The giant arc statistic in the threeyear WMAP cosmological model

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The giant arc statistic in the three-year WMAP
cosmological model
Guoliang Li
Shanghai Astronomic Observatory
November 1st, 2006
COLLABORATORS Shude mao (JBO) Yipeng Jing, Xi
Kang, Weipeng Lin (SHAO) Matthias Bartelmann,
Massimo Menegentti (Heidelberg) Liang Gao (Durham)
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A2218
Z0.175
Giant arcs are background galaxies distorted into
long arcs by foreground clusters
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A1689
Z0.18
Observations can determine, arc L/W ratio, width,
source redshift arc frequency
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Why do we study giant arcs?

• Giant arcs probe the largest bound structures in
  the universe
• Their numbers and positions are a sensitive probe
  of cluster properties including their abundance
  and mass profiles
• Their numbers are also sensitive to the
  cosmogony, particularly the power-spectrum
  normalisation s8
• Clusters are nature telescope, allow us to study
  high-z background objects

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Observational samples of giant arcs

• Luppino et al. found strong lensing in eight out
  of 38 X-ray selected clusters (Bartelmann(1998)
  predicted the frequency is 7x10-3deg-2 but the
  observation is 3.75.6x10-2deg-2 )
• Zaritsky Gozalez (2003) using LCRS and Gladders
  et al. (2003) using RCS also found high fractions
• Sand, Ellis, Treu, Smith (2005) found 104
  candidate tangential arcs in 128 clusters with
  HST
• Giant arcs appear common in massive clusters and
  the discrepancy with Bartelmann is kept.

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How do we model giant arcs?

• Earlier studies used analytical spherical models
  (e.g. Wu Hammer 1993 Wu Mao 1996).
• But clusters are complex (ellipticities,
  substructures, mergers).
• More realistic studies use numerical simulated
  clusters
• Bartelmann and associates (1998-)
• Dalal et al. (2004)
• Li, Mao, Jing, Bartelmann, Kang, Meneghetti
  (2005)
• Wambsganss, Ostriker, Bode (2004) 3D ray-tracing

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High resolution simulations

• Numerical simulations performed by Jing (2000)
• Dark matter only, 5123 particles
• Box size 300/h Mpc, 30/h kpc (comoving)
  resolution
• 200 massive clusters are selected using the
  friends-of-friends algorithm, from redshift 0.1,
  0.2, , 2.5
• Background source population
• At redshift 0.6, 1.0, 1.4, ., 7
• Sources have 0.5, 1, 1.5 arcsecond effective
  diameter
• Ellipticity 1-b/a, from 0.5 to 1
• Integrate the cross-sections of all clusters to
  get the total lensing cross sections.

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Optical depth as a function of source redshift

• Strong zs dependence
• Weaker dependence on ellipticity and source size

• Optical depth 10-7 for zs1, but 10-6 for zs4
• Several previous values are too high due to
  incorrect assumptions of sigma_8 and L/W
  definition
• Consistent with Dalal et al. (2004)

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Optical depth as a function of lens redshift

• For sources at high z, probe clusters at high
  redshift
• Gladders et al. who found all of their lensing
  clusters were at zgt0.62 understood if source z
  is high.

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• Comparing with Bartelmann (1998), Dalal et al.
  (2004) pointed that the numbers of lens and
  should be increased by a factor of 2. The giant
  arcs number which they predicted is in good
  agreement with almost all of the observations.
• What will happen in the three-year WMAP universe?

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Giant arcs in the WMAP3 cosmology

• The WMAP three-year model has lower ?m and ?8
  compared with the WMAP one-year model.
• The lower ?m (0.238) and ?8 (0.74) both reduce
  the number of giants
• We compared the arc predictions in the usual LCDM
  and WMAP three-year model
• Using two 300/h Mpc N-body simulations
• The predicted number is reduced by a factor of
  about six in the WMAP three year model
• Easily understood due to the abundance of clusters

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Predicted number of giant arcs

• Effect of star formation? Likely a factor of 2
• Source redshift distribution, size,
  ellipticity(modest)

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The way to increase the lensing efficiency

• The asysmetric of lens----------------ok
• The merger effect------------------- --ok
• The substructure-----------------------ok
• The redshift distribution of source ---ok
• The size and shape of source ---modest
• The mass around the line of sight----lt7
• The baryon effect ---not very clear(2)

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Summary

• Optical depth may be too low in the WMAP
  three-year model (with ?80.74)
• We need many larger giant arc unbiased samples --
  they will come as by-products of weak lensing
  surveys.

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• Thanks !