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Atacama Cosmology Telescope: A measurement of galaxy cluster temperatures through relativistic corrections to the thermal Sunyaev-Zeldovich effect

William R. Coulton ^1,2,3, Adriaan J. Duivenvoorden^4,3,5, Zachary Atkins ⁵, Nicholas Battaglia ⁶, Elia Stefano Battistelli ⁷, J Richard Bond⁸, Hongbo Cai⁹, Erminia Calabrese ¹⁰, Steve K. Choi¹¹ et al.

Kevin T. Crowley¹², Mark J. Devlin ¹³, Jo Dunkley ^5,14, Simone Ferraro ^15,16, Yilun Guan¹⁷, Carlos Hervías-Caimapo¹⁸, J. Colin Hill ^19,3, Matt Hilton ^20,21, Adam D. Hincks ^22,23, Arthur Kosowsky ⁹, Mathew S. Madhavacheril¹³, Joshiwa van Marrewijk ²⁴, Fiona McCarthy^2,1,3, Kavilan Moodley ²¹, Tony Mroczkowski ²⁵, Michael D. Niemack^26,6, Lyman A. Page ⁵, Bruce Partridge ²⁷, Emmanuel Schaan ^28,29, Neelima Sehgal ³⁰, Blake D. Sherwin^2,1, Cristóbal Sifón ³¹, David N. Spergel ^3,14, Suzanne T. Staggs⁵, Alexander Van Engelen³², Eve M. Vavagiakis ²⁶, and Edward J. Wollack ³³

¹Kavli Institute for Cosmology Cambridge, Madingley Road, Cambridge CB3 0HA, United Kingdom
²DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 OWA, United Kingdom
³Center for Computational Astrophysics, Flatiron Institute, 162 5th Avenue, New York, New York 10010, USA
⁴Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Strasse 1, 85748 Garching, Germany
⁵Joseph Henry Laboratories of Physics, Jadwin Hall, Princeton University, Princeton, New Jersey 08544, USA
⁶Department of Astronomy, Cornell University, Ithaca, New York 14853, USA
⁷Sapienza University of Rome, Physics Department, Piazzale Aldo Moro 5, 00185 Rome, Italy
⁸Canadian Institute for Theoretical Astrophysics, University of Toronto, Toronto, Ontario, Canada M5S 3H8
⁹Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
¹⁰School of Physics and Astronomy, Cardiff University, The Parade, Cardiff, Wales CF24 3AA, United Kingdom
¹¹Department of Physics and Astronomy, University of California, Riverside, California 92521, USA
¹²Department of Astronomy and Astrophysics, University of California San Diego, La Jolla, California 92093, USA
¹³Department of Physics and Astronomy, University of Pennsylvania, 209 South 33rd Street, Philadelphia, Pennsylvania 19104, USA
¹⁴Department of Astrophysical Sciences, Peyton Hall, Princeton University, Princeton, New Jersey 08544, USA
¹⁵Lawrence Berkeley National Laboratory, One Cyclotron Road, Berkeley, California 94720, USA
¹⁶Berkeley Center for Cosmological Physics, Department of Physics, University of California, Berkeley, California 94720, USA
¹⁷Dunlap Institute for Astronomy and Astrophysics, University of Toronto, 50 St. George Street, Toronto, Ontario M5S 3H4, Canada
¹⁸Instituto de Astrofísica and Centro de Astro-Ingeniería, Facultad de Fìsica, Pontificia Universidad Católica de Chile, Avenida Vicuña Mackenna 4860, 7820436 Macul, Santiago, Chile
¹⁹Department of Physics, Columbia University, New York, New York 10027, USA
²⁰Wits Centre for Astrophysics, School of Physics, University of the Witwatersrand, Private Bag 3, 2050, Johannesburg, South Africa
²¹Astrophysics Research Centre, School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban 4001, South Africa
²²David A. Dunlap Department of Astronomy and Astrophysics, University of Toronto, 50 St. George Street, Toronto, Ontario M5S 3H4, Canada
²³Specola Vaticana (Vatican Observatory), V-00120 Vatican City State
²⁴Leiden Observatory, Leiden University, P.O. Box 9513, 2300 RA Leiden, The Netherlands
²⁵European Southern Observatory, Karl-Schwarzschild-Strasse 2, D-85748, Garching, Germany
²⁶Department of Physics, Cornell University, Ithaca, New York 14853, USA
²⁷Department of Physics and Astronomy, Haverford College, Haverford, Pennsylvania 19041, USA
²⁸SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, California 94025, USA
²⁹Kavli Institute for Particle Astrophysics and Cosmology, 382 Via Pueblo Mall, Stanford, California 94305-4060, USA
³⁰Physics and Astronomy Department, Stony Brook University, Stony Brook, New York 11794, USA
³¹Instituto de Física, Pontificia Universidad Católica de Valparaíso, Casilla 4059, Valparaíso, Chile
³²School of Earth and Space Exploration, Arizona State University, Tempe, Arizona 85287, USA
³³NASA/Goddard Space Flight Center, Greenbelt, Maryland 20771, USA

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Phys. Rev. D 113, 043520 – Published 18 February, 2026

DOI: https://doi.org/10.1103/n7p5-pc66

Abstract

The high electron temperature in galaxy clusters ( $> 1 keV$ or $> 10^{7} K$ ) leads to corrections at the level of a few percent in their thermal Sunyaev-Zeldovich effect signatures. Both the size and frequency dependence of these corrections, which are known as relativistic temperature corrections, depend upon the temperature of the objects. In this work we exploit this effect to measure the average temperature of a stack of Compton- $y$ selected clusters. Specifically, we apply the “spectroscopic method” and search for the temperature that best fits the clusters’ signal measured at frequencies from 30 to 545 GHz by the Atacama Cosmology Telescope and Planck satellite. We measure the average temperature of clusters detected in the Atacama Cosmology Telescope maps to be $8.5 \pm 2.4 keV$ , with an additional systematic error of comparable amplitude dominated by passband uncertainty. Upcoming surveys, such as the Simons Observatory and CMB-S4, have the potential to dramatically improve upon these measurements and thereby enable precision studies of cluster temperatures with millimeter observations. The key challenge for future observations will be mitigating instrumental systematic effects, which already limit this analysis.

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Phys. Rev. D 113, 043520– Published 18 February, 2026

Vol. 113, Iss. 4 — 15 February 2026

Received 18 November 2024
Accepted 23 December 2025

DOI: https://doi.org/10.1103/n7p5-pc66

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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Atacama Cosmology Telescope: A measurement of galaxy cluster temperatures through relativistic corrections to the thermal Sunyaev-Zeldovich effect

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