Frequency domain model of f -mode dynamic tides in gravitational waveforms from compact binary inspirals

Abstract

The recent detection of gravitational waves (GWs) from the neutron star binary inspiral GW170817 has opened a unique avenue to probe matter and fundamental interactions in previously unexplored regimes. Extracting information on neutron star matter from the observed GWs requires robust and computationally efficient theoretical waveform models. We develop an approximate frequency-domain GW phase model of a main GW signature of matter: dynamic tides associated with the neutron stars' fundamental oscillation modes (f -modes). We focus on nonspinning objects on circular orbits and demonstrate that, despite its mathematical simplicity, the new "f -mode tidal" (fmtidal) model is in good agreement with the effective-one-body dynamical tides model up to GW frequencies of 1 kHz and gives physical meaning to part of the phenomenology captured in tidal models tuned to numerical-relativity. The advantages of the fmtidal model are that it makes explicit the dependence of the GW phasing on the characteristic equation-of-state parameters, i.e., tidal deformabilities and f -mode frequencies, is computationally efficient, and can readily be added to any frequency-domain baseline waveform. The fmtidal model is easily amenable to future improvements and provides the means for a first step towards independently measuring additional fundamental properties of neutron star matter beyond the tidal deformability as well as performing novel tests of General Relativity from GW observations. PACS numbers: 04.80.Nn, 95.85.Sz, 04.30.Tv, 97.60.Jd, 26.60.Kp * pschmidt@star.sr.bham.ac.uk † t.hinderer@uva.nl 1 Oscillation modes are characterized by three integers (n, , m),where n denotes the number of radial nodes in the mode function and m is the azimuthal integer. In the nonspinning case, the mode frequency is independent of m, and for the f -modes n = 0, hence our notation ω n m | f −mode = ω . arXiv:1905.00818v1 [gr-qc]

Gravitational-wave asteroseismology with fundamental modes from compact binary inspirals

“…' 5 , implying that small values of f ℓ result in hyper-excited dynamical tides that are inconsistent with the data. This is reflected in the shape of the posterior (green curve), where we see a dramatic drop in posterior support as f → 0.…”

“…16 ) augmented with the dynamical f-mode tidal contribution to the phase developed in ref. 5 (see Methods, Waveform Model). We perform coherent Bayesian inference using the nested sampling algorithm implemented in LALINFERENCE 17,18 , as summarised in Methods, Parameter Estimation.…”

“…48 , where contributions from higher multipoles are omitted and a number of unknown terms appearing at 7PN are neglected. In this paper, we also incorporate a recently derived closed-form expression for the dynamical tidal contribution to the phase 5 . This enables us to include the tidal excitation of the neutron stars fundamental oscillation modes at quadrupolar (ℓ = 2) and octupolar (ℓ = 3) order.…”

“…As the binary evolves towards merger, additional dynamical tidal effects become important when variations in the tidal fields occurring on the orbital timescale approach a resonance with the star's internal oscillation modes, giving rise to new characteristic signatures in the GWs associated with specific modes. Among these modes, the fundamental (f ℓ -)modes have the strongest tidal coupling and lead to a f-mode frequency-dependent amplification of tidal signatures in the GW signal that starts to accumulate long before the resonance [3][4][5] . In General Relativity (GR), and for a range of proposed nuclear EoSs for NSs, the f ℓ -mode frequencies are empirically found to be related to Λ ℓ through approximate universal relations (URs) 6,7 .…”

“…Here we show direct constraints on f-modes from the GW data alone, without the assumption of URs, by using a model for the GW signal that explicitly depends both on the tidal deformability and the f-mode frequency 5 . In this UR-independent analysis, we find that the data from GW170817 disfavours anomalously small values of f ℓ .…”