[Paper Review] Measuring cosmic distances with galaxy clusters

S. W. Allen, Mantz, A. B.+6 more|arXiv (Cornell University)|Jul 30, 2013

Galaxies: Formation, Evolution, Phenomena9 references10 citations

TL;DR

This paper reviews two X-ray-based methods for measuring cosmic distances using galaxy clusters: the X-ray gas mass fraction ($f_{\text{gas}}$) and combined X-ray/mm-wave Sunyaev-Zel'dovich (XSZ) measurements. It projects that with a new X-ray observatory, $f_{\text{gas}}$ measurements could improve dark energy constraints by a factor of 6–7, offering model-independent constraints on $\Omega_{\text{m}}$ and competitive precision to Type Ia supernovae and BAO studies.

ABSTRACT

In addition to cosmological tests based on the mass function and clustering of galaxy clusters, which probe the growth of cosmic structure, nature offers two independent ways of using clusters to measure cosmic distances. The first uses measurements of the X-ray emitting gas mass fraction, which is an approximately standard quantity, independent of mass and redshift, for the most massive clusters. The second uses combined millimeter (mm) and X-ray measurements of cluster pressure profiles. We review these methods, their current status and the prospects for improvements over the next decade. For the first technique, which currently provides comparable dark energy constraints to type Ia supernova studies, improvements of a factor of 6 or more should be readily achievable, together with tight constraints on the mean matter density that are largely independent of the cosmological model assumed. Realizing this potential will require a coordinated, multiwavelength approach, utilizing new cluster surveys, X-ray, optical and mm facilities, and a continued emphasis on improved hydrodynamical simulations.

Motivation & Objective

• To assess the current and future potential of galaxy clusters as cosmological distance indicators using X-ray and millimeter-wave data.
• To evaluate the $f_{\text{gas}}$ method's ability to constrain $\Omega_{\text{m}}$ and dark energy independently of cosmological model assumptions.
• To project improvements in dark energy constraints from $f_{\text{gas}}$ measurements using a next-generation X-ray observatory with enhanced collecting area and spectral resolution.
• To compare the $f_{\text{gas}}$ and XSZ methods in terms of systematic error control and cosmological sensitivity.
• To identify key observational and simulation requirements for maximizing the cosmological power of cluster-based distance measurements over the next decade.

Proposed method

• Measure the X-ray gas mass fraction ($f_{\text{gas}}$) in massive, dynamically relaxed clusters using X-ray surface brightness and temperature profiles to infer gas mass and total mass.
• Use the $f_{\text{gas}}$-distance relation $f_{\text{gas}} \propto d^{1.5}$ to infer distances from observed $f_{\text{gas}}$ values, assuming $\Omega_{\text{b}}$ from CMB or nucleosynthesis.
• Combine X-ray and millimeter-wave (e.g., SPT, ACT) observations to measure cluster pressure profiles via the Sunyaev-Zel'dovich effect (XSZ), enabling independent distance estimates.
• Apply MCMC methods to analyze cosmological constraints, incorporating priors on $\Omega_{\text{b}}h^2$ and $h$, and accounting for degeneracies and systematics.
• Simulate future observations with a next-generation X-ray observatory, assuming 10 Ms of Chandra-equivalent observing time and improved hydrodynamical simulations.
• Project cosmological figure of merit (FoM) improvements by comparing current data with projected data sets of 450 clusters at 7.5% ($f_{\text{gas}}$) precision, down to 5% with improved velocity resolution.

Experimental results

Research questions

• RQ1 Can the $f_{\text{gas}}$ method provide competitive dark energy constraints compared to SN Ia and BAO surveys?
• RQ2 To what extent can the intrinsic scatter in $f_{\text{gas}}$ be reduced by measuring bulk and turbulent gas motions with high-resolution X-ray spectrometers?
• RQ3 What level of improvement in cosmological constraints can be expected from a next-generation X-ray observatory with greater collecting area and spectral resolution?
• RQ4 How do the $f_{\text{gas}}$ and XSZ methods compare in terms of systematic error budget and cosmological sensitivity?
• RQ5 Can $f_{\text{gas}}$ measurements provide a model-independent constraint on $\Omega_{\text{m}}$?

Key findings

• Current $f_{\text{gas}}$ measurements for ~40 hot, relaxed clusters provide dark energy constraints comparable to those from BAO and SN Ia studies.
• Expanding the sample to ~100 clusters with 15% precision in the 0.8–1.2 $r_{2500}$ shell would improve the dark energy figure of merit by a factor of 4–6.
• A future X-ray observatory with 7.5% $f_{\text{gas}}$ precision could improve the figure of merit by a factor of 6–7 over current results.
• In the optimistic scenario, reducing intrinsic scatter to 5% via high-resolution X-ray spectrometry would yield a 22.6 figure of merit for a flat, evolving $w$ model.
• The $f_{\text{gas}}$ method provides a tight, cosmology-independent constraint on $\Omega_{\text{m}}$, with uncertainties reduced to ~6% in the optimistic case.
• The XSZ method is expected to yield more modest improvements due to high intrinsic scatter in cluster pressure profiles, making it less impactful than $f_{\text{gas}}$ for next-decade cosmology.