The effect of Poisson noise on SPH calculations

A simple algorithm is presented which generates a lattice-like, regular spacing of smoothed particle hydrodynamics (SPH) particles in discs, with any prescribed density gradient. Using this for comparison we demonstrate the effect of Poisson noise on SPH estimates of density, pressure and viscous forces when calculated using randomly distributed particles. The standard deviation of density and pressure is typically increased by greater than an order of magnitude. In a disc with a Keplerian velocity profile, the effectiveness of the Balsara switch in reducing the shear component of SPH artificial viscosity is greatly enhanced when the particles are properly spaced, reducing the magnitude of viscosity by two orders of magnitude. Noise problems are exacerbated, not removed, by increasing the numbers of SPH particles, if the number of neighbours used is kept constant. However, comparison of the evolution of a disc created using perfectly spaced particles and a disc with identical parameters but randomly placed particles, reveals very similar results. Although there are subtle differences in the evolution, and the smooth disc takes longer to begin developing structure, in both cases the identical number of objects is created by gravitational collapse. SPH disc simulations do not depend on initial density disturbances to evolve objects by gravitational collapse, which gives added credence to the validity of the results. It also appears that complicated disc settling procedures are unnecessary.