Opacity effects and shock-in-jet modelling of low-level activity in   Cygnus X-3
  We present simultaneous dual-frequency radio observations of Cygnus X-3 during a phase of low-level activity. We constrain the minimum variability timescale to be 20 minutes at 43 GHz and 30 minutes at 15 GHz, implying source sizes of 2 to 4 AU. We detect polarized emission at a level of a few per cent at 43 GHz which varies with the total intensity. The delay of approximately 10 minutes between the peaks of the flares at the two frequencies is seen to decrease with time, and we find that synchrotron self-absorption and free-free absorption by entrained thermal material play a larger role in determining the opacity than absorption in the stellar wind of the companion. A shock-in-jet model gives a good fit to the lightcurves at all frequencies, demonstrating that this mechanism, which has previously been used to explain the brighter, longer-lived giant outbursts in this source, is also applicable to these low-level flaring events. Assembling the data from outbursts spanning over two orders of magnitude in flux density shows evidence for a strong correlation between the peak brightness of an event, and the timescale and frequency at which this is attained. Brighter flares evolve on longer timescales and peak at lower frequencies. Analysis of the fitted model parameters suggests that brighter outbursts are due to shocks forming further downstream in the jet, with an increased electron normalisation and magnetic field strength both playing a role in setting the strength of the outburst. 
James C. A. Miller-Jones (1), Michael P. Rupen (1), Marc T\"urler   (2,3), Elina J. Lindfors (4,5), Katherine M. Blundell (6...