On the correlation between the X-ray and gamma-ray emission in TeV blazars

Aims: The observations of TeV blazars published recently show an unexpected quadratic or even cubic correlation between the X-ray and gamma-ray emission. A standard model of the synchrotron self-Compton emission of a compact source inside a jet is not able to explain such a correlation. Therefore, we propose an alternative scenario where the emission of at least two independent compact components is observed at the same time.
Methods: We compare two different models. The first model assumes the injection of relativistic particles into a downstream region of a shock wave inside a jet that creates the emitting source. The model precisely describes the evolution of the particle energy spectrum inside the source and takes into account a light-crossing time effect for the produced radiation. The second model assumes an intrinsically constant emission of a homogeneous source that travels inside the jet along a curved trajectory, where the activity is produced simply by different values of the source's Doppler factor. To verify the two models we use recently published observations of Mrk 421.
Results: Our simulations show that simultaneous radiation of at least two independent sources, where the first source dominates the emission in the X-ray range and the second source radiates strongly in the gamma-ray range, can explain the observed correlations. However, the injection model provides inadequate results because it gives different values for the correlation of the rise and decay of a flare. This problem is negligible in the scenario that uses the Doppler boosting effect. Therefore, this approach yields much better results.