Constraints on the Physical Parameters of TeV Blazars

We consider the constraints that can be derived from the spectral shape and variability of TeV blazars on the homogeneous synchrotron self–Compton (SSC) model. Assuming that the relativistic electron spectrum is a broken power law, where the break energy is a free parameter, we write analytical formulae that allow to connect observable quantities to the physical parameters of the model.We give approximate analytic formulae also for the case of Compton scattering occurring in the Klein Nishina regime, which is particularly relevant for TeV blazars. In particular we find that even in the latter regime a power law component can be present at the highest energies. Further restrictions in the parameter space are set assuming that the break energy results from a balance between cooling and escape and that the soft photon lags measured in some sources derive from radiative cooling of high energy particles. The constraints can be summarized as allowed regions in the Doppler factor – magnetic field parameter space and are in principle sufficient to univocally determine the model parameters and their uncertainties. We apply the method to three well studied sources Mkr 421, PKS 2155–304 and Mkr 501. For Mrk 421 the available data are sufficient to fully constrain the model. The additional restrictions are found to be consistent with the model parameters, supporting the proposed interpretation. In the case of PKS 2155–304, not yet detected in the TeV band, we estimate the peak frequency of the Compton component (≃ 40 GeV) and the expected TeV flux. The derived physical parameters are similar for the two sources, with a relatively large value of the Doppler factor (δ ∼ 25) and a magnetic field of B ≃ 0.2 G. For Mrk 501 we consider both the historical low state and the flaring state observed in April 1997. In the first case consistency between the various assumptions is reached for δ ≃ 10 and B ≃ 0.3 G. For the high state a similar value of the Doppler factor and a somewhat larger value of the magnetic field are indicated, while the