\rho }_c$. The inset shows the $I\text{−}M$ relations.

Figure 11

The redshift $z$ as a function of the central density ${\rho }_c$. The inset shows the $z\text{−}M$ relations.