Luminosity enhancement in relativistic jets and altered luminosity functions for beamed objects

Due to relativistic effects, the observed emission from relativistic jets is quite different from the rest frame emission. We discuss systematic differences between the observed and intrinsic intensities of sources in which jet phenomena are occurring. Assuming that jets have a power-law luminosity function of slope ..beta.., we calculate the observed luminosity distribution as a function of the velocity of the jet, the spectral index of the rest frame emission, and the range of angles of the jets relative to our line of sight. The result is well approximated by two power laws, the higher luminosity end having the original power law index ..beta.. and the lower luminosity end having a flattened exponent independent of ..beta.. and only slightly greater than 1. We then investigate a model consisting of beamed emission from a jet and unbeamed emission from a stationary central component. The luminosity functions for these two-component sources are calculated for two ranges of angles. For sources in which beaming is important, the luminosity function is much flatter. Because of this, the relative numbers of ''beamed'' and ''unbeamed'' sources detected on the sky depend strongly on the luminosity at which the comparison is made.