The differences of baryonic and dark matter scaling relations in galaxy clusters between IllustrisTNG simulations and observations

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 $0.0 \leq z \leq 1.5$ and $M_{200c} \geq 7 \times 10^{13} M_{\odot}$, we fit the scaling relations using Simple Power Law (SPL), Broken Power Law (BPL), and General Double Power Law (GDPL) models through non-linear 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 $1{-}2\sigma$, suggesting comparable baryonic scaling slopes. We identify $\sim$13.8$-$14.1 per cent of baryons as "missing", primarily in the form of intracluster light (ICL) across all halo masses and warm gas in low-mass haloes. High-mass haloes ($\log_{10}(M_{500c}/M_{\odot}) \geq 14$) adhere to self-similarity, while low-mass haloes exhibit deviations, with the breakpoint occurring at $\log_{10}(M_{500c}/M_{\odot}) \sim 14$, 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.