Axial quasinormal modes of scalarized neutron stars with realistic equations of state

We compute the axial quasinormal modes of static neutron stars in scalar tensor theory. In particular, we employ various realistic equations of state including nuclear, hyperonic and hybrid matter. We investigate the fundamental curvature mode and compare the results with those of general relativity. We find that the frequency of the modes and the damping time are reduced for the scalarized neutron stars. In addition, we confirm and extend the universal relations for quasinormal modes known in general relativity to this wide range of realistic equations of state for scalarized neutron stars and confirm the universality of the scaled frequency and damping time in terms of the scaled moment of inertia as well as compactness for neutron stars with and without scalarization.

Figure 1

Total mass $M$ in solar masses $M_{\odot }$ versus the physical radius $R_s$ in km of the neutron star models for all the EOSs considered for GR configurations (red) and the scalarized solutions for $A=e^{\frac{1}{2}\beta {\phi }^2}$ with $\beta =-4.5$ (blue).

Figure 2

Frequency ${\omega }_R$ in kHz (a) and damping time $\tau$ in $\mu \mathrm{s}$ (b) versus the total mass $M$ in solar masses $M_{\odot }$ of the neutron star models for all the EOSs considered for GR configurations (red) and the scalarized solutions for $A=e^{\frac{1}{2}\beta {\phi }^2}$ with $\beta =-4.5$ (blue).

Figure 3

Frequency ${\omega }_R$ in kHz (a) and damping time $\tau$ in $\mu \mathrm{s}$ (b) both scaled by the mass in $M_{\odot }$ versus the compactness $\mathcal{C}=M/R_s$ of the neutron star models for all the EOSs considered for GR configurations (black) and the scalarized solutions for $A=e^{\frac{1}{2}\beta {\phi }^2}$ with $\beta =-4.5$ (blue). The upper panels show the scaled values (symbols) together with the fitted curves (dotted) of the universal relations. The lower panels show the deviations from the fits, $|1-F/F_{\mathrm{fit}}|$.

Figure 4

The scaled quantity $10^{3}M/\tau$ (in $10^3{M}_{\odot }/\mu \mathrm{s}$) as a function of $M{\omega }_R$ (in $M_{\odot }\mathrm{kHz}$). GR configurations are in black and the scalarized solutions for $A=e^{\frac{1}{2}\beta {\phi }^2}$ with $\beta =-4.5$ in blue.

Figure 5

Relation between the imaginary part of the eigenvalue $\omega$ with the real part, when both are normalized with respect to the central pressure of the neutron star (${\tilde{\omega }}_I$ vs ${\tilde{\omega }}_R$). GR configurations are in black and the scalarized solutions for $A=e^{\frac{1}{2}\beta {\phi }^2}$ with $\beta =-4.5$ in blue. The upper panel shows the scaled values (symbols) together with the fitted curve (dotted) of the universal relation. The lower panel shows the deviations from the fit, $|1-F/F_{\mathrm{fit}}|$.

Figure 6

Frequency ${\omega }_R$ in kHz (a) and inverse damping time $\tau$ in $\mu \mathrm{s}$ (b) both scaled by the mass in $M_{\odot }$ versus the scaled moment of inertia $\eta =\sqrt{M^3/I}$ of the neutron star models for all the EOSs considered for GR configurations (black) and the scalarized solutions for $A=e^{\frac{1}{2}\beta {\phi }^2}$ with $\beta =-4.5$ (blue). The upper panels show the scaled values (symbols) together with the fitted curves (dotted) of the universal relations. The lower panels show the deviations from the fits, $|1-F/F_{\mathrm{fit}}|$.