2-BODY HEATING IN NUMERICAL GALAXY FORMATION EXPERIMENTS

We show that discreteness effects related to classical two-body relaxa tion produce spurious heating of the gaseous component in numerical si mulations of galaxy formation. A simple analytic calculation demonstra tes that this artificial heating will dominate radiative cooling in an y simulation where the mass of an individual dark matter particle exce eds a certain critical value, This maximum mass depends only on the co oling function of the gas, on the fraction of the material in gaseous form, and (weakly) on typical temperatures in the gas. It is comparabl e to, or smaller than, the dark matter particle masses employed in mos t published simulations of cosmological hydrodynamics and galaxy forma tion. Any simulation that violates this constraint will be unable to f ollow cooling flows, although catastrophic cooling of gas may still oc cur in regions with very short cooling times. We use a series of N-bod y/smoothed particle hydrodynamics simulations to explore this effect. In simulations that neglect radiative cooling, two-body heating causes a gradual expansion of the gas component. When radiative effects are included, we find that gas cooling is almost completely suppressed for dark matter particle masses above our limit. Although our test simula tions use smoothed particle hydrodynamics, similar effects, and a simi lar critical mass, are expected in any simulation where the dark matte r is represented by discrete particles.