CMB lensing reconstruction biases from masking extragalactic sources
  Observed Cosmic Microwave Background (CMB) maps are contaminated by
foregrounds, some of which are usually masked to perform cosmological analyses.
If masks are correlated to the lensing signal, such as those removing
extragalactic emissions located in matter overdensities, measurements over the
unmasked sky may give biased estimates. We quantify the impact of these
mask-induced biases for the reconstructed CMB lensing auto- and
cross-correlation power spectra with external matter tracers. We show that they
arise both from changes in the lensing power, and via modifications to the
reconstruction power spectrum corrections, $N_L^{(0)}$, $N_L^{(1)}$ and
$N_L^{(3/2)}$). For direct masking of the CMB lensing field, we derive simple
analytic models of the masking effect and show that it is potentially large. We
show that mask-induced biases are significantly reduced by optimal filtering of
the CMB maps in the lensing reconstruction. 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 the lensing auto spectrum, masking biases can only be measured with a
statistical significance $\lesssim 3\sigma$ for future data sets. The same
applies to the cross-correlation power spectra between CMB lensing and tSZ and
CIB even though biases are larger (up to ~30%). We find that masking
tSZ-selected galaxy clusters leads to the largest mask biases, potentially
detectable with high significance. We find that the calibration of cluster
masses using CMB lensing, in particular for objects at $z\lesssim 0.6$, 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.
