Properties of rapidly rotating hot neutron stars with antikaon condensates at constant entropy per baryon

We consider a neutrino-free hot neutron star that contains antikaon condensates in its core and is at finite entropy per baryon. We find the equation of state for a range of entropies and antikaon optical potentials and generate the mass profile of static as well as rotating stars. Rotation induces many changes in the stellar equilibrium, and hence its structural properties evolve. In this work, we report the effect of rotation on the mass and shape of a hot neutron star for different equations of state and thermodynamic conditions. The temperature profile of a hot, static neutron star is also explored. We also make a crude estimate of the amplitude of gravitational waves emitted by an axisymmetric rotating NS with high magnetic field.

Figure 1

(a) The EoS with pressure plotted against number density for np and npK ($U_{\overline{K}}=-100\mathrm{MeV}$) for a NS core at zero temperature state ($T=0$ MeV) and at adiabatic state (entropy per baryon $s=1$, 4, and 5). (b) The mass sequences against number densities for the np and npK ($U_{\overline{K}}=-100\mathrm{MeV}$) EoS, for total entropy $S=0$, 3, 5, and 7 $M_{\mathrm{solar}}$. The dashed lines are for np matter and solid lines are for npK matter for $U_{\overline{K}}=-100$ MeV in both the panels.

Figure 2

The EoS is plotted for a range of values of $U_{\overline{K}}=-60\text{MeV}$ to $-150\text{MeV}$ (a) for lower $s=1$ and (b) for higher $s=4$. In both the plots np EoS is also included as the dashed line for comparison.

Figure 3

The mass-number density profiles for EoS with np and npK matter at different optical potentials at for (a) $\mathrm{S}=3M_{\mathrm{solar}}$ and (b) $S=7M_{\mathrm{solar}}$.

Figure 4

Fraction of different particles in a $\beta$-equilibrated NS matter with n, p, e, $\mu$, and antikaon condensates of $K^{-}$ and $K^T$; for $U_{\overline{K}}=-60$ MeV; plotted as a function of the baryon density for (a) $s=1$ and (b) $s=4$.

Figure 5

Particle fractions vs baryon number density as in Fig 4, but for a deeper $U_{\overline{K}}=-150$ MeV for (a) $s=1$ and (b) $s=4$.

Figure 6

Temperature in a NS is plotted as a function of baryon density $n_b$, for a given thermodynamic state, (a) $s=1$ and (b) $s=4$.

Figure 7

The evolution of mass with rotation for a NS with npK ($U_{\overline{K}}=-100\mathrm{MeV}$) and at (a) $S=3M_{\mathrm{solar}}$ and (b) $S=7M_{\mathrm{solar}}$. The sequences are plotted for NS rotating with different angular momenta starting from $J=0$ (static case) to $J=1G{M}_{\mathrm{solar}}^2/c$ and $2G{M}_{\mathrm{solar}}^2/c$.

Figure 8

Energy density iso-contours of a rotating NS with baryon mass of $2M_{\mathrm{solar}}$. Top (bottom) panel shows static NS with EoS for $U_{\overline{K}}=-60(-150)$ MeV, with $s=1$.

Figure 9

Energy density iso-contours of a rotating NS as in Fig. 8, but with higher entropy per baryon state $s=4$

Figure 10

Effect of rotation on NS shape. Energy density iso-contours for a NS with npK ($U_{\overline{K}}=-150\mathrm{MeV}$, $s=1$) rotating at $J=0.02G{M}_{\mathrm{solar}}^2/c$ (top) and $0.5G{M}_{\mathrm{solar}}^2/c$ (bottom).

Figure 11

Energy density isocontours for a NS as in Fig. 10 rotating at $J=1.8G{M}_{\mathrm{solar}}^2/c$ (top) and $2.23G{M}_{\mathrm{solar}}^2/c$ (bottom).

Figure 12

Fluid energy density isocontours for NS ($U_{\overline{K}}=-150$ MeV, $s=4$) rotating at $J=0.02G{M}_{\mathrm{solar}}^2/c$ (top) and at $J=1.8G{M}_{\mathrm{solar}}^2/c$ (bottom).