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.