Hierarchical numerical cosmology with hydrodynamics: Resolving X-ray clusters

A two-level nested grid code is applied to resolve X-ray clusters in a standard critically closed cold dark matter-dominated universe. The physical dimension of the larger periodically identified box is set to 50 Mpc as a compromise to providing both adequate sampling of long-wavelength perturbations and sufficient small-scale resolution. A refined grid with smaller cell dimensions is constructed within the larger cube to resolve a single rich cluster (arising from a 3 sigma peak fluctuation) in greater detail as the larger scale structure evolves on the parent grid. We performed a sequence of runs at consistently higher resolution to test for the convergence of various physical attributes, including the core radius, distribution profiles, mass fractions, X-ray luminosity, Sunyaev-Zel'dovich decrement, and beta-model parameters. We find no evidence of convergence in the inner core regions even at the most refined subgrid resolution of 100 kpc, effectively a 512(3) grid covering the cluster. However, false convergence is seen in several runs which fail to adequately resolve the collapse of fluctuations at high redshifts-a result which may explain the discrepancy between our finding and the results of Navarro, Frenk, & White (1995). Averaged radial profiles of the gas and dark matter densities and the gas temperature are consistent with Bertschinger's (1985) self-similar solution at small radii down to the force softening length. We also investigate the reliability of reconstructing the numerical data based solely on the ''observed'' X-ray luminosities and the isothermal and hydrostatic equilibrium assumptions made in the standard beta-models. This work is carried out in a developing framework to explore the advantages and limitations of nested grid methods as applied to cosmological simulations.