Radio spectra of extragalactic sources and the relativistic beaming model

We present a correlation between the spectral index, spectral curvature, and the degree of variability measured from multi-epoch radio spectra of 308 extragalactic radio sources taken from the 1-Jy catalogue. The analysis indicates that these three quantities are statistically interdependent and are characteristic for different classes of sources, such as galaxies, quasars, optically violent variable sources (OVVs), and BL Lac objects. Following this order we find an increase in spectral index, spectral curvature, and the degree of variability. The distributions of these quantities allows us to distinguish between galaxies and the remaining sources with a reliability of 75–80 per cent. The differences between quasars, OVVs and BL Lacs are less marked. The spectral properties are explained in the framework of a relativistic beaming model involving a non-variable, steep spectrum $$(\alpha\le-0.5, \enspace S \propto \nu^\alpha)$$ component and a core component with an inverted spectrum $$(\alpha\ge0.0)$$ exhibiting an intrinsic variability of about 30 per cent. At 5 GHz the flux density ratio between the core component, seen at an angle of $$\theta=90^\circ$$, to the steep-spectrum component is of the order of 0.03 or larger.