Accounting for selection effects in the BH-bulge relations: No evidence
  for cosmological evolution
  The redshift evolution of the black hole - bulge relations is an essential
observational constraint for models of black hole - galaxy coevolution. In
addition to the observational challenges for these studies, conclusions are
complicated by the influence of selection effects. We demonstrate that there is
presently no statistical significant evidence for cosmological evolution in the
black hole-bulge relations, once these selection effects are taken into account
and corrected for. We present a fitting method, based on the bivariate
distribution of black hole mass and galaxy property, that accounts for the
selection function in the fitting and is therefore able to recover the
intrinsic black hole - bulge relation unbiased. While prior knowledge is
restricted to a minimum, we at least require knowledge of either the sample
selection function and the mass dependence of the active fraction, or the
spheroid distribution function and the intrinsic scatter in the black hole -
bulge relation. We employed our fitting routine to existing studies of the
black hole-bulge relation at z~1.5 and z~6, using our current best knowledge of
the distribution functions. There is no statistical significant evidence for
positive evolution in the MBH-M* ratio out to z~2. At z~6 the current
constraints are less strong, but we demonstrate that the large observed
apparent offset from the local black hole-bulge relation at z~6 is fully
consistent with no intrinsic offset. The method outlined here provides a tool
to obtain more reliable constraints on black hole - galaxy co-evolution in the
future.
