The joint likelihood of observable cluster signals reflects the astrophysical evolution of the coupled baryonic and dark matter components in massive halos, and its knowledge will enhance cosmological parameter constraints in the coming era of large, multi-wavelength cluster surveys. We present a computational study of intrinsic covariance in cluster properties using halo populations derived from Millennium Gas Simulations (MGS). The MGS are re-simulations of the original 500 h −1 Mpc Millennium Simulation performed with gas dynamics under two different physical treatments: shock heating driven by gravity only (GO) and a second treatment with cooling and preheating (PH). We examine relationships among structural properties and observable X-ray and Sunyaev-Zel'dovich (SZ) signals for samples of thousands of halos with M 200 ≥ 5 × 10 13 h −1 M ⊙ and z < 2. While the X-ray scaling behavior of PH model halos at low-redshift offers a good match to local clusters, the model exhibits non-standard features testable with larger surveys, including weakly running slopes in hot gas observable-mass relations and ∼ 10% departures from self-similar redshift evolution for 10 14 h −1 M ⊙ halos at redshift z ∼ 1. We find that the form of the joint likelihood of signal pairs is generally well-described by a multivariate, log-normal distribution, especially in the PH case which exhibits less halo substructure than the GO model. At fixed mass and epoch, joint deviations of signal pairs display mainly positive correlations, especially the thermal SZ effect paired with either hot gas fraction (r = 0.88/0.69 for PH/GO at z = 0) or X-ray temperature (r = 0.62/0.83). The levels of variance in X-ray luminosity, temperature and gas mass fraction are sensitive to the physical treatment, but offsetting shifts in the latter two measures maintain a fixed 12% scatter in the integrated SZ signal under both gas treatments. We discuss halo mass selection by signal pairs, and find a minimum mass scatter of 4% in the PH model by combining thermal SZ and gas fraction measurements.

The physical processes that define the spine of the galaxy cluster X‐ray luminosity–temperature (L–T) relation are investigated using a large hydrodynamical simulation of the universe. This simulation models the same volume and phases as the millennium simulation and has a linear extent of 500 h−1 Mpc. We demonstrate that mergers typically boost a cluster along but also slightly below the L–T relation. Due to this boost, we expect that all of the very brightest clusters will be near the peak of a merger. Objects from near the top of the L–T relation tend to have assembled much of their mass earlier than an average halo of similar final mass. Conversely, objects from the bottom of the relation are often experiencing an ongoing or recent merger.

We follow the growth of baryonic structure in the presence of a magnetic field within an approximate cosmological magnetohydrodynamic simulation, produced by adding an (isotropic) magnetic pressure related to the local gas pressure. We perform an ensemble of these simulations to follow the amplification of the field with time. By using a variety of initial field strengths and changing the slope of the power law that governs the way the field grows with increasing density, we span the range of current observations and demonstrate the size of the effect realistic magnetic fields could have on the central density of groups and clusters. A strong magnetic field significantly reduces the central gas density which, in turn, reduces observable quantities such as the X‐ray luminosity.

The comparison between observations of galaxy clusters thermo-dynamical properties and theoretical predictions suggests that non-gravitational heating needs to be added into the models. We implement an internally self-consistent heating scheme into GADGET-2 for the third (and fourth) run of the Millennium gas project (Pearce et al. in preparation), a set of four hydrodynamical cosmological simulations with N=2(5x10^8) particles and with the same volume (L=500 h-1 Mpc) and structures as the the N-body Millennium Simulation (Springel et al. 2005). Our aim is to reproduce the observed thermo-dynamical properties of galaxy clusters.Comment: 3 pages, 2 figures, To appear in the Proceedings of "Heating vs. Cooling in Galaxies and Clusters of Galaxies", August 2006, Garching (Germany

We follow the passive evolution of magnetic fields in SPH simulations to study their role in structure formation and galaxy clusters properties. Despite magnetic fields are not dynamically important for massive objects, they can still affect the properties of group-size objects and core regions and also affect particle's entropy.