We revisit the possibility and detectability of a stochastic gravitational wave (GW) background produced by a cosmological population of newborn neutron stars (NSs) with r-mode instabilities. The NS formation rate is derived from both observational and simulated cosmic star formation rates (CSFRs). We show that the resultant GW background is insensitive to the choice of CSFR models, but depends strongly on the evolving behavior of CSFR at low redshifts. Nonlinear effects such as differential rotation, suggested to be an unavoidable feature which greatly influences the saturation amplitude of the r-mode, are considered to account for GW emission from individual sources. Our results show that the dimensionless energy density ΩGW could have a peak amplitude of ≃(1-3.5) × 10-8 in the frequency range (200-1000) Hz, if the smallest amount of differential rotation corresponding to a saturation amplitude of order unity is assumed. However, such a high-mode amplitude is unrealistic as it is known that the maximum value is much smaller and at most 10-2. A realistic estimate of ΩGW should be at least four orders of magnitude lower (∼10-12), which leads to a pessimistic outlook for the detection of the r-mode background. We consider different pairs of terrestrial interferometers (IFOs) and compare two approaches to combine multiple IFOs in order to evaluate the detectability of this GW background. Constraints on the total emitted GW energy associated with this mechanism to produce a detectable stochastic background (a signal-to-noise ratio of 2.56 with 3 year cross-correlation) are ∼10-3 M⊙ 1 c 2 for two co-located advanced LIGO detectors, and 2 × 10-5 M⊙ 1 c 2 for two Einstein telescopes. These constraints may also be applicable to alternative GW emission mechanisms related to oscillations or instabilities in NSs depending on the frequency band where most GWs are emitted.
- formation stars
- miscellaneous gravitational waves stars