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 k0. 1 h^-1 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 ``nonlinear linear alignment'' 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.