The K-band Hubble diagram for brightest cluster galaxies in X-ray clusters

This paper concerns the K-band Hubble diagram for the brightest cluster galaxies (BCGs) in a sample of X-ray clusters covering the redshift range 0.05<z<0.8. We show that BCGs in clusters of high X-ray luminosity are excellent standard candles: the intrinsic dispersion in the raw K-band absolute magnitudes of BCGs in clusters with L_X>2.3x10^44 erg s^-1 (in the 0.3-3.5 keV band) is no more than 0.22 mag, and is not significantly reduced by correcting for the BCG structure parameter, alpha, or for X-ray luminosity. This is the smallest scatter in the absolute magnitudes of any single class of galaxy, and demonstrates the homogeneity of BCGs in high-L_X clusters. By contrast, we find that the brightest members of low-L_X systems display a wider dispersion (~0.5 mag) in absolute magnitude than commonly seen in previous studies, which arises from the inclusion, in X-ray flux-limited samples, of poor clusters and groups which are usually omitted from low-redshift studies of BCGs in optically rich clusters. Spectral synthesis models reveal the insensitivity of K-band light to galaxy evolution, and this insensitivity, coupled with the tightness of its Hubble relation, and the lack of evidence of significant growth by merging (shown by the absence of a correlation between BCG structure parameter, alpha, and redshift), makes our sample of BCGs in high-L_X clusters ideal for estimating the cosmological parameters Omega_M and Omega_L, free from many of the problems that have bedevilled previous attempts using BCGs. The BCGs in our high-L_X clusters yield a value of Omega_M=0.28+/-0.24 if the cosmological constant Lambda=0. For a flat Universe we find Omega_M=0.55^+0.14_-0.15 with a 95 per cent confidence upper limit to the cosmological constant corresponding to Omega_Lambda<0.73. These results are discussed in the context of other methods used to constrain the density of the Universe, such as Type Ia supernovae.