Using the Bright Ultrahard XMM-Newton survey to define an IR selection of luminous AGN based on WISE colours

We present a highly complete and reliable mid-infrared (MIR) colour selection of luminous active galactic nucleus (AGN) candidates using the 3.4, 4.6 and 12 mu m bands of the Wide-field Infrared Survey Explorer (WISE) survey. The MIR colour wedge was defined using the wide-angle Bright Ultrahard XMMNewton survey (BUXS), one of the largest complete flux-limited samples of bright (f4.5--10 keV >6x10-14 erg s-1 cm -2) ultrahard (4.510? keV) X-ray-selected AGN to date. The BUXS includes 258 objects detected over a total sky area of 44.43?deg2 of which 251 are spectroscopically identified and classified, with 145 being type 1 AGN and 106 type 2 AGN. Our technique is designed to select objects with red MIR power-law spectral energy distributions (SEDs) in the three shortest bands of WISE and properly accounts for the errors in the photometry and deviations of the MIR SEDs from a pure power-law. The completeness of the MIR selection is a strong function of luminosity. At L210?keV >1044 ? erg?s-1, where the AGN is expected to dominate the MIR emission, 97.1-4.8+2.2 and 76.5-18.4+13.3 per cent of the BUXS type 1 and type 2 AGN, respectively, meet the selection. Our technique shows one of the highest reliability and efficiency of detection of the X-ray-selected luminous AGN population with WISE amongst those in the literature. In the area covered by BUXS our selection identifies 2755 AGN candidates detected with signal-to-noise ratio =5 in the three shorter wavelength bands of WISE with 38.5 per cent having a detection at 210?keV X-ray energies. We also analysed the possibility of including the 22? mu m WISE band to select AGN candidates, but neither the completeness nor the reliability of the selection improves. This is likely due to both the significantly shallower depth at 22 mu m compared with the first three bands of WISE and star formation contributing to the 22 mu m emission at the WISE 22 mu m sensitivity.