The distribution of twodimensional eccentricity of SunyaevZeldovich Effect and Xray surf.pdfVIP

The distribution of two-dimensional eccentricity of Sunyaev-Zeldovich Effect and X-ray surface brightness profiles Y.-G. Wang and Z.-H. Fan Department of Astronomy, Peking University, Beijing 100871, China 4 wangyg@bac.pku.edu.cn,fan@bac.pku.edu.cn 0 0 2 ABSTRACT p e S With the triaxial density profile of dark matter halos and the corresponding 8 equilibrium gas distribution, we derive two-dimensional Sunyaev-Zeldovich (SZ) 2 effect and X-ray surface brightness profiles for clusters of galaxies. It is found v 5 that the contour map of these observables can be well approximated by a series 4 of concentric ellipses with scale-dependent eccentricities. The statistical distri- 1 9 bution of their eccentricities (or equivalently axial ratios) is analyzed by taking 0 into account the orientation of clusters with respect to the line of sight and the 4 0 distribution of the axial ratios and the concentration parameters of dark mat- / h ter halos. For clusters of mass 1013h−1M⊙ at redshift z = 0, the axial ratio is p- peaked at η ∼ 0.9 for both SZ and X-ray profiles. For larger clusters, the devia- o tion from circular distributions is more apparent, with η peaked at η ∼ 0.85 for r t M = 1015h−1M . To be more close to observations, we further study the axial- s ⊙ a : ratio distribution for mass-limited cluster samples with the number distribution v i of clusters at different redshifts described by a modified Press-Schechter model. X For a mass limit of value Mlim