The Three Hundred Project: Modeling Baryon and Hot-Gas Fraction Evolution in Simulated Clusters

TL;DR

This work uses The Three Hundred cosmological hydrodynamical simulations to model how the baryon and hot-gas fractions in galaxy clusters depend on total mass and redshift across overdensities Δ=2500, 500, and 200, from z≈0 to z≈1.3. It tests three mass-scaling forms (linear, parabola, logarithmic in log space) and two redshift-evolution schemes ((1+z) and E(z)), finding that simple power-laws fail to capture the observed curvature, especially in core regions. Parabolic and logarithmic fits accurately describe the mass dependence, with redshift evolution being mild and more pronounced in inner regions; the study also demonstrates good agreement with observations and contrasts with other simulations, providing practical fitting formulas for cosmology and ICM physics. These results highlight the impact of baryonic processes, particularly AGN feedback, on the distribution of baryons and hot gas in clusters and offer robust tools for interpreting upcoming group- and cluster-scale observations.

Abstract

The baryon fraction of galaxy clusters is a powerful tool to inform on the cosmological parameters while the hot-gas fraction provides indications on the physics of the intracluster plasma and its interplay with the processes driving galaxy formation. Using cosmological hydrodynamical simulations from The Three Hundred collaboration of about 300 simulated massive galaxy clusters with median mass $M_{500}\approx7 \times 10^{14}$M$_{\odot}$ at $z=0$, we model the relations between total mass and either baryon fraction or the hot gas fractions at overdensities $Δ= 2500$, $500$, and $200$ with respect to the cosmic critical density, and their evolution from $z\sim 0$ to $z\sim 1.3$. We fit the simulation results for such scaling relations against three analytic forms (linear, quadratic, and logarithmic in a logarithmic plane) and three forms for the redshift dependence, considering as a variable both the inverse of cosmic scale factor, $(1+z)$, and the Hubble expansion rate, $E(z)$. We show that power-law dependencies on cluster mass poorly describe the investigated relations. A power-law fails to simultaneously capture the flattening of the total baryon and gas fractions at high masses, their drop at the low masses, and the transition between these two regimes. The other two functional forms provide a more accurate description of the curvature in mass scaling. The fractions measured within smaller radii exhibit a stronger evolution than those measured within larger radii. From the analysis of these simulations, we conclude that as long as we include systems in the mass range herein investigated, the baryon or gas fraction can be accurately related to the total mass through either a parabola or a logarithm in the logarithmic plane. The trends are common to all modern hydro simulations, although the amplitude of the drop at low masses might differ [Abridged].

Figures (15)

• Figure 1: Baryon fraction (top panels) and hot-gas fraction (bottom panels) relative to the cosmic fraction versus the cluster mass within $\Delta=2500$ (left panels) and $\Delta=200$ (right panels). Data for $z=0.07$ (pink circles), $z=0.59$ (yellow diamonds), $z=0.98$ (green squares) and $z=1.32$ (navy triangles) are shown. The median values of the $z=0.07$ and $z=1.32$ subsamples are shown with a solid line. For reference: in both panels the maximum value of the y-axis is $1.1$ and the horizontal line marks the cosmic baryon fraction.
• Figure 2: Baryon fraction (left panel) and gas fraction (right panel) relative to the cosmic fraction versus the cluster mass within $R_{500}$ at $z=0.07$ (black dots) and $z=1.32$ (navy dots). The legend associates colors and symbols to the shortenings of the observational papers of reference that include both local and distant clusters: Zha for zhang.etal.2011SF, GoP for gonzalez.etal.2013, Lin for lin.etal.2003, Chiu for chiu.etal.2018, Mul for mulroy.etal.2019, Eckm for eckmiller.etal.2011, Lov for Lovisari.etal.2020, Pra for pratt.etal.2009, Mau for maughan.etal.2008, Mah for mahdavi.etal.2013, Sun for sun.etal.2009, Ge for ge.etal.2018, San for sanderson.etal.2013, Ecke for eckert.etal.2019, Ett for ettori.etal.2009, Vik for vikhlinin.etal.2006, Man for mantz.etal.2016b. The red band is from eckert.etal.2021, and the purple, dark green, and cyan lines are, respectively, from popesso.etal.2024arxiv, andreon.etal.2017, and akino.etal.2022.
• Figure 3: Averaged residuals at $R_{2500}$ of the fitting function in Eq. \ref{['eq:glob']} (top panel), Eq. \ref{['eq:stanek']} (middle panel), and Eq. \ref{['eq:log']} (bottom panel). The shaded area represent 1$\sigma$ deviation from the mean.
• Figure 4: Best-fit functions of Eq. \ref{['eq:glob']} (red solid line), Eq. \ref{['eq:stanek']} (brown dot-dashed line), and Eq. \ref{['eq:log']} (light-blue dashed line) at the four redshifts specified in each panel. Individual clusters are shown with gray empty circles, while the median values are shown with black squares. Error bars indicate $\sigma_\mu$ and $\sigma_\eta$. The residuals of the best-fit functions with respect to the median values are shown at the bottom of each panel.
• Figure 5: Average and 1$\sigma$ deviation of the residuals of the baryon fraction at $R_{2500}$ at fixed mass-bin number. Eq. \ref{['eq:glob']}, Eq. \ref{['eq:stanek']}, and Eq. \ref{['eq:log']} are shown in the first, second, and third panel from the top, respectively, once the evolution is parametrized through $(1+z)$ as a shift in the normalization (Eq. \ref{['eq:exty']}). The dotted lines represent in the first panel the $E(z)$ evolution for the linear fit and in the second and third panels the residuals of Eq. \ref{['eq:extx']}. The bottom panel shows the results of using Eq. \ref{['eq:log']}, but after adopting $E(z)$ in the expression for the redshift dependence provided by Eq. \ref{['eq:extx']}. Residuals have been aligned towards the first bin on the left panels and towards the last bin on the right panels.