Abstract: | The lensing-induced $B$-mode signal is a valuable probe of the dark matter
distribution integrated back to the last-scattering surface, with a broad
kernel that peaks at $zsimeq2$. It also constitutes an important contaminant
for the extraction of the primary CMB $B$-modes from inflation. Combining
all-sky coverage and high resolution and sensitivity, Planck provides accurate
nearly all-sky measurements of both the polarization $E$-mode signal and the
integrated mass distribution via the reconstruction of the CMB gravitational
lensing. By combining these two data products, we have produced an all-sky
template map of the secondary CMB $B$-modes using a real-space algorithm that
minimizes the impact of sky masks. The cross-correlation of this template with
an observed (primordial and secondary) $B$-mode map can be used to measure the
lensing $B$-mode power spectrum at all angular scales. In particular when
cross-correlating with the $B$-mode contribution directly derived from the
Planck polarization maps, we obtain lensing-induced $B$-mode power spectrum
measurements at a significance of $12,sigma$, which are in agreement with the
theoretical expectation derived from the Planck best-fit $Lambda$CDM model.
This unique nearly all-sky secondary $B$-mode template, which includes the
lensing-induced information from intermediate to small ($10lesssim
elllesssim 1000$) angular scales, is delivered as part of the Planck 2015
public data release. It will be particularly useful for experiments searching
for primordial $B$-modes, such as BICEP2/Keck Array or LiteBIRD, since it will
enable an estimate to be made of the secondary (i.e., lensing) contribution to
the measured total CMB $B$-modes. |