Quantifying and controlling biases in dark matter halo concentration
  estimates
  We use bootstrapping to estimate the bias of concentration estimates on
N-body dark matter halos as a function of particle number. We find that
algorithms based on the maximum radial velocity and radial particle binning
tend to overestimate the concentration by 15%-20% for halos sampled with 200
particles and by 7% - 10% for halos sampled with 500 particles. To control this
bias at low particle numbers we propose a new algorithm that estimates halo
concentrations based on the integrated mass profile. The method uses the full
particle information without any binning, making it reliable in cases when low
numerical resolution becomes a limitation for other methods. This method
reduces the bias to less than 3% for halos sampled with 200-500 particles. The
velocity and density methods have to use halos with at least 4000 particles in
order to keep the biases down to the same low level. We also show that the
mass-concentration relationship could be shallower than expected once the
biases of the different concentration measurements are taken into account.
These results show that bootstrapping and the concentration estimates based on
the integrated mass profile are valuable tools to probe the internal structure
of dark matter halos in numerical simulations.
