We discuss the correlation between the evolution of the TeV emission and X-ray radiation observed in high-energy peaked BL Lac objects. We describe such a correlation by a simple power law F_TeV(t) propto F^x_X-ray(t). In the first part of this work we present correlations obtained for the activity of Mrk 501 observed in 1997 April and for the activity of Mrk 421 observed in 2000 February. Our results obtained for Mrk 501 show that the index of the correlation (x) may strongly depend on the width and position of the spectral bands used for the comparison. The result of the correlation which we have obtained for Mrk 421 is not informative. However, we discuss results of similar correlation obtained for this source by other authors. They report an almost quadratic (x ∼ 2) correlations observed between the evolution of the TeV and X-ray emission. In the second part of this paper we present a phenomenological model which describes the evolution of the synchrotron and inverse Compton emission of a simple spherical homogeneous source. Neglecting the radiative cooling of the particles we derive analytical expressions that describe the evolution. Then we use a numerical code to investigate the impact of radiative cooling on the evolution. We show that different forms of correlations can be obtained depending on the assumed evolution scenario and the spectral bands used for the calculation. However, the quadratic correlation observed during the decay phase of the flare observed in Mrk 421 on 2001 March 19 appears problematic for this basic modeling. The quadratic correlation can be explained only for specific choices of the spectral bands used for the calculation. Therefore, looking for more robust solutions, we investigate the evolution of the emission generated by a cylindrical source. However this model does not provide robust solutions for the problem of a quadratic correlation. In principle the problem could be solved by the TeV emission generated by the self Compton scattering in the Thomson limit. However, we show that such a process requires unacceptably large values of the Doppler factor. Finally we briefly discuss the possible influence of the light travel time effect on our results.

We present calculations of the spectral and temporal radiative signatures expected from ultrarelativistic protons in compact sources. The coupling between the protons and the leptonic component is assumed to occur via Bethe-Heitler pair production. This process is treated by modeling the results of Monte-Carlo simulations and incorporating them in a time-dependent kinetic equation, that we subsequently solve numerically. Thus, the present work is, in many respects, an extension of the leptonic “one-zone” models to include hadrons. Several examples of astrophysical importance are presented, such as the signature resulting from the cooling of relativistic protons on an external black-body field and that of their cooling in the presence of radiation from injected electrons. We also investigate and refine the threshold conditions for the “Pair Production/Synchrotron” feedback loop which operates when relativistic protons cool efficiently on the synchrotron radiation of the internally produced Bethe-Heitler pairs. We demonstrate that an additional component of injected electrons lowers the threshold for this instability.