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

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We examine the effects of Doppler beaming on flux-limited samples of compact radio sources representative 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 (Γ). These enhancements allow us to compare observable parameters other than simply apparent velocity with the data. The predictions of L-Γ-independent (LGI) models are compared to those of a L-Γ-dependent (LGD) scenario in which the Lorentz factor and luminosity are related by the form L Γξ. This is accomplished using Monte Carlo simulations, where we compare the predicted flux density, redshift, monochromatic emitted luminosity, and apparent velocity distributions of flux-limited samples to the Caltech-Jodrell Bank sample of bright, flat-spectrum, radio core-dominated AGNs (CJ-F). The LGI model predictions are consistent with the CJ-F data if we adopt parent Lorentz factor distributions of the form N(Γ) Γa, where -1.5 a -1.75, or, alternatively N(Γ) (Γ - 1)a, where -0.5 a -1. These models reproduce, via selection effects, a deficit of sources having both low apparent velocity (βapp) and high monochromatic emitted luminosity (P) seen in the CJ-F sample, as reported by Vermeulen in 1995. We examine two possible cases for the LGD scenario, the first of which employs a positive correlation between unbeamed synchrotron luminosity and Lorentz factor (the LGC model), and the second of which employs an anticorrelation (the LGA model). The LGA models do not predict enough low-P sources to be consistent with the CJ-F data and do not reproduce the P versus βapp envelope. The predictions of the best-fit LGC model, on the other hand, are very similar to our best-fit LGI models and provide as good fits to the CJ-F data, with the important exception that very few high-viewing angle sources are predicted. This in conflict with the large fraction (11%) of radio galaxies present in the CJ-F sample, whose jet axes are predicted by the unified AGN model to be at angles greater than ~45° to the line of sight. At present, the observational data on the CJ-F sample are otherwise insufficient to distinguish between the LGI and LGC models. Our simulations indicate, however, that the LGC models predict a larger number of high (δ > 20) Doppler factor sources in flux-limited samples. Furthermore, the predicted median variability timescale of the high (βapp > 10 h-1) objects is only ~20 times faster than the low βapp < 2.5 h-1 objects in the LGC models, whereas the LGI models predict a ratio of ~200. We find that all of our models predict a very large parent population for the CJ-F sample: on the order of 107-107.7 objects are required to produce 293 objects with flux densities greater than 350 mJy for the LGC and LGI models, respectively. This translates into parent population space densities on the order of (1.3-5.9) × 10-5 Mpc-3 for H0 = 65 km s-1 Mpc-1 and q0 = 0.