Stellar mass -- halo mass relation and star formation efficiency in
  high-mass halos
  We study relation between stellar mass and halo mass for high-mass halos
using a sample of galaxy clusters with accurate measurements of stellar masses
from optical and IR data and total masses from X-ray observations. We find that
stellar mass of the brightest cluster galaxies (BCGs) scales as M*BCG\propto
M500^a_BCG with the best fit slope of a_BCG~0.35+-0.1 and scatter of M*BCG at a
fixed M500 of ~0.2 dex. We show that M*-M relations from abundance matching or
halo modelling reported in recent studies underestimate stellar masses of BCGs
by a factor of ~2-4, because these studies used stellar mass functions (SMF)
based on photometry that severely underestimates the outer surface brightness
profiles of massive galaxies. We show that M*-M relation derived using
abundance matching with the recent SMF calibration by Bernardi et al. (2013)
based on improved photometry is in a much better agreement with the relation we
derive. The total stellar mass of galaxies correlates with total mass M500 with
the slope of \approx 0.6+-0.1 and scatter of 0.1 dex. This indicates that
efficiency with which baryons are converted into stars decreases with
increasing cluster mass. We show that for a fixed choice of the initial mass
function (IMF) total stellar fraction in clusters is only a factor of ~3-5
lower than the peak stellar fraction reached in M\approx 10^12 Msun halos, and
only a factor of ~1.5-3 if the IMF becomes progressively more bottom heavy with
increasing mass in early type galaxies, as indicated by recent observations.
The larger normalization and slope of the M*-M relation derived in this study
shows that the overall efficiency of star formation in massive halos is
suppressed much less than was thought before and that feedback and associated
suppression of star formation in massive halos should be weaker than assumed in
most of the current semi-analytic models and simulations.
