Tidal alignment of galaxies

TL;DR

This paper advances intrinsic alignment modeling by formulating a nonlinear tidal-alignment framework that incorporates one-loop perturbative corrections, density weighting, and smoothing of the tidal field. It carefully treats the alignment epoch and redshift evolution, and separates perturbative contributions from nonperturbative halo-scale physics to extend IA predictions down to the one-halo regime. The authors demonstrate that density weighting is a dominant nonlinear effect, inducing a bias-dependent IA amplitude and B-mode power, and they show improved agreement with IA measurements of luminous red galaxies compared with linear and nonlinear alignment models. A complementary halo-based approach for small scales reveals saturation of the IA signal inside halos, with implications for cosmic shear analyses and future mitigation strategies.

Abstract

We develop an analytic model for galaxy intrinsic alignments (IA) based on the theory of tidal alignment. We calculate all relevant nonlinear corrections at one-loop order, including effects from nonlinear density evolution, galaxy biasing, and source density weighting. Contributions from density weighting are found to be particularly important and lead to bias dependence of the IA amplitude, even on large scales. This effect may be responsible for much of the luminosity dependence in IA observations. The increase in IA amplitude for more highly biased galaxies reflects their locations in regions with large tidal fields. We also consider the impact of smoothing the tidal field on halo scales. We compare the performance of this consistent nonlinear model in describing the observed alignment of luminous red galaxies with the linear model as well as the frequently used "nonlinear alignment model," finding a significant improvement on small and intermediate scales. We also show that the cross-correlation between density and IA (the "GI" term) can be effectively separated into source alignment and source clustering, and we accurately model the observed alignment down to the one-halo regime using the tidal field from the fully nonlinear halo-matter cross correlation. Inside the one-halo regime, the average alignment of galaxies with density tracers no longer follows the tidal alignment prediction, likely reflecting nonlinear processes that must be considered when modeling IA on these scales. Finally, we discuss tidal alignment in the context of cosmic shear measurements.

Figures (5)

• Figure 1: The linear theory result, NLA correction, and all additional $\mathcal{O}(P_{\rm lin}^2)$ corrections are shown for $w_{g+}$ ( top panel) and $w_{++}$ ( bottom panel), with $b_1=2.1$ and $b_2=0.5$. Overall normalization for both statistics, determined by $C_1$, is chosen to match the LOWZ $w_{g+}$ measurement of singh14, while the value of $\sigma_S^2$ is calculated using the smoothing discussed in section \ref{['sec:smoothing']}, with $k_{\rm sm}=1.0$$h\,{\rm Mpc}^{-1}$. Contributions are labeled using the associated pre-factors in eqs. \ref{['eq:PgE1']}-\ref{['eq:PBB1']}, and the $\sigma_S^2P_{\rm lin}$ contribution (black) is separated from the other tracer density weighting terms (green). Note that the "NLA corr." term shows the difference between the NLA (Halofit) and linear theory predictions. Dashed lines indicate a negative value.
• Figure 2: Data points show the LRG measurements of $w_{g+}$ ( top panel) and $w_{++}$ ( bottom panel) from okumura09aokumura09b. The solid lines show the best fit linear, NLA, and total model predictions, with $b_1=2.1$ and $b_2=0.5$. For comparison, dashed lines indicate the linear and NLA models with no smoothing of the tidal field. The alignment amplitude and $\sigma^2_S$ is fit separately to $w_{g+}$ and $w_{++}$.
• Figure 3: Data points show the LOWZ measurements of $w_{g+}$ ( top panel) and $w_{++}$ ( bottom panel) from singh14. For $w_{g+}$, the solid lines show the best fit linear, NLA, and total model predictions, with $b_1=1.8$ and $b_2=0.5$. For comparison, dashed lines indicate the linear and NLA models with no smoothing of the tidal field. The linear and NLA models for $w_{++}$ are shown, normalized using the fit to $w_{g+}$ due to low signal-to-noise in $w_{++}$.
• Figure 4: Model results for ${\langle {\gamma}_+ \rangle^{\rm trac}_{r_p}}$, shown for an NFW profile for $M_{180b}=1.51\times10^{13} h^{-1} M_{\odot}$, is compared with the observational results from the LOWZ sample singh14. The dashed blue line shows the continuation of the tidal alignment prediction below $R_{200c}$ (indicated by the vertical line). Predictions from the full SPT model of section \ref{['sec:tidal_alignment']}, as well as the NLA model (dashed line indicates no smoothing), are shown for comparison. As discussed in the text, the NLA model does not account for density weighting, and the associated prediction for ${\langle {\gamma}_+ \rangle^{\rm trac}_{r_p}}$ does not include $w_{gg}$.
• Figure 5: Predictions for $w_{\delta +}$ are shown for both the SPT and non-perturbative models. Shape tracers are assumed to have the same bias and alignment properties as the LOWZ galaxies singh14. As discussed in the text, $\langle \gamma_+\rangle$ saturates below $r_p=R_{200c}$, and results are shown for $w_{g \delta}$ predicted using both Halofit (with linear bias) and an NFW profile. For reference, the $\langle \gamma_+\rangle$ line (blue) shows the alignment effect without shape tracer clustering.