The halo-model description of marked statistics

Marked statistics allow sensitive tests of how galaxy properties correlate with environment, as well as of how correlations between galaxy properties are affected by environment. A halo-model description of marked correlations is developed, which incorporates the effects which arise from the facts that typical galaxy marks (e.g. luminosity, colour, star formation rate, stellar mass) depend on the mass of the parent halo, and that massive haloes extend to larger radii and populate denser regions. Comparison with measured marked statistics in semi-analytic galaxy formation models shows good agreement on scales smaller than a megaparsec, and excellent agreement on larger scales. The halo-model description shows clearly that the behaviour of some low-order marked statistics on these scales encodes information about the mean galaxy mark as a function of halo mass, but is insensitive to mark gradients within haloes. Higher-order statistics encode information about higher-order moments of the distribution of marks within haloes. This information is obtained without ever having to identify haloes or clusters in the galaxy distribution. On scales smaller than a megaparsec, the halo-model calculation shows that marked statistics allow sensitive tests of whether or not central galaxies in haloes are a special population. A prescription for including more general mark gradients in the halo-model description is also provided. The formalism developed here is particularly well suited to interpretation of marked statistics in astrophysical data sets, because it is phrased in the same language that is currently used to interpret more standard measures of galaxy clustering.