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Astrophysics, High Energy Astrophysical Phenomena, astro-ph.HE
Abstract:
We analyze the impact of a proposed tidal instability coupling $p$-modes and
$g$-modes within neutron stars on GW170817. This non-resonant instability
transfers energy from the orbit of the binary to internal modes of the stars,
accelerating the gravitational-wave driven inspiral. We model the impact of
this instability on the phasing of the gravitational wave signal using three
parameters per star: an overall amplitude, a saturation frequency, and a
spectral index. Incorporating these additional parameters, we compute the Bayes
Factor ($\ln B^{pg}_{!pg}$) comparing our $p$-$g$ model to a standard one. We
find that the observed signal is consistent with waveform models that neglect
$p$-$g$ effects, with $\ln B^{pg}_{!pg} = 0.03^{+0.70}_{-0.58}$ (maximum a
posteriori and 90% credible region). By injecting simulated signals that do not
include $p$-$g$ effects and recovering them with the $p$-$g$ model, we show
that there is a $\simeq 50\%$ probability of obtaining similar $\ln
B^{pg}_{!pg}$ even when $p$-$g$ effects are absent. We find that the $p$-$g$
amplitude for 1.4 $M_\odot$ neutron stars is constrained to $\lesssim
\text{few}\times10^{-7}$, with maxima a posteriori near $\sim 10^{-7}$ and
$p$-$g$ saturation frequency $\sim 70\, \mathrm{Hz}$. This suggests that there
are less than a few hundred excited modes, assuming they all saturate by wave
breaking. For comparison, theoretical upper bounds suggest a $p$-$g$ amplitude
$\lesssim 10^{-6}$ and $\lesssim 10^{3}$ modes saturating by wave breaking.
Thus, the measured constraints only rule out extreme values of the $p$-$g$
parameters. They also imply that the instability dissipates $\lesssim 10^{51}\,
\mathrm{ergs}$ over the entire inspiral, i.e., less than a few percent of the
energy radiated as gravitational waves.