The luminosity-weighted or ‘marked’ correlation function

Abstract

We present measurements of the redshift-space luminosity-weighted or `marked' correlation function in the SDSS. These are compared with a model in which the luminosity function and luminosity dependence of clustering are the same as that observed, and in which the form of the luminosity-weighted correlation function is entirely a consequence of the fact that massive halos populate dense regions. We do this by using mock catalogs which are constrained to reproduce the observed luminosity function and the luminosity dependence of clustering, as well as by using the language of the redshift-space halo-model. These analyses show that marked correlations may show a signal on large scales even if there are no large-scale physical effects--the statistical correlation between halos and their environment will produce a measureable signal. Our model is in good agreement with the measurements, indicating that the halo mass function in dense regions is top-heavy; the correlation between halo mass and large scale environment is the primary driver for correlations between galaxy properties and environment; and the luminosity of the central galaxy in a halo is different from (in general, brighter than) that of the other objects in the halo. Thus our measurement provides strong evidence for the accuracy of these three standard assumptions of galaxy formation models. These assumptions also form the basis of current halo-model based interpretations of galaxy clustering.