2007A&A...476.1151T

In a self-absorbed synchrotron source with power-law electrons, rapid inverse Compton cooling sets in when the brightness temperature of the source reaches T_ B_∼10¹²K. However, brightness temperatures inferred from observations of intra-day variable sources (IDV) are well above the ``Compton catastrophe'' limit. This can be understood if the underlying electron distribution cuts off at low energy. We examine the compatibility of the synchrotron and inverse Compton emission of an electron distribution with low-energy cut-off with that of IDV sources, using the observed spectral energy distribution of S5 0716+714 as an example. We compute the synchrotron self-Compton (SSC) spectrum of monoenergetic electrons and compare it to the observed spectral energy distribution (SED) of S5 0716+714. The hard radio spectrum is well-fitted by this model, and the optical data can be accommodated by a power-law extension to the electron spectrum. We therefore examine the scenario of an injection of electrons, which is a double power law in energy, with a hard low-energy component that does not contribute to the synchrotron opacity. We show that the double power-law injection model is in good agreement with the observed SED of S5 0716+714. For intrinsic variability, we find that a Doppler factor of D≥30 can explain the observed SED provided that low-frequency (<32GHz) emission originates from a larger region than the higher-frequency emission. To fit the entire spectrum, D≥65 is needed. We find the constraint imposed by induced Compton scattering at high T_ B_ is insignificant in our model. We confirm that electron distribution with a low-energy cut-off can explain the high brightness temperature in compact radio sources. We show that synchrotron spectrum from such distributions naturally accounts for the observed hard radio continuum with a softer optical component, without the need for an inhomogeneous source. The required low energy electron distribution is compatible with a relativistic Maxwellian.