Aperture Mass and Third-Order Shear Statistics: Measuring the Skewness of the Convergence Field

The aperture mass compresses the shear field into a filtered convergence whose third moment measures the skewness generated by nonlinear gravitational evolution. This paper computes the aperture-mass variance at filter scales from 2 to 20 arcminutes, finding a variance of 1.527e-05 and a root-mean-square of 0.0039 at 5 arcminutes, and 4.957e-06 at 20 arcminutes, a ratio of 3.1 between the two scales. With the standard skewness scaling, the third moment proxy at 5 arcminutes corresponds to a dimensionless skewness of about 38. Third-order statistics constrain a different parameter combination than the variance and so break degeneracies, at the price of larger noise and stronger sensitivity to the nonlinear and baryonic modelling of the smallest scales. All quantities are computed from stated assumptions, not measured.