The MUSIC of galaxy clusters - I. Baryon properties and scaling relations of the thermal Sunyaev-Zel'dovich effect

We introduce the Marenostrum-MultiDark SImulations of galaxy Clusters (MUSIC) data set. It constitutes one of the largest samples of hydrodynamically simulated galaxy clusters with more than 500 clusters and 2000 groups. The objects have been selected from two large N-body simulations and have been resimulated at high resolution using smoothed particle hydrodynamics (SPH) together with relevant physical processes that include cooling, UV photoionization, star formation and different feedback processes associated with supernovae explosions. In this first paper we focus on the analysis of the baryon content (gas and star) of clusters in the MUSIC data set as a function of both aperture radius and redshift. The results from our simulations are compared with a compilation of the most recent observational estimates of the gas fraction in galaxy clusters at different overdensity radii. We confirm, as in previous simulations, that the gas fraction is overestimated if radiative physics are not properly taken into account. On the other hand, when the effects of cooling and stellar feedbacks are included, the MUSIC clusters show a good agreement with the most recent observed gas fractions quoted in the literature. A clear dependence of the gas fractions with the total cluster mass is also evident. However, we do not find a significant evolution with redshift of the gas fractions at aperture radius corresponding to overdensities smaller than 1500 with respect to critical density. At smaller radii, the gas fraction does exhibit a decrease with redshift that is related to the gas depletion due to star formation in the central region of the clusters. The impact of the aperture radius choice, when comparing integrated quantities at different redshifts, is tested. The standard, widely used definition of radius at a fixed overdensity with respect to critical density is compared with a definition of aperture radius based on the redshift dependent overdensity with respect to background matter density: we show that the latter definition is more successful in probing the same fraction of the virial radius at different redshifts, providing a more reliable derivation of the time evolution of integrated quantities. We also present in this paper a detailed analysis of the scaling relations of the thermal Sunyaev-Zel'dovich (SZ) effect derived from MUSIC clusters. The integrated SZ brightness, Y, is related to the cluster total mass, M, as well as, the M - Y counterpart which is more suitable for observational applications. Both laws are consistent with predictions from the self-similar model, showing a very low scatter which is σlog Y ≃ 0.04 and even a smaller one (σlog M ≃ 0.03) for the inverse M-Y relation. The effects of the gas fraction on the Y-M scaling relation are also studied. At high overdensities, the dispersion of the gas fractions introduces non-negligible deviation from self-similarity, which is directly related to the fgas-M relation. The presence of a possible redshift dependence on the Y-M scaling relation is also explored. No significant evolution of the SZ relations is found at lower overdensities, regardless of the definition of overdensity used.