Constraints on relativistic beaming from estimators of the unbeamed flux

Abstract

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 > 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 cannot be reasonably explained by Doppler boosting alone.