Gaussian Peaks and Clusters of Galaxies: Mass Function, Correlation Funcion, Evolution and Beyond

Details Gaussian Peaks and Clusters of Galaxies: Mass Function, Correlation Funcion, Evolution and Beyond Gaussian Peaks and Clusters of Galaxies: Mass Function, Correlation Funcion, Evolution and Beyond

May 1998

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1998aas...192.4203c&link_type=abstract

American Astronomical Society, 192nd AAS Meeting, #42.03; Bulletin of the American Astronomical Society, Vol. 30, p.872

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We develop and test a method to compute the cluster mass and correlation functions from linear density fluctuations, based on the formalism of Gaussian peaks (Bardeen, et al 1986). The essential, new ingredient in the current study is a simultaneous and unique fixture of the size of the smoothing window for the density field and the critical height for collapse of a density peak for a given cluster mass (enclosed within the sphere of a given radius rather than the virial radius, which is hard to measure observationally). The former depends on both the mass of the cluster in question and Omega , whereas the latter is a function of only Omega and Lambda . These two parameters have formerly been treated as free parameters. Thus, for the first time, the Gaussian Peak Method becomes unambiguous, and more importantly, accurate, as is shown here. The method may be applicable to objects on other scales provided that the implicit assumption that merger is unimportant is not violated or merger does not affect the concerned results, (for example, total mass of some collapsed objects defined within some fixed radius). We then apply this method to arrive at several useful constraints and predictions concerning all variants of the Gaussian cold dark matter cosmological model. One important prediction is that we seem to be on the verge of being able to make dramatic tests of all models in the foreseeable future using a large set of independent observations, mostly at high redshift.

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