New Class of Quasinormal Modes of Neutron Stars in Scalar-Tensor Gravity

Detection of the characteristic spectrum of pulsating neutron stars can be a powerful tool not only to probe the nuclear equation of state but also to test modifications to general relativity. However, the shift in the oscillation spectrum induced by modified theories of gravity is often small and degenerate with our ignorance of the equation of state. In this Letter, we show that the coupling to additional degrees of freedom present in modified theories of gravity can give rise to new families of modes, with no counterpart in general relativity, which could be sufficiently well resolved in frequency space to allow for clear detection. We present a realization of this idea by performing a thorough study of radial oscillations of neutron stars in massless scalar-tensor theories of gravity. We anticipate astrophysical scenarios where the presence of this class of quasinormal modes could be probed with electromagnetic and gravitational wave measurements.

Figure 1

ADM mass of sequences of equilibrium stellar configurations in M1 and M2, with (a) $\beta =-5$ and (b) $\beta =100$, parametrized by their central rest-mass density ${\tilde{\rho }}_c$. Branches of scalarized solutions appear at sufficiently high densities. In (b), we display only the first families of scalarized solutions, labeled by the number $n$ of nodes in their scalar field profile; see Refs. [26, 34] for details.

Figure 2

Frequency (a) and inverse damping time (b) of the three lowest-frequency radial modes of stellar models in STTs, for M1 and M2 with $\beta =-5$, as a function of compactness. Lines (points) represent values computed with frequency (time) domain techniques. Panel (c) focuses on the fundamental $\varphi$ mode, showing its real and imaginary parts as a function of stellar compactness.

Figure 3

Same as Fig. 2, except for $\beta =100$. Panels (a) and (b) refer to Model 1 alone since all scalarized stars in Model 2 are unstable (see SM [41]). For the sake of presentation, in panel (c), we plot the absolute value of the $\varphi$-mode frequencies only, scaled by the sign of the imaginary part of $\omega$ to help distinguish between stable and unstable modes. Note that scalarized solutions in M2 with $n=0$ cease to exist at the same critical compactness $M/R\approx 0.292$, where scalarized solutions in M1 first appear [cf. Fig. 1].