Statistics of the Weak-lensing Convergence Field

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

• Shear-Selected Galaxy Clusters
• Projection Effects
• Alternative Method
• Systematic Errors
• Results and Conclusions

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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-Zeldovich effect (SZE)
• Weak gravitational lensing (WL)
• Mass-observable relation is one potential
  problem.
• Self-calibration Majumdar Mohr (2003)
• Scatter and bias Lima Hu (2005)

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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)

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Projection Effects
Projection!
Hennawi Spergel (2005)
WL is sensitive to all masses along the line of
sight.
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Press-Schecter Formalism

• Original P-S formalism
• Primordial matter density (d) field
  Gaussian p.d.f.
• Spherical collapse dc 1.69
• One-parameter family sM
• Universal mass function (N-body simulation)
• ?CDM, tCDM models Jenkins et al. (2001)
• w-dependence Linder Jenkins (2003)
• accuracy 10 level

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Alternative Approach

• Analogies
• 3D matter density field 2D convergence (?)
  field
• dc S/N threshold
• Jenkins et al. mass function universal
  p.d.f. for ?
• (?min and s?)
• Valageas (2000)
• Munshi Jain (2000)
• Wang, Holz, Munshi (2002)

Flat ?CDM Om0.3 zs 1.0
One-point p.d.f. tail Fractional area of high
S/N points Projection effects incorporated
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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)

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Systematic Errors

• Reduced shear (direct observable)
• high ? 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?

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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

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Fisher Matrix

• Formalism
• Background galaxy redshift bins (i, j)
• Signal-to-noise thresholds (µ,?)

Covariance matrix estimated using log-normal
approximation (work in progress to estimate it
from simulations)
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Fractional Area
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Results
LSST-like WL survey performed by a ground based
telescope. Sky coverage 18000 deg2 Background
galaxies 50 /arcmin2.
Three background galaxy redshift bins (zs 0.6,
1.1, 1.9) with S/N thresholds 2.0, 2.5, 3.0
future CMB anisotropy measurements
(Planck) ?(w0) 0.03, ?(wa)
0.1 Constraints from CMB alone ?(w0) 0.3,
?(wa) 1.
Constraints from clusters ?(w0) 0.03,
?(wa) 0.09.
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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.