Influence of differential rotation on the detectability of gravitational waves from ther-mode instability

Abstract

Recently, it was shown that differential rotation is an unavoidable feature of nonlinear r -modes. We investigate the influence of this differential rotation on the detectability of gravitational waves emitted by a newly born, hot, rapidly-rotating neutron star, as it spins down due to the r -mode instability. We conclude that gravitational radiation may be detected by the advanced laser interferometer detector LIGO if the amount of differential rotation at the time the r -mode instability becomes active is not very high.PACS numbers: 04.30. Db, 95.85.Sz, 97.10.Sj, 97.60.Jd

Gravitational waves from r-modes

“…This quantity, in turn, plays a crucial role in the evolution model of the r-mode instability (Sá and Tomé 2005). Within this model one can determine the time evolution of the star's angular velocity and the mode's amplitude, two quantities which are used to compute the gravitational wave amplitude (Sá and Tomé 2006). Assuming matched filtering, the characteristic amplitude of the signal (related, in a simple way, to the gravitational wave amplitude in the frequency domain) is compared to the rms strain noise in the detector, showing that the signal-to-noise ratio decreases as the initial amount of differential rotation associated to r-modes increases (Sá and Tomé 2006).…”

“…Within this model one can determine the time evolution of the star's angular velocity and the mode's amplitude, two quantities which are used to compute the gravitational wave amplitude (Sá and Tomé 2006). Assuming matched filtering, the characteristic amplitude of the signal (related, in a simple way, to the gravitational wave amplitude in the frequency domain) is compared to the rms strain noise in the detector, showing that the signal-to-noise ratio decreases as the initial amount of differential rotation associated to r-modes increases (Sá and Tomé 2006). Therefore, one can conclude that differential rotation induced by r-modes plays a fundamental role in the evolution of the mode's instability, making it more difficult to detect the…”

“…The initial amplitude of the r-mode perturbation, the initial angular velocity and temperature of the star are chosen to be, respectively, α 0 = 10 −6 , Ω 0 = Ω K and T 0 = 10 11 K. The r-mode instability is active from t ≈ 0 to t = t f , where t f lies between 3.6 × 10 6 s, for K = −5/4, and 7.1 × 10 6 s, for K 1 (Sá and Tomé 2006). Solving numerically the above system of differential equations we arrive at the conclusion that (Sá and Tomé 2005): (i) initially, the amplitude of the r-mode grows exponentially (as expected, according to the results of the linearized theory, discussed in Sect.…”

“…Afterwards, Arras et al (2003) and Brink et al (2004Brink et al ( , 2005 showed that nonlinear mode-mode interactions limit the r-mode saturation amplitude to values much lower than unity, implying that the detection of such gravitational waves is more difficult than initially supposed. Recently, the issue of detectability of these gravitational waves was again addressed, but taking into account another nonlinear effect, namely, differential rotation induced by r-modes (Sá and Tomé 2006). In this article we discuss these recent results, showing that differential rotation may also limit the saturation amplitude of r-modes to values much lower than unity, making it more difficult to detect gravitational waves from newly born neutron stars.…”

“…We now investigate the possibility of detecting these gravitational waves using the Advanced Laser Interferometer Gravitational Wave Observatory (in what follows referred to simply as Advanced LIGO), whose planned noise power spectral density (Abramovici et al 1992) is well approximated, for 50 Hz ≤ f ≤ 1200 Hz, by the analytical expression (Sá and Tomé 2006)…”