Position-Dependent Correlation Function of Weak Lensing Convergence
We provide a systematic study of the position-dependent correlation function in weak lensing convergence maps and its relation to the squeezed limit of the three-point correlation function (3PCF) using state-of-the-art numerical simulations. We relate the position-dependent correlation function to its harmonic counterpart, i.e., the position-dependent power spectrum or equivalently the integrated bispectrum. We use a recently proposed improved fitting function, BiHalofit, for the bispectrum to compute the theoretical predictions as a function of source redshifts. In addition to low redshift results ($z_s=1.0-2.0$), we also provide results for maps inferred from lensing of the cosmic microwave background, i.e., $z_s=1100$. We include a {\em Euclid}-type realistic survey mask and noise. In agreement with the recent studies on the position-dependent power spectrum, we find that the results from simulations are consistent with the theoretical expectations when appropriate corrections are included. Performing a rough estimate, we find that the (S/N) for the detection of the position-dependent correlation function from {\em Euclid}-type mask with $f_{sky}=0.35$, can range between $6-12$ depending on the value of the intrinsic ellipticity distribution parameter $σ_ε = 0.3-1.0$. For reconstructed $κ$ maps using an ideal CMB survey the (S/N) $\approx 1.8$. We also found that a $10\%$ deviation in $σ_8$ can be detected using IB for the optimistic case of $σ_ε=0.3$ with a (S/N) $\approx 5$. The (S/N) for such detection in case of $Ω_M$ is lower.