Statistical Effects of Doppler Beaming and Malmquist Bias on Flux‐limited Samples of Compact Radio Sources

We examine the e†ects of Doppler beaming on Ñux-limited samples of compact radio sources repre-sentative of relativistic jets found in active galactic nuclei (AGNs). We expand upon past studies by incorporating a luminosity function and redshift distribution for the parent population and by allowing the unbeamed synchrotron luminosity L of a relativistic jet to be related to its bulk Lorentz factor (!). These enhancements allow us to compare observable parameters other than simply apparent velocity with the data. The predictions of L-!Èindependent (LGI) models are compared to those of a L-!È dependent (LGD) scenario in which the Lorentz factor and luminosity are related by the form L P!m. This is accomplished using Monte Carlo simulations, where we compare the predicted Ñux density, red-shift, monochromatic emitted luminosity, and apparent velocity distributions of Ñux-limited samples to the CaltechÈJodrell Bank sample of bright, Ñat-spectrum, radio core-dominated AGNs (CJ-F). The LGI model predictions are consistent with the CJ-F data if we adopt parent Lorentz factor dis-tributions of the form N(!)P!a, where or, alternatively N(!) P (! [ 1)a, where[1.5 [ a [[1.75, These models reproduce, via selection e†ects, a deÐcit of sources having both low[0.5 [ a [ [1. apparent velocity and high monochromatic emitted luminosity (P) seen in the CJ-F sample, as(bapp)reported by Vermeulen in 1995.