Journal Article

Spherically averaging ellipsoidal galaxy clusters in X-ray and Sunyaev–Zel’dovich studies – I. Analytical relations

David A. Buote and Philip J. Humphrey

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 420, issue 2, pages 1693-1705
Published in print February 2012 | ISSN: 0035-8711
Published online January 2012 | e-ISSN: 1365-2966 | DOI:
Spherically averaging ellipsoidal galaxy clusters in X-ray and Sunyaev–Zel’dovich studies – I. Analytical relations

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This is the first of two papers investigating the deprojection and spherical averaging of ellipsoidal galaxy clusters. We specifically consider applications to hydrostatic X-ray and Sunyaev–Zel’dovich (SZ) studies, though many of the results also apply to isotropic dispersion-supported stellar dynamical systems. Here we present analytical formulae for galaxy clusters described by a gravitational potential that is a triaxial ellipsoid of constant shape and orientation. For this model type we show that the mass bias due to spherically averaging X-ray observations is independent of the temperature profile, and for the special case of a scale-free logarithmic potential, there is exactly zero mass bias for any shape, orientation and temperature profile. The ratio of spherically averaged intracluster medium (ICM) pressures obtained from SZ and X-ray measurements depends only on the ICM intrinsic shape, projection orientation and H0, which provides another illustration of how cluster geometry can be recovered through a combination of X-ray and SZ measurements. We also demonstrate that YSZ and YX have different biases owing to spherical averaging, which leads to an offset in the spherically averaged relation. A potentially useful application of the analytical formulae presented is to assess the error range of an observable (e.g. mass, YSZ) accounting for deviations from assumed spherical symmetry, without having to perform the ellipsoidal deprojection explicitly. Finally, for dedicated ellipsoidal studies, we also generalize the spherical onion peeling method to the triaxial case for a given shape and orientation.

Keywords: cosmological parameters; cosmology: observations; dark matter; X-rays: galaxies; X-rays: galaxies: clusters

Journal Article.  7150 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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