Dark sirens and the impact of redshift precision

TL;DR

This paper evaluates how redshift measurement precision and catalog completeness affect the accuracy of the Hubble constant estimation using dark sirens in gravitational wave astronomy.

Contribution

It demonstrates the importance of spectroscopic-like redshifts over photometric redshifts and analyzes the impact of catalog completeness on $H_0$ measurement accuracy.

Findings

Spectroscopic-like redshifts improve $H_0$ precision, especially in small localization areas.

Redshift outliers do not bias $H_0$ estimates.

Reduced catalog completeness increases uncertainty, with 50% completeness negating benefits.

Abstract

With the growing number of gravitational wave detections, achieving a competitive measurement of $H_0$ with dark sirens is becoming increasingly feasible. The expansion of the Ligo-Virgo-KAGRA Collaboration into a four detector network will reduce both the localisation area and the luminosity distance uncertainty associated with each gravitational wave event. It is therefore essential to identify and mitigate other major sources of error that could increase the uncertainty in $H_0$. In this work, we explore three scenarios relevant to the dark siren method in future observing runs. First, we demonstrate that there is a precision gain offered by a catalogue of spectroscopic-like redshifts compared to photometric-like redshifts, with the greatest improvements observed in smaller localisation areas. Second, we show that redshift outliers (as occur in realistic photometric redshift catalogues), do not introduce bias into the measurement of $H_0$. Finally, we find that uniformly sub-sampling spectroscopic-like redshift catalogues increases the uncertainty in $H_0$ as the completeness fraction is decreased; at a completeness of 50% the benefit of spectroscopic redshift precision is outweighed by the degradation from incompleteness. In all three scenarios, we obtain unbiased estimates of $H_0$. We conclude that a competitive measurement of $H_0$ using the dark siren method will require a hybrid catalogue of both photometric and spectroscopic redshifts, at least until highly complete spectroscopic catalogues become available. This, however, will come at the cost of a more complex selection function.