Intrinsic ellipticity correlation     of luminous red galaxies       and misalignment with          ...
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Intrinsic ellipticity correlation of luminous red galaxies and misalignment with their host dark matter halos. The 8 th Sino – German workshop Teppei O KUMURA (SHAO) Collaborators: Yipeng Jing (SHAO) & Cheng Li (MPA). References:.

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The 8 th Sino – German workshop Teppei O KUMURA (SHAO)

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Intrinsic ellipticity correlation of luminous red galaxies and misalignment with their host dark matter halos

The 8th Sino – German workshop


Collaborators: Yipeng Jing (SHAO) & Cheng Li (MPA)


Okumura, Jing, & Li, ApJ, 694, in press (arXiv:0809.3790) Okumura & Jing, ApJL, accepted (arXiv:0812.2935)

Tidal field, …


  • Weak gravitational lensing by large-scale structure

    • Directly probe the matter distribution

  • Observable

    • Ellipticity of galaxies eobs





  • Intrinsic ellipticity – ellipticity (II) correlation can be a contamination for weak lensing observations.

SDSS luminous red galaxies (LRG)

  • Properties of LRGs

    • Giant ellipticals (not contaminated by spirals)

    • Almost all the LRGs are central galaxies (~ 95%)

    • LRGs preferentially reside in massive halos which have stronger ellipticity correlation (Jing2002).

  • We use 83,773 LRGs at 0.16 < z < 0.47 and –23.2 < Mg < –21.2 from the SDSS DR6 sample.

Measuring the II correlation


  • Definitions

    • Ellipticity of galaxies

    • II correlation function

    • c22 is calculated in the same way and cross-correlations, c12 and c21, should vanish on all scales.

axis ratio


= 0 : line = 1 : spherical

q = a / b

  • Stronger correlations can be seen in the brighter sample although the error bars are large.

The II correlation function of LRGs

Bright sample

  • Positive c11 on small scales

  • Brighter LRGs tend to reside in more massive halos

  • More massive halos have stronger ellipticity correlations (Jing2002).

Faint sample

Halo occupation distribution for LRGs (Seo+2008, Zheng+)

Galaxies assigned


  • Mock LRG catalog

    • Then modeled ellipticity correlation functions can be calculated.

Modeling the II correlation from N-body simulation

  • Mock halo catalog from N-body simulation (Jing et al. 2007)

    • Concordance LCDM model was assumed

    • Ellipticity of each halo is computed by tracing all the particles in the halo.

Jing & Suto (2000)

Comparison of observation with model

4 times smaller

  • First we assume that all central LRGs are completely aligned with their host halos.

  • There are significant discrepancies in the amplitude between observation and model.



  • We will model the II correlation by considering the misalignment of central LRGs with their host halos.

Misalignment between central LRGs and their host halos

  • Misalignment angle parameter σθ

    • Assumption that the PDF of the misalignment angle θ follows Gaussian,

Calculation of model c11(r ;σθ) for LRGs


Δc11(r ;σθ) = c11model(r ;σθ) – c11obs(r)


σθ = 0 model

σθ = 35 model

Constraints on misalignment

  • A model which the central galaxies and their host halos are completely aligned is strongly rejected by our analysis.

Implications for weak lensing surveys

Dependence of II correlation on halo mass (Jing 2002)

  • An example

    • CFHTLS weak lensing survey (zs ~ 1 and RAB=24.5). (Fu+)

    • Central galaxies in the DEEP2 are in dark halos ~ 4×1011h–1 Msun (Zheng+)

  • If these central galaxies have the same misalignment distribution as the SDSS LRGs, the II correlation can contribute by 5 – 10% to the shear correlation.

Hirata & Seljak (2004), Pengjie’s talk

Distant source (G)

Nearby source (I)

GI terms

Another contamination; Gravitational shear – intrinsic ellipticity correlation

  • Observables

    • Ellipticity of galaxies

  • Unlike II correlation, GI correlation can exist between galaxies at very different redshifts.



Measuring the GI correlations


  • Definitions

    • Ellipticity of galaxies

    • Projected GI correlation function

    • In observation

Directly related to the GI term of the shear power spectrum.

This relation is indeed valid on large scales.

Galaxy biasing ~2 for LRGs

The GI correlation functions of LRGs in observation and in LCDM model

  • The GI correlation is better determined than the II correlation in observation.

  • The GI correlation can be well modeled in the current LCDM model if the misalignment angle parameter follows

  • This correlation increases the amplitude by ~15%.

Correlation of the LRG shape and orientation

  • Normalized GI correlation function

    • If there is no correlation

      between q and β, we expect

axis ratio



  • II correlation

    • The correlation was determined up to 30h–1Mpc.

    • Luminosity dependence was also detected.

    • We constrained the misalignment parameter

    • If not corrected, the II correlation can lead to contamination at 5~10% levels to cosmic shear.

  • GI correlation

    • The correlation was also measured accurately.

    • By comparing with a simulation,we found the GI correlation can be well modeled in the current LCDM model if the misalignment angle

    • We found a correlation between the axis ratios and orientations of LRGs which amplifies the GI correlation by ~15 %.

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