Two-body heating in numerical galaxy formation experiments

We show that discreteness effects related to classical two-body relaxationproduce spurious heating of the gaseous component in numerical simulations ofgalaxy formation. A simple analytic model demonstrates that this artificialheating will dominate radiative cooling in any simulation where the mass of anindividual dark matter particle exceeds a certain critical value. This maximummass depends only on the cooling function of the gas, on the fraction of thematerial in gaseous form, and (weakly) on typical temperatures in the gas. Itis comparable to, or smaller than, the dark matter particle masses employed inmost published simulations of cosmological hydrodynamics and galaxy formation.Any simulation which violates this constraint will be unable to follow coolingflows, although catastrophic cooling of gas may still occur in regions withvery short cooling times. We use a series of N--body/smoothed particlehydrodynamics simulations to explore this effect. In simulations which neglectradiative cooling, two--body heating causes a gradual expansion of the gascomponent. When radiative effects are included, we find that gas cooling isalmost completely suppressed for dark matter particle masses above our limit.Although our test simulations use smoothed particle hydrodynamics, similareffects, and a similar critical mass, are expected in any simulation where thedark matter is represented by discrete particles.