The importance of the cosmic web and halo substructure for power spectra
  In this work we study the relevance of the cosmic web and substructures on
the matter and lensing power spectra measured from halo mock catalogues
extracted from the N-body simulations. Since N-body simulations are
computationally expensive, it is common to use faster methods that approximate
the dark matter field as a set of halos. In this approximation, we replace mass
concentrations in N-body simulations by a spherically symmetric
Navarro-Frenk-White halo density profile. We also consider the full mass field
as the sum of two distinct fields: dark matter halos ($M>9\times
10^{12}~M_{\odot}$/h) and particles not included into halos. Mock halos
reproduce well the matter power spectrum, but underestimate the lensing power
spectrum on large and small scales. For sources at $z_{\rm s}=1$ the lensing
power spectrum is underestimated by up to 40% at $\ell\approx 10^4$ with
respect to the simulated halos. The large scale effect can be alleviated by
combining the mock catalogue with the dark matter distribution outside the
halos. In addition, to evaluate the contribution of substructures we have
smeared out the intra-halo substructures in a N-body simulation while keeping
the halo density profiles unchanged. For the matter power spectrum the effect
of this smoothing is only of the order of 5%, but for lensing substructures are
much more important: for $\ell\approx 10^4$ the internal structures contribute
30% of the total spectrum. These findings have important implications in the
way mock catalogues have to be created, suggesting that some approximate
methods currently used for galaxy surveys will be inadequate for future weak
lensing surveys.
