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Giant Arcs: A Probe for Clusters and Cosmogony

Giant Arcs: A Probe for Clusters and Cosmogony. Shude Mao. Jodrell Bank Observatory. Sept 28, 2006. COLLABORATORS: Guoliang Li , Yipeng Jing, Xi Kang, Weipeng Lin (SHAO) Matthias Bartelmann, Massimo Menegentti (Heidelberg) Liang Gao (Durham). A2218. Z=0.175.

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Giant Arcs: A Probe for Clusters and Cosmogony

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  1. Giant Arcs: A Probe for Clusters and Cosmogony Shude Mao Jodrell Bank Observatory Sept 28, 2006 COLLABORATORS: Guoliang Li, 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. Observational samples of giant arcs • Luppino et al. (1999) found strong lensing in eight out of 38 X-ray selected clusters • Optically, Zaritsky & Gozalez (2003) using LCRS and Gladders et al. (2003) using RCS 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

  5. 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, allowing us to study faint, high-redshift background objects behind clusters

  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). • Most recent studies use numerically simulated clusters • Bartelmann and associates (1998-) • Dalal et al. (2004) • Wambsganss, Ostriker, Bode (2004): 3D ray-tracing • Li, Mao, Jing, Bartelmann, Kang, Meneghetti (2005)

  7. Numerical simulation • N-body simulation was performed by Jing (2000) in CDM cosmology (m=0.3, 8=0.9) • 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 diameters • Ellipticity (=1-b/a), uniformly distributed from 0.5 to 1 • Calculate the cross-section for each cluster, and then integrate to obtain the total lensing optical depth.

  8. A high-resolution numerical cluster Clusters are complex (e.g. tri-axial with significant substructures) Jing (2000)

  9. From particles to smooth density fields • Simulations give discreet particle positions • Need an efficient and high-fidelity smoothing algorithm from position to density field • We proposed an adaptive smoothing algorithm based on the scatter interpretation of SPH (Li et al. 2006) • First partitions particle weights in 3D grids according to SPH (for Nneighbor=32, 64). • Then integrate along the line of sight to obtain surface density • Fully adaptive, and better preserves substructures than other methods

  10. Caustics and critical curves z=0.3, M~1015/h Msun

  11. Optical depth as a function of source redshift • Optical depth ~ 10-7 for deff=0.5”, for zs=1; but 10-6 for zs=3 • Lower than several previous studies • Agree with Dalal et al. (2004), who claimed consistency with observations in the CDM cosmology. • Strong zs dependence • Weaker dependence on ellipticity and source size

  12. Optical depth as a function of cluster mass • Cutoffs at both low-mass and high-mass tails • Need to sample the mass function sufficiently

  13. Optical depth as a function of lens redshift • For sources at high z, probe clusters at high redshift • Hoekstra et al. who found all three of their lensing clusters were at z>0.62; understood if source z is high.

  14. Width of giant arcs • ~ r-β, width/diameter ~ 1/(β-1) • If β =2 (isothermal sphere), width/diameter=1 • Width can be used as a probe of the cluster potential and the background source population

  15. Observed size distribution from HST Ferguson et al. (2004) Half-light radius Appears to be consistent with HST CDF/HDF observations of high-z galaxies

  16. Giant arcs in the WMAP three year cosmology • The WMAP three-year model has lower m and 8 compared with the usual LCDM model. • The lower m (0.238) and 8 (0.74) both reduce the number of giants • We compared arc predictions in the usual CDM and WMAP three-year models: • 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

  17. Predicted number of giant arcs Z=0.3 A factor of 6 • Effects of source size and ellipticity are modest • Effect of star formation? Maybe a factor of 2 (Meneghetti et al. 2003). Overcooling. • Largest uncertainty: source redshift distribution

  18. Summary • Optical depth may be too low in the WMAP three-year model (with 8=0.74) • But the source redshift distribution and effects of star formation are still uncertain • Properties of giant arcs (e.g., widths) can be used to probe of the intrinsic size of high-redshift sources and the cluster potential. • We need many larger giant arc samples, which will come as by-products of weak lensing surveys. • A combination of strong and weak lensing can probe clusters more robustly.

  19. Future works • What is the effect of baryons? • More realistic comparisons with observations • In particular, giant arcs in x-ray selected clusters • Are lensed clusters typical? Tests of the NFW profile. • Explore how the width of giant arcs can be used to probe properties of clusters and high-redshift source population • Constrain the power-spectrum normalisation and cosmogony

  20. Effects of source ellipticity • Effect of ellipticity is around 30-50%

  21. Effects of source size • Source size change results by a factor of ~1.5-2

  22. Comparison with previous studies • Two previous studies claim their predictions are consistent with observations • Our optical depth is lower than Bartelmann et al. (1998) by a factor of 10 because their σ8 (1.12) is too high • Sensitive to cosmogony & dark energy

  23. Comparison with previous studies • Wambsganss, Ostriker & Bode (2004) • Too high by a factor of ten • Assumption L/W=μ is incorrect • More or less consistent with Dalal et al. (2004), but their simulation volume may be too small (box size: 100/h Mpc)!

  24. Dark matter (energy) discussions • Do we really need it? MOND? • Evidence for dark matter in galaxies & clusters • Disc galaxies (rotation curve, satellite galaxies) • Elliptical galaxies (dynamics, lensing, x-ray) • Clusters (x-ray, lensing) • Large-scale structure, CMB • Substructures: • too many predicted? • Implications of new satellites found by SDSS in the MW. • Density profiles of dark matter haloes? • Density slopes? Too concentrated (from rotation curve, Tully-Fisher relation)? • Distribution of dark matter in galaxies as a function of radius • Maximal or minimal disks? • Fast bar pattern speed? • Galactic microlesning • What is it? • Cold, hot or warm? Collisionless or self-interacting? • Experimental status of direct search

  25. New satellites in the MW Belokurov et al. 2006

  26. CDM direct search

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