Chandra Cluster Cosmology Project III: Cosmological Parameter Constraints

TL;DR

This paper leverages the evolution and normalization of the galaxy cluster mass function from Chandra observations to constrain cosmological parameters, focusing on dark energy through the equation of state $w$ and the geometry of the Universe. By combining cluster growth information with distance priors from SN, BAO, and CMB data, the authors achieve tighter $w$ constraints and competitive limits on $\,Σ m_ν$, while also delivering precise measurements of $Ω_M h$ and $σ_8$. The analysis demonstrates that cluster data provide independent, complementary leverage on cosmology, reducing statistical and systematic uncertainties when integrated with external datasets and highlighting the role of X-ray mass proxies such as $T_X$, $M_{gas}$, and $Y_X$. The work also maps systematic error sources, discusses future improvements, and shows that the results remain consistent with a flat $\\Lambda$CDM framework, with $w_0$ near $-1$ and tight neutrino mass bounds.

Abstract

Chandra observations of large samples of galaxy clusters detected in X-rays by ROSAT provide a new, robust determination of the cluster mass functions at low and high redshifts. Statistical and systematic errors are now sufficiently small, and the redshift leverage sufficiently large for the mass function evolution to be used as a useful growth of structure based dark energy probe. In this paper, we present cosmological parameter constraints obtained from Chandra observations of 36 clusters with <z>=0.55 derived from 400deg^2 ROSAT serendipitous survey and 49 brightest z=~0.05 clusters detected in the All-Sky Survey. Evolution of the mass function between these redshifts requires Omega_Lambda>0 with a ~5sigma significance, and constrains the dark energy equation of state parameter to w0=-1.14+-0.21, assuming constant w and flat universe. Cluster information also significantly improves constraints when combined with other methods. Fitting our cluster data jointly with the latest supernovae, WMAP, and baryonic acoustic oscillations measurements, we obtain w0=-0.991+-0.045 (stat) +-0.039 (sys), a factor of 1.5 reduction in statistical uncertainties, and nearly a factor of 2 improvement in systematics compared to constraints that can be obtained without clusters. The joint analysis of these four datasets puts a conservative upper limit on the masses of light neutrinos, Sum m_nu<0.33 eV at 95% CL. We also present updated measurements of Omega_M*h and sigma_8 from the low-redshift cluster mass function.

Figures (13)

• Figure 1: Estimated mass functions for our cluster samples computed for the $\Omega_{\rm M}=0.25$, $\Omega_\Lambda=0.75$, $h=0.72$ cosmology. Solid lines show the mass function models (weighted with the survey volume as a function of $M$ and $z$), computed for the same cosmology with only the overall normalization, $\sigma_8$, fitted. The deficit of clusters in the distant sample near $M_{500}=3\times10^{14}\,h^{-1}\,M_\odot$ is a marginal statistical fluctuation --- we observe 4 clusters where 9.5 are expected, a $2\sigma$ deviation (cf. Fig. 17 in vikhlinin08).
• Figure 2: Illustration of sensitivity of the cluster mass function to the cosmological model. In the left panel, we show the measured mass function and predicted models (with only the overall normalization at $z=0$ adjusted) computed for a cosmology which is close to our best-fit model. The low-$z$ mass function is reproduced from Fig. \ref{['fig:mfun']}, which for the high-$z$ cluster we show only the most distant subsample ($z>0.55$) to better illustrate the effects. In the right panel, both the data and the models are computed for a cosmology with $\Omega_\Lambda=0$. Both the model and the data at high redshifts are changed relative to the $\Omega_\Lambda=0.75$ case. The measured mass function is changed because it is derived for a different distance-redshift relation. The model is changed because the predicted growth of structure and overdensity thresholds corresponding to $\Delta_{\rm crit}=500$ are different. When the overall model normalization is adjusted to the low-$z$ mass function, the predicted number density of $z>0.55$ clusters is in strong disagreement with the data, and therefore this combination of $\Omega_{\rm M}$ and $\Omega_\Lambda$ can be rejected.
• Figure 3: Constraints on the $\sigma_8$ and $\Omega_M$ parameters in a flat $\Lambda$CDM cosmology from the total (both low and high-redshift) cluster sample. The inner solid region corresponds to $-2\Delta \ln L=1$ from the best-fit model (indicates the 68% CL intervals for one interesting parameter, see footnote \ref{['fn:chi2']}) and the solid contour shows the one-parameter 95% CL region ($-2\Delta \ln L=4$). The dashed contour shows how the inner solid confidence region is modified if the normalization of the absolute cluster mass vs. observable relations is changed by $+9\%$ (our estimate of the systematic errors).
• Figure 4: Comparison with other $\sigma_8$ measurements. Solid region is our 68% CL region reproduced from Fig. \ref{['fig:OmegaM-h']} (this and all other confidence regions correspond to $\Delta\chi^2=1$, see footnote \ref{['fn:chi2']} on page \ref{['fn:chi2']}). Blue contours show the WMAP 3 and 5-year results from 2007ApJS..170..377S and 2008arXiv0803.0586D (dotted and solid contours, respectively). For other measurements, we show the general direction of degeneracy as a solid line and a 68% uncertainty in $\sigma_8$ at a representative value of $\Omega_M$. Filled circles show the weak lensing shear results from 2006ApJ...647..116H and 2008AA...479....9F (dashed and solid lines, respectively). Open circle shows results from a cluster sample with galaxy dynamics mass measurements 2007ApJ...657..183R. Finally, open square shows the results from 2002ApJ...567..716R.
• Figure 5: Constraints for non-flat $\Lambda$CDM cosmology from evolution of the cluster mass function. The results using only the evolution information (change in the number density of clusters between $z=0$ and $z\approx0.55$) are shown in blue and green from the $M_{\text{gas}}$ and $T_{\!X}$-based total mass estimates. The degeneracies in these cases are different because these proxies result in very different distance-dependence of the estimated masses (see text for details). The constraints from the $Y_{\mkern -1mu X}$-based mass function are between those for $M_{\text{gas}}$ and $T_{\!X}$ (Fig. \ref{['fig:OmegaM-OmegaL:Yx']}). Adding the shape of the mass function information breaks degeneracies with $\Omega_{\rm M}$, significantly improving constraints from $M_{\text{gas}}$ and $Y_{\mkern -1mu X}$ with little effect on the $T_{\!X}$ results.