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) Dataset, one of the largest sample 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 SPH together with relevant physical processes (cooling, UV photoionization, star formation and different feedback processes). We focus on the analysis of the baryon content (gas and star) of clusters in the MUSIC dataset both as a function of aperture radius and redshift. The results from our simulations are compared with the most recent observational estimates of the gas fraction in galaxy clusters at different overdensity radii. 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. The impact of the aperture radius choice, when comparing integrated quantities at different redshifts, is tested: the standard definition of radius at a fixed overdensity with respect to critical density is compared with a definition based on the redshift dependent overdensity with respect to background density. We also present a detailed analysis of the scaling relations of the thermal SZ (Sunyaev Zel'dovich) 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, more suitable for observational applications. Both laws are consistent with predictions from the self-similar model, showing a very low scatter. The effects of the gas fraction on the Y-M scaling and the presence of a possible redshift dependence on the Y-M scaling relation are also explored.