Cosmological simulations with scale-free initial conditions. I. Adiabatic hydrodynamics

We analyze hierarchical structure formation based on scale-free initial con ditions in an Einstein-de Sitter universe, including a baryonic component w ith Omega(bary) = 0.05. We present three independent, smoothed particle hyd rodynamics (SPH) simulations, performed at two resolutions (32(3) and 64(3) dark matter and baryonic particles) and with two different SPH codes (Tree SPH and P3MSPH). Each simulation is based on identical initial conditions, which consist of Gaussian-distributed initial density fluctuations that hav e a power spectrum P(k) proportional to k(-1). The baryonic material is mod eled as an ideal gas subject only to shock heating and adiabatic heating an d cooling; radiative cooling and photoionization heating are not included. The evolution is expected to be self-similar in time, and under certain res trictions we identify the expected scalings for many properties of the dist ribution of collapsed objects in all three realizations. The distributions of dark matter masses, baryon masses, and mass- and emission-weighted tempe ratures scale quite reliably. However, the density estimates in the central regions of these structures are determined by the degree of numerical reso lution. As a result, mean gas densities and Bremsstrahlung luminosities obe y the expected scalings only when calculated within a limited dynamic range in density contrast. The temperatures and luminosities of the groups show tight correlations with the baryon masses, which we find can be well repres ented by power laws. The Press-Schechter (PS) approximation predicts the di stribution of group dark matter and baryon masses fairly well, though it te nds to overestimate the baryon masses. Combining the PS mass distribution w ith the measured relations for T(M) and L(M) predicts the temperature and l uminosity distributions fairly accurately, though there are some discrepanc ies at high temperatures/luminosities. In general the three simulations agr ee well for the properties of resolved groups, where a group is considered resolved if it contains more than 32 particles.