Be careful in multi-messenger inference of the Hubble constant: A path forward for robust inference

TL;DR

This paper examines systematic uncertainties in multi-messenger measurements of the Hubble constant from binary neutron star mergers, proposing methods to improve the robustness of such inferences.

Contribution

It identifies key sources of bias in inclination angle inference and introduces joint inference techniques to mitigate these biases for more accurate Hubble constant measurements.

Findings

Inclination angle inference from EM afterglows can be precise but not necessarily accurate.

Small misalignments between GW and EM system inclinations can bias H0 inference.

Joint inference of inclination mismatch improves robustness of H0 measurement.

Abstract

Multi-messenger observations of coalescing binary neutron stars (BNSs) are a direct probe of the expansion history of the universe and carry the potential to shed light on the disparity between low- and high-redshift measurements of the Hubble constant $H_0$. To measure the value of $H_0$ with such observations requires pristine inference of the luminosity distance and the true source redshift with minimal impact from systematics. In this analysis, we carry out joint inference on mock gravitational wave (GW) signals and their electromagnetic (EM) afterglows from BNS coalescences and find that the inclination angle inferred from the afterglow light curve and apparent superluminal motion can be precise, but need not be accurate and is subject to systematic uncertainty that could be as large as $1.5\sigma$. This produces a disparity between the EM and GW inferred inclination angles, which if not carefully treated when combining observations can bias the inferred value of $H_0$. We also find that already small misalignments of $3^{\circ}-6^{\circ}$ between the inherent system inclinations for the GW and EM emission can bias the inference by $\mathcal{O}(1-2\sigma)$ if not taken into account. As multi-messenger BNS observations are rare, we must make the most out of a small number of events and harness the increased precision, while avoiding reduced accuracy. We demonstrate how to mitigate these potential sources of bias by jointly inferring the mismatch between the GW- and EM-based inclination angles and $H_0$.