Gravitational-wave asteroseismology with fundamental modes from compact binary inspirals

Abstract

Gravitational waves (GWs) from binary neutron stars encode unique information about ultra-dense matter through characterisic signatures associated with a variety of phenomena including tidal effects during the inspiral. The main tidal signature depends predominantly on the equation of state (EoS)-related tidal deformability parameter Λ, but at late times is also characterised by the frequency of the star's fundamental oscillation mode (f-mode). In General Relativity and for nuclear matter, Λ and the f-modes are related by universal relations which may not hold for alternative theories of gravity or exotic matter. Independently measuring Λ and the f-mode frequency enables tests of gravity and the nature of compact binaries. Here we present directly measured constraints on the f-mode frequencies of the companions of GW170817. We also show that future GW detector networks will measure f-mode frequencies to within tens of Hz, enabling precision GW asteroseismology with binary inspiral signals alone.

Fig. 1. Results for the larger-mass object of GW170817.

a The black shaded region shows the two-dimensional probability distribution function (PDF) for the f₂-mode frequency and quadrupolar tidal deformability of the larger companion Λ_2,1, where the subscripts denote the multipolar index ℓ = 2 and the larger mass object's label A = 1. The solid lines correspond to the 90% credible regions, where the black curve corresponds to the analysis in which f_2,A are treated as independent parameters and the yellow one to imposing the universal relations, i.e., fixing f_2,A given Λ_2,A. The posteriors are overlaid with UR predictions for three EoS for NSs (coloured solid curves), and three massive BSs (coloured dashed curves) denoted (m_b/m_n, λ_b), with m_n = 1.675 × 10⁻²⁷kg being the neutron mass, where all curves are restricted to the 90% interval of the component mass posterior, m₁ ∈ [1.37, 1.63] M_⊙. b Marginalised one-dimensional PDF for the f₂-mode frequency. We show results for the following three tidal phase models as listed in Table 1: (i) purely adiabatic tides with URs imposed (pink), (l) adiabatic and dynamical tides with UR imposed (blue) and (f) adiabatic and dynamical tides without UR assumed (green). The dashed lines indicate the corresponding 90% lower bound (green) for the UR-independent analysis or credible interval (pink and blue) for the results with the UR imposed. The green shaded region indicates how the lower bound changes in the UR-independent analysis when a different upper limit on the prior for Ω_2,A, ranging between 0.182 and 0.5, is assumed.

Fig. 2. 1D posterior probability for the f₂-mode frequency of a GW170817-like binary in different detector networks.

The vertical dashed line indicates the true value of f₂ = 2.04 kHz for the larger mass. The detector networks considered are: LIGO-Virgo at design sensitivity (HLV), three A+ detectors^,, three 4 km L-shaped LIGO detectors with improved high-frequency sensitivity^, (HF4S), one triangular Einstein Telescope D-configuration, one Cosmic Explorer (CE) and a network consisting of two CEs and one ET-D.