Why the fundamental plane of black hole activity is not simply a distance driven artifact

The fundamental plane of black hole activity is a non-linear correlation among radio core luminosity, X-ray luminosity and mass of all accreting black holes, both of stellar mass and supermassive, found by Merloni et al. [Merloni, A., Heinz, S., di Matteo, T. 2003. MNRAS 345, 1057 (MHD03)] and, independently, by Falcke et al. [Falcke, H., Körding, E., Markoff, S., 2004. A& A 414, 895]. Here we further examine a number of statistical issues related to this correlation. In particular, we discuss the issue of sample selection and quantify the bias introduced by the effect of distance in two of the correlated quantities. We demonstrate that the fundamental plane relation cannot be a distance artifact, and that its non-linearity must represent an intrinsic characteristic of accreting black holes. We also discuss possible future observational strategies to improve our understanding of this correlation.