Astrophysical constraints on neutron star $f$-modes with a nonparametric equation of state representation

We constrain the fundamental-mode ($f$-mode) oscillation frequencies of nonrotating neutron stars using a phenomenological Gaussian process model for the unknown dense-matter equation of state conditioned on a suite of gravitational-wave, radio and X-ray observations. We infer the quadrupolar $f$-mode frequency preferred by the astronomical data as a function of neutron star mass, with error estimates that quantify the impact of equation of state uncertainty, and compare it to the contact frequency for inspiralling neutron-star binaries, finding that resonance with the orbital frequency can be achieved for the coalescences with the most unequal mass ratio. For an optimally configured binary neutron star merger, we estimate the gravitational waveform's tidal phasing due to $f$-mode dynamical tides as $7^{+2}_{-3}$ rad at merger. We assess prospects for distinguishing $f$-mode dynamical tides with current and future-generation gravitational-wave observatories.