A Joy Ride in the Large Scale Structure of the Universe

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A Joy Ride in the Large Scale Structure of the
Universe

• Niayesh Afshordi
• Institute for Theory and Computation
• Harvard-Smithsonian Center for Astrophysics

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Outline

• Galaxies
• Spectrum, Color, Redshift, Shape, Scalings, Bias
  Phenomenology
• Correlations
• Real/Fourier, CF/PS Measurements, Two/Many Points
• Linear and Non-Linear Dynamics
• Linear Theory, Zeldovich Approximation,
  Adhesion, Top hat model, N-Body Simulations
• Peculiar motion
• Velocity Surveys, POTENT, kSZ prospects
• Non-Linear Structures and Bias
• Press-Schecter and Variants, Bias, Clusters and
  Virialization (number counts, ICM)
• Halo Model
• Galaxy Formation and Reionization
• Lyman-Alpha Forest/Weak Lensing (Uros Talk)

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Sound Waves in the LSS

• The imprint of sound horizon at last scattering
  can be seen in the galaxy auto-correlation
  (SDSS/2dF)
• Spectacular triumph of Linear Theory of Structure
  Formation (Roberts Lecture)

Sloan Digital Sky Survey (SDSS) Luminous Red
Galaxies (LRGs)
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Sound Waves in the LSS
CMB Power Spectrum (WMAP 1st yr)
2dF Galaxy Power Spectrum
Acoustic Oscillations In Baryon-Photon Fluid
turn into small imprints in dark matter power
spectrum
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Galaxies Cosmological Molecules

• Poorly understood Inner dynamics and formation
  mechanism
• Used as tracers of LSS using a phenomenological
  understanding of their properties (most robust,
  historically and so far)

http//cosmo.nyu.edu/blanton/
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Galaxy Spectra ?redshift ? distance (up to
peculiar motion)
Population Synthesis Models for Galaxy Spectra
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Photometric Redshifts
If spectrum can be parameterized by a few
numbers, redshift can be expressed in terms of
colors.
redshift
u g r i z

• Much more efficient if you dont want
• exact redshift, e.g., weak lensing surveys,
• CMB cross-correlation

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Scaling of Galaxy Properties

• Tully-Fisher/Faber Jackson

• Other Scalings

Standard Candles?
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Bias Phenomenology

• Large Scales? Independent Patches of the
  Universe
• Bias can be different for different
• galaxy populations

Bias bgal(t)
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Correlation Function/ Power Spectrum

• Correlation Function
• Excess Probability of finding galaxies at
  distance r
• P(x,xr) d3x d3r 2 (1?(r)) d3x d3r
• Power Spectrum
• Magnitude of Fourier Amplitude
• ?k -1 s d3x n(x) exp(-ik.x)
• Statistical Homogeneity (see Amirs Talk)?
• (2?)3 ?3(k-k) P(k)
• You can then easily verify P(k) s d3x ?(r)
  exp(-ik.x)
• ?2(k) (k3 /2?2)P(k) ?(?/r)

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Explicit Example SDSS Galaxies
bias
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One Power Spectrum Many Probes
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Higher Order Statistics

• May probe primordial non-Gaussianity (test
  inflation) or non-linear structure formation
  (e.g. measure bgal)
• Three Point Function/ Bispectrum
• Minkowski Functionals
• Galaxy Clusters

(2dF) Jing Borner 04
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Linear and Non-Linear Dynamics

• Newtonian Structure Formation
• (Roberts Lectures)
• Zeldovich Approximation
• (? does not feel small scale non-linearities)

Pancakes in the Sky
Caustics Zeldovich Pancake
Example 2dF Survey
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Top-Hat Collapse Model (Gunn Gott 72)
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c

• At ?lin ?c ' 1.6, spherical domains collpase to
  a point
• Before this happens, aspherical inner structure
  causes the halo to virialize at ? ? ' 200

simulations
log (c)
Spherical Collapse
log(Mh/M)
Afshordi Cen 2002
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N-Body Simulations

• Navarro-Frenk-White (NFW) dark matter profiles
• Cusp-Core controversy
• Cusp-Cusp controversy
• X-ray Scalings
• Everything Else !
• Problems
• Resolution
• Cooling
• Star Formation Feedback
• AGN Feedback

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Peculiar Motion

• Zeldocich formula
• Velocity Surveys
• Redshift Space correlation function
• kSZ prospects

SuZIE
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Making Virialized Haloes

• Gaussian Initial Conditions and Press-Schecter
• Ellipsoidal collapse modifying Press-Schecter
• Haloes are biased w.r.t. dark matter
• b(M) d log n(M)/d?c
• DM caustics ? gas shocks ? hot haloes
• Gaussian Tail of perturbations ? Cluster Mass
  Function is a sensitive probe of the cosmic
  evolution (X-ray/SZ surveys)
• Understanding Intra-Cluster Medium is a
  prerequisite

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Halo Model

• For the first time, gave theorists an analytic
  framework to deal with fully non-linear structure
  formation
• Structure Comprises of NFW haloes, which cluster
  according to the linear theory with a constant
  bias
• (See Cooray Sheth 2002 for a review)

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Halo Model
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Halo Model

• Using prescriptions to occupy haloes with
  galaxies or gas, we can reproduce their
  non-linear structure as well

Komatsu Seljak 01
Kravstov et al. 05
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Reionization

• Gunn-Peterson effect The universe is transparent
  to Ly-? photons up to z ' 6 (Ly-? forest)
• ? Hydrogen Neutral Fraction in Inter-Galactic
  Medium (IGM) xHI
• ? Hydrogen was reionized by Light from Galaxies

http//casa.colorado.edu/gnedin/
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Gunn-Peterson trough
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Gunn-Peterson Trough
z 3.7
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Reionization

• WMAP sees signatures of scattering of CMB by free
  electrons at z ' 17 4
• ? Reionization started at z20, and was
  completed by z6
• 21cm hyperfine transition is considered as a
  promising method to probe reionization

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Final Thoughts

• The (quasi)-linear nature of LSS along with its
  transparency, makes it an excellent test bed for
  cosmological theories
• CMB is in 2D, but LSS is in 3D ? It contains much
  more information
• In combination with CMB, LSS provides countless
  ways of confirming LCDM paradigm, leaving little
  room for alternative interpretations