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Abstract

The quest for distinguishing black holes (BH) from horizonless compact
objects using gravitational wave (GW) signals from coalescing compact binaries
can be helped by utilizing the phenomenon of tidal heating (TH), which leaves
its imprint on binary waveforms through the horizon parameters. We investigate
the effects of TH on GWs to probe the observability of the horizon parameters,
mainly using Fisher matrix analysis to determine the errors and covariances
between them. The horizon parameters are defined as $H_1$ and $H_2$ for the two
binary components, with $H_{1,2} \in [0,1]$, and combined with the component
masses and spins to form two new parameters, $H_{\rm eff5}$ and $H_{\rm eff8}$,
to minimize their covariances in parameter estimation studies. In this work, we
add the phase contribution due to TH in terms of $H_{\rm eff5}$ and $H_{\rm
eff8}$ to a post-Newtonian waveform and examine the variation of their
measurement errors with the binary's total mass, mass ratio, luminosity
distance, and component spins. Since the Fisher matrix approach works well for
high signal-to-noise ratio, we focus mainly on third-generation (3G) GW
detectors Einstein Telescope and Cosmic Explorer and use LIGO and Virgo for
comparison. We find that the region in the total binary mass where measurements
of $H_{\rm eff5}$ and $H_{\rm eff8}$ are most precise are $\sim 20 - 30M_\odot$
for LIGO-Virgo and $\sim 50 - 80M_\odot$ for 3G detectors. Higher component
spins allow more precise measurements of $H_{\rm eff5}$ and $H_{\rm eff8}$. For
a binary situated at 200 Mpc with component masses $12M_\odot$ and $18M_\odot$,
equal spins $\chi_1=\chi_2=0.8$, and $H_{\rm eff5}=0.6$, $H_{\rm eff8}=12$, the
1-$\sigma$ errors in these two parameters are $\sim 0.01$ and $\sim 0.04$,
respectively, in 3G detectors. We substantiate our results from Fisher studies
with a set of Bayesian simulations.