HIFLUGCS: Galaxy cluster scaling relations between X-ray luminosity, gas mass, cluster radius, and velocity dispersion

We present relations between X-ray luminosity and velocity dispersion (L - sigma), X-ray luminosity and gas mass (L - M-gas), and cluster radius and velocity dispersion (r(500) - sigma) for 62 galaxy clusters in the HIFLUGCS, an X-ray flux-limited sample minimizing bias toward any cluster morphology. Our analysis in total is based on similar to 1.3Ms of clean X-ray XMM-Newton data and 13439 cluster member galaxies with redshifts. Cool cores are among the major contributors to the scatter in the L - sigma relation. When the cool-core-corrected X-ray luminosity is used the intrinsic scatter decreases to 0.27 dex. Even after the X-ray luminosity is corrected for the cool core, the scatter caused by the presence of cool cores dominates for the low-mass systems. The scatter caused by the non-cool-core clusters does not strongly depend on the mass range, and becomes dominant in the high-mass regime. The observed L - sigma relation agrees with the self-similar prediction, matches that of a simulated sample with AGN feedback disregarding six clusters with <45 cluster members with spectroscopic redshifts, and shows a common trend of increasing scatter toward the low-mass end, i.e., systems with sigma <= 500 km s(-1). A comparison of observations with simulations indicates an AGN-feedback-driven impact in the low-mass regime. The best fits to the L - M-gas relations for the disturbed clusters and undisturbed clusters in the observational sample closely match those of the simulated samples with and without AGN feedback, respectively. This suggests that one main cause of the scatter is AGN activity providing feedback in different phases, e.g. during a feedback cycle. The slope and scatter in the observed r(500) - sigma relation is similar to that of the simulated sample with AGN feedback except for a small offset but still within the scatter.