Constraining the r-mode saturation amplitude from a hypothetical detection of r-mode gravitational waves from a newborn neutron star - sensitivity study

TL;DR

This paper explores how detecting r-mode gravitational waves from a newborn neutron star can constrain the star's internal physics, including its moment of inertia, equation of state, and oscillation amplitude, and proposes a detection strategy.

Contribution

It derives a method to infer neutron star properties from hypothetical r-mode detections and presents a search strategy using simulated data for advanced gravitational wave detectors.

Findings

Maximum detection distance with aLIGO is 1 Mpc for ^{-1} amplitude.

Maximum detection distance with ET is 10 Mpc for ^{-1} amplitude.

Detection could provide insights into neutron star EOS and cooling mechanisms.

Abstract

This paper consists of two related parts: In the first part we derive an expression of the moment of inertia (MOI) of a neutron star as a function of observables from a hypothetical r-mode gravitational wave detection. For a given r-mode detection we show how the value of the MOI of a neutron star constrains the equation of state (EOS) of the matter in the core of the neutron star. Subsequently, for each candidate EOS, we derive a possible value of the saturation amplitude, \alpha, of the r-mode oscillations on the neutron star. Additionally, we argue that a r-mode detection will provide clues about the cooling rate mechanism of the neutron star. The above physics that can be derived from a hypothetical r-mode detection constitute our motivation for the second part of the paper. In that part we present a detection strategy to efficiently search for r-modes in gravitational-wave data. R-mode signals were injected into simulated noise colored with the advanced LIGO (aLIGO) and Einstein Telescope (ET) sensitivity curves. The r-mode waveforms used are those predicted by early theories based on a polytropic equation of state (EOS) neutron star matter. In our best case scenario \alpha of order 10^{-1}, the maximum detection distance when using the aLIGO sensitivity curve is 1 Mpc (supernova event rate of 3-4 per century) while the maximum detection distance when using the ET sensitivity curve is 10 Mpc (supernova event rate of 1-2 per year).