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Decade-long monitoring of blazars at optical and infrared (OIR) wavelengths with the Small and Moderate Aperture Research Telescope System (SMARTS) in Chile and in $gamma$-rays with the Fermi Large Area Telescope (LAT) has enabled the systematic study of their multi-wavelength long-term variability. In this work we investigate, from a theoretical perspective, the long-term variability properties of blazar emission by introducing an observationally motivated time-dependence to four main parameters of the one-zone leptonic model: injection luminosity of relativistic electrons, strength of magnetic field, Doppler factor, and external photon field luminosity. For the first time, we use both the probability density function and the power spectral density of the 10 year-long Fermi-LAT light curves to create variation patterns for the model parameters. Using as test beds two bright blazars from the SMARTS sample (PKS 2155-304 and 3C 273), we compute 10 year-long OIR, X-ray, and $gamma$-ray model light curves for different varying parameters. We compare the findings of our theoretical investigation with multi-wavelength observations using various measures of variability. While no single-varying parameter simulation can explain all multi-wavelength variability properties, changes in the electron luminosity and external radiation field in PKS 2155-304 and 3C 273, respectively, can account for most of them. Our results motivate future time-dependent studies with coupling between two or more physical parameters to describe the multi-wavelength long-term blazar variability.
The long-term optical, X-ray and $gamma$-ray data of blazar 3C 279 have been compiled from $Swift$-XRT, $RXTE$ PCA, $Fermi$-LAT, SMARTS and literature. The source exhibits strong variability on long time scales. Since 1980s to now, the optical $R$ ba
Time variability of the photon flux is a known feature of active galactic nuclei (AGN) and in particular of blazars. The high frequency peaked BL Lac (HBL) object PKS 2155-304 is one of the brightest sources in the TeV band and has been monitored reg
We study the multi-band variability and correlations of the TeV blazar Mrk 421 on year time scales, which can bring additional insight on the processes responsible for its broadband emission. We observed Mrk 421 in the very high energy (VHE) gamma-ra
A study of the gravitationally lensed blazar PKS 1830-211 was carried out using multi waveband data collected by Fermi-LAT, Swift-XRT and Swift-UVOT telescopes between MJD 58400 to MJD 58800 (9 Oct 2018 to 13 Nov 2019). Flaring states were identified
A detailed analysis of the optical polarimetric variability of the TeV blazar 1ES 1959+650 from 2007 October 18 to 2011 May 5 is presented. The source showed a maximum and minimum brightness states in the R-band of 14.08$pm$0.03 mag and 15.20$pm$0.03