We examine the validity of the hydrostatic equilibrium (HSE) assumption for galaxy clusters using one of the highest-resolution cosmological hydrodynamical simulations. We define and evaluate several effective mass terms corresponding to the Euler equations of the gas dynamics, and quantify the degree of the validity of HSE in terms of the mass estimate. We find that the mass estimated under the HSE assumption (the HSE mass) deviates from the true mass by up to ∼ 30 %. This level of departure from HSE is consistent with the previous claims, but our physical interpretation is rather different. We demonstrate that the inertial term in the Euler equations makes a negligible contribution to the total mass, and the overall gravity of the cluster is balanced by the thermal gas pressure gradient and the gas acceleration term. Indeed the deviation from the HSE mass is well explained by the acceleration term at almost all radii. We also clarify the confusion of previous work due to the inappropriate application of the Jeans equations in considering the validity of HSE from the gas dynamics extracted from cosmological hydrodynamical simulations.

We revisit the non-sphericity of cluster-mass scale halos from cosmological N-body simulation on the basis of triaxial modelling. In order to understand the difference between the simulation results and the conventional ellipsoidal collapse model (EC), we first consider the evolution of individual simulated halos. The major difference between EC and the simulation becomes appreciable after the turn-around epoch. Moreover, it is sensitive to the individual evolution history of each halo. Despite such strong dependence on individual halos, the resulting nonsphericity of halos exhibits weak but robust mass dependence in a statistical fashion; massive halos are more spherical up to the turn-around, but gradually become less spherical by z = 0. This is clearly inconsistent with the EC prediction; massive halos are usually more spherical. In 1 addition, at z = 0, inner regions of the simulated halos are less spherical than outer regions, i.e., the density distribution inside the halos is highly inhomogeneous and therefore not self-similar (concentric ellipsoids with the same axis ratio and orientation). This is also inconsistent with the homogeneous density distribution that is commonly assumed in EC. Since most of previous fitting formulae for the probability distribution function (PDF) of axis ratio of triaxial ellipsoids have been constructed under the self-similarity assumption, they are not accurate. Indeed, we compute the PDF of projected axis ratio a 1 /a 2 directly from the simulation data without the self-similarity assumption, and find that it is very sensitive to the assumption. The latter needs to be carefully taken into account in direct comparison with observations, and therefore we provide an empirical fitting formula for the PDF of a 1 /a 2 . Our preliminary analysis suggests that the derived PDF of a 1 /a 2 roughly agrees with the current weak-lensing observations. More importantly, the present results will be useful in future exploration of the non-sphericity of clusters in X-ray and optical observations.

We characterize the non-sphericity of galaxy clusters by the projected axis ratio of spatial distribution of star, dark matter, and X-ray surface brightness (XSB). We select 40 simulated groups and clusters of galaxies with mass larger than 5 × 10 13 M ⊙ from the Horizon simulation that fully incorporates the relevant baryon physics, in particular, the AGN feedback. We find that the baryonic physics around the central region of galaxy clusters significantly affects the non-sphericity of dark matter distribution even beyond the central region, approximately up to the half of the virial radius. Therefore it is very difficult to predict the the probability density 1 function (PDF) of the projected axis ratio of XSB from dark-matter only N-body simulations as attempted in previous studies. Indeed we find that the PDF derived from our simulated clusters exhibits much better agreement with that from the observed X-ray clusters. This indicates that our present methodology to estimate the non-sphericity directly from the Horizon simulation is useful and promising. Further improvements in both numerical modeling and observational data will establish the non-sphericity of clusters as a cosmological test complementary to more conventional statistics based on spherically averaged quantities.

The top-hat spherical collapse model (TSC) is one of the most fundamental analytical frameworks to describe the non-linear growth of cosmic structure. TSC has motivated, and been widely applied in, various researches even in the current era of precision cosmology. While numerous studies exist to examine its validity against numerical simulations in a statistical fashion, there are few analyses to compare the TSC dynamics in an individual object-wise basis, which is what we attempt in the present paper. We extract 100 halos at z = 0 from a cosmological N-body simulation according to the conventional TSC criterion for the spherical over-density. Then we trace back their spherical counter-parts at earlier epochs. Just prior to the turn-around epoch of the halos, their dynamics is well approximated by TSC, but their turn-around epochs are systematically delayed and the virial radii are larger by ∼ 20% on average relative to the TSC predictions. We find that this systematic deviation is mainly ascribed to the non-uniformity/inhomogeneity of dark matter density profiles and the non-zero velocity dispersions, both of which are neglected in TSC. In particular, the inside-outcollapse and shell-crossing of dark matter halos play an important role in generating the significant velocity dispersion. The implications of the present result are briefly discussed.