Towards Reliably Measuring the Mass-Size Relation of Dark Matter Halos: Impact of projection, miscentering and Eddington bias
Abstract
In the conventional spherical overdensity definition of a dark matter halo, masses and radii, e.g. M200m and r200m, are equivalent. However, halos do exhibit a physical boundary at the splashback radius rsp, which manifests as a sharp drop in density. Splashback radii are now routinely measured in stacked weak lensing profiles, but the expected trend of decreasing rsp/r200m with mass has not been verified in observed galaxy groups or clusters. In this work, we show that several observational effects conceal the predicted mass-size relation. In particular, we quantify the impact of systematics on the mean density and lensing profiles of mock-observed halo samples, which are created by applying a realistic cluster-finding procedure to dark matter-only simulations. We reproduce the known impact of projection: preferentially observing systems in overdense regions. But, differing from previous works, we show that the same projection effect, combined with scatter in observed luminosities, causes a significant Eddington bias in the derived mass-observable relation and a complex suppression in mean density profiles over all radial scales. The magnitude of this effect is mass-dependent and coupled to the cluster-finding procedure and survey properties, making it challenging to model simply and motivating full forward-modeling of observed group and cluster samples. However, we demonstrate that a simple mitigation approach, effectively a weak lensing mass calibration, does well in approximately recovering the true mass-size relation. Finally, we show that only severe miscentering can bias the measurement of the halo size, but any miscentering can increase the measurement uncertainty.
Related
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BibTeX
@misc{mpetha2026towards,
title = {{Towards Reliably Measuring the Mass-Size Relation of Dark Matter Halos: Impact of projection, miscentering and Eddington bias}},
author = {Charlie T. Mpetha and Benedikt Diemer},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.36531},
eprint = {2610.36531},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.36531},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Towards Reliably Measuring the Mass-Size Relation of Dark Matter Halos: Impact of projection, miscentering and Eddington bias
AU - Charlie T. Mpetha
AU - Benedikt Diemer
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.36531
UR - https://arxiv.org/abs/2610.36531
AB - In the conventional spherical overdensity definition of a dark matter halo, masses and radii, e.g. M_200m and r_200m, are equivalent. However, halos do exhibit a physical boundary at the splashback radius r_sp, which manifests as a sharp drop in density. Splashback radii are now routinely measured in stacked weak lensing profiles, but the expected trend of decreasing r_sp/r_200m with mass has not been verified in observed galaxy groups or clusters. In this work, we show that several observational effects conceal the predicted mass-size relation. In particular, we quantify the impact of systematics on the mean density and lensing profiles of mock-observed halo samples, which are created by applying a realistic cluster-finding procedure to dark matter-only simulations. We reproduce the known impact of projection: preferentially observing systems in overdense regions. But, differing from previous works, we show that the same projection effect, combined with scatter in observed luminosities, causes a significant Eddington bias in the derived mass-observable relation and a complex suppression in mean density profiles over all radial scales. The magnitude of this effect is mass-dependent and coupled to the cluster-finding procedure and survey properties, making it challenging to model simply and motivating full forward-modeling of observed group and cluster samples. However, we demonstrate that a simple mitigation approach, effectively a weak lensing mass calibration, does well in approximately recovering the true mass-size relation. Finally, we show that only severe miscentering can bias the measurement of the halo size, but any miscentering can increase the measurement uncertainty.
ER -