Discreteness effects in simulations of Hot/Warm dark matter

In Hot or Warm Dark Matter universes the density fluctuations at early times contain very little power below a characteristic wavelength related inversely to the particle mass. We study how discreteness noise influences the growth of nonlinear structures smaller than this coherence scale in N-body simulations of cosmic structure formation. It has been known for 20 years that HDM simulations in which the initial uniform particle load is a cubic lattice exhibit artifacts related to this lattice. In particular, the filaments which form in such simulations break up into regularly spaced clumps which reflect the initial grid pattern. We demonstrate that a similar artifact is present even when the initial uniform particle load is not a lattice, but rather a glass with no preferred directions and no long-range coherence. Such regular fragmentation also occurs in simulations of the collapse of idealised, uniform filaments, although not in simulations of the collapse of infinite uniform sheets. In HDM or WDM simulations all self-bound nonlinear structures with masses much smaller than the free streaming mass appear to originate through spurious fragmentation of filaments. These artificial fragments form below a characteristic mass which scales as $m_p^{1/3}k_{peak}^{-2}$, where $m_p$ is the $N$-body particle mass and $k_{peak}$ is the wavenumber at the maximum of $k^3 P(k)$ ($P(k)$ is the power spectrum). This has the unfortunate consequence that the effective mass resolution of such simulations improves only as the cube root of the number of particles employed.