Non-parametric estimation of the baryon gas fraction and the cosmological bias with clusters

Abstract

X-ray observations of galaxy clusters allow us to estimate the gas fraction, and thus the baryon fraction, and its evolution over time. This offers an additional cosmological probe as well as a probe of the gas behaviour in massive halos at the end of structure formation. However, cosmological and astrophysical effects are degenerate, and both should be modeled in order to explain observations; otherwise, the chosen baryonic model can potentially bias the cosmological results. We propose to quantify this effect by adopting a model-independent framework. We utilize Type Ia Supernovae to reconstruct the cosmic expansion history and apply the iterative smoothing method to infer the mass and redshift evolution of the hydrostatic mass bias. Our results confirm previous findings and show that the bias should evolve with time to reproduce CMB cosmological constraints.

Figures (7)

• Figure 1: Smooth reconstructions of $\mu(z)$, $\mathcal{D}(z)$, and $h(z)$ from the Pantheon+ sample. The reconstructions are color-coded by $\Delta\chi^2=\chi^2-\chi^2_{\Lambda\text{CDM}}$, where the $\Lambda\text{CDM}$ best-fit is indicated as a dashed red line.
• Figure 2: MCMC posteriors for equation \ref{['eq:fgas_model']} in the Wicker model (blue) and using smooth reconstructions with $\Delta\chi^2 =\Delta\chi^2_\text{min}=-9.5$ (red).
• Figure 3: We present the MCMC results for the 1NP model using normal ($\mathcal{N}$) and uniform ($\mathcal{U})$ priors, as specified in Table \ref{['tab:1NP prior']}.
• Figure 4: Bias data as a function of redshift (left) and mass (right). The blue line shows the Wicker et al. best-fit to the data, together with the shaded $1\sigma$ uncertainties. The colored solid lines show the reconstructed $\hat{B}(M,z)$ from Eq. \ref{['eqn:smooth_2d']}, color-coded by $\Delta\chi^2$. The curves are evaluated at fixed mass slices for the redshift plots (left): $M=M_{75}$ (top-left) and $M=M_{25}$ (bottom-left). The curves are evaluated at fixed redshift slices for the mass plots (right): $z=z_{75}$ (top-right) and $z=z_{25}$ (bottom-right). The data points correspond to the subsamples $M \geq M_{50}$ (top-left), $M < M_{50}$ (bottom-left), $z \geq z_{50}$ (top-right), and $z < z_{50}$ (bottom-right).
• Figure 5: Reconstructed bias normalized by the Wicker 2023 model. The left column shows the redshift evolution at $M=M_{75}, M_{50},$ and $M_{25}$ respectively in the top, middle, and bottom panels. The right column shows the mass evolution at $z=z_{75}, z_{50},$ and $z_{25}$ respectively. The olive line (Bias reconstruction) corresponds to the reconstruction based on equation \ref{['eq:B(z)']} using the bias data derived with the Planck prior. The cyan line (Bias + SN reconstruction) represents the reconstruction based on equation \ref{['eq:B(z)']} using bias data inferred from the SN reconstruction. In both cases, the ratio $\Omega_b / \Omega_m$ is computed using the Planck prior.