# Constraining the Noise-Free Distribution of Halo Spin Parameters

## TL;DR

This paper develops a model to quantify and correct for particle noise in N-body simulations, enabling more accurate estimation of the true distribution of halo spin parameters.

## Contribution

It introduces a calibrated noise model for halo spin measurements that improves the accuracy of inferred noise-free spin distributions in cosmological simulations.

## Key findings

- The noise-free median halo spin is 3% lower than the measured median.
- Measuring individual halo spin to 10% accuracy requires at least 40,000 particles.
- For halos with 200 particles, the spin measurement error is about 100%.

## Abstract

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.