Towards establishing the presence or absence of horizons in coalescing binaries of compact objects by using their gravitational wave signals

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.