We review the statistical properties of relativistic Doppler boosting relevant for studies of relativistic jets from compact objects based on radio–X-ray ( –mass ) correlations , such as that found in black-hole X-ray binaries in the low/hard state , or the “ fundamental plane ” of Merloni , Heinz , & DiMatteo .
We show that the presence of only moderate scatter in such relations does not necessarily imply low Lorentz factors of the jets producing the radio emission in the samples under consideration .
Applying Doppler beaming statistics to a large sample of XRBs and AGN , we derive a limit on the width of the Lorentz factor distribution of black holes with relativistic jets : If the X-rays are unbeamed ( e.g. , if they originate in the accretion disk or in the slower , innermost part of the jet ) , the width of the \beta \Gamma distribution should be about one order of magnitude or less .
If the scatter about the “ fundamental plane ” is entirely dominated by relativistic beaming , a lower limit on the mean Lorentz factor \langle \beta \Gamma \rangle > 5 can be derived .
On the other hand , if the X-rays are boosted by the same factor as the radio emission , we show that the observed scatter can not be reasonably explained by Doppler boosting alone .