Constraining Doppler factors of blazars

Determine the Doppler factors of blazars more reliably despite the unobservability of the plasma velocity and viewing angle, thereby resolving the remaining uncertainty in Doppler-factor estimation.

Background

The paper uses radio Doppler factors to interpret the distribution of blazars on the broad-band spectral-index plane and to compare jet properties across FSRQs, LBLs, IBLs, and HBLs. These Doppler factors are compiled from several studies that use different estimation methods, and some values are extrapolated between radio bands using an empirical accelerated- or decelerated-jet prescription.

Because the Doppler factor depends on the plasma velocity and viewing angle, both of which are difficult to observe directly, uncertainty in its value affects interpretations of the relationship between Doppler beaming, synchrotron-peak frequency, and blazar subclass. The paper notes that existing methods consistently recover an anti-correlation between radio Doppler factor and synchrotron-peak frequency, but does not resolve the broader problem of obtaining robust, direct Doppler-factor constraints.

References

It is well-known that the Doppler factor of blazars is notoriously difficult to estimate due to the unobservability of $\beta$ and $\theta$. Although many previous studies have proposed different methods for estimating the Doppler factor \citep[e.g.,][]{Ghisellini1993ApJ,Hovatta2009,Fan2014RAA,Liodakis2017MN,Liodakis2018ApJ,Ye2021PASJ,Pei2022ApJ}, the constraint of the Doppler factor of blazars is still an open question.

The Jet Properties and Accretion Regime for the Blazar Sequence  (2609.03435 - Long, 3 Sep 2026) in Section 4.3, Discussion of Uncertainties in Our Analysis and Possible Alternative Interpretations