(Abridged) We examine the X-ray luminosity scaling relations of 31 nearby galaxy clusters from the Representative XMM-Newton Cluster Structure Survey (REXCESS). The objects are selected in X-ray luminosity only, optimally sampling the cluster luminosity function; temperatures range from 2 to 9 keV and there is no bias toward any particular morphological type. Pertinent values are extracted in an aperture corresponding to R_500, estimated using the tight correlation between Y_X and total mass. The data exhibit power law relations between bolometric X-ray luminosity and temperature, Y_X and total mass, all with slopes that are significantly steeper than self-similar expectations. We examine the causes for the steepening, finding that the primary driver appears to be a systematic variation of the gas content with mass. Scatter about the relations is dominated in all cases by the presence of cool cores. The natural logarithmic scatter about the raw X-ray luminosity-temperature relation is about 70%, and about the X-ray luminosity-Y_X relation it is 40%. Cool core and morphologically disturbed systems occupy distinct regions in the residual space with respect to the best fitting mean relation, the former lying systematically to the high luminosity side, the latter to the low luminosity side. Exclusion of the central regions serves to reduce the scatter by more than 50%. Using Y_X as a mass proxy, we derive a Malmquist bias corrected luminosity-mass relation and compare with previous determinations. Our results indicate that luminosity can be a reliable mass proxy with controllable scatter, which has important implications for upcoming all-sky cluster surveys, such as those to be undertaken with Planck and eROSITA, and ultimately for the use of clusters for cosmological purposes.
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