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.