Foreground-immune CMB lensing with shear-only reconstruction

CMB lensing from current and upcoming wide-field CMB experiments such as AdvACT, SPT-3G and Simons Observatory relies primarily on temperature, rather than polarization. In this regime, foreground contamination to the temperature maps produces significant lensing biases, which cannot be fully controlled by multi-frequency component separation, masking or bias hardening. In this letter, we use the different symmetries of the lensed CMB and foregrounds to argue that a shear-only estimator should be approximately immune to foregrounds. Using simulations, we build a new method to compute separately and without noise the primary, secondary and trispectrum biases to CMB lensing. We show that the shear estimator is indeed insensitive to foregrounds, even when applied to a single-frequency temperature map contaminated with CIB, tSZ, kSZ and radio point sources. This dramatic reduction in foreground biases allows us to include higher temperature multipoles than with the standard quadratic estimator, thus increasing the overall statistical power of lensing measurements. In addition, the corresponding magnification-only estimator is highly sensitive to foregrounds, and therefore provides a useful diagnostic for potential residuals.