We present results from a new set of 30 cosmological simulations of galaxy clusters, including the effects of radiative cooling, star formation, supernova feedback, black hole growth and AGN feedback. We first demonstrate that our AGN model is capabl
e of reproducing the observed cluster pressure profile at redshift, z~0, once the AGN heating temperature of the targeted particles is made to scale with the final virial temperature of the halo. This allows the ejected gas to reach larger radii in higher-mass clusters than would be possible had a fixed heating temperature been used. Such a model also successfully reduces the star formation rate in brightest cluster galaxies and broadly reproduces a number of other observational properties at low redshift, including baryon, gas and star fractions; entropy profiles outside the core; and the X-ray luminosity-mass relation. Our results are consistent with the notion that the excess entropy is generated via selective removal of the densest material through radiative cooling; supernova and AGN feedback largely serve as regulation mechanisms, moving heated gas out of galaxies and away from cluster cores. However, our simulations fail to address a number of serious issues; for example, they are incapable of reproducing the shape and diversity of the observed entropy profiles within the core region. We also show that the stellar and black hole masses are sensitive to numerical resolution, particularly the gravitational softening length; a smaller value leads to more efficient black hole growth at early times and a smaller central galaxy.
Recent results by the Planck collaboration have shown that cosmological parameters derived from the cosmic microwave background anisotropies and cluster number counts are in tension, with the latter preferring lower values of the matter density param
eter, $Omega_mathrm{m}$, and power spectrum amplitude, $sigma_8$. Motivated by this, we investigate the extent to which the tension may be ameliorated once the effect of baryonic depletion on the cluster mass function is taken into account. We use the large-volume Millennium Gas simulations in our study, including one where the gas is pre-heated at high redshift and one where the gas is heated by stars and active galactic nuclei (in the latter, the self-gravity of the baryons and radiative cooling are omitted). In both cases, the cluster baryon fractions are in reasonably good agreement with the data at low redshift, showing significant depletion of baryons with respect to the cosmic mean. As a result, it is found that the cluster abundance in these simulations is around 15 per cent lower than the commonly-adopted fit to dark matter simulations by Tinker et al (2008) for the mass range $10^{14}-10^{14.5}h^{-1} mathrm{M}_odot$. Ignoring this effect produces a significant artificial shift in cosmological parameters which can be expressed as $Delta[sigma_8(Omega_mathrm{m}/0.27)^{0.38}]simeq -0.03$ at $z=0.17$ (the median redshift of the $mathit{Planck}$ cluster sample) for the feedback model. While this shift is not sufficient to fully explain the $mathit{Planck}$ discrepancy, it is clear that such an effect cannot be ignored in future precision measurements of cosmological parameters with clusters. Finally, we outline a simple, model-independent procedure that attempts to correct for the effect of baryonic depletion and show that it works if the baryon-dark matter back-reaction is negligible.
We have exploited the large-volume Millennium Gas cosmological N-body hydrodynamics simulations to study the SZ cluster population at low and high redshift, for three models with varying gas physics. We confirm previous results using smaller samples
that the intrinsic (spherical) Y_{500}-M_{500} relation has very little scatter (sigma_{log_{10}Y}~0.04), is insensitive to cluster gas physics and evolves to redshift one in accord with self-similar expectations. Our pre-heating and feedback models predict scaling relations that are in excellent agreement with the recent analysis from combined Planck and XMM-Newton data by the Planck Collaboration. This agreement is largely preserved when r_{500} and M_{500} are derived using the hydrostatic mass proxy, Y_{X,500}, albeit with significantly reduced scatter (sigma_{log_{10}Y}~0.02), a result that is due to the tight correlation between Y_{500} and Y_{X,500}. Interestingly, this assumption also hides any bias in the relation due to dynamical activity. We also assess the importance of projection effects from large-scale structure along the line-of-sight, by extracting cluster Y_{500} values from fifty simulated 5x5 square degree sky maps. Once the (model-dependent) mean signal is subtracted from the maps we find that the integrated SZ signal is unbiased with respect to the underlying clusters, although the scatter in the (cylindrical) Y_{500}-M_{500} relation increases in the pre-heating case, where a significant amount of energy was injected into the intergalactic medium at high redshift. Finally, we study the hot gas pressure profiles to investigate the origin of the SZ signal and find that the largest contribution comes from radii close to r_{500} in all cases. The profiles themselves are well described by generalised Navarro, Frenk & White profiles but there is significant cluster-to-cluster scatter.
