AMICO galaxy clusters in KiDS-DR3: The impact of estimator statistics on the luminosity-mass scaling relation

¹ Leiden Observatory, Leiden University, PO Box 9513 2300 RA Leiden, The Netherlands
e-mail: msmit@strw.leidenuniv.nl
² Ruhr University Bochum, Faculty of Physics and Astronomy, Astronomical Institute (AIRUB), German Centre for Cosmological Lensing, 44780 Bochum, Germany
³ INAF – Osservatorio Astronomico di Padova, vicolo dell’Osservatorio 5, Padova 35122, Italy
⁴ Zentrum für Astronomie, Universität Heidelberg, Philosophenweg 12, 69120 Heidelberg, Germany
⁵ Dipartimento di Fisica e Astronomia “Augusto Righi” – Alma Mater Studiorum Università di Bologna, Via Piero Gobetti 93/2 40129 Bologna, Italy
⁶ INAF – Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Gobetti Piero 93/3, 40129 Bologna, Italy
⁷ INFN – Sezione di Bologna, viale Berti Pichat 6/2, 40127 Bologna, Italy

Received: 24 June 2021
Accepted: 18 September 2021

Abstract

Context. As modern-day precision cosmology aims for statistical uncertainties of the percent level or lower, it becomes increasingly important to reconsider estimator assumptions at each step of the process, along with their consequences on the statistical variability of the scientific results.

Aims. We compare L¹ regression statistics to the weighted mean, the canonical L² method based on Gaussian assumptions, to infer the weak gravitational shear signal from a catalog of background ellipticity measurements around a sample of clusters, which has been a standard step in the processes of many recent analyses.

Methods. We use the shape measurements of background sources around 6925 AMICO clusters detected in the KiDS third data release. We investigate the robustness of our results and the dependence of uncertainties on the signal-to-noise ratios of the background source detections. Using a halo model approach, we derive lensing masses from the estimated excess surface density profiles.

Results. The highly significant shear signal allows us to study the scaling relation between the r-band cluster luminosity, L₂₀₀, and the derived lensing mass, M₂₀₀. We show the results of the scaling relations derived in 13 bins in L₂₀₀, with a tightly constrained power-law slope of ∼1.24 ± 0.08. We observe a small, but significant, relative bias of a few percent in the recovered excess surface density profiles between the two regression methods, which translates to a 1σ difference in M₂₀₀. The efficiency of L¹ is at least that of the weighted mean and increases with higher signal-to-noise shape measurements.

Concluions. Our results indicate the relevance of optimizing the estimator for inferring the gravitational shear from a distribution of background ellipticities. The interpretation of measured relative biases can be gauged by deeper observations, and the increased computation times remain feasible.