The Skewness of the Aperture Mass Statistic

Abstract

We present simple formulae for calculating the skewness and kurtosis of the aperture mass statistic for weak lensing surveys which is insensitive to masking effects of survey geometry or variable survey depth. The calculation is the higher order analog of the formula given by Schneider et al (2002) which has been used to compute the variance of the aperture mass from several lensing surveys. As our formula requires the three-point shear correlation function, we also present an efficient tree-based algorithm for measuring it. We show how our algorithm would scale in computing time and memory usage for future lensing surveys. Finally, we apply the procedure to our CTIO survey data, originally described in Jarvis et al (2003). We find that the skewness is positive (inconsistent with zero) at the 2 sigma level. However, the signal is too noisy from this data to usefully constrain cosmology.