The relation between radio luminosity and spectrum for extended extragalactic radio sources

We have investigated the relation between radio spectrum and radio luminosity for samples of extragalactic radio sources selected at 178 and 2700 MHz. Spectra were derived for the extended regions of emission in these sources, which we have also classified by morphological type. At low frequencies the degree of spectral curvature is found to be correlated with luminosity for sources with hot-spots. The spectra of powerful sources show downward curvature which is greatest for the most luminous objects, whereas weak sources have spectra which steepen at low frequencies. At high frequencies, the correlation between spectral index and luminosity is confirmed and is shown to extend throughout the luminosity range considered. This relation is due mainly to sources with hot-spots and implies an even stronger relation for the hot-spots themselves.