An Order Statistics Approach to the Halo Model for Galaxies

Abstract

We use the Halo Model to explore the implications of assuming that galaxy luminosities in groups are randomly drawn from an underlying luminosity function. We show that even the simplest of such order statistics models -one in which this luminosity function p(L) is universal -naturally produces a number of features associated with previous analyses based on the 'central plus Poisson satellites' hypothesis. These include the monotonic relation of mean central luminosity with halo mass, the Lognormal distribution around this mean, and the tight relation between the central and satellite mass scales. In stark contrast to observations of galaxy clustering, however, this model predicts no luminosity dependence of large scale clustering. We then show that an extended version of this model, based on the order statistics of a halo mass dependent luminosity function p(L|m), is in much better agreement with the clustering data as well as satellite luminosities, but systematically under-predicts central luminosities. This brings into focus the idea that central galaxies constitute a distinct population that is affected by different physical processes than are the satellites. We model this physical difference as a statistical brightening of the central luminosities, over and above the order statistics prediction. The magnitude gap between the brightest and second brightest group galaxy is predicted as a by-product, and is also in good agreement with observations. We propose that this order statistics framework provides a useful language in which to compare the Halo Model for galaxies with more physically motivated galaxy formation models.

Study of QCD generalized ghost dark energy in FRW universe

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Mining the Information Content of Member Galaxies in Halo Mass Modeling

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Mining the information content of member galaxies in the halo mass modelling

“…Such ranks and their corresponding sizes naturally appear as function values and random variables in the cumulative mass or luminosity functions. Such a connection have been exploited before to derive the distribution of magnitude gaps as well as that of the BCGs by drawing from the global or conditional luminosity functions (More 2012;Paranjape & Sheth 2012;Hearin et al 2013;Shen et al 2014;Paul et al 2017). 6.…”