Abstract

We compare the self-similar baryonic mass fraction scaling relations between galaxy clusters from the South Pole Telescope Sunyaev Zel dovich (SPT-SZ) survey and the IllustrisTNG state-of-the-art magnetohydrodynamical cosmological simulations. Using samples of 218 (TNG100) and 1605 (TNG300) friends-of-friends (FoF) haloes within 0.0 ? z ? 1.5 and M200c ? 7 1013 M, we fit the scaling relations using Simple Power Law (SPL), Broken Power Law (BPL), and General Double Power Law (GDPL) models through nonlinear least squares regression. The SPL model reveals null slopes for the baryonic fraction as a function of redshift, consistent with self-similarity. Observations and simulations agree within 1-2, suggesting comparable baryonic scaling slopes. We identify 13.8-14.1 per cent of baryons as missing , primarily in the form of intracluster light (ICL) across all halo masses and warm gas in low-mass haloes. High-mass haloes (log10(M500c/M) ? 14) adhere to self-similarity, while low-mass haloes exhibit deviations, with the breakpoint occurring at log10(M500c/M) 14, where baryons are redistributed to the outskirts. Our findings suggest that the undetected warm-hot intergalactic medium (WHIM) and baryon redistribution by feedback mechanisms are complementary solutions to the missing baryon problem. © 2025 EDP Sciences. All rights reserved.