Beyond linear galaxy alignments
  Galaxy intrinsic alignments (IA) are a critical uncertainty for current and
future weak lensing measurements. We describe a perturbative expansion of IA,
analogous to the treatment of galaxy biasing. From an astrophysical
perspective, this model includes the expected large-scale alignment mechanisms
for galaxies that are pressure-supported (tidal alignment) and
rotation-supported (tidal torquing) as well as the cross-correlation between
the two. Alternatively, this expansion can be viewed as an effective model
capturing all relevant effects up to the given order. We include terms up to
second order in the density and tidal fields and calculate the resulting IA
contributions to two-point statistics at one-loop order. For fiducial
amplitudes of the IA parameters, we find the quadratic alignment and
linear-quadratic cross terms can contribute order-unity corrections to the
total intrinsic alignment signal at $k\sim0.1\,h^{-1}{\rm Mpc}$, depending on
the source redshift distribution. These contributions can lead to significant
biases on inferred cosmological parameters in Stage IV photometric weak lensing
surveys. We perform forecasts for an LSST-like survey, finding that use of the
standard "NLA" model for intrinsic alignments cannot remove these large
parameter biases, even when allowing for a more general redshift dependence.
The model presented here will allow for more accurate and flexible IA treatment
in weak lensing and combined probes analyses, and an implementation is made
available as part of the public FAST-PT code. The model also provides a more
advanced framework for understanding the underlying IA processes and their
relationship to fundamental physics.
