Reconciling inverse-Compton Doppler factors with variability Doppler factors in blazar jets

Abstract

Context. Blazar population models have shown that the inverse-Compton and variability Doppler factor estimates yield consistent results at the population level for flat spectrum radio quasars (FSRQs). The two methods, however, are inconsistent when compared on a source-by-source basis.Aims. In this work, we attempt to understand the source of the discrepancy by tracing the potential sources of systematic and statistical error for the inverse-Compton Doppler factors. By eliminating these sources of error, we provide stronger constrains on the value of the Doppler factor in blazar jets.Methods. We re-estimate the inverse-Compton Doppler factor for 11 sources that meet certain criteria for their synchrotron peak frequency and the availability of Doppler factor estimates in the literature. We compare these estimates with the average of two di ff erent estimates of the variability Doppler factor obtained using various datasets and methodologies to identify any discrepancies and, in each case, trace their sources in the methodology or assumptions adopted.Results. We identify three significant sources of error for the inverse-Compton Doppler factors: a) contamination of the X-ray flux by non-synchrotron self-Compton emission; b) radio observations at frequencies other than the synchrotron turnover frequency; c) non-simultaneity between radio and X-ray observations. We discuss key aspects in the correct application of the inverse-Compton method in light of these potential errors. We are able to constrain the Doppler factor of 3C 273, 3C 345, 3C 454.3, PKS 1510-089, and PKS 1633 + 382 e ff ectively, since all available estimates from both methods converge to the same values for these five sources.