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A B S T R A C TWe present results of an extensive study of the X-ray spectral properties of sources detected in the RIXOS survey, which is a large, nearly complete sample of objects detected serendipitously in ROSAT PSPC fields down to a flux limit of 3 Â 10 214 erg cm 22 s 21 (0.5± 2 keV). We show that for X-ray surveys containing sources with low count rate, such as RIXOS, spectral slopes estimated using simple hardness ratios in the ROSAT band can be biased. Instead, we analyse three-colour X-ray data using statistical techniques appropriate to the Poisson regime which remove the effects of this bias. We also show that the use of three-colour data enables some discrimination between thermal and non-thermal spectra. We have then applied this technique to the RIXOS survey to study the spectral properties of the sample.For the AGN we find an average energy index of 1X05^0X05Y with no evidence for spectral evolution with redshift. Individual AGN are shown to have a range of properties, including soft X-ray excesses and intrinsic absorption. Narrow-emission-line galaxies (NELGs) also seem to fit to a power-law spectrum, which may indicate a non-thermal origin for their X-ray emission. We infer that most of the clusters in the sample have a bremsstrahlung temperature .3 keVY although some show evidence for a cooling flow. The stars deviate strongly from a power-law model but fit to a thermal model. Finally, we have analysed the whole RIXOS sample (extending the flux cut-off to the sensitivity threshold of each individual observation) containing 1762 sources to study the relationship between spectral slope and flux. We find that the mean spectral slope of the sources hardens at lower fluxes, in agreement with results from other samples. However, a study of the individual sources demonstrates that the majority have relatively soft spectra even at faint flux levels, and the hardening of the mean is caused by the appearance of a population of very hard sources at the lowest fluxes. This has implications for the nature of the soft X-ray background.

A sample of 47 faint Gigahertz Peaked Spectrum (GPS) radio sources selected from the Westerbork Northern Sky Survey (WENSS) has been imaged in the optical and near‐infrared, resulting in an identification fraction of 87 per cent. The R − IR − K colours of the faint optical counterparts are as expected for passively evolving elliptical galaxies, assuming that they follow the R‐band Hubble diagram as determined for radio‐bright GPS galaxies. We find evidence that the radio spectral properties of the GPS quasars are different from those of GPS galaxies. The observed distribution of radio spectral peak frequencies for GPS sources optically identified with bright stellar objects (presumably quasars) is shifted compared with GPS sources identified with faint or extended optical objects (presumably galaxies), in the sense that a GPS quasar is likely to have a higher peak frequency than a GPS galaxy. This means that the true peak frequency distribution is different for the GPS galaxies and quasars, because the sample selection effects are independent of optical identification. The correlation between peak frequency and redshift that has been suggested for bright sources has not been found in this sample; no correlation exists between R magnitude (and therefore redshift) and peak frequency for the GPS galaxies. We therefore believe that the claimed correlation is actually caused by the dependence of the peak frequency on optical host, because the GPS galaxies are generally at lower redshifts than the quasars. The difference in the peak frequency distributions of the GPS galaxies and quasars is further evidence against the hypothesis that they form a single class of object.