[Paper Review] The velocity dispersion profiles of clusters of galaxies: a cosmological test and the sampling effect

Y. P. Jing, Gerhard Börner|arXiv (Cornell University)|Aug 23, 1995

Galaxies: Formation, Evolution, Phenomena3 citations

TL;DR

This paper investigates velocity dispersion profiles in galaxy clusters across seven cosmological models to test their sensitivity to cosmological parameters, particularly Ω and Λ. It finds that while profiles differ significantly with Ω and Λ in principle, limited sampling and small cluster samples degrade discriminative power, making models with Ω ≥ 0.2 indistinguishable with current data.

ABSTRACT

In this paper we investigate the velocity dispersion profiles of clusters of galaxies for seven cosmological models. One model is the SCDM model, and the others are six low-density models with the density parameter $Ω=0.1$, 0.2 or 0.3 and with or without a cosmological constant $Λ=1-Ω$. We find that the velocity dispersion profiles depend both on $Ω$ and on $Λ$. For $Λ=0$, the profiles are steeper in a lower-$Ω$ model than in a higher-$Ω$ one. The cosmological constant significantly weakens the dependence on $Ω$: the difference in the profile distributions between two flat models is much smaller than that between the two corresponding open models with the same $Ω$. These results in principle can be used to constrain the cosmological parameters when a large sample of the velocity dispersion profiles is available. Motivated by the practical situation that a sample of $\sim 100$ clusters with $\sim 100$ measured redshifts per cluster is still the best sample available in the foreseen future, we examine carefully to what degree the cosmological parameters can be constrained with the velocity dispersion profiles of such a sample of clusters. The limited sampling around clusters and the limited number of clusters seriously degrade the discriminative power of the velocity dispersion profiles among cosmological models. We find that the five models of $Ω\ge 0.2$ cannot be distinguished by this type of observation. Due to the limited sampling, one should be very cautious in extracting information about the density profile and/or the dynamics around single clusters from the diluted velocity dispersion profiles

Motivation & Objective

• To evaluate the sensitivity of galaxy cluster velocity dispersion profiles to cosmological parameters Ω and Λ.
• To assess the practical feasibility of using observed velocity dispersion profiles to distinguish between competing cosmological models.
• To quantify the impact of limited cluster sampling (e.g., ~100 clusters with ~100 redshifts each) on cosmological parameter constraints.
• To examine how sampling effects distort the inferred dynamical structure and density profiles around individual clusters.

Proposed method

• Simulating velocity dispersion profiles for seven cosmological models: one SCDM model and six low-density models with Ω = 0.1, 0.2, 0.3 and Λ = 1−Ω.
• Using N-body simulations to model cluster dynamics under different cosmological assumptions.
• Analyzing the radial dependence of velocity dispersion profiles to detect differences across models.
• Assessing the impact of finite sampling (limited redshifts per cluster) on profile reconstruction and model discrimination.
• Comparing the discriminative power of observed profiles across models with varying Ω and Λ, especially in flat vs. open universes.
• Evaluating the reliability of extracting dynamical and density structure from diluted, sparsely sampled velocity profiles.

Experimental results

Research questions

• RQ1 How do velocity dispersion profiles in galaxy clusters vary with the cosmological parameters Ω and Λ?
• RQ2 To what extent can velocity dispersion profiles distinguish between flat and open cosmological models with the same Ω?
• RQ3 How do finite sampling effects (limited number of redshifts per cluster and small cluster sample size) degrade the ability to constrain cosmological parameters?
• RQ4 Can reliable dynamical or density structure be inferred from velocity dispersion profiles when sampling is sparse?
• RQ5 What is the minimum level of model distinction achievable with current observational data limits?

Key findings

• Velocity dispersion profiles depend significantly on both Ω and Λ, with steeper profiles in lower-Ω models when Λ = 0.
• The cosmological constant Λ reduces the sensitivity of profiles to Ω, making differences between flat models (e.g., Ω=0.3, Λ=0.7) smaller than between corresponding open models.
• With current observational limits (≈100 clusters, ≈100 redshifts per cluster), models with Ω ≥ 0.2 cannot be distinguished using velocity dispersion profiles.
• Sampling limitations severely degrade the discriminative power of velocity dispersion profiles for cosmological model testing.
• Diluted velocity dispersion profiles from sparse sampling introduce significant uncertainty in inferring the true dynamical and density structure around individual clusters.
• The study cautions against overinterpreting velocity dispersion profiles from limited data when extracting cosmological or dynamical information.