On the dependence of the spectral parameters on the observational conditions in homogeneous time dependent models of the TeV blazars

Aims. Most of current models of TeV blazars emission assume a Synchrotron Self-Compton mechanism where relativistic particles emit both synchrotron radiation and Inverse Compton photons. For sake of simplicity, these models usually consider only steady state emission. The spectral features are thus only related to the shape of the particle distribution, and do not depend on the timing of observations. Methods. In this letter, we study the effect of, firstly, the lag between the beginning of the injection of the fresh particles and the trigger of the observation, and secondly, of a finite injection duration. We illustrate these effects considering an analytical time-dependent model of the synchrotron emission by a monoenergetic distribution of leptons. Results. We point out that the spectral shape can be in fact very dependent on observational conditions if the particle injection term is time-dependent, particularly taking into account the effect of the time averaging procedure on the final shape of the SED. Consequences on the acceleration process are also discussed.