A complete sample of Seyfert galaxies selected at 0.25 keV

We have used the ROSAT Bright Source Catalogue to extract a complete sample of sources selected in the band from 0.1-0.4 keV. This 0.25 keV-selected s ample is composed of 54 Seyfert galaxies, 25 BL Lacertae objects, 4 cluster s and 27 Galactic stars or binaries. Seyfert-type galaxies with 'ultrasoft' X-ray spectra can very often be classed optically as narrow-line Seyfert 1 s (NLS1s). Such objects are readily detected in 0.25 keV surveys; the sampl e reported here contains 20 NLS1s, corresponding to a 40 per cent fraction of the Seyferts. Optical spectra of the Seyfert galaxies were gathered for correlative analysis, which confirmed the well-known relations between X-ra y slope and optical spectral properties (e.g. [0 III]/H/beta ratio; Fe II s trength, H beta width). The various intercorrelations are most likely drive n, fundamentally, by the shape of the photoionizing continuum in Seyfert nu clei. We argue that a steep X-ray spectrum is a better indicator of an 'ext reme' set of physical properties in Seyfert galaxies than is the narrowness of the optical H beta line. The correlation studies were also used to isolate a number of Seyfert galax ies with apparently 'anomalous' properties. Of particular interest are the six objects with relatively weak permitted line emission (H beta and Fe II) and weak optical continua. Such objects are rare in most surveys, but two of these (IC 3599 and NGC 5905) are known to be transient active galactic n uclei in which the X-ray flux has faded by factors similar to 100. If the o ther four objects also turn out to be transient, this would demonstrate tha t 0.25 keV surveys provide an efficient way of finding an interesting class of object. Finally, the luminosity function of the 0.25 keV-selected Seyfert galaxies was determined and broken down into subsamples to investigate the relative space densities of Seyferts when separated on the basis of either X-ray slo pe or H beta linewidth.