Non-spherical BUFFALOs: a weak lensing view of the Frontier Field clusters and associated systematics

TL;DR

This study leverages the BUFFALO HST data set to produce high-density weak-lensing catalogues for six extreme Frontier Field clusters, enabling individual $M_{200}$ estimates via NFW modelling and systematic tests (centre choice, $N(z)$, contamination, miscentring, ellipticity, and multimodality). By integrating strong-lensing information in the cores where available, the authors demonstrate improved mass constraints and highlight the nontrivial impact of complex morphologies on mass inferences. The work provides a comprehensive framework to quantify and mitigate key systematics in weak-lensing cluster masses, informing upcoming wide-field surveys like Euclid and LSST. Overall, the largest biases arise in disturbed systems (e.g., A2744), motivating careful multimodal modelling and cross-calibration with strong-lensing data for reliable cosmological applications.

Abstract

Galaxy clusters are tracers of the large scale structures of the Universe, making the time evolution of their mass function dependent on key cosmological parameters, such as the cosmic matter density or the amplitude of density fluctuations $σ_8$. Accurate measurements of cluster's total masses are therefore essential, yet they can be challenging, particularly for clusters with complex morphologies, as simple mass profiles are often adopted to fit the measurements. In this work, we focus on the Frontier Fields galaxy clusters: a sample of six extremely massive systems, that, in most cases, exhibit highly complex mass distributions. The BUFFALO survey extended the Hubble Space Telescope observations for the Frontier Fields galaxy clusters, providing high-resolution multi-band imaging within a few Mpc. Combining this high-quality imaging dataset with ancillary spectroscopy, we produce weak-lensing catalogues with very high source densities, about 50 sources/arcmin$^2$. This allows us to robustly estimate the individual weak-lensing cluster masses and quantify the sensitivity of these measurements on different factors, such as the cluster centring, the uncertainty on the redshift distribution or the foreground contamination and boost factor correction. This provides a data-driven analysis of the different sources of systematics that can impact such measurements. We find that the largest sources of systematic bias arise for the most disturbed clusters, such as the multi-modal, merging galaxy cluster Abell 2744. This analysis sets a comprehensive framework for assessing the impact of systematics on the weak-lensing estimates of cluster masses, and in particular, in the case of unrelaxed clusters. This can play a key role in forthcoming cosmological analyses based on wide-field surveys such as Euclid and the Legacy Survey of Space and Time of the Rubin Observatory.

Figures (12)

• Figure 1: BUFFALO observations in the ACS/F814W band for the six galaxy clusters (which also incorporates the data taken within the HFF and other ancillary programmes). The fiducial cluster centres, corresponding to the X-ray surface-brightness peaks, are shown as black crosses, while the circles have a radius of 1 comoving Mpc. The mosaic pattern of the BUFFALO observations can be seen on the image, with the two adjacent fields for each cluster, the main and the parallel, each $\sim 5 ~\rm arcmin^2$. Note the small gap in the mosaic between the two fields.
• Figure 2: Background galaxy selections for the cluster AS1063. Top: Colour-colour diagram ($m_{\mathrm{F814W}}$-$m_{\mathrm{F160W}}$) vs ($m_{\mathrm{F606W}}$-$m_{\mathrm{F160W}}$) for objects with good WFC3/F160W, ACS/F814W and ACS/F606W photometry. Grey dots represent all galaxies with both ACS and WFC3 imaging. Non-lensed galaxies, diluting the shear signal, are marked by different colours: galaxies identified as foreground with spectroscopic redshifts $z < 0.34$ (blue), and galaxies classified as cluster members due to their spectroscopic redshifts $0.34 < z < 0.4$ (red). As only a small number of foreground contaminants are identified in each field, to better calibrate the colour-colour selection we show in addition all galaxies with $z < 0.4$ in the six BUFFALO fields and in the Candels dataset ('Foreground ext', in green). The solid black lines delineate the colour-colour-cut defined for this work to mitigate shear dilution by non-lensed galaxies. Bottom: Colour-magnitude diagram $m_{\mathrm{F814W}}$vs ($m_{\mathrm{F606W}}-m_{\mathrm{F814W}}$) for galaxies within the ACS field without WFC3 imaging. The same colour code as above is applied. The bright source cut is shown as a dashed horizontal line.
• Figure 3: Redshift distribution function $N(z)$ for the background galaxy population. Top panel: redshift distribution for the background source distribution for each cluster, estimated from galaxies with either a measured spectroscopic or photometric redshift. Dashed vertical lines represent the weighted mean of the redshift distribution for each cluster. Bottom panel: the black histogram represents the $N(z)$ for all six galaxy clusters combined, where error bars show the standard deviation between clusters. The blue curve represents the fit of a smail1995 distribution to the histogram, and the orange curve of a log-normal distribution. In both cases, the best-fit parameters are given in the legend between brackets. The dashed green curve represents the smail1995 distribution with the original parameters, also given in brackets. We note the small but statistically significant peak at $z\sim 4.3$, which could be due to a systematic bias in the photometric-redshift estimation, but would require further investigations.
• Figure 4: Top panel: in black, $\Delta\Sigma_r$ profiles for each of the six galaxy clusters. The error bars account for the uncertainty coming from the missing redshift information for a fraction of the sources, as well as the statistical errors. Only bins where the number of background sources is higher than a given threshold are used to fit the model (solid line). For each cluster, we represent the best-fit NFW model with the darragh-ford2023$M-c$ relation as a solid orange line, and 1000 models corresponding to randomly drawn MCMC samples to show the dispersion. In addition, for A370 and AS1063 the "Flat $c$ prior" best-fit models are shown with blue dashed lines. Finally, the green dot-dashed lines correspond to the Singular Isothermal Sphere (SIS) models described in Sect. \ref{['sec:SIS']}. Bottom panel: number of background sources used to compute the lensing signal in each radial bin. The y-axis is in linear scale.
• Figure 5: Excess surface density profiles for the six BUFFALO clusters, combining the weak lensing shear measurement at large radial scales (blue 'x's) and strong-lensing mass models at small scales (orange '+'s). The best-fit model is shown as a black solid line, and 1000 models corresponding to randomly drawn MCMC samples are represented in grey to show the dispersion. $\Delta\Sigma$ is in $hM_{\odot}\rm{pc}^{-2}$. The profiles shown on the left panels are measured around the fiducial centres, i.e. X-ray brightness peaks, and around the brightest BCGs (named C0) on the right panels.