Time-dependent simulations of emission from FSRQ PKS1510-089: multiwavelength variability of external Compton and SSC models

[ abridged] We present results of modeling the SEDand multiwavelength variability of the bright FSRQ PKS1510-089 with our time-dependent multizone Monte Carlo/Fokker-Planck code (Chen et al. 2001). As primary source of seed photons for inverse Compton scattering, we consider radiation from the broad line region (BLR), from the molecular torus, and the local synchrotron radiation (SSC). Different scenarios are assessed by comparing simulated light curves and SEDswith one of the best flares by PKS1510-089, in March 2009. The time-dependence of our code and its correct handling of light travel time effects allow us to fully take into account the effect of the finite size of the active region, and in turn to fully exploit the information carried by time resolved observed SEDs, increasingly available since the launch of Fermi. We confirm that the spectrum adopted for the external radiation has an important impact on the modeling of the SED, in particular for the lower energy end of the Compton component, observed in the X-ray band, which in turn is one of the most critical bandsto assess the differences between EC and SSC emission. In the context of the scenario presented here, where the flaring is caused by the increase of the number of relativistic electrons ascribed to the effect of the interaction of a portion of the jet ( blob) with a shock, we can not firmly discriminate the three main scenarios for gamma-ray emission. However, results show clearly the differences produced by a more realistic treatment of the emitting source in the shape of SEDsand their time variability over relevant, observable time-scales, and demonstrate the crucial importance of time-dependent multi-zone models to advance our understanding of the physics of these sources, by taking full advantage of the wealth of information offered by the high quality data of current multiwavelength campaigns.