LIGO Document P1800246-v8

Constraining the p-mode--g-mode tidal instability with GW170817

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We analyze the impact of a proposed tidal instability coupling p-modes and g-modes within neutron stars on GW170817. This nonresonant instability transfers energy from the orbit of the binary to internal modes of the stars, accelerating the gravitational-wave driven inspiral. We model the impact of this instability on the phasing of the
gravitational wave signal using three parameters per star: an overall amplitude, a saturation frequency, and a spectral index. Incorporating these p-g additional parameters, we compute the Bayes factor (lnB) comparing our p-g model to a standard
one. We find that the observed signal is consistent with waveform models that neglect p-g effects, with lnB = 0.03 +0.70 −0.58. By injecting simulated signals that do not include p-g effects and recovering them with the p-g model, we show that there is a 50% probability of obtaining similar lnB even when p-g effects are absent. We find that the p-g amplitude for 1.4 M neutron stars is constrained to few 10^−7 , with maxima a posteriori near ∼ 10^−7 and p-g saturation frequency ∼ 70 Hz. This suggests that there are less than a few hundred excited modes, assuming they all saturate by wave breaking. For comparison, theoretical upper bounds suggest a p-g amplitude 10^−6 and 10^3 modes saturating by wave breaking. Thus, the measured constraints only rule out extreme values of the p-g parameters. They also imply that the instability dissipates 10^51 ergs over the entire inspiral, i.e., less than a few percent of the energy radiated as gravitational waves
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