From 0801.1170. The luminosity-halo mass relation for brightest cluster galaxies, Brough et al.
The authors measure the K-band luminosity and the halo mass (from X-ray emission) of 146 BGG and BCGs. They find that L_K is proportional to M^grad. They have plotted their data points (open circles) as well as other studies (squares) and models (stars) against redshift. They find no evolution in the luminosity-halo mass relation up to a redshift of 1. This suggests that the early-type BCGs grow steadily with the growth of their host cluster. A slope of 0.3 suggests that BCG growth is limited by the timescale on which dynamical friction causes satellite galaxies to fall into the centre. These observations are consistent with BCGs accreting 10-20% of their stellar mass as their host cluster doubles in size. Hence they can grow by less than 50% since z~1 i.e. most of the stellar mass in these massive red galaxies is already in place by z~1.

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