Gravitational wave asteroseismology with fast rotating neutron stars

We investigate damping and growth times of the quadrupolar $f$ mode for rapidly rotating stars and a variety of different polytropic equations of state in the Cowling approximation. This is the first study of the damping/growth time of these types of oscillations for fast-rotating neutron stars in a relativistic treatment where the spacetime degrees of freedom of the perturbations are neglected. We use these frequencies and damping/growth times to create robust empirical formulae which can be used for gravitational-wave asteroseismology. The estimation of the damping/growth time is based on the quadrupole formula and our results agree very well with Newtonian ones in the appropriate limit.

Figure 1

Splitting of the power spectral density (normalized units) for nonaxisymmetric $|m|=2$ modes in a comoving reference frame with corresponding mode frequency ${\sigma }_c$. The mass-shedding limit for this particular sequence is reached for $\Omega /2\pi =2.18\mathrm{kHz}$.

Figure 2

Co- and counterrotating branches of the different polytropic EoS studied in this paper. Panel (i): Mode frequencies in the inertial frame; the solid line of each EoS depicts the more compact sequence, while the dashed line traces the less compact configurations. Panel (ii): Normalized mode frequencies and fitting curve in the comoving frame; the larger circles represent again the more compact models, while the small circles stand for the less compact ones. ${\sigma }_0$ is the frequency in the nonrotating limit, ${\Omega }_K$ represents the Kepler-limit.

Figure 3

Scaling of the $f$-mode frequency with mean density in the nonrotating limit. $M$ and $R$ are given in km, ${\sigma }_0$ in kHz.

Figure 4

Model-independent relations for the damping time. Larger circles represent the more compact models, while small circles stand for the less compact configurations of each EoS. Panel (i): Damping times for the counterrotating branch, ${\sigma }_i^u$ is the mode frequency in the inertial frame. Panel (ii): Damping times for the corotating branch, ${\sigma }_c^s$ is the mode frequency in the comoving frame.

Figure 5

Scaling of the $f$-mode damping time in the nonrotating limit. $M$, $R$, and ${\tau }_0$ are given in km.

Figure 6

Power spectral density of $H$ (normalized units) for the quadrupolar $f$ mode and a nonrotating background configuration.

Figure 7

Mass-radius diagram for the six EoS and in our sample. The 12 different background sequences (two for every EoS) are marked as circles which branch off their corresponding nonrotating equilibrium curve.

Figure 8

Comparison between literature values and our results for $c_{\tau }$ (see (c1) for the definition). In the limit of small compactness, the Newtonian value of $c_{\tau }=8.46$ is approached.