The thermal and kinematic Sunyaev-Zeldovich effect in galaxy clusters and filaments using multifrequency temperature maps of the cosmic microwave background: Abell 399--Abell 401 cluster pair case study

TL;DR

This work develops a modular, multifrequency, multi-instrument framework to jointly model thermal and kinematic Sunyaev-Zeldovich effects in galaxy clusters and cosmic filaments, incorporating relativistic corrections and dust foregrounds. By fitting a per-pixel physical model across ACT and Planck data (30–545 GHz), the authors disentangle tSZ and kSZ signals, constrain gas properties with X-ray priors, and measure filament optical depth with high significance. Applied to the Abell 399–Abell 401 system, the method yieldstSZ results consistent with prior Compton-$y$ analyses, detects the inter-cluster bridge with $8.5\sigma$, and yields competitive peculiar-velocity constraints ( uncertainties $\lesssim 600$ km s$^{-1}$). The study demonstrates robust parameter recovery, careful treatment of covariance, and a scalable approach poised for future facilities and broader wavelength coverage.

Abstract

We present a multifrequency and multi-instrument methodology to study the physical properties of galaxy clusters and cosmic filaments using cosmic microwave background observations. Our approach enables simultaneous measurement of both the thermal (tSZ) and kinematic Sunyaev-Zeldovich (kSZ) effects, incorporates relativistic corrections, and models astrophysical foregrounds such as thermal dust emission. We do this by jointly fitting a single physical model across multiple maps from multiple instruments at different frequencies, rather than fitting a model to a single Compton-$y$ map. We demonstrate the success of this method by fitting the Abell 399-Abell 401 galaxy cluster pair and filament system using archival data from the Planck satellite and new, targeted deep data from the Atacama Cosmology Telescope, covering 11 different frequencies over 14 maps from 30 GHz to 545 GHz. Our tSZ results are consistent with previous work using Compton-$y$ maps. We measure the line-of-sight peculiar velocities of the cluster-filament system using the kSZ effect and find statistical uncertainties on individual cluster peculiar velocities of $\lesssim $600 km s$^{-1}$, which are competitive with current state-of-the-art measurements. Additionally, we measure the optical depth of the filament component with a signal-to-noise of 8.5$σ$ and reveal hints of its morphology. This modular approach is well-suited for application to future instruments across a wide range of millimeter and sub-millimeter wavebands.

Figures (22)

• Figure 1: Thermal and kinematic SZ effect including relativistic corrections. We assume an optical depth of $\tau_{\rm e} = 0.01$ for these calculations. The vertical dotted line is at the tSZ null at 217 GHz. For illustration, the vertical lines show the bands of the ACT and Planck frequency maps we used in this work.
• Figure 2: A coadded temperature map of ACT 98 GHz PA5 showing the A399--A401 cluster pair and regions around the pair used for estimating the signal and noise covariance. The sensitivity contours are from the combined coadded variance maps from ACT and show that the data are deeper towards the center due to the 31.5 hours of dedicated observations of this system.
• Figure 3: The modified blackbody spectrum from thermal dust emission in galaxy clusters (normalized to 545 GHz) and the impact of variations in the dust temperature and emissivity index. The observation bands in this work lie in the Rayleigh-Jeans regime, so small changes in the dust temperature and emissivity index do not have a significant impact on the spectral shape.
• Figure 4: Bandpasses of the ACT and Planck maps used in this work. These bandpasses have been normalized to have a peak of one.
• Figure 5: An illustrative schematic of part of the covariance matrix required for the multifrequency approach in this work. We show the portion of the covariance matrix that includes maps from ACT PA5 (98, 150 GHz), ACT PA6 (150 GHz), and Planck (353 and 545 GHz). The orange and blue elements are cases for which covariant noise must be included, whereas the signal covariance is computed for all matrix elements. The noise covariance is assumed to be zero for the matrix elements in white.