Prospects for characterizing Population III remnants with next-generation gravitational-wave observatories

The most distant gravitational-wave (GW) detection by LIGO, Virgo and KAGRA so far is a binary black hole (BBH) merger at a redshift of $z\sim 1.1$, corresponding to a luminosity distance of $D_L \sim 8 \, \rm Gpc$. The next-generation GW detectors, the Einstein Telescope (ET) and Cosmic Explorer (CE), will detect mergers beyond the peak of star formation at $z_{\rm peak}\sim 2$, enabling the direct detection of the remnants of the first stars in the early Universe. Realising this science potential requires accurate inference of the redshift, sky localization and intrinsic properties of the most distant mergers. In this work, using a fully Bayesian framework and an astrophysically motivated model, we study Population III remnants with an ET-CE detector network and quantify the measurement uncertainties in redshift, sky localisation, intrinsic masses and spins for BBHs at $z \geq 15$. Considering an optimistic ($5\, \rm Hz$) and pessimistic ($10\,\rm Hz$) lower cutoff frequency for the detectors' sensitivity, we show that the $5\, \rm Hz$ configuration consistently improves the redshift inference for spin-precessing binaries. We also find that the source-frame component masses can be measured to within $\sim 12\%$ on average, and that the highest-redshift sources in the population can be reliably characterised. In contrast, we find only modest constraints on the BH spins. The improved low-frequency sensitivity also extends the redshift reach of the detector network, enabling events injected at $z_{\rm true}\simeq19.8$ to be confidently identified as originating beyond $z\simeq18.5$ at $90\%$ credibility, compared to a maximum lower-bound redshift of $z\simeq17.5$ for the $10\,\rm Hz$ configuration. Improved detector sensitivity below $10\, \rm Hz$ also reduces the sky-localisation uncertainties, which are essential for cosmological cross-correlation.