Precision Measurements of the Cluster Red Sequence using an Error
  Corrected Gaussian Mixture Model
  The red sequence is an important feature of galaxy clusters and plays a
crucial role in optical cluster detection. Measurement of the slope and scatter
of the red sequence are affected both by selection of red sequence galaxies and
measurement errors. In this paper, we describe a new error corrected Gaussian
Mixture Model for red sequence galaxy identification. Using this technique, we
can remove the effects of measurement error and extract unbiased information
about the intrinsic properties of the red sequence. We use this method to
select red sequence galaxies in each of the 13,823 clusters in the maxBCG
catalog, and measure the red sequence ridgeline location and scatter of each.
These measurements provide precise constraints on the variation of the average
red galaxy populations in the observed frame with redshift. We find that the
scatter of the red sequence ridgeline increases mildly with redshift, and that
the slope decreases with redshift. We also observe that the slope does not
strongly depend on cluster richness. Using similar methods, we show that this
behavior is mirrored in a spectroscopic sample of field galaxies, further
emphasizing that ridgeline properties are independent of environment.
