1. Cluster Strong Lensing Neal Dalal IAS

2. Cluster Strong Lensing Images of background galaxies strongly distorted by potential of foreground massive cluster Typically 2-3 images merged together into “giant arcs” Canonical giant arcs have l/w > 10 Usually azimuthally oriented but radial arcs are also observed

3. Lensing surveys SurveyRedshiftsArea (deg 2 )DepthObserved EMSS0.15 < z < 0.6~ 360V < 228 LCDCS0.5 < z < 0.769R < 21.52 RCSz < 0.6 z > 0.6 90  R < 24 0404 Comparison of Previous Arc Surveys Ongoing and future surveys (e.g. SDSS, MACS, RCS-2, CFHTLS, DES) increase area and number of detected arcs by many orders of magnitude!

4. SDSS Arcs

5. What good are arcs for cosmology? 1.Study properties of clusters Calibrate mass-observable relations Measure DM properties (e.g. radial profile, triaxiality, etc.) 2.Cosmological parameters Statistics Geometrical measure

6. modelling of individual systems Abell 1689 (Broadhurst et al. 2004) By fitting 100’s of lensed images, can reconstruct non-parametric mass model

7. Strong lens selection Strong lensing can give a precise determination of cluster mass profile. But which clusters are selected with a lens-selected sample? Related: which cluster properties are important in determining lensing cross-section?

8. Ray Tracing Simulations Ran 1024 3 cosmological N-body simulation in 320 h -1 Mpc box Compute surface density and ray- trace from source plane to image plane (~14000 ray-traces for z l =0.4, z s =1) Lens Plane Massive Cluster Identify massive cluster halos, measure structural properties (e.g. ~900 clusters at z=0.4)

9. Shallow density cusps imply: –SL cross section is a steep function of mass and concentration –Extreme sensitivity to fluctuations caused by substructure and halo triaxiality –Large spread in cross sections as a function of viewing angle and among clusters of similar mass Strong Lensing by CDM Halos For NFW: r crit exponentially sensitive to small variations in  20” rsrs r vir h  i /  crit

10. Analog Halos Spherical No Substructure Simulated Triaxial

11. Analog Halos Hennawi et al. (2005) in prep Replace each halo with analog halo. Ray trace and compare number of arcs to original simulated clusters Substructure identified by FOF algorithm with b = 0.05 Triaxiality boosts cross sections by factor 4-25 compared to spherical Analytical models under predict arc abundance by –up to 50 for spherical models –up to 2 for triaxial models Halo Triaxiality much more important than projections of substructure onto small radii Source plane: z s = 2.0; Lens Plane: z d = 0.41 N(>  ) Number of Arcs 10”15”20”25”30” Real/No Subs1.061.101.131.181.24 Real/Triaxial1.311.401.531.742.04 Real/Spherical4.765.096.4311.251.7

12. Biases in Lensing Selected Samples With a sample of well studied lensing clusters we can measure distributions of cluster properties. However lenses are biased with respect to.... Mass Concentration Orientation Substructure M vir c/c(M) M sub M 1/2 = 4.5  10 14 [c/c(M)] 1/2 = 1.18 [M sub ] 1/2 = 0.045 [M sub ] 1/2 = 0.041 |cos  | |cos  | 1/2 = 0.50 |cos  | 1/2 = 0.67 q 2  lower third q 2  middle third q 2  upper third

13. 2-D vs. 3-D quantities We measure 2-D profile and infer 3-D parameters. Because of triaxiality and projection bias, our 3-D inferences are biased. Can this explain the oddly high concentrations seen in detailed analyses of many lensing clusters (e.g. A1689, CL0024, RCS0224)? Note c vir ¼ 14 Broadhurst et al. (2004)

14. 2-D vs. 3-D quantities Note that concentrations of 15-20 are very unlikely

15. How important are mergers? It has been claimed that mergers can enhance lensing cross section by 10 £. Is this true? most massive substructure virial mass  mass in substructure virial mass

16. Line-of-sight projections Multi-plane Single plane Large-scale structure can significantly affect shear-selected cluster samples (Hennawi & Spergel 2005). Is this also the case for strong-lens selected clusters (e.g. Wambsganss et al. 2004)?

17. Giant Arc Abundance SurveyRedshiftsArea (deg 2 )DepthObservedPredicted EMSS0.15 < z < 0.6~ 360V < 2288.2 LCDCS0.5 < z < 0.769R < 21.521.2 RCSz < 0.6 z > 0.6 90  R < 24 0404 2121 Dalal, Holder, & Hennawi (2004) based on GIF simulations Comparison of Arc Surveys to Ray Trace Predictions EMSS: 8 of 38 clusters with L X > 2  10 44 ergs/s show giant arcs. Extrapolating gives ~ 900 over full sky. Ray tracing sims + HDF galaxy counts predicts ~ 1000 NO GIANT ARC PROBLEM! –Previous claim of order of magnitude discrepancy incorrectly extrapolated EMSS and used lower source density N(>r) Number of Arcs r [arcsecs] Solid: EMSS Dashed: Simulations

18. Conclusions Cluster lensing is a powerful probe of the distribution of dark matter on ~ 100 kpc/h scales Shallow density cusps of CDM clusters imply SL cross sections are extremely sensitive to ellipticity/triaxiality of dark matter halos Abundance of giant arcs behind low-z clusters agrees with prediction for LCDM. Hint of an excess for high-z clusters (Gladders/RCS) Search for clusters lenses in SDSS Gpc 3 volume will yield > 200 new giant arcs and ~ 8 new wide separation multiply image quasars

19. modelling of individual systems MS 2137-23 (Gavazzi et al. 2003) Even with just 1 or 2 arcs, it is still possible to derive interesting interesting constraints with high resolution imaging! DM inner slope Dalal & Keeton (2004)

20. Modelling individual systems With ground-based imaging, it is harder to match up images, making modeling more difficult. But systems with multiple arcs can still be useful: Example 1: tangential arcs roughly measure enclosed mass : so can we use multiple arcs to measure M(r) and hence radial slope? error in M(r) is O(e) dashed: 30% ellipticity solid: 15% ellipticity RCS 0224-0002 (Gladders et al. 2002) super-concentrated (c vir ~15)? 15% ellipticity 30% ellipticity isothermal flat example 2: combining tangential & radial arcs for spherical lenses: the ratio of radial critical line to tangential critical line gives slope. However, this is strongly affected by ellipticity

21. Cluster Lenses in the SDSS SDSS quasar samples –Spectro: 50,000 quasars -- 4000 deg 2 –Photo: 400,000 quasars -- 7000 deg 2 Search for companions around quasars with similar colors Follow up spectroscopy (ARC 3.5m) required because of fiber collisions SDSS 2.5m ARC 3.5m Jim Gunn Multiply Imaged Quasars Giant Arcs Apache Point Observatory UH 2.2m SDSS cluster sample –Richness selected clusters out to z < 0.6 -- 7000 deg 2 or ~ Gpc 3 –Photo-z’s good to within dz = 0.02 Deep imaging (  g < 26) of richest clusters on 4m class imagers Arc redshifts from Magellan and MMT HST imaging of lenses discovered? WIYN 3.5m

22. SDSS Arcs Extreme example of minor axis cusp? Or instead, is BCG off-center? Lin et al. (2005) in preparation Counter Image? Brightest arc (  g ~ 22 )  = 11” Discovered by visual inspection of SDSS southern coadd data (r < 24) Magellan spectroscopy –BCG galaxy @ z = 0.65 –Arc A @ z = 1.14 Preliminary models prefer the BCG to be off center? WIYN gri composite - seeing ~ 0.6” 30”

23. SDSS Arcs A B 30” WIYN g + i composite - seeing ~ 1.2” Arcs at  = 35” and  = 12” Abell cluster @ z = 0.28. L X = 8.7  10 44 (NORAS) Models prefer high ellipticities (q < 0.5) for inner slopes typical of CDM halos (n ~ 0.5) Hennawi et al. (2005) in preparation

24. N(>r) Number of Arcs r [arcsecs] Cosmology with Cluster Lenses Why is Cluster Strong Lensing interesting for Cosmology? –Natural Gravitational Telescopes magnify high-z galaxies –Measure Cosmological Parameters?? –Constrain distribution of dark matter in clusters on small scales where density is highest For a giant arc with  ~ 20” YES: For wide separation arcs, all cluster lensing observables can be predicted ab initio NO: Need to simulate effects of cooling and star formation on dark matter. Ask A. Kravtsov?

25. Strong Lensing Statistics Detailed Modeling of Individual Lenses –Measure structural parameters of cluster (concentration, ellipticity/triaxiality, inner slope) for each cluster lens. Compare to analogous distributions in N-body simulations Abundance –Count the number of lensed arcs (QSOs?) per deg 2 as a function of angular separation and compare to prediction from N-body sims CONS Arcs identified by eye. Selection function very difficult to quantify (QSOs?) Uncertainty in cluster mass scale creeps in unless entire survey area is deeply imaged PROS Simplest ‘one-point’ statistic Requires ground based imaging of most massive clusters PROS Isolates parameters of halos breaking ‘degeneracies’ which could produce the same abundance Does not require knowledge of selection function of arcs CONS Requires multiple arcs. Imaging from space required to obtain tight constraints Even with multiple arcs degeneracies between model parameters complicates comparison to simulations