On the Correlations of Massive Black Holes with their Host Galaxies

We address the correlations of black hole (BH) mass with four different host-galaxy properties from eleven existing data sets. To guide theoretical understanding, we first try to quantify the tightness of the intrinsic correlations. Given the estimated measurement errors, we evaluate the probability distribution of the residual variance in excess of that expected from the measurement errors. Our central result is that the current data sets do not allow definite conclusions regarding the quality of the true correlations because the obtained probability distributions for the residual variance overlap for most quantities. We then consider which of the relations offer the best inferences of BH mass when there is no direct measurement available. As with the residual variances, we find that the probability distribution of expected uncertainty in inferred BH masses overlaps significantly for most of the relations. Photometric methods would then be preferred because the data are easier to obtain, as long as bulge-disk decomposition or detailed modeling of the photometric profile (as in \citet{graham:01}) do not present problems. Determining which correlation offers the best inferences requires reducing the uncertainty in the expected error in the inferred BH masses (the ``error on the error''). This uncertainty is currently limited by uncertainty in the residual variance for all of the relations.