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Cluster abundance normalization from observed mass-temperature relation

Uros Seljak

TL;DR

This paper addresses the sensitivity of cluster-based power-spectrum normalization to the assumed M–T relation by adopting an empirical $M_{500}$–$T$ relation derived from X-ray mass measurements. It connects the observed masses to the theoretical virial mass function using a CDM halo profile and a universal halo mass function $f(\sigma)$, enabling a data-driven estimate of $\sigma_8$ with reduced reliance on uncertain gas physics. The authors find $\sigma_8 = 0.7$ for a fiducial flat model, with a parametric form $\sigma_8 = 0.7 (\Omega_m/0.35)^{-0.44} (\Gamma/0.2)^{0.08}$ and a statistical uncertainty of $\pm 0.06$, which is lower than some previous local-cluster estimates and more consistent with CMB/LSS constraints. They emphasize that systematic uncertainties in mass determinations remain substantial and advocate for larger, well-measured cluster-mass samples via lensing and hydrostatic methods (BeppoSAX, Chandra, XMM-Newton) to solidify this empirical normalization method.

Abstract

Abundance of rich clusters in local universe is currently believed to provide the most robust normalization of power spectrum at a scale of 10 Mpc. This normalization depends very sensitively on the calibration between virial mass M and temperature T, which is usually taken from simulations. Uncertainties in the modelling, such as gas cooling and heating, can lead to a factor of two variations in the normalization and are thus not very reliable. Here we use instead an empirical M_{500}-T relation derived from X-ray mass determinations to calibrate the method. We use results from dark matter simulations to relate the virial mass function to the mass function at observed M_{500}. We find that the best fitted value in flat models is sigma_8=(0.7 \pm 0.06) (Ω_m/0.35)^{-0.44}(Γ/0.2)^{0.08}, where only the statistical error is quoted. This is significantly lower than previously obtained values from the local cluster abundance. This lower value for sigma_8 is in a better agreement with cosmic microwave background and large scale structure constraints and helps alleviate small scale problems of CDM models. Presently the systematic uncertainties in the mass determination are still large, but ultimately this method should provide a more reliable way to normalize the M-T relation. This can be achieved by obtaining a larger sample of well measured cluster masses out to a significant fraction of virial radius with BeppoSAX, Chandra and XMM-Newton.

Cluster abundance normalization from observed mass-temperature relation

TL;DR

This paper addresses the sensitivity of cluster-based power-spectrum normalization to the assumed M–T relation by adopting an empirical – relation derived from X-ray mass measurements. It connects the observed masses to the theoretical virial mass function using a CDM halo profile and a universal halo mass function , enabling a data-driven estimate of with reduced reliance on uncertain gas physics. The authors find for a fiducial flat model, with a parametric form and a statistical uncertainty of , which is lower than some previous local-cluster estimates and more consistent with CMB/LSS constraints. They emphasize that systematic uncertainties in mass determinations remain substantial and advocate for larger, well-measured cluster-mass samples via lensing and hydrostatic methods (BeppoSAX, Chandra, XMM-Newton) to solidify this empirical normalization method.

Abstract

Abundance of rich clusters in local universe is currently believed to provide the most robust normalization of power spectrum at a scale of 10 Mpc. This normalization depends very sensitively on the calibration between virial mass M and temperature T, which is usually taken from simulations. Uncertainties in the modelling, such as gas cooling and heating, can lead to a factor of two variations in the normalization and are thus not very reliable. Here we use instead an empirical M_{500}-T relation derived from X-ray mass determinations to calibrate the method. We use results from dark matter simulations to relate the virial mass function to the mass function at observed M_{500}. We find that the best fitted value in flat models is sigma_8=(0.7 \pm 0.06) (Ω_m/0.35)^{-0.44}(Γ/0.2)^{0.08}, where only the statistical error is quoted. This is significantly lower than previously obtained values from the local cluster abundance. This lower value for sigma_8 is in a better agreement with cosmic microwave background and large scale structure constraints and helps alleviate small scale problems of CDM models. Presently the systematic uncertainties in the mass determination are still large, but ultimately this method should provide a more reliable way to normalize the M-T relation. This can be achieved by obtaining a larger sample of well measured cluster masses out to a significant fraction of virial radius with BeppoSAX, Chandra and XMM-Newton.

Paper Structure

This paper contains 4 sections, 6 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Theory
  3. Results
  4. Discussion and conclusions

Figures (2)

  • Figure 1: $M_{\Delta}/M_{\Delta_c}$ versus $\Delta$ for $c_{\Delta_c}=3.7$ (short dashed), $c_{\Delta_c}=5$ (solid) and $c_{\Delta_c}=7.5$ (dotted) for $\Delta_c=108$. Also shown is isothermal profile $M_{\Delta}/M_{\Delta_c} = (\Delta/\Delta_c)^{-1/2}$ as long dashed line.
  • Figure 2: Cumulative temperature function constructed by 2001MNRAS.325...77P compared to the best fitted model for a flat cosmology with $\Omega_m=0.35$.