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Measuring the Growth Factor via Gravitational Lensing

Measuring the Growth Factor via Gravitational Lensing. James Taylor University of Waterloo. Origins of Dark Energy Origins Institute, May 14-17 2007. Observational Paths to Dark Energy. }. geometry. }. growth of structure. line-of-sight distances, e.g. D L (a) from SNe

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Measuring the Growth Factor via Gravitational Lensing

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  1. Measuring the Growth Factor via Gravitational Lensing James Taylor University of Waterloo Origins of Dark Energy Origins Institute, May 14-17 2007

  2. Observational Paths to Dark Energy } geometry } growth of structure line-of-sight distances, e.g. DL(a) from SNe physical scales, e.g. the sound horizon from Baryon Acoustic Oscillations volumes, e.g. from cluster number counts? the growth of potential fluctuations (ISW) the growth of linear fluctuations (cosmic shear) the abundance of non-linear fluctuations (cluster number counts) the differential growth of non-linear structure Both ultimately measure H(a) or i(a), but with very different redshift weighting. Origins of Dark Energy Origins Institute, May 14-17 2007

  3. Probes of Structure Formation Horellou & Berge 2005 Initial perturbations are small, grow linearly to amplitude D(a): Growth Factor: (normalized to 1 at the a = 1), where D is the amplitude of the growing mode. For EdS, g = 1 at all times For other e.o.s., varies with a: Origins of Dark Energy Origins Institute, May 14-17 2007

  4. Probes of structure growth using gravitational lensing: 1) Cosmic shear from weak lensing  linear and non-linear fluctuations on a range of scales (complicated inversion problems) 2) Cluster detection and characterization from weak and strong lensing  abundance of high peaks in the density field (degenerate in 8 andgrowth) 3) Differential growth of non-linear structure (interesting, but may be hard to calibrate?) Origins of Dark Energy Origins Institute, May 14-17 2007

  5. overdenseunderdense B-mode (systematic) Cosmic Shear, etc. Mass overdensity produces tangential distortion of light rays from background objects; underdensity produces radial distortion. Effect always small, so need to average over 100s of objects (i.e. galaxies)  limit to scales probed, intrinsic shape noise. * Can look at resulting signal statistically: shear correlation measuring correlation of overdense/underdense regions as a function of angular scale. * Can also make smoothed maps of resulting shear or convergence. Redshift dependence of effect is very slow, producing a very broad kernel in redshift space: Origins of Dark Energy Origins Institute, May 14-17 2007

  6. zs = 0.8 zs = 1.0 3D Lensing Tomography sensitivity 1/c Single source plane produces one weighted measurement of mass along the l.o.s. In principle, differences between planes can produce a 3D mass map or more indirect 3D shear statistics Some problems from extent of redshift kernel, inaccuracies in photo-zs Origins of Dark Energy Origins Institute, May 14-17 2007

  7. The COSMOS SurveyP.I. Nick Scoville Origins of Dark Energy Origins Institute, May 14-17 2007

  8. The COSMOS Survey • 2 square degree ACS mosaic • current lensing results from 1.64 square degrees • 2-3 million galaxies down to F814WAB = 26.6 • 15-band photometry, photo-zs with dz ~ 0.03(1+z) to z = 1.4 and IF814W = 24 • follow-up in X-ray, radio, IR, UV Origins of Dark Energy Origins Institute, May 14-17 2007

  9. WL Convergence MapsMassey, Rhodes, Leauthaud Capak, Koekemoer, Scoville, Refregier • cut catalogue down to 40 galaxies/arcmin2 to remove bad zs • correct for PSF variations, CTE • Get lensing maps, low-resolution 3D maps, various measures of power in 2D and restricted 3D • results compare well with baryonic distributions (e.g. galaxy distribution) Origins of Dark Energy Origins Institute, May 14-17 2007

  10. instrumental systematics a major and unanticipated headache (PSF variations, CTE) Systematics Origins of Dark Energy Origins Institute, May 14-17 2007

  11. The Final Result E-modes (left) versus B-modes (right) Origins of Dark Energy Origins Institute, May 14-17 2007

  12. actually quite complicated to show the growth of structure going forward in time Seeing the Growth of Structure Directly Origins of Dark Energy Origins Institute, May 14-17 2007

  13. Measuring the Growth of Structure Calculate the shear correlation function divided by the integrated lensing sensitivity to a given slice, and rescale to a fixed physical scale, assuming the signal is coming from the redshift of peak sensitivity. Get (rather noisy) measure of the growth of structure: Massey et al. 2007b Origins of Dark Energy Origins Institute, May 14-17 2007

  14. Final result: first 3D map of the mass (or potential) distribution in a large volume. Note this is only 1.6 square degrees on the sky. 3D Mass Distribution Massey et al. 2007a Origins of Dark Energy Origins Institute, May 14-17 2007

  15. Shear vs. photo-z around peaks, along promising lines of sight Origins of Dark Energy Origins Institute, May 14-17 2007

  16. Shear vs. photo-z around peaks, along promising lines of sight N.B. angular-diameter distance-z relation Taylor et al. in prep. Origins of Dark Energy Origins Institute, May 14-17 2007

  17. 2D Can get constraints on the amplitude of fluctuations: Need a larger volume to get constraints on the equation of state (current estimate: w = -1 ± 1 with this volume) Working from space does not automatically make systematics vanish. Physically, projection effects and photo-z errors a major issue. Summary 3D Origins of Dark Energy Origins Institute, May 14-17 2007

  18. Count the number of high peaks in the universe • In principle a very sensitive measure • In practice, mass calibrations a problem • Also constrained to do this at fairly low redshift (esp. for x-ray) and fairly large mass N.B. Press-Schechter: Second Method: Cluster Number Counts Weller & Battye 2003 How to break sigma-growth factor degeneracy? Origins of Dark Energy Origins Institute, May 14-17 2007

  19. Dark matter halos achieve a different degree of relaxation depending on their growth rate (mass accretion rate versus crossing time?) • The change between the mixed and unmixed regions corresponds to a change in the slope of the density profile: r-1 to r-3 • This is measured as halo concentration: c  rs/rvir; rs where slope is r-2 • Thus the concentration of the density profile contains information about prior growth • Other structural features (substructure, elongation, spin?) track this one parameter Third Method: Differential Growth Origins of Dark Energy Origins Institute, May 14-17 2007

  20. Andrei Kravtsov

  21. Some reassuring simplifications in the non-linear regime: e.g. a single-parameter density profile Navarro et al. 2004 Similarly, a single-parameter mass-accretion history? cf. van den Bosch, Wechsler et al., Mo et al. Origins of Dark Energy Origins Institute, May 14-17 2007

  22. So how do haloes grow? Extended Press-Schechter (e.g. Lacey & Cole 1993) mass accretion history = random walk in  / (where   c/D) high increasing barrier height low  : height of barrier perturbation has to cross to collapse (M) : variance on mass scale M big small decreasing scale Origins of Dark Energy Origins Institute, May 14-17 2007

  23. What does concentration measure? Mass accretion histories correspond to linear trajectories in- space Transformation to M - a introduces curvature concentration depends on epoch where transition from fast to slow accretion starts Depends mainly on dlnD/dlna Origins of Dark Energy Origins Institute, May 14-17 2007

  24. What does concentration measure? ac slow Concentration set in transition from fast to slow accretion curvature in log(M/M0) vs. log(a) mainly due to curvature in D(a) So in effect we can measure dlnD/dln(a) with some weighting. fast cNFW ~ 4 (ao/ac) Origins of Dark Energy Origins Institute, May 14-17 2007

  25. Concentration versus mass accretion history Wechsler et al. 2002: ac/ao vs concentration Zhao et al. 2003a: better fitting function Origins of Dark Energy Origins Institute, May 14-17 2007

  26. Can we measure concentration? Comerford & Natarajan 2007: X-ray and Lensing concentrations for O(100) clusters Origins of Dark Energy Origins Institute, May 14-17 2007

  27. N.B. other age indicators: Halo Substructure The “radial period” (period for subsequent pericentric passages)is the fundamental timescale for subhalo evolution  substructuretracks tH Radius/Rvir M/Minf Energy/Vc2 Taylor & Babul 2004 Origins of Dark Energy Origins Institute, May 14-17 2007

  28. Substructure reflects balance between accretion and disruption Taylor & Babul 2005a Origins of Dark Energy Origins Institute, May 14-17 2007

  29. Overall effect of age on the substructure mass function: Taylor & Babul 2005a Origins of Dark Energy Origins Institute, May 14-17 2007

  30. Global Substructure vs. Age Relation Overall correlation between age and substructure fraction: number of massive satellites strongly correlated with recent merger history Zentner et al. 2005 Origins of Dark Energy Origins Institute, May 14-17 2007

  31. Three Lensing Surveys: * COSMOS(Scoville PI, Ellis, Massey, Rhodes, Leauthaud, Finoguenov) 2 deg2 ACS weak lensing, plus X-ray & other supporting observations ~150 extended X-ray peaks, ~ 20 in lensing map, z = 0.15 –0.85, M 5e13. * Suprime22(Miyazaki/Ellis, Green, Hamana, Massey) 22 deg2 Subaru weak lensing, some x-ray, Keck/Subaru redshifts ~80 objects from lensing (with masses to ~50%), z = 0.15–0.8, , M 1e14 * LoCuSS(Smith PI) ~all sky, nearby massive cluster survey z = 0.15–0.25, Lx limited, ACS snapshot lensing, some ground-based NIR, XMM & archival Chandra x-ray, objects typically 5e14, current sample of 30 clusters, final sample of ~100 Origins of Dark Energy Origins Institute, May 14-17 2007

  32. Pilot (XBACs): JPK+ GO:8249 LoCuSS (BCS+eBCS+REFLEX): GPS+ GO:10881 LoCuSS: Sample Original Idea: • Target = 100 clusters • Brightest X-ray clusters over a narrow z range suited to f.o.v. of WFPC/ACS • 21 archival HST clusters • 143 SNAPSHOT targets • ~50% observed by mid-2008 Current Status: • More or less complete data on 43 clusters • Many are strong lensing systems Origins of Dark Energy Origins Institute, May 14-17 2007

  33. Why the diversity of cluster morphologies? What is happening physically? (Smith et al. 2005) Origins of Dark Energy Origins Institute, May 14-17 2007

  34. Smith et al., 2005, MNRAS, 359, 417 Disturbed Versus Undisturbed Undisturbed uni-modal (3/10) Disturbed multi-modal (4/10) Disturbed uni-modal (3/10) Mass Ndm 1 2 1 fsub 0.03±0.01 0.23±0.01 0.04±0.01 Ttot/Tann 0.8±0.1 1.0±0.1 1.0±0.2 Δr (kpc) <4 40±8 88±4 X-ray Origins of Dark Energy Origins Institute, May 14-17 2007

  35. Structural segregation [~40%] Possible Systematics? [~10-20%] Structural segregation in the M-T relation? • Mass measurement wrong for non-SL clusters? • Core-related phenomena? • Pederson et al., 0603260 • Cluster-cluster mergers? • Ricker & Sarazin 2001, Randall et al. 2003 • What else? Smith et al., 2005, MNRAS, 359, 417 Origins of Dark Energy Origins Institute, May 14-17 2007

  36. Compare main central component to the substructure:A wide range of substructure fractions  age difference? (Smith et al. 2005) Overall, seems likely that substructure and possibly X-ray scaling offsets provide another way of quantifying age obsevationally. Origins of Dark Energy Origins Institute, May 14-17 2007

  37. Summary The measuring the growth factor provides a complimentary estimate of the equation of state, with different redshift weighting. At least three methods exist; the third relies on the statistics of halo growth and the effect of mass accretion rates on halo profiles, substructure and other properties (spin? X-ray scaling offsets? AGN activity?). Whether this third method can be calibrated to a useful degree is not clear; then again similar problems exist with cluster mass measurements. Origins of Dark Energy Origins Institute, May 14-17 2007

  38. 8 6 Recent Suprime22 Results(Green et al. 2006) 3  worse seeing  better seeing Log(volume) Origins of Dark Energy Origins Institute, May 14-17 2007

  39. COSMOS Xray-lensing comparison(Finoguenov et al. 2006, Taylor et al in prep.) 8 6 3 Log(volume) Origins of Dark Energy Origins Institute, May 14-17 2007

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