Beyond linear galaxy alignments

Abstract

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.

Figures (3)

• Figure 1: The components of the $z=0$, II power spectra from are shown. The pre-factors in Eqs. \ref{['eq:EEtot']}-\ref{['eq:BBtot']} are included, with $C_1 = C_{1\delta} = -1$ and $C_2 = 5$, corresponding to the fiducial relative scaling between $C_1$ and $C_2$, without the factor of $\bar{C_1}\rho_{\rm crit}\Omega_{\rm m}$ in Eqs. \ref{['eq:C1amp']}-\ref{['eq:C2amp']}. We assume transverse modes ($\mu_k = 0$). Negative values are indicated with dashed lines. Left panel: contributions from tidal alignment ($C_1$ and $C_{1\delta}$). Right panel: contributions from tidal torquing ($C_2$) and mixed terms. For reference, in both panels the leading tidal alignment contribution $C_1^2 P_{\delta}$ is shown, with the solid line for $P_{\rm NL}$ (the NLA model) and the dotted line for $P_{\rm lin}$.
• Figure 2: IA contributions to the angular auto- and cross-power spectra for two source bins with Gaussian $n(z)$, with means $\langle z \rangle=0.4$ and 0.8 and width $\Delta z=0.1$. Dashed lines indicate negative values, and $B$-modes are denoted "BB." For reference, the lensing contribution is shown in black.
• Figure 3: Constraints on cosmological and intrinsic alignment parameters for an idealized LSST-like cosmic shear survey. Dashed lines indicate the input parameter values used to create the data vectors. Green outlined contours use a data vector and model without intrinsic alignment contributions, case (i). The orange outlined contour uses a data vector with contamination by the full intrinsic alignment model, with fiducial amplitudes (see Sec. \ref{['sec:impact']}), but uses a model which assumes the NLA model for the intrinsic alignment contribution, case (ii). The black contour is the same as the orange, except the model also includes a free power law in redshift, case (iii). The purple contour uses the same data vector as orange and black, but uses the full intrinsic alignment modeling, thereby recovering unbiased parameter constraints, case (iv).