Blazars and Optical Depth in a non-linear, time-dependent injection and cooling scenario

TL;DR

This study calculates optical depths in blazars considering various photon fields within a time-dependent, non-linear injection model, finding that only a constant external photon field notably affects high-energy radiation.

Contribution

It introduces a comprehensive time-dependent model for optical depths in blazars, accounting for multiple photon fields and analyzing their impact on high-energy spectra.

Findings

External photon field significantly influences high-energy radiation.

Internal radiation fields have minor or negligible effects under typical conditions.

Time-dependent synchrotron-self absorption is complex and hard to constrain.

Abstract

In this paper the optical depths in blazars due to photo-pair production is calculated for a time-dependent, non-linear injection model. Several target photon fields are taken into account, namely the internal synchrotron, synchrotron-self Compton and external Compton radiation, as well as a constant external soft photon field. By applying the optical depths to theoretical blazar spectra only the constant external photon field turns out to significantly influence the radiation at high energies. The impact of the internal time-dependent radiation fields is either minor or requires extreme parameter settings. Additionally, the synchrotron-self absorption turn-over energy for low synchrotron energies is calculated, which is inherently time-dependent. It would be challenging to use it to constrain free parameters, since precise knowledge of the observation time relative to the injection time is needed. In conclusion, optical depth does not significantly influence the non-linear, time-dependent injection and cooling model.