Modelling the $γ$-ray variability of 3C 273

We investigate MeV-GeV $γ$-ray outbursts in 3C 273 in the frame of a time-dependent one-zone synchrotron self-Compton (SSC) model. In this model, electrons are accelerated to extra-relativistic energy through the stochastic particle acceleration and evolve with the time, nonthermal photons are produced by both synchrotron and inverse Compton scattering of synchrotron photons. Moreover, nonthermal photons during a quiescent are produced by the relativistic electrons in the steady state and those during a outburst are produced by the electrons whose injection rate is changed at some time interval. We apply the model to two exceptionally luminous $γ$-ray outbursts observed by the Fermi-LAT from 3C 273 in September, 2009 and obtain the multi-wavelength spectra during the quiescent and during the outburst states, respectively. Our results show that the time-dependent properties of outbursts can be reproduced by adopting the appropriate injection rate function of the electron population.

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