On Constraining the Smoothed Particle Hydrodynamics Kernel Radius in Galaxy Simulations

Abstract

In simulations of galaxy formation that use smoothed particle hydrodynamics (SPH) to model the gas component, a lower limit on the value of the kernel smoothing radius h is often imposed, usually equal to the gravitational softening length . In this paper we analyze a series of benchmark hydrodynamics problems and test galaxy formation simulations, aimed at quantifying the effects of imposing such a constraint on h. We have found that in some circumstances, such an approach can severely degrade the accuracy of solutions. In such cases, using large values of h results in an over-smoothed density field, i.e., a decrease in the calculated values of density ρ and density gradients ∇ρ, which unphysically decreases the ∇ρ/ρ part of pressure accelerations. In simulations of galaxy disks, constrained h may also result in unphysical angular momentum transfer, affecting the gross structure of the numerical galaxy. Such an effect occurs because particles in the central regions of the disk sample the velocity field in SPH summations over too large a range in velocities. We demonstrate here that when h is allowed to evolve freely to maintain a constant number of neighbors in SPH summations, such unwanted effects can be avoided and accuracy improved. At the same time, significant savings in computational cost can also be made by using the unconstrained h approach.