Cluster gravitational redshifts: uncertainties and survey requirements

TL;DR

This paper assesses how observational uncertainties affect the use of cluster gravitational redshifts to test modified gravity, highlighting survey design considerations and the importance of accurate cluster centering.

Contribution

It introduces an end-to-end forecasting pipeline to evaluate uncertainties in gravitational redshift measurements for modified gravity constraints.

Findings

Redshift precision beyond σ_z ~ 10^{-4}(1+z) offers no further improvement.

Shallow, narrow spectroscopic surveys outperform deep, wide photometric ones for this purpose.

Accurate cluster centering is crucial to avoid systematic biases.

Abstract

We investigate the impact of observational and theoretical uncertainties in cluster gravitational redshifts as a probe of modified gravity using an end-to-end forecasting pipeline. We use a generative model to build a halo catalogue with $M_{500}\ge 3\times 10^{13}\,M_\odot$, populate haloes with member galaxies via a five-parameter halo occupation distribution (HOD), assign projected positions from radial density profiles, apply survey-like selections, and infer a linear rescaling of the gravitational potential, $\alpha_\mathrm{MG}$, to parameterise modifications to general relativity (GR). We vary redshift uncertainties, radial and mass-redshift completeness, member abundance, minimum mass and maximum redshift, as well as mis-specify the clusters density and velocity profiles, centres, and mass function. We find that the intracluster velocity dispersion sets an effective floor: improving redshift precision beyond $\sigma_z\sim 10^{-4}(1+z)$ brings no improvement in the precision of $\alpha_\mathrm{MG}$. Realistic redshift and mass cuts primarily remove low-mass haloes and have minimal impact on the $\alpha_\mathrm{MG}$ precision. In this setting, we find that shallow, narrower spectroscopic surveys are preferable to deep, wide photometric ones for precise modified gravity constraints. We further find that mis-centring can mimic significant departures from GR. Baryonic deviations from a Navarro-Frenk-White profile and velocity anisotropies do not introduce appreciable biases. In the high-S/N regime of upcoming surveys, accurate determination of cluster centres will be essential to avoid interpreting systematic effects as new physics. The Spectroscopic Stage-5 Experiment and the Widefield Spectroscopic Telescope provide a clear route toward establishing gravitational redshifts as a competitive probe of modified gravity.