Contamination of early-type galaxy alignments to galaxy lensing-CMB
  lensing cross-correlation
  Galaxy shapes are subject to distortions due to the tidal field of the
Universe. The cross-correlation of galaxy lensing with the lensing of the
Cosmic Microwave Background (CMB) cannot easily be separated from the
cross-correlation of galaxy intrinsic shapes with CMB lensing. Previous work
suggested that the intrinsic alignment contamination can be $15\%$ of this
cross-spectrum for the CFHT Stripe 82 (CS82) and Atacama Cosmology Telescope
surveys. Here we re-examine these estimates using up-to-date observational
constraints of intrinsic alignments at a redshift more similar to that of CS82
galaxies. We find a $\approx$ $10\%$ contamination of the cross-spectrum from
red galaxies, with $\approx$ $3\%$ uncertainty due to uncertainties in the
redshift distribution of source galaxies and the modelling of the spectral
energy distribution. Blue galaxies are consistent with being unaligned, but
could contaminate the cross-spectrum by an additional $9.5\%$ within current
$95\%$ confidence levels. While our fiducial estimate of alignment
contamination is similar to previous work, our work suggests that the relevance
of alignments for CMB lensing-galaxy lensing cross-correlation remains largely
unconstrained. Little information is currently available about alignments at
$z>1.2$. We consider the upper limiting case where all $z>1.2$ galaxies are
aligned with the same strength as low redshift luminous red galaxies, finding
as much as $\approx$ $60\%$ contamination.
