Impact of magnification and size bias on the weak lensing power spectrum and peak statistics

The weak lensing power spectrum is a powerful tool to probe cosmological parameters. Additionally, lensing peak counts contain cosmological information beyond the power spectrum. Both of these statistics can be affected by the preferential selection of source galaxies in patches of the sky with high magnification, as well as by the dilution in the source galaxy surface density in such regions. If not accounted for, these biases introduce systematic errors for cosmological measurements. Here we quantify these systematic errors, using convergence maps from a suite of ray-tracing N-body simulations. At the cutoff magnitude m of ongoing and planned major weak lensing surveys, the logarithmic slope of the cumulative number counts s d log n(> m)/d log m is in the range 0.1 less than or similar to s less than or similar to 0.5. At s approximate to 0.2, expected in the I band for Large Synoptic Survey Telescope, the inferred values of Omega(m), w, and sigma(8) are biased by many sigma (where sigma denotes the marginalized error), and therefore the biases will need to be carefully modeled. We also find that the parameters are biased differently in the (Omega(m), w, sigma(8)) parameter space when the power spectrum and the peak counts are used. In particular, w derived from the power spectrum is less affected than w derived from peak counts, while the opposite is true for the best-constrained combination of sigma(8)Omega(gamma)(m) (with gamma = 0.62 from the power spectrum and gamma = 0.48 from peak counts). This suggests that the combination of the power spectrum and peak counts can help mitigate the impact of magnification and size biases.