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 ρ 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 α^5.0_2.7 > 0.4VV_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 ~30 in ρ between a peak redshift α^5.0_2.7 < 0.5_z~2.5 and y = log₁₀S_νΣ²_i=0 a_ixⁱ, z~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-ρ (no cut-off) models and models with cut-offs as abrupt as those envisaged by Shaver et al. are outside the 90per cent confidence region. The inference that the decline in ρ is most likely to be gradual, by a factor ~4 between α^5.0_2.7 ≈= 0.26_z~2.5 and α^5.0_2.7 ≈= 0.4_z~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.