Statistics of gravitational potential perturbations: A novel approach to deriving the X-ray temperature function

Free access article

Issue		A&A Volume 494, Number 2, February I 2009


Page(s)		461 - 470
Section		Cosmology (including clusters of galaxies)
DOI		http://dx.doi.org/10.1051/0004-6361:200809562
Published online		22 December 2008

A&A 494, 461-470 (2009)
DOI: 10.1051/0004-6361:200809562

Statistics of gravitational potential perturbations: A novel approach to deriving the X-ray temperature function

C. Angrick and M. Bartelmann

Zentrum für Astronomie, ITA, Universität Heidelberg, Albert-Überle-Str. 2, 69120 Heidelberg, Germany
e-mail: cangrick@ita.uni-heidelberg.de

Received 12 February 2008 / Accepted 5 December 2008

Abstract
Context. While the halo mass function is theoretically a very sensitive measure of cosmological models, masses of dark-matter halos are poorly defined, global, and unobservable quantities.
Aims. We argue that local, observable quantities such as the X-ray temperatures of galaxy clusters can be directly compared to theoretical predictions without invoking masses. We derive the X-ray temperature function directly from the statistics of Gaussian random fluctuations in the gravitational potential.
Methods. We derive the abundance of potential minima constrained by the requirement that they belong to linearly collapsed structures. We then use the spherical-collapse model to relate linear to non-linear perturbations, and the virial theorem to convert potential depths to temperatures. No reference is made to mass or other global quantities in the derivation.
Results. Applying a proper high-pass filter that removes large enough modes from the gravitational potential, we derive an X-ray temperature function that agrees very well with the classical Press-Schechter approach on relevant temperature scales, but avoids the necessity of measuring masses.
Conclusions. This first study shows that and how an X-ray temperature function of galaxy clusters can be analytically derived, avoiding the introduction of poorly defined global quantities such as halo masses. This approach will be useful for reducing scatter in observed cluster distributions and thus in cosmological conclusions drawn from them.

Key words: cosmology: theory -- methods: analytical -- galaxies: clusters: general -- cosmology: dark matter -- X-rays: galaxies: clusters -- cosmology: cosmological parameters

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