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

Abstract

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.

Figures (7)

• Figure 1: Mean (solid) quadrupolar $f$-mode frequency and symmetric 90% credible interval (shaded) as a function of neutron star mass, as inferred from different astrophysical datasets. For the PSR dataset, we show only the 90% credible interval. Every realization (dashed) of the $f_2(m)$ relation is monotonically increasing, but the mean of the distribution turns over above 2 $M_\odot$ because the EOSs that support larger neutron star masses are stiffer than average and thus have systematically lower $f_2$.
• Figure 2: Comparison between the inferred quadrupolar $f$-mode frequency and the gravitational-wave frequencies at contact for a realistic population of binary neutron star coalescences. The PSR+GW+NICER constraints from Fig. \ref{['fig:Envelope Plot']} are shown. Resonance of the orbit with the $f$-mode only occurs if $f_2$ is below the contact frequency.
• Figure 3: Inferred two-dimensional marginal posterior distributions over mass and quadrupolar $f$-mode frequency for the primary (solid) and secondary (dashed) components of GW170817. The distributions are conditioned on three different observational datasets. Contours delimit 90% credibility regions.
• Figure 4: Inferred two-dimensional marginal posterior distributions over the radius of canonical (top) or TOV-mass (bottom) neutron stars and the corresponding quadrupolar $f$-mode frequency. The distributions are conditioned on three different observational datasets. Contours delimit 90% credibility regions. The value of $f_{1.4}$ is strongly (anti-)correlated with $R_{1.4}$. A similar correlation is observed between $f_{\rm TOV}$ and $R_{\rm TOV}$. The correlation coefficients are quoted in the legend.
• Figure 5: EOS-averaged tidal phase at merger from quadrupolar $f$-mode dynamical tides as a function of binary neutron star component masses. The tidal phase is evaluated at the contact frequency with the fmtidal model from Ref. SchmidtHinderer2019. The EOS distribution is informed by the PSR+GW+NICER dataset.