The skewness of the aperture mass statistic

By Michael J. Jarvis, G. Bernstein, B. Jain. 2003

224 citations recorded by the source corpus.

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 calculations are the higher order analogues of the formula given by Schneider, van Waerbeke & Mellier, 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. We also apply the procedure to our Cerro Tololo Inter-American Observatory (CTIO) survey data, originally described by Jarvis et al. We find that the skewness is positive (inconsistent with zero) at the 2a level. However, the signal is too noisy from this data to usefully constrain cosmology.

Subfields: Astronomy and Astrophysics, Instrumentation

View Paper: https://www.semanticscholar.org/paper/862938013e801c2696ee80a2863ab27e744bf2bf

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

In Instrumentation

Citations in the corpus

The Intrinsic Alignment of Galaxies and its Impact on Weak Gravitational Lensing in an Era of Precision Cosmology (2014, methodology): “Explicitly taking into account photometric redshift uncertainties in the measurement of intrinsic alignment correlations, Joachimi et al. (2011) used the MegaZ-LRG photometric galaxy sample (Collister et al.”
KiDS+VIKING-450: Cosmic shear tomography with optical and infrared data (2018, methodology): “The 2-point shear correlation function between two tomographic bins i and j is measured with the public treecorr code (Jarvis et al. 2004), which implements the following estimator: ξ̂ i j ± (θ) = ∑ ab wawb [ it (xa) j t (xb) ± i×(xa) j ×(xb) ]∑ ab wawb (4) where t,× are the tangential and cross…”
The first-year shear catalog of the Subaru Hyper Suprime-Cam Subaru Strategic Program Survey (2017, methodology): “This acts as a wrapper for the software TreeCorr18 (Jarvis et al. 2004), performing different kinds of correlation functions with appropriate parameter values.”
Weak Gravitational Lensing (2012, background): “• The skewness and the kurtosis of the aperture mass 〈M ap〉: Similarly to the aperture mass variance described in the previous section, the skewness and the kurtosis of the aperture mass have also been introduced to weak lensing analyses to constrain cosmological parameters (see for example [38, 73]”