RMS-Flux Relation and Disc-Jet Connection in Blazars in the Context of
  the Internal Shocks Model
  Recent analysis of blazar variability has revealed a proportionality between
the mean flux and the root mean squared (rms) fluctuations about the mean flux.
Although such rms-flux relation has been previously observed in the accretion
disc/corona variability of X-ray binaries and Seyfert galaxies, and has been
extensively modelled, its emergence in the jet light curves of blazars calls
for a revised theoretical understanding of this feature. In this work, we
analyse the time variability properties of realistic multi-wavelength jet light
curves, simulated in the context of a simplified version of the internal shocks
model, particularly focusing on the rms-flux relation. These shocks accelerate
the jet electrons to relativistic energies, which then cool radiatively via
synchrotron and inverse-Compton processes. We find that the rms-flux relation
may be consistently recovered in the cases, in which the shocks have different
amplitudes based on the speed of the colliding blobs generating them as opposed
to all shocks having the same amplitude. We observe that the slope of the
rms-flux relation depends on the wavelength at which the variability is
observed and the energy distribution of the electron population. We find that
the accretion disc and the jet variability are anti-correlated, with the latter
lagging that of the disc. Our results provide crucial constraints on the
physical properties of the jet, and the mode of connection through which the
accretion disc and jet may be related.
