Steep radio spectra in high-redshift radio galaxies

The generic spectrum of an optically thin synchrotron source steepens by 0.5 in spectral index from low frequencies to high whenever the source lifetime is greater than the energy-loss timescale for at least some of the radiating electrons. Three effects tend to decrease the frequency nu(b) of this spectral bend as the source redshift increases: (1) for fixed bend frequency nu* in the rest frame, nu(b) = nu*/(1 + z); (2) losses due to inverse Compton scattering the microwave background rise with redshift as (1 + z) exp 4, so that, for fixed residence time in the radiating region, the energy of the lowest energy electron that can cool falls rapidly with increasing redshift; and (3) if the magnetic field is proportional to the equipartition field and the emitting volume is fixed or slowly varying, flux-limited samples induce a selection effect favoring low nu* at high z because higher redshift sources require higher emissivity to be included in the sample, and hence have stronger implied fields and more rapid synchrotron losses. A combination of these effects may explain the trend observed in the 3CR sample for higher redshift radio galaxies to have steeper spectra, and the successful use of ultrasteep spectrum surveys to locate high-redshift galaxies.