CMB lensing reconstruction biases from masking extragalactic sources

Observed cosmic microwave background (CMB) temperature and polarization maps can be powerful cosmological probes and used for CMB lensing reconstruction. However, the CMB maps are inevitably contaminated by foregrounds, some of which are usually masked to perform the analysis. If this mask is correlated to the lensing signal, measurements over the unmasked sky may give biased estimates and hence biased cosmological inferences. For example, masking extragalactic astrophysical emissions associated with objects located in dark matter halos will systematically remove parts of the sky that have a mass density higher than average. This can lead to a modified lensed CMB power spectrum over the unmasked area and biased measurements of lensing reconstruction auto- and cross-correlation power spectra with external matter tracers (both from the direct impact on the lensing power and via modifications to the lensing-dependent reconstruction power spectrum corrections, N-L((0)), N-L((1)), N-L((3/2))). For direct masking of the CMB lensing field, we give an approximate halo-model prediction of the size of the effect and derive simple analytic models for point sources and threshold masks constructed on a correlated Gaussian foreground field. We show that biases are significantly reduced by optimal filtering of the CMB maps in the lensing reconstruction, which effectively fills hack some of the infomiation in small mask holes. We test the resulting lensing power spectrum biases on numerical simulations, masking radio sources, and peaks of thermal Sunyaev-Zeldovich (tSZ) and cosmic infrared background (CIB) emission. For radio point sources, the remaining bias is negligible, but a temperature lensing reconstruction power spectrum bias remains at the 0.5%-5% level if clusters with a mass larger than similar to 10(14) M-circle dot/h are masked or if peaks in the CIB and tSZ maps are removed with f(sky)(mask) similar or equal to 0.5-7%. In any case, these biases can only he measured with a statistical significance less than or similar to 2 sigma for future datasets. Moreover, we quantified the impact of the mask biases in the cross-correlation power spectrum between CMB lensing and tSZ and C113 and found them to be larger (up to similar to 30%). We found that masking tSZ -selected galaxy clusters leads to the largest mask biases, potentially detectable with high significance, and should therefore be avoided as much as possible. For the most realistic masks we considered, masking biases can only be measured with marginal significance. We found that the calibration of cluster masses using CMB lensing, in particular for objects at z less than or similar to 0.6, might be significantly affected by mask biases for near future observations if the lensing signal recovered inside the mask holes is used without further corrections. Conversely, mass calibration of high redshift objects will still deliver unbiased results.