Weak Lensing

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Weak Lensing

• Pan-STARRS Seminar Series
• Nick Kaiser, IfA, U. Hawaii
• Dec 12th, 2004

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Outline

• Overview Goals of WL
• The standard model for cosmology
• Background model
• Theory of structure formation
• Probes of large-scale structure
• Galaxy-clustering CMB bulk flows WL
• Applications of WL
• Implications for Pan-STARRS

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Overview Goals of WL

• WL is the distortion of shapes (and sizes) of
  distant galaxies (the cosmic wallpaper) by
  intervening mass structure
• Potent probe of mass distribution on a wide range
  of scales (10kpc - 100Mpc)
• Goals
• Constrain cosmological parameters
• Evolution of clusters
• Geometrical tests
• Test theories of structure formation
• Statistics of large-scale structure

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WL Movie
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Cosmological background model

• Inflation
• Early dynamics dominated by a relativistic scalar
  field (the inflaton) ?
• Analogous to electromagnetic vector field A?
  (also bosonic)
• Field is defined by its potential V(?)
• Might just be a mass term m?2, or self
  interaction ??4
• Initial conditions (chaotic inflation)
• Finite region with large ?, small ???and ?? /?t
• Expanding da /dt 0
• ?slow roll inflation a exp(Ht) with H, H2
  G? constant
• Reheating
• Decay of energy in the inflaton field to ordinary
  matter
• ? radiation era ? matter era ? late-time
  inflation?

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Cosmological structure formation

• Zero point fluctuations ? ??, ?? /?t ???
• A region with ?? 0 will undergo more inflation
  and will end up with larger volume
• ? spatial curvature fluctuations
• Constancy of conditions during inflation ?
  scale invariant spectrum of curvature
  fluctuations (fractal-like)
• At end of inflation, curv. Fluctuations are
  frozen in on super-horizon scales
• Fluctuations re-enter horizon as density
  fluctuations
• Curvature peculiar Newtonian gravitational
  potential
• Post-inflation evolution depends on scale
• Small scale ? re-enter horizon in rad era ?
  acoustic oscillations in baryon/plasma fluid,
  stagnation of DM growth
• Large scales grow continuously preserving initial
  spectrum
• Critical scale is horizon size at zeq
  super-cluster scale

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Inflationary cosmology predictions

• Big, old, spatially flat Universe
• Specific predictions for the nature and spectrum
  of density fluctuations (seeds for structure
  formation)
• Gaussian fluctuations (random phases)
• (Nearly) scale invariant fluctuations on large
  scales
• Detailed form (tilt) depends on scalar
  potential
• break at zeq horizon scale
• Sub zeq horizon spectrum depends on
• matter content, ?m ?rad, ??
• Matter type - cold, warm DM etc

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Probes of cosmological structure

• Galaxy Clustering
• Cosmic Microwave Background Anisotropy
• Bulk Flows
• Weak Lensing

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Galaxy clustering

• Measure P(k) (or ?(r)) directly from galaxy
  distribution
• Low-z redshift surveys (SDSS, 2df)
• In projection as w???from angular surveys
• Moderate z redshift surveys (e.g. DEEP) ?
  evolution of structure
• Problem of bias
• Different galaxy types are known to cluster
  differently on small scales
• Clusters are rich in early type galaxies
• Clusters have anomalously large clustering ?(r)

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Semi-analytic galaxy formation

• Semi-analytic galaxy formation theory
• MPA group
• Early type (low star formation rate) galaxies
  reside in densest regions

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CMB anisotropy

• Large-scales
• Gravitational redshift ?T/T 1/3 ????G??/R
• Direct map of curvature/Newtonian potential
  perturbations
• Small-scales
• Acoustic oscillations (Doppler peaks)
• Sensitive to matter content
• Probe of conditions around decoupling
• Later for very large scales

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Bulk Flows

• Growth of density perturbations ???????a(t)
  implies departures from pure Hubble expansion
• ?? ?v2 constant ??v?v G?M/R ???v HR ????
• Measuring H is hard, measuring ?H is very hard
• Can only be measured locally ??large cosmic
  (a.k.a. sampling) variance

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Weak Lensing

• In weak gravity, effective refractive index is
  n1-2??
• For a single blob of size R the deflection
  angle is ??????G?M/Rc2
• The deflection is not directly measurable, but
  the gradient of the deflection is - this is
  called the (image) shear ?
• For 1 blob this is ?1 ??/? G?M D/R2c2
  (H2RD/c2) ????, where D is the distance.
• Similar to the velocity perturbations ?v/v for D
  c/H
• However, we generally have N D/R such blobs
  along the line of sight, so the rms effect is
• ? (H2 R1/2 D3/2 / c2) ????

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Applications of WL

• Mass distribution (and Mass vs Light) on
  supercluster scales
• Extended haloes of early type galaxies vs CDM
  theory
• Cosmic shear variance
• Equivalent to power-spectrum measurements

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Mass vs Light (early type galaxies)
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Boxes mass Circles light Early type
galaxies trace the mass
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Mass vs Light in MACS Clusters

• MACS cluster sample
• SUBARU/SUPRIME imaging
• Donovan thesis
• Relation between mass and light distributions?
• Can we use Lx as a proxy for mass?

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MACS Cluster Sample(Harald Ebeling)
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MACSJ2243mass contours over light
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MACSJ2243tangentialshear surface density
profiles
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Light vs Mass in MACSJ2243
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Masses of early type haloesfrom the UH 8K survey
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Early-type halo mass profile
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• Cosmic Shear ca 04/00
• 4 groups
• Good agreement at small scales
• UH results lower at large angles

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Combo-17(Brown et al)
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CTIO-75

• 75 sq deg
• Jarvis et al

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WL with Pan-STARRS

• WL will surpass current surveys (e.g. CFHT-LS) by
  orders of magnitude in area coverage
• All sky (30,000 sq deg) ecliptic plane (7,000
  squ deg) surveys
• Cosmic variance for P(k) will be greatly reduced
• Thousands of mass selected clusters - ?m, ??
• Selected medium deep field will allow higher
  order moments, evolutionary tests
• WL is usually systematics limited
• Correction for (generally color, position
  dependent) anisotropic PSF
• PS will take many, many short exposures and
  combine these
• Each galaxy will be observed under range of
  conditions (telescope orientation, position on
  focal plane)
• Systematics can be either measured and corrected
  for (if deterministic) or will average down like
  root(N) (if not)

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The End