A hybrid GNA instability

Abstract

A semi-analytic admixed model formalism to study the stability effects of the inner crust regions against the local collective perturbations in non-rotating neutron stars is proposed. It consists of the viscoelastic heavy neutron-rich nuclei, superfluid neutrons, and degenerate quantum electrons. A normal spherical mode analysis yields a generalized linear dispersion relation multiparametrically mimicking the inner crust features of neutron stars. A hybrid gravito-nucleo-acoustic (GNA) instability mode is found to be excited. It is demonstrated that the electron density and the inner crust curvature act as its accelerating and antidispersive agents. In contrast, the heavy neutron-rich nucleus and neutron densities act as decelerating factors. The heavy nucleus density, electron density, and geometric curvature act as its destabilizers. It is only the neutron density that acts as the GNA stabilizing agent. The heavy neutron-rich nucleus and neutron densities are found to act as dispersive broadening factors to it. The high-[Formula: see text] regions are the more unstable spectral windows indicating that the GNA mode plays a dominant role in the inner crust zone towards the local stability. Its fair reliability is indicated in light of the recent astronomic observed scenarios. It could be useful to explore acoustic mode signatures in non-rotating neutron stars and similar other compact astroobjects.

Figure 1

Profile of the Jeans-normalized (a) real frequency $({\mathrm{\Omega }}_r)$, (b) imaginary frequency $({\mathrm{\Omega }}_i)$, (c) phase velocity $(v_p)$, and (d) group velocity $(v_g)$ of the fluctuations with variation in the Jeans-normalized wavenumber $(K)$ for the different ${\rho }_{h0}$-values. The distinct lines link to ${\rho }_{h0}=5\times {10}^{14}$ kg m⁻³ (solid blue line), ${\rho }_{h0}=7\times {10}^{14}$ kg m⁻³ (red dash-dash line), and ${\rho }_{h0}=9\times {10}^{14}$ kg m⁻³ K (black dotted line), respectively.

Figure 2

Same as Fig. 1, but for ${\rho }_{h0}=5\times {10}^{14}$ kg m⁻³ (fixed). The different lines link to ${\rho }_{n0}=1\times {10}^{17}$ kg m⁻³ (solid blue line), ${\rho }_{n0}=2\times {10}^{17}$ kg m⁻³ (red dash-dash line), and ${\rho }_{n0}=3\times {10}^{17}$ kg m⁻³ (black dotted line), respectively.

Figure 3

Same as Fig. 1, but for ${\rho }_{h0}=1\times {10}^{15}$ kg m⁻³ (fixed). The different lines link to ${\rho }_{e0}=1\times {10}^9$ kg m⁻³ (solid blue line), ${\rho }_{e0}=2\times {10}^{19}$ kg m⁻³ (red dash-dash line), and ${\rho }_{e0}=3\times {10}^9$ kg m⁻³ (black dotted line), respectively.

Figure 4

Same as Fig. 1, but for ${\rho }_{h0}=5\times {10}^{14}$ kg m⁻³ (fixed). The different lines link to different Jeans-normalized radial space coordinates as $\xi =0.1$ (solid blue line), $\xi =0.2$ (red dash-dash line), and $\xi =0.3$ (black dotted line), respectively.

Figure 5

Spectral profile of the Jeans-normalized (a) real frequency $({\mathrm{\Omega }}_r)$, (b) imaginary frequency $({\mathrm{\Omega }}_i)$, (c) phase velocity $(v_p)$, and (d) group velocity $(v_g)$ of the GNA fluctuations in a colour phase space functionally defined by the Jeans-normalized angular wavenumber $(K)$ and the rescaled heavy nuclear material density $({\rho }_h^{\ast })$.

Figure 6

Same as Fig. 5, but showing the ${\rho }_n^{\ast }$-variation with a fixed ${\rho }_h^{\ast }$.

Figure 7

Same as Fig. 5, but showing the ${\rho }_e^{\ast }$-variation with a fixed ${\rho }_h^{\ast }$.

Figure 8

Same as Fig. 5, but showing the $\xi$-variation with a fixed ${\rho }_h^{\ast }$.