Synchrotron and inverse-Compton emission from blazar jets I: a uniform   conical jet model
  In the first of a series of papers investigating emission from blazar jets from radio to high-energy {\gamma}-rays, we revisit the class of models where the jet has a uniform conical ballistic structure. We argue that by using simple developments of these models, in the context of new multi-frequency data extending to gamma-ray energies, valuable insights may be obtained into the properties that fully realistic models must ultimately have. In this paper we consider the synchrotron and synchrotron-self-Compton emission from the jet, modelling the recent simultaneous multi-wavelength observations of BL Lac. This is the first time these components have been fitted simultaneously for a blazar using a conical jet model.   In the model we evolve the electron population dynamically along the jet taking into account the synchrotron and inverse-Compton losses. The inverse-Compton emission is calculated using the Klein-Nishina cross section and a relativistic transformation into the jet frame, and we explicitly show the seed photon population. We integrate synchrotron opacity along the line of sight through the jet plasma, taking into account the emission and opacity of each section of the jet. In agreement with previous studies of radio emission, we find that a conical jet model which conserves magnetic energy produces the characteristic blazar flat radio spectrum, however, we do not require any fine-tuning of the model to achieve this. Of particular note, in our model fit to BL Lac--which at ~10^37W is a relatively low jet-power source--we find no requirement for significant re-acceleration within the jet to explain the observed spectrum. 
William J. Potter and Garret Cotter
astro-ph.HE astro-ph.CO astro-ph.GA