Mass-Temperature Relation of Galaxy Clusters: A Theoretical Study

Abstract

Combining conservation of energy throughout nearly-spherical collapse of galaxy clusters with the virial theorem, we derive the mass-temperature relation for X-ray clusters of galaxies $T=C{M}^{2/3}$. The normalization factor $C$ and the scatter of the relation are determined from first principles with the additional assumption of initial Gaussian random field. We are also able to reproduce the recently observed break in the M-T relation at $T \sim 3 \keV$, based on the scatter in the underlying density field for a low density $\Lambda$CDM cosmology. Finally, by combining observational data of high redshift clusters with our theoretical formalism, we find a semi-empirical temperature-mass relation which is expected to hold at redshifts up to unity with less than 20% error.

43 pages, 13 figures, One figure is added and minor changes are made. Accepted for Publication in ApJ

References in corpus (5)

• The Power Spectrum Dependence of Dark Matter Halo Concentrations
• The effect of radiative cooling on scaling laws of X-ray groups and clusters
• The Postcollapse Equilibrium Structure of Cosmological Haloes in a Low-Density Universe
• The Mass-Temperature Relation of 22 Nearby Clusters
• The Effect of Formation Redshifts on the Cluster Mass-Temperature Relation

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• Entropy "floor" and effervescent heating of intracluster gas
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• Evolution of spherical overdensities in holographic dark energy models
• Aging Halos: Implications of the Magnitude Gap on Conditional Statistics of Stellar and Gas Properties of Massive Halos
• Equilibrium Models of Galaxy Clusters with Cooling, Heating and Conduction
• Mass-Temperature relation in $\Lambda$CDM and modified gravity
• Hierarchy in the Phase Space and Dark Matter Astronomy
• Clustering in the Phase Space of Dark Matter Haloes. II. Stable Clustering and Dark Matter Annihilation
• Universal clustering of dark matter in phase space
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• The anatomy of the NGC 5044 group - I. Group membership and dynamics
• Superclusters with thermal SZ effect surveys
• Implications of Halo Inside-out Growth on the X-Ray Properties of Nearby Galaxy Systems within the Preheating Scenario
• The mass and temperature functions in a moving barrier model
• Parameterization Effects in the analysis of AMI Sunyaev-Zel'dovich Observations
• The Halo Mass-Temperature Relation for Clusters, Groups, and Galaxies
• Implications of the Universal Temperature Profile for Galaxy Clusters
• The Effect of Interacting Dark Energy on Mass-Temperature Relation in Galaxy Clusters
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• Entropy of the intracluster medium at high redshift
• Relativistic virial relation for cosmological structures
• Measuring Omega_m using clusters evolution
• Sensitivity and Insensitivity of Galaxy Cluster Surveys to New Physics
• Cosmological constraints from clustering properties of galaxy clusters
• Super Interacting Dark Sector: An Improvement on Self-Interacting Dark Matter via Scaling Relations of Galaxy Clusters
• Luminosity-Temperature Relation as a Probe for Modified Gravity
• Intracluster Medium through three years of WMAP