Population statistics of beamed sources – I. A new model for blazars

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Abstract
Observations of blazar jets are shrouded in relativistic effects, thus hindering our understanding of their intrinsic properties and dominant physical processes responsible for their generation, evolution, radiation and particle emission. In this work, we focus on extracting information about time-scales in the jet rest frame using a population-modelling approach. We employ Monte Carlo simulations to derive a simple population model for the intrinsic unbeamed luminosities and the Lorentz Γ of blazar jets that adequately describe the observed redshift and apparent superluminal speed distributions for flux-limited blazar samples. We derive separate models for BL Lacs and flat spectrum radio quasars (FSRQs). We then use these models to compute the predicted distribution of Doppler factors in each blazar class, and address the following questions: (a) What is the relativistically induced spread in observed time-scales (e.g. event duration, time lags) in a flux-limited sample of relativistic jets? (b) Could differences between BL Lacs and FSRQs observed in the time domain be attributed to differences in beaming between the two populations? (c) Is there a statistically preferred amount of beaming in a flux-limited sample? How large are statistical deviations from that preferred value? We use our findings to propose promising approaches in phenomenological studies of time-scales in blazar jets.

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