The LBDS Hercules sample of mJy radio sources at 1.4 GHz - II. Redshift distribution, radio luminosity function, and the high-redshift cut-off

A combination of spectroscopy and broad-band photometric redshifts is used to find the complete redshift distribution of the Hercules sample of millijansky radio sources. These data are used to examine the evolution of the radio luminosity function (RLF) and its high-redshift cut-off. We report the results of recent spectroscopic observations of the Hercules sample, drawn from the 1.4-GHz Leiden-Berkeley Deep Survey (LBDS) with a flux-density limit of 1 mJy. New redshifts have been measured for 11 sources, and a further 10 were detected in continuum emission from which upper limits to the redshift are given, derived from the absence of a Lyman-limit break in their spectra. The total number of sources with known redshifts in the sample is now 47 (65 per cent). We calculated broad-band photometric redshifts for the remaining one-third of the sample, using a two-component (old stellar population plus starburst) spectral synthesis model. We use the resulting redshift distribution of this complete sample to investigate the cosmological evolution of radio sources. For the luminosity range probed by the present study (P_1.4GHz > 10^24.5 W Hz^-1 sr^-1), we use the V/V_max test to show conclusively that there is a deficit of high-redshift (z > 2-2.5) objects. Comparison with the model RLFs of Dunlop & Peacock shows that our data can now exclude pure luminosity evolution as a viable description of the cosmological evolution of the RLF. However, two of the models of DP90 successfully predict the redshift-dependent evolution of the millijansky population and are approximately consistent with its observed luminosity dependence. These models, and the RLF deduced by direct binning of the data, both favour a luminosity dependence for the high-redshift cut-off, with lower luminosity sources (P_1.4GHZ ≃ 10²⁴ W Hz^-1 sr^-1) in decline by z ≃ 1-1.5, while higher luminosity sources (P_{1.4 GHz} ≃ 10_25-26 W Hz^-1 sr^-1) decline in comoving number density beyond z ≃ 2-2.5.