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

## TL;DR

This paper introduces a simple, efficient frequency-domain gravitational wave phase model capturing neutron star matter effects via $f$-mode dynamic tides, aiding in extracting neutron star properties from GW data.

## Contribution

The paper develops the first approximate frequency-domain $f$-mode tidal GW phase model that explicitly relates to neutron star matter parameters, improving computational efficiency and interpretability.

## Key findings

- Model agrees with dynamical tides up to 1 kHz.
- Explicit dependence on tidal deformability and $f$-mode frequency.
- Facilitates future measurements of neutron star properties.

## 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 $\gtrsim 1$ 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; it is computationally efficient; and it 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.