The impact of the formation channel on gravitational-wave-galaxy cross-correlations

The angular, harmonic cross-correlation between gravitational wave (GW) events and galaxy catalogues contains rich information on the large-scale structure and the origin of compact binary mergers. In this work, we study how uncertainties in the binary formation channel affect the predicted cross-correlation signal for both current-generation and next-generation networks of detectors. We generate five mock GW catalogues for which we vary the progenitor-to-remnant mass-transfer function and the time-delay probability distribution between progenitor and remnant. We then cross-correlate these catalogues with galaxy samples modelled on the 2MASS Photometric Redshift catalogue (2MPZ) and the Gaia-unWISE quasar catalogue (Quaia). We find that the mass-transfer function has negligible effect on the cross-correlation signal, with differences remaining within redshift uncertainties. In contrast, the time-delay distribution dramatically affects the redshift distribution of the GW events and, with it, the cross-correlation signal, particularly for shallow galaxy catalogues. In particular, current-generation facilities can achieve significant detections only for the longest time delays when cross-correlated with 2MPZ, whilst all cross-correlations with the deeper Quaia catalogue are marginally detectable or consistent with zero. Our exploratory results thus demonstrate that forecasts on cosmological or astrophysical parameters derived from GW-galaxy cross-correlations are, as expected, strongly sensitive to the assumed binary formation history.