Appendix A: debeaming and the broad band spectral slopes
In the case of a one-component model, and under the assumption that the local spectral indices are constant, we can derive the transformation law for the change of the spectral slope due to relativistic beaming. If the flux density in the frame comoving with the emitting region is , the observed one is
where is the beaming factor of the same object for different lines of sight (i.e. observed as BL Lac or as radio galaxy). Substituting these transformations in the definition of the broad-band spectral index (where 1 and 2 refer to radio, optical or X-ray flux), one obtains
which can be written as
where and are the local spectral indices.
© European Southern Observatory (ESO) 2000
Online publication: June 26, 2000