Radio-<i>γ</i>-ray response in blazars as a signature of adiabatic blob expansion

Multiwavelength light curves in long-term campaigns have shown that, for several blazars, the radio emission occurs with a significant delay w.r.t. to $\gamma$-ray band, timescales ranging from weeks years. Such observational evidence has been matter of debate years and usually is interpreted as signature originating upstream jet, emitting region becoming transparent at larger scales. In this paper, we show, by means self-consistent numerical modelling, that adiabatic expansion relativistic blob can explain these delays. We use JetSeT framework reproduce modelling radiative/accelerative processes, reproducing temporal evolution, initial flaring activity, subsequent expansion. follow spectral evolution curves, investigating relations among observed parameters, rise, time, decay identifying link physical parameters. find when active, lags due shift synchrotron frequency occur, an offset equal distance time between onset beginning expansion, whilst rising decaying depend on velocity required source exhibit self-absorption frequency. derive inter-band response function, investigate effects competitions radiative cooling response. apply function $\gamma-$ray Mrk 421, 501 3C 273, finding satisfactory agreement log-term behaviour, Monte Carlo Markov Chain approach, estimate some relevant discuss applications polarization measurements, jets collimation profile kinematics.