Constraining the Noise-Free Distribution of Halo Spin Parameters
  Any measurement made using an N-body simulation is subject to noise due to
the finite number of particles used to sample the dark matter distribution
function, and the lack of structure below the simulation resolution. This noise
can be particularly significant when attempting to measure intrinsically small
quantities, such as halo spin. In this work we develop a model to describe the
effects of particle noise on halo spin parameters. This model is calibrated
using N-body simulations in which the particle noise can be treated as a
Poisson process on the underlying dark matter distribution function, and we
demonstrate that this calibrated model reproduces measurements of halo spin
parameter error distributions previously measured in N-body convergence
studies. Utilizing this model, along with previous measurements of the
distribution of halo spin parameters in N-body simulations, we place
constraints on the noise-free distribution of halo spins. We find that the
noise-free median spin is 3% lower than that measured directly from the N-body
simulation, corresponding to a shift of approximately 40 times the statistical
uncertainty in this measurement arising purely from halo counting statistics.
We also show that measurement of the spin of an individual halo to 10%
precision requires at least $4\times 10^4$ particles in the halo - for halos
containing 200 particles the fractional error on spins measured for individual
halos is of order unity.
