1. Statistics of the Weak-lensing Convergence Field Sheng Wang Brookhaven National Laboratory Columbia University Collaborators: Zoltán Haiman, Morgan May, and John Kehayias

2. Outline Shear-Selected Galaxy Clusters Projection Effects Alternative Method Systematic Errors Results and Conclusions

3. Cluster of Galaxies Abundance of galaxy clusters (redshift evolution) is exponentially sensitive to matter density fluctuations thus the growth of structure. X-ray or Sunyaev-Zel’dovich effect (SZE) Weak gravitational lensing (WL) Mass-observable relation is one potential problem. Self-calibration Majumdar & Mohr (2003) Scatter and bias Lima & Hu (2005)

4. Shear-Selected Galaxy Clusters WL — coherent distortion of background galaxy images Depends on gravity only (“cleanest” technique) Automatic mass estimates Projection Effects Efficiency — false detections Completeness — missing clusters White, van Waerbeke, & Mackey (2002) Hennawi & Spergel (2004) Hamana, Takada, & Yoshida (2004)

5. Projection Effects WL is sensitive to all masses along the line of sight. Hennawi & Spergel (2005) Projection!

6. Press-Schecter Formalism Original P-S formalism Primordial matter density (δ) field — Gaussian p.d.f. Spherical collapse — δ c ~ 1.69 One-parameter family — σ M Universal mass function (N-body simulation) ΛCDM, τCDM models Jenkins et al. (2001) w-dependence Linder & Jenkins (2003) accuracy: 10% level

7. Analogies 3D matter density field — 2D convergence (κ) field δ c — S/N threshold Jenkins et al. mass function — universal p.d.f. for κ (κ min and σ κ ) Valageas (2000) Munshi & Jain (2000) Wang, Holz, & Munshi (2002) Alternative Approach Flat ΛCDM Ω m =0.3 z s = 1.0 One-point p.d.f. tail Fractional area of high S/N points Projection effects incorporated

8. Shear → Convergence Reconstruction of “mass map” (WL regime) Tangential shear (linear) Kaiser & Squires (1993) Maximum likelihood Bartelmann et al. (1996) Intrinsic ellipticity noise Gaussian random field (KS/maximum likelihood) van Waerbeke (2000)

9. Systematic Errors Reduced shear (direct observable) high κ — non-linear inversion Seitz & Schneider (1995) Universality — Stable-clustering ansatz valid for tail? (work in progress looking at simulations) Baryon effects cooling — different density distribution Intrinsic ellipticity noise Intrinsic ellipticity alignment / shear-ellipticity alignment?

10. Comparison of Technique Vs. shear-shear correlation (tomography) Simple one-point statistics yet extra information Different systematic errors Vs. number counts of galaxy clusters Closely related (galaxy clusters “mean” high S/N) Projection effects included as signals

11. Fisher Matrix Covariance matrix estimated using log-normal approximation (work in progress to estimate it from simulations) Formalism Background galaxy redshift bins (i, j) Signal-to-noise thresholds (μ,ν)

12. Fractional Area

13. Results LSST-like WL survey performed by a ground based telescope. Sky coverage: 18000 deg 2 ; Background galaxies: ~ 50 /arcmin 2. Three background galaxy redshift bins (z s ~ 0.6, 1.1, 1.9) with S/N thresholds = 2.0, 2.5, 3.0 + future CMB anisotropy measurements (Planck): Δ(w 0 ) ~ 0.03, Δ(w a ) ~ 0.1; Constraints from CMB alone: Δ(w 0 ) ~ 0.3, Δ(w a ) ~ 1. Constraints from clusters: Δ(w 0 ) ~ 0.03, Δ(w a ) ~ 0.09.

14. Conclusion Future galaxy cluster surveys using WL, such as LSST, will suffer from the projection effects when searching for clusters. To determine the selection function to ~ N -1/2 will be challenging. We propose an alternative, more robust one-point statistic using points in mass maps with high signal-to-noise. Compared with conventional statistics, they contain extra information and suffer from different systematics. This statistic, combined with future CMB anisotropy measurements, such as Planck, can place constraints on cosmological parameters, such as the evolution of dark energy, that are comparable to those from clusters.