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

Abstract

The quest for distinguishing black holes from horizonless compact objects using gravitational wave signals from coalescing compact binaries can be helped by utilizing the phenomenon of tidal heating, which leaves its imprint on the binary waveforms through the horizon parameters. These parameters, defined as ${H}_{1}$ and ${H}_{2}$ with ${H}_{1,2}\ensuremath{\in}[0,1]$ for the two compact objects, are combined with the binary components' masses and spins to form two new parameters, ${H}_{\mathrm{eff}5}$ and ${H}_{\mathrm{eff}8}$, to minimize their covariances in parameter estimation studies. In this work, we investigate the effects of tidal heating on gravitational waves to probe the observability of these effective parameters. We use a post-Newtonian waveform that includes the phase contribution due to tidal heating as a function of ${H}_{\mathrm{eff}5}$ and ${H}_{\mathrm{eff}8}$, and we examine their $1\ensuremath{\sigma}$ measurement errors as well as the covariances between them mainly using the Fisher matrix approach. Since this approach works well for high signal-to-noise ratios, we focus primarily on the third-generation (3G) gravitational wave detectors Einstein Telescope and Cosmic Explorer and use the second-generation (2G) detector network of LIGO (Hanford, Livingston) and Virgo for comparison. We study how the errors vary with the binaries' total mass, mass ratio, luminosity distance, and component spins. We find that the regions in the total binary mass where measurements of ${H}_{\mathrm{eff}5}$ and ${H}_{\mathrm{eff}8}$ are most precise are $\ensuremath{\sim}20--30\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$ for LIGO-Virgo and $\ensuremath{\sim}50--80\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$ for the 3G detectors. Higher component spins allow more precise measurements of ${H}_{\mathrm{eff}5}$ and ${H}_{\mathrm{eff}8}$. For a binary situated at 200 Mpc with component masses $12\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$ and $18\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$, equal spins ${\ensuremath{\chi}}_{1}={\ensuremath{\chi}}_{2}=0.8$, and ${H}_{\mathrm{eff}5}=0.6$, ${H}_{\mathrm{eff}8}=12$, the $1\ensuremath{\sigma}$ errors in these two parameters are $\ensuremath{\sim}0.01$ and $\ensuremath{\sim}0.04$, respectively, in 3G detectors. These estimates suggest that precise measurements of the horizon parameters are possible in third-generation detectors, making tidal heating a potential tool to identify the presence or absence of horizons in coalescing compact binaries. We substantiate our results from Fisher studies with a set of Bayesian simulations.

Topics & Concepts