The Gravitational Shear--Intrinsic Ellipticity Correlation Functions of Luminous Red Galaxies in Observation and in the $Λ$CDM Model

TL;DR

This study tests whether the gravitational shear–intrinsic ellipticity (GI) correlation of luminous red galaxies (LRGs) can be modeled with a Gaussian misalignment angle within the ΛCDM framework. By measuring the GI signal in SDSS DR6 and comparing it to ΛCDM mocks using halo occupation and halo triaxiality, the authors find best-fit misalignment width $σ_θ≈34.9^{+1.9}_{-2.1}$ degrees, yielding GI predictions that match observations and aligning with prior intrinsic-ellipticity results. Additionally, they uncover a correlation between galaxy axis ratios and intrinsic alignments that enhances GI by about 15%, highlighting an important effect for weak-lensing modeling. The findings support the ΛCDM misalignment scenario and provide practical guidance for mitigating GI contamination in future surveys, via the relation $w_{g+}=b_g w_{\delta+}$ with $b_g\approx2$.

Abstract

We examine whether the gravitational shear--intrinsic ellipticity (GI) correlation function of the luminous red galaxies (LRGs) can be modeled with the distribution function of a misalignment angle advocated recently by Okumura et al. For this purpose, we have accurately measured the GI correlation for the LRGs in the Data Release 6 (DR6) of the Sloan Digital Sky Survey (SDSS), which confirms the results of Hirata et al. who used the DR4 data. By comparing the GI correlation functions in the simulation and in the observation, we find that the GI correlation can be modeled in the current $Λ$CDM model if the misalignment follows a Gaussian distribution with a zero mean and a typical misalignment angle $σ_θ=34.9^{+1.9}_{-2.1}$ degrees. We also find a correlation between the axis ratios and intrinsic alignments of LRGs. This effect should be taken into account in theoretical modeling of the GI and intrinsic ellipticity--ellipticity correlations for weak lensing surveys.

Figures (3)

• Figure 1: Projected galaxy-galaxy correlation function for the LRG sample at $0.16<z<0.36$. For comparison, the data of Zehavi2005 and Hirata2007 are also plotted.
• Figure 2: Projected GI correlation functions from the SDSS central LRGs, $w_{g+}(r_p)$ and $w_{g\times}(r_p)$. The dashed and solid lines are respectively the model predictions for $w_{g+}$ obtained from the mock LRGs with $\sigma_\theta=0^{\circ}$ and $35^{\circ}$. Mixed logarithmic and linear scalings are used for the vertical axis. The horizontal axis at the top shows the corresponding angular scale when the transverse separations are located at $z=0.5$.
• Figure 3: Normalized GI correlation functions $\bar{w}_{g+}(r_p;q)$. All the lines are the model predictions with $\sigma_\theta=35^{\circ}$. The dotted blue line is the one with $q_{\rm mock}$ shuffled randomly. The circles/squares have been respectively offset in the horizontally negative/positive direction for clarity.