The largescale structure of the universe 2

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The large-scale structure of the universe - 2

• Matthew Colless
• The New Cosmology
• Physics Summer School 2003

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Lecture 2 - Outline

• Redshift-space distortions.
• The correlation function and power spectrum.
• Gaussianity and topology.
• Open questions and new surveys.
• LSS cosmology with the 2dF Galaxy Redshift
  Survey.
• Mass motions - the 6dF Galaxy Survey.

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Redshift-space distortions
zobs ztrue vpec/c where vpec? ?0.6 dr/r
(?0.6/b) dn/n
bias
Real-space
linear
nonlinear
turnaround
Regime
Redshift space
Observer
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Redshift-space distortion of the CF

• Because of peculiar velocities, the redshift
  space CF is distorted w.r.t. the real-space CF
• In real space the contours of the CF are
  circular.
• Coherent infall on large scales (in linear
  regime) squashes the contours along the line of
  sight.
• Rapid motions in collapsed structures on small
  scales stretch the contours along the line of
  sight.

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Distortions and P(k)

• Because of peculiar velocities, the PS in
  redshift space, Ps(k) is distorted w.r.t. the PS
  in real space, P(k).
• Far from the observer (plane- approx.)
  Ps(k) (1bmk2)2 P(k)
  where b W0.6/b and mk is cosine of Ð
  between k and radial l.o.s. (Note Ps depends on
  k, not just k, because no longer isotropic.)
• The Ð-averaged z-space PS, Ps(k)
  (4p)-1 ò Ps(k) dqk ,
  is then given by
  Ps(k) (1 2/3 b 1/5 b2) P(k) ,
  so the ratio of the z-space
  and real-space PS (in the linear regime)
  constrains b W0.6/b (the mass density, up to
  biasing).
• With z-survey, measuring Ps(k) not P(k)
• doesnt affect shape analysis (since they are
  proportional)
• to use distortions for b need P(k) can obtain by
  inverting angular PS w(q), or by linearly
  evolving the CMB mass PS.

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x(s), x(?,?) and x(r)

• The spatial CF x(r) can be recovered from the
  z-space CF x(s) by computing x(s) as a function
  of the separations in plane of sky, s, and the
  line of sight, p, to obtain x s(s,p).
• The projection of x s(s,p) onto the s-axis is
  w(s) 2
  ò x s(s,p) dp
  2 ò x r (s2y2)1/2 dy
• For a power-law, x(r) (r/r0)-g , and we have
  ?(s) w(s)/s
  x r(s) G(1/2)G((g-1)/2)/G(g/2)
  where G is the standard gamma
  function.

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Small scales - x(r)

• On scales lt20 h-1 Mpc x(r) is well-fitted by a
  power law x(r) (r/5.4 h-1
  Mpc)-1.8 Þ s2(8 Mpc) ? 1.0
  (optical) x(r) (r/3.8 h-1 Mpc)-1.6
  Þ s2(8 Mpc) ? 0.6 (IR)
• This is just a reflection of the
  morphology-density relation (E/S0Sp as density
  ) E/S0s clustered much more strongly than
  Sp/Irrs at small scales (lt few Mpc).
• Low-L galaxies are more weakly clustered than L
  galaxies high-L galaxies are more strongly
  clustered.

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Large scales - P(k)

• P(k) is preferred to x(r) on large scales it is
  more robust to compute, the covariance between
  scales is simpler, and the error analysis is
  easier.
• Fits to P(k) give G ? 0.2, implying ? ? 0.3 if h
  ? 0.7, but the turnover in P(k) around 200 h-1
  Mpc (the horizon scale at matter-radiation
  equality) is not well determined.

• Can reconcile P(k) for IR, optical and radio
  galaxies and clusters on scales gt10 h-1 Mpc,
  assuming
• relative biases bAbellbradiobopticalbIRAS
  4.51.91.31
• P(k) shape consistent with G0.25 CDM and COBE
  normalisation.

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Measuring b from P(k)

• z-space distortions produce Fingers of God on
  small scales and compression along the line of
  sight on large scales.
• Can get b W0.6/b from the ratio of the z-space
  to real-space PS Ps(k)/P(k) (1 2/3 b 1/5
  b2)
• Or can measure the degree of distortion of x s in
  s-p plane from ratio of quadrupole to monopole
  P2s(k) 4/3b 4/7b 2
  P0s(k) 1 2/3b 1/5b 2
• Estimates of b from P(k) using linear z-space
  distortions

• from IR z-surveys b 0.80.2
• from optical z-surveys b 0.50.1
• thus boptical/bIRAS 1.5

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Gaussianity and topology

• On large scales, all the evidence appears
  consistent with random phases (Gaussian
  fluctuations) on large scales - but this is not
  yet compelling.
• On small scales, non-linear evolution of the
  density field occurs
• the 34-point correlation functions are found to
  be non-zero Þ non-random phases.
• hierarchical scaling appears to relate the
  N-point, spherically-averaged correlation
  functions
  ltxN(V)gt SNltx2(V)gtN-1
  as predicted by perturbation
  theory for Gaussian initial conditions and
  gravitational instability.
• Topology use g(n), the genus as function of
  density contour g holes - pieces 1
  
• on small scales, there is a slight meatball
  shift w.r.t. Gaussian g(n), as expected from
  non-linear evolution
• on large scales, this will provide another test
  of Gaussianity.

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Open questions in LSS

• What is the shape of the power spectrum?
• what is the nature of the DM?
• what is the value of G Wh?
• Mass and bias
• what is the value of b W0.6/b?
• can we obtain W and b independently of each
  other?
• what are the relative biases of different galaxy
  populations?
• Can we check the gravitational instability
  paradigm?
• Were the initial density fluctuations
  random-phase (Gaussian)?
• What is the non-linear evolution of the galaxy
  and mass distributions?
• Can we link galaxy properties (luminosity, mass,
  type) to local density and/or large-scale
  structure?
• which properties are primordial?
• which are contingent on detailed evolution?

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Major new LSS surveys

• Massive surveys at low z (105-106 galaxies ltzgt ?
  0.1)
• 2dF Galaxy Redshift Survey and Sloan Digital Sky
  Survey
• high-precision LSS and cosmology measure P(k) on
  large scales and b from z-space distortions to
  give ? and b.
• low-z galaxy population F and x as joint
  functions of luminosity, type, local density and
  star-formation rate
• Massive surveys at high redshift (ltzgt ? 0.5-1.0
  or higher)
• VIMOS and DEIMOS surveys (and others)
• evolution of the galaxy population
• evolution of the large-scale structure
• Mass and motions survey (6dF Galaxy Survey)
• NIR-selected z-survey of local universe, together
  with...
• measurements of s for 15000 E/S0 galaxies
  
  Þ masses
  and distances from Fundamental Plane Þ
  density/velocity field to 15000 km/s (150 h-1 Mpc)

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CfA/SSRS z-survey 15000 zs
Earlier large redshift surveys
CfA Survey 15000 zs
Las Campanas Redshift Survey 25000 zs
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Comparison of redshift surveys
2dGRS
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2dF Galaxy Redshift Survey
2000 sq.deg. to bJ19.45 250,000 galaxies
Stripsrandom fields 1x108 h-3 Mpc3 Volume in
strips 3x107 h-3 Mpc3
NGP
SGP
NGP 75?x7.5? SGP 75?x15? Random 100x2?Ø
70,000 140,000 40,000
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2dF Galaxy Redshift Survey
May 2002 221,283 galaxies
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Fine detail 2-deg NGP slices (1-deg steps)
2dFGRS bJ lt 19.45
SDSS r lt 17.8
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?CDM bias 1
SCDM bias 1
Cosmology by eye!
Observed
SCDM bias 2
?CDM bias 2
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?m ?? ?k ? 1
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2dFGRS LSS Cosmology Highlights

• The most precise determination of the large-scale
  structure of the galaxy distribution on scales up
  to 600 h-1 Mpc.
• Detection of acoustic oscillations in the galaxy
  distribution due to baryon/photon coupling in the
  early universe.
• Unambiguous detection of coherent collapse on
  large scales, confirming structures grow via
  gravitational instability.
• Measurements of ? (mean mass density) from the
  power spectrum and redshift-space distortions ?
  0.29 ? 0.05
• A measurement of the baryon fraction from the
  acoustic oscillations in the power spectrum
  ?b/? 0.15 ? 0.07
• First measurement of galaxy bias parameter b
  1.00 ? 0.09
• An new upper limit on the neutrino fraction, ?n/?
  lt 0.13, and a limit on the mass of all neutrino
  species, mn lt 1.8 eV.

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CDM Model Fits to Power Spectrum
Fit model CDM P(k) (with n1) after convolution
with survey window function. Fit parameters (1)
?mh (2) ?b/?m (3) h (marginalise) Window flattens
P(k) and damps baryon features. Fits limited
to 0.015ltklt0.15.
model P(k)
Non-linear regime
Large errors
Ratio to ?mh0.25 no-baryon CDM model
model P(k) after window convolution
Wavenumber 2?/scale
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Confidence Limits on ? and ?b/?m
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Redshift-Space Correlation Function

• Small ? ? non-linear Finger-of-God effect
• Large ? ? flattening along line of sight due to
  coherent infall
• Fit to r 8-30 h-1 Mpc gives (after correction
  for ltzgt0.15, ltLgt1.4L) ? ?0.6/b 0.47?0.09
  and pair-wise vel. dispersion ?p 495 ? 52 km/s
• For b ? 1 ? ? ? 0.21
• For ? ? 0.3 ? b ? 1.2

Separation along the line of sight, ? (Mpc/h)
Separation on the sky, ? (Mpc/h)
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Measuring Bias - 2dFGRS CMB
Assume dn/n b dr/r (blinear bias). Then
Pgal(k)b2Pm(k), so can get the bias parameter by
comparing the relative normalizations (s8) of the
mass PS from CMB (linearly evolved to z0) and
the galaxy PS from 2dFGRS.
Do galaxies trace mass?
b b(L) 0.96 0.08
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Cosmology from 2dFGRS CMB
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2dFGRSCMB fits - flat cosmology

• Fits assume ?k0 and use CMB 2dFGRS only (no
  priors)
• Preferred model is scalar-dominated and almost
  scale-invariant
• Best-fit normalization is ?8 (0.72 ? 0.04)
  exp ?

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Constraints on the neutrino mass
P(k) gives an upper limit on the total mass of
all n species
Wn/Wm lt 0.13 ? mn,tot lt 1.8 eV (95
confidence)
Best previous bound
Wn/Wmlt 0.13
Elgaroy et al., 2002, astro-ph/0204152
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The dark energy equation of state

• Dark energy equation of state w(z)? p/?
• ?(z) ? (1?z)n , n ? 3(1?w)
• cosmological constant has w ? -1 and n ? 0.
• The combined constraint on ?w?, assuming a flat
  universe, from the CMB and 2dFGRS power spectra
  plus the HST key project H0, is
  ?w? ? -0.52 (95 c.l.)

2dFGRS CMB
2dFGRS CMB HST
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Clustering/bias variation with luminosity
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Passive (non-starforming) galaxies
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Active (starforming) galaxies
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Power spectrum and galaxy type
Non-linear regime
passive
active
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Redshift-space distortions and galaxy type
Passive ? ?0.6/b 0.46 ? 0.13 ?p
618 ? 50 km s-1
Active ? ?0.6/b 0.54 ? 0.15 ?p
418 ? 50 km s-1
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The 2dF Galaxy Redshift Survey

• Final data release June 2003
• www.mso.anu.edu.au/2dFGRS

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Mass and motions - 6dF Galaxy Survey

• Redshift survey
• sample from 2MASS ( DENIS B Sky Survey)
• cover whole southern sky with bgt10º
• galaxies with Klt13.0 (also Jlt14.0, Ilt15, Blt16.5)
• ? 150,000 galaxies
• Peculiar velocity survey
• volume-limited sample of early-type galaxies with
  czlt15,000 km/s
  ? 15,000
  galaxies
• measure velocity dispersions, combine with 2MASS
  photometry ? Dn-? distances/velocities

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6dF observed velocity field (15,000 galaxies)
PSCz predicted velocity field (15,000 galaxies)
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Bulk flows and LSS

• Bulk flow is mean motion of a given volume.
• Bulk flows are due to very large-scale structure.
• Compare the scales at which the mass power
  spectrum P(k) contributes most to the rms mass
  fluctuation and the rms bulk flow within a
  spherical region of radius R
• ?(?M/M)2?(R) ? P(k) W2(kR) (dk/2?)3
• ?v2?(R) 4?(H0?0.6)2 ? k-2 P(k) W2(kR) (dk/2?)3
• The bulk flow is dominated by fluctuations in the
  mass distribution at smaller k (i.e. larger
  scales) than the density field.

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Observed bulk flows
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Cosmological constraints
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The 6dF Galaxy Survey Early Data Release
http//www.mso.anu.edu.au/6dFGS