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This paper consists of two related parts: In the first part we derive anexpression of the moment of inertia (MOI) of a neutron star as a function ofobservables from a hypothetical r-mode gravitational wave detection. For agiven r-mode detection we show how the value of the MOI of a neutron starconstrains the equation of state (EOS) of the matter in the core of the neutronstar. Subsequently, for each candidate EOS, we derive a possible value of thesaturation amplitude, \alpha, of the r-mode oscillations on the neutron star.Additionally, we argue that a r-mode detection will provide clues about thecooling rate mechanism of the neutron star. The above physics that can bederived from a hypothetical r-mode detection constitute our motivation for thesecond part of the paper. In that part we present a detection strategy toefficiently search for r-modes in gravitational-wave data. R-mode signals wereinjected into simulated noise colored with the advanced LIGO (aLIGO) andEinstein Telescope (ET) sensitivity curves. The r-mode waveforms used are thosepredicted by early theories based on a polytropic equation of state (EOS)neutron star matter. In our best case scenario \alpha of order 10^{-1}, themaximum detection distance when using the aLIGO sensitivity curve is 1 Mpc(supernova event rate of 3-4 per century) while the maximum detection distancewhen using the ET sensitivity curve is 10 Mpc (supernova event rate of 1-2 peryear).

astrophysical journal/the astrophysical journal

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