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 different 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 3C273, 3C345, 3C454.3, PKS1510-089, and PKS1633+382 effectively, since all available estimates from both methods converge to the same values for these five sources.

Constraining the Limiting Brightness Temperature and Doppler Factors for the Largest Sample of Radio-bright Blazars

“…There are several methods in the literature for estimating the Doppler factor in blazar jets, some of which are mentioned in section 1. Although a broader comparison study between the different methods similar to Liodakis & Pavlidou (2015b); Liodakis et al (2017c) could be beneficial, we focus on recent results from the radio regime and SED modeling. The most recent attempts in estimating the variability Doppler factor for a large number of sources are Hovatta et al (2009); Liodakis et al (2017d) (hereafter H09 and L17 respectively).…”

“…However, different methods often yield discrepant results due to either assumptions that do not hold or the wrongful application of the methods (see e.g., Liodakis et al 2017c). Liodakis & Pavlidou (2015b) using blazar population models (Liodakis & Pavlidou 2015a;Liodakis et al 2017a) evaluated a number of these methods and found that the variability Doppler factor method Hovatta et al 2009) is the most accurate and can describe both flat spectrum radio quasar (FSRQ) and BL Lac object (BL Lacs) populations.…”

RadioAstron observations of 3C 345

“…3C 345 was successfully imaged with RadioAstron with sub-mas resolution, corresponding to a projected distance of 1.9 pc or ∼5000 gravitational radii for a black hole mass of 4 × 10 9 M [15]. The visibility amplitudes imply the presence of emitting regions with observed brightness temperature in excess of 3.4 × 10 13 K, well above the inverse Compton limit of 10 11.5 K. Considering the redshift z = 0.59 and the Doppler factor δ = 9.1 [16] of the source, the intrinsic brightness temperature T b,min ∼ 6 × 10 12 K, which is still above the theoretical limit. This suggests locally efficient injection or re-acceleration of particles in the jet to counter the inverse Compton cooling, or an unusual geometry of the jet.…”

Probing the innermost regions of AGN jets and their magnetic fields with RadioAstron

“…The Doppler factor is denoted by δ = 1 − β 2 (1 − β cos(θ)) −1 , where β is the jet bulk velocity in units of the speed of light and θ is the jet viewing angle. We take δ = 9.1 ± 1.9 as reported in Liodakis et al (2017), calculated from variability arguments. They also constrain the Doppler factor with assumptions on the IC emission (Ghisellini et al 1993), yielding similar results.…”