Cosmic shear and halo abundances: Analytical versus numerical results

TL;DR

This study compares analytical predictions and numerical simulations of the aperture mass in weak lensing, finding good agreement for some metrics and highlighting limitations in quasi-linear predictions, thereby aiding cosmological model testing.

Contribution

It evaluates the accuracy of analytical models for aperture mass against large N-body simulations, confirming their reliability for certain measures and identifying their limitations.

Findings

Analytical predictions for dispersion and halo abundance match simulations well.

Predictions for skewness are less accurate due to quasi-linear approximation.

The aperture mass distribution decreases exponentially for large values.

Abstract

The aperture mass has been shown in a series of recent publications to be a useful quantitative tool for weak lensing studies, ranging from cosmic shear to the detection of a mass-selected sample of dark matter haloes. Quantitative analytical predictions for the aperture mass have been based on a number of simplifying assumptions. In this paper, we test the reliability of these assumptions and the quality of the analytic approximations, using ray-tracing simulations through a cosmological density field generated by very large N-body simulations. We find that those analytic predictions which take into account the non-linear evolution of the matter distribution, such as the dispersion of the aperture mass and the halo abundance, are surprisingly accurately reproduced with our numerical results, whereas the predictions for the skewness, based on quasi-linear theory, are rather imprecise. In particular, we verify numerically that the probability distribution of the aperture mass decreases exponentially for values much larger than the rms. Given the good overall agreement, comparisons between the observed distribution of the aperture mass and the theoretical values provide a powerful tool for testing cosmological models.