Testing the tidal alignment model of galaxy intrinsic alignment

TL;DR

The paper tackles intrinsic galaxy alignment as a systematic in weak lensing by testing the linear tidal alignment (LA) model against SDSS measurements. It develops predictions for GI/II correlations, the E/B-mode decomposition, and the orientation-dependent alignment function $w_g(r_p,\theta)$, comparing them to data and finding consistency on scales $r_p\gtrsim10\,h^{-1}$Mpc, with nonlinear corrections via Halofit improving smaller-scale fits. A clear luminosity dependence emerges, with more luminous red galaxies showing stronger alignment, while the angular dependence reduces to $\cos(2\theta)$ as predicted for Gaussian fields; stochastic misalignment can damp higher-order angular terms. Overall, the LA model captures a substantial portion of observed IA, offering insights into galaxy formation physics and informing weak-lensing analyses, with implications for modeling IA in future surveys.

Abstract

Weak gravitational lensing has become a powerful probe of large-scale structure and cosmological parameters. Precision weak lensing measurements require an understanding of the intrinsic alignment of galaxy ellipticities, which can in turn inform models of galaxy formation. It is hypothesized that elliptical galaxies align with the background tidal field and that this alignment mechanism dominates the correlation between ellipticities on cosmological scales (in the absence of lensing). We use recent large-scale structure measurements from the Sloan Digital Sky Survey to test this picture with several statistics: (1) the correlation between ellipticity and galaxy overdensity, w_{g+}; (2) the intrinsic alignment auto-correlation functions; (3) the correlation functions of curl-free, E, and divergence-free, B, modes (the latter of which is zero in the linear tidal alignment theory); (4) the alignment correlation function, w_g(r_p,theta), a recently developed statistic that generalizes the galaxy correlation function to account for the angle between the galaxy separation vector and the principle axis of ellipticity. We show that recent measurements are largely consistent with the tidal alignment model and discuss dependence on galaxy luminosity. In addition, we show that at linear order the tidal alignment model predicts that the angular dependence of w_g(r_p,theta) is simply w_{g+}*cos(2*theta) and that this dependence is consistent with recent measurements. We also study how stochastic nonlinear contributions to galaxy ellipticity impact these statistics. We find that a significant fraction of the observed LRG ellipticity can be explained by alignment with the tidal field on scales >~10 h^-1 Mpc. These considerations are relevant to galaxy formation and evolution.

Figures (5)

• Figure 1: Measurements of okumura09b and LA model prediction for $w_{g+}$. The black dashed line is calculated using the linear theory $P_{\delta}(k)$, and the red solid line uses the Halofit model.
• Figure 2: Measurements of okumura09a and model predictions for $w_{++}$ ( left panel) and $w_{\times \times}$ ( right panel). The measurements have been projected along the line-of-sight. Open circles, indicating the original measurements without the $\left( 1+\xi_g(r)\right)$ correction, are only shown for $w_{++}$ and on small scales where there is an appreciable difference. For clarity, these points have a small horizontal offset. Line convention is the same as in figure \ref{['fig:wg+']}. A linear $y$-axis is used for $w_{\times \times}$. The normalization of the LA prediction for both statistics is set from the fit to $w_{++}$.
• Figure 3: Left panel:$E$-mode auto-correlation statistic. Line convention and LA model normalization are the same as in figure \ref{['fig:auto']}. Inset shows more detail above $r_p=10$$h^{-1}$Mpc. Right panel:$B$-mode auto-correlation statistic is compared with the LA prediction of zero. The observations are consistent with the prediction above 10 $h^{-1}$Mpc.
• Figure 4: Top panel: The best-fit LA model prediction for $w_g(r_p,\theta)/w_g(r_p)$ compared with the measurements of faltenbacher09 for 4 luminosity bins. The Halofit $P_{\delta}(k)$ is used. Solid curves include redshift-space distortions, while dashed curves do not. The measurements are divided into 3 angular bins. Bottom panel: Deviations from the prediction of $\cos(2\theta)$ angular dependence. See section 4.2 for more information. For clarity, small horizontal offsets have been introduced to circle and diamond points.
• Figure 5: The LA model prediction for $\gamma_{\rm rms}$ plotted as a function of the cut-off value $k_{\rm max}$. Solid lines are calculated using the Halofit $P_{\delta}(k)$, while the dashed lines are calculated with the linear $P_{\delta}(k)$. The prediction is normalized assuming the best-fit LRG value for $C_1$. Black lines assume a level of stochasticity consistent with okumura09a, while red lines assume that no stochasticity is present. For reference, the observed LRG value of $\gamma_{\rm rms}\approx 0.17$ is plotted (horizontal blue dotted line).