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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.