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The g iant a rc statistic in the three-year WMAP cosmological model

The g iant a rc 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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The g iant a rc statistic in the three-year WMAP cosmological model

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  1. The giant arc statistic in the three-year WMAP cosmological model Guoliang Li Shanghai Astronomic Observatory November1st, 2006 COLLABORATORS: Shude mao (JBO) Yipeng Jing, Xi Kang, Weipeng Lin (SHAO) Matthias Bartelmann, Massimo Menegentti (Heidelberg) Liang Gao (Durham)

  2. A2218 Z=0.175 Giant arcs are background galaxies distorted into long arcs by foreground clusters

  3. A1689 Z=0.18 Observations can determine, arc L/W ratio, width, source redshift & arc frequency

  4. 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 σ8 • Clusters are nature telescope, allow us to study high-z background objects

  5. 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 3.7~5.6x10-2deg-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.

  6. 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

  7. 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.

  8. Optical depth as a function of source redshift • Optical depth ~ 10-7 for zs=1, but 10-6 for zs=4 • Several previous values are too high due to incorrect assumptions of sigma_8 and L/W definition • Consistent with Dalal et al. (2004) • Strong zs dependence • Weaker dependence on ellipticity and source size

  9. 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 z>0.62; understood if source z is high.

  10. 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?

  11. 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

  12. Predicted number of giant arcs • Effect of star formation? Likely a factor of 2 • Source redshift distribution, size, ellipticity(modest)

  13. 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----<7% • The baryon effect ---not very clear(~2)

  14. Summary • Optical depth may be too low in the WMAP three-year model (with 8=0.74) • We need many larger giant arc unbiased samples -- they will come as by-products of weak lensing surveys.

  15. Thanks !

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