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Examining the influence of anisotropy on the fundamental mode of nonradial oscillation in neutron stars on a complete general relativistic scheme

José D. V. Arbañil, Gabriel O. Cavalheiro, Victor B. T. Alves, Juan M. Z. Pretel, César O. V. Flores, César H. Lenzi

Abstract

The anisotropic influence on the $f$-mode frequency of oscillations and dimensionless tidal deformability of neutron stars are analyzed by employing the nonradial oscillation equations for the complete general relativity frame and tidal deformability equations, which are derived and modified from their standard form to introduce the anisotropic factor. The fluid inside the compact star obeys an equation of state constructed by matching microscopic nuclear and perturbative QCD calculations through a piecewise polytropic interpolating scheme. For the anisotropic function, we use a local anisotropy, which is regular along the whole star and is null both at the center and on the star's surface. We show that the $f$-frequency of oscillation and dimensionless tidal deformability change considerably with the anisotropy. Finally, we investigate the correlation between the dimensionless tidal deformability of the GW$170817$ event with the anisotropy.

Examining the influence of anisotropy on the fundamental mode of nonradial oscillation in neutron stars on a complete general relativistic scheme

Abstract

The anisotropic influence on the -mode frequency of oscillations and dimensionless tidal deformability of neutron stars are analyzed by employing the nonradial oscillation equations for the complete general relativity frame and tidal deformability equations, which are derived and modified from their standard form to introduce the anisotropic factor. The fluid inside the compact star obeys an equation of state constructed by matching microscopic nuclear and perturbative QCD calculations through a piecewise polytropic interpolating scheme. For the anisotropic function, we use a local anisotropy, which is regular along the whole star and is null both at the center and on the star's surface. We show that the -frequency of oscillation and dimensionless tidal deformability change considerably with the anisotropy. Finally, we investigate the correlation between the dimensionless tidal deformability of the GW event with the anisotropy.

Paper Structure

This paper contains 18 sections, 48 equations, 4 figures, 3 tables.

Table of Contents

  1. Introduction
  2. General relativistic equations
  3. The static equilibrium equations
  4. Nonradial perturbation equations
  5. Tidal deformability
  6. Equation of state and anisotropic profile
  7. Equation of state
  8. Anisotropic profile
  9. Anisotropic effects on the equilibrium, frequency of oscillations, and tidal deformability
  10. General remarks
  11. Equilibrium configurations and frequency of oscillations
  12. On the detectability of the fundamental mode signal
  13. Tidal deformability
  14. Conclusions
  15. Nonradial perturbations of relativistic spherically symmetric stars in the presence of an anisotropic fluid
  16. ...and 3 more sections

Figures (4)

  • Figure 1: The total gravitational mass, in Sun's masses, against the central energy density and as a function of the total radius are plotted on the left and right panels, respectively. In both panels, nine different anisotropic parameters $\alpha$ are employed. The solid purple and black curves indicate the $95\%$ confidence intervals for the masses and radii of PSR J$0030+0451$riley2019miller2019, while the orange and gray curves show the same for PSR J$0740+6620$riley2021miller2021, both measured by the NICER collaboration. In all cases, the outer lines offer a greater likelihood of containing the true value but with lower precision, whereas the inner lines provide higher accuracy but with lower statistical coverage.
  • Figure 2: The $f$-mode frequency of oscillations and the normalized $\omega_f$ with the average density $(M/R^3)^{0.5}$ against the total mass are presented on the left and right panels, respectively. In both panels, nine different anisotropic parameters $\alpha$ are used.
  • Figure 3: Left: Dimensionless tidal deformability against the total mass for different values of $\alpha$. Right: Oscillation frequency $f_f$ as a function of the dimensionless tidal deformability for nine values of $\alpha$. In both panels, the vertical dashed line depicts dimensionless tidal deformability $\Lambda_{1.4}=190^{+390}_{-120}$ from the event GW$170817$ reported by LVC in Ref. 2018PhRvL.121p1101A.
  • Figure 4: The dimensionless tidal deformabilities of the GW$170817$ event components are shown for different values of the anisotropic parameter $\alpha$. The yellow line depicts the LIGO-Virgo confidence curves abbott2017_4, while the dotted diagonal line marks the points where $\Lambda_1 = \Lambda_2$.