Intrinsic Ellipticity Correlation of SDSS Luminous Red Galaxies and Misalignment with their Host Dark Matter Halos

TL;DR

This study measures intrinsic ellipticity correlations of SDSS LRGs to assess how central galaxies align with their host halos. By combining SDSS observations with an $N$-body simulation and a halo occupation distribution, the authors predict ellipticity signals under different misalignment scenarios and constrain the misalignment angle. The best-fit Gaussian misalignment width is $σ_θ = 35.4^{+4.0}_{-3.3}$ degrees, indicating centrals are not perfectly aligned with halos and rejecting perfect alignment. The results imply a few-percent level impact on weak lensing shear measurements at typical high-redshift survey depths, emphasizing the need to model intrinsic alignments in cosmological analyses and informing theories of massive elliptical formation.

Abstract

We investigate the orientation correlation of giant elliptical galaxies by measuring the intrinsic ellipticity correlation function of 83,773 luminous red galaxies (LRGs) at redshifts 0.16 -- 0.47 from the Sloan Digital Sky Survey. We have accurately determined the correlation up to 30 $h^{-1}$Mpc. Luminosity dependence of the ellipticity correlation is also detected although the error bars are large, while no evidence is found for its redshift evolution between $z=0.2$ and $z=0.4$. Then we use a cosmological $N$-body simulation to examine misalignment between the central LRGs and their parent dark matter halos. Central and satellite galaxies are assigned to simulated halos by employing a halo occupation distribution model for the LRGs. The ellipticity correlation is predicted to have the same shape as but an amplitude about 4 times higher than our observation if the central LRGs are perfectly aligned with their host halos. This indicates that the central LRG galaxies are preferentially but not perfectly aligned with their host halos. With the assumption that there is a misalignment angle between a central LRG and its host halo which follows a Gaussian distribution with a zero mean and a width $σ_θ$, we obtain a tight constraint on the misalignment parameter, $σ_θ={35.4}^{+4.0}_{-3.3}$ deg. This type of intrinsic ellipticity correlation, if not corrected, can lead to contamination at 5% level to the shear power spectrum in weak lensing surveys of limiting magnitude $R_{AB}=24.5$ if the source central galaxies follow the same misalignment distribution as the LRGs.

Figures (7)

• Figure 1: Top: ellipticity correlation functions for the central LRG sample. Bottom: as the top panel, but setting $q=0$ when the ellipticity of the LRGs is measured in equation (\ref{['eq:ellip']}). The dashed black line shows $c_{11}$ for the combined sample of central and satellite LRGs. To clearly show the fluctuations of $c_{22}$ and $(c_{12}+c_{21})/2$, mixed logarithmic and linear scalings are used for the vertical axis. Bins in $r$ are in logarithmic separation of 0.25. The circles/triangles have been respectively offset in the negative/positive direction for clarity.
• Figure 2: Normalized covariance matrix for the $c_{11}(r)$ measurement of the central LRG sample. Contour spacing is 0.2 going from 1 on the diagonal (thick line) down to 0. The dashed line denotes the 0.4 contour. This is a similar plot to Figure 7 of Zehavi2005 who focused on the LRG clustering.
• Figure 3: Luminosity dependence of $c_{11}(r)$ of the LRGs for $0.16<z<0.36$. Here both the central and satellite LRGs are used for the calculation. Note that the vertical axis mixes logarithmic and linear scalings.
• Figure 4: Redshift dependence of $c_{11}(r)$ of the LRGs for the absolute magnitude of $-23.2<M_g<-21.2$. Here both the central and satellite LRGs are used for the calculation. Note that the vertical axis mixes logarithmic and linear scalings.
• Figure 5: Comparison of the real space correlation functions between the observed and mock LRGs. The black points with the error bars show the observed correlation function Zehavi2005. The dashed line is that of the mock galaxy catalog using the best-fit HOD model for the LRGs Seo2008.