On the redshift cut-off for flat-spectrum radio sources

We use data from the Parkes Half-Jansky Flat-Spectrum (PHJFS) sample to constrain the cosmic evolution in the comoving space density rho of radio sources in the top decade of the flat-spectrum radio luminosity function (RLF). A consistent picture for the high-redshift evolution is achieved using both simple parametric models, which are the first to allow for distributions in both radio luminosity and spectral index, and variants of the V/V-max test, some of which incorporate the effects of radio spectral curvature. For the most luminous flat-spectrum objects, the PHJFS sample is extremely similar to that used by Shaver et al. to argue for an abrupt 'redshift cut-off': a decrease by a factor similar to 30 in rho between a peak redshift z similar to 2.5 and z similar to 5. Our analysis finds that the observable comoving volume is too small to make definitive statements about any redshift cut-off for the most luminous flat-spectrum sources, although both constant-rho (no cut-off) models and models with cut-offs as abrupt as those envisaged by Shaver et al. are outside the 90 per cent confidence region. The inference that the decline in rho is most likely to be gradual, by a factor similar to4 between z similar to 2.5 and z similar to 5, is in accordance with previous work on the RLF by Dunlop & Peacock, but different from the abrupt decline favoured by studies of optically selected quasars. Dust obscuration provides one explanation for this difference. We show that a significant fraction of the most radio-luminous flat-spectrum objects are Gigahertz Peaked Spectrum (GPS) rather than Doppler-Boosted (DB) sources, complicating any interpretation of the redshift cut-off. Studies based on objects extending into the next lower decade of the flat-spectrum RLF are likely to be more fruitful, but will require a separation of the GPS and DB populations, careful radio selection and analysis of K-corrections, and larger sky-area redshift surveys than those currently available.