Blazar variability power spectra from radio up to TeV photon energies: Mrk 421 and PKS 2155-304.

We present the results of the power spectral density (PSD) analysis for the blazars Mrk\,421 and PKS\,2155$-$304, using good-quality, densely sampled light curves at multiple frequencies, covering 17 decades of the electromagnetic spectrum, and variability timescales from weeks up to a decade. The data were collected from publicly available archives of observatories at radio from OVRO, optical and infrared (B, V, R, I, J, H, and K-bands), X-rays from the {\it Swift} and the {\it Rossi} X-ray Timing Explorer, high and very high energy $\gamma-$rays from the {\it Fermi} and Very Energetic Radiation Imaging Telescope Array System as well as the High Energy Stereoscopic System. Our results are: (1) the power-law form of the variability power spectra at radio, infra-red and optical frequencies have slopes $\sim$1.8, indicative of random-walk type noise processes; (2) the power-law form of the variability power spectra at higher frequencies, from X-rays to very high energy \,$\gamma$-rays, however, have slopes $\sim$1.2, suggesting a flicker noise type process; (3) there is significantly more variability power at X-rays, high and very high energy $\gamma$-rays on timescales $\lesssim$ 100 days, as compared to lower energies. Our results do not easily fit into a simple model, in which a single compact emission zone is dominating the radiative output of the blazars across all the timescales probed in our analysis. Instead, we argue that the frequency-dependent shape of the variability power spectra points out a more complex picture, with highly inhomogeneous outflow producing non-thermal emission over an extended, stratified volume.