The luminosity-weighted or ‘marked’ correlation function

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. When the same galaxies are weighted by their u−, g−, or r−band luminosities, then the marked correlation function is stronger in the redder bands. When the weight is galaxy color rather than luminosity, then the data suggest that close pairs of galaxies tend to have redder colors. This wavelength dependence of marked correlations is in qualitative agreement with galaxy formation models, and reflects the fact that the mean luminosity of galaxies in a halo depends more strongly on halo mass in the r−band than in u. The u−band luminosity is a tracer of star formation, so our measurement suggests that the correlation between star formation rate and halo mass is not monotonic. In particular, the luminosity and color dependence we find are consistent with models in which the galaxy population in clusters is more massive and has a lower star formation rate than does the population in the field. The virtue of this measurement of environmental trends is that it does not require classification of galaxies into field, group and cluster environments.