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Large-scale structure and matter in the universe
John Peacock Royal Society January 2003
The distribution of the galaxies
1930s:
Hubble proves galaxies have a non-random distribution
1950s:
Shane & Wirtanen spend 10 years counting 1000,000 galaxies by eye
- filamentary patterns?
Redshift surveysInverting v = cz = Hd gives an approximate distance.
Applied to galaxies on a strip on the sky, gives a ‘slice of the universe’
Spectrum of inhomogeneities
x
Primordial power-law spectrum (n=1?)
Transfer function
Transfer function Key scales:
* Horizon at zeq :
16 (mh2)-1 Mpc
(observe mh)
* Free-stream length : 80 (M/eV)-1 Mpc
(m h2 = M / 93.5 eV)
* Acoustic horizon : sound speed < c/31/2
* Silk damping
M sets damping scale - reduced power rather than cutoff if DM is mixed
Generally assume adiabatic
Parameters: d b v neutrino h w n M
Limiting WDM
m > 0.75 keV from the Ly-alpha forest
(Narayanan et al. 2000)
Galaxies at z>6 need <100 kpc damping length
The universe
according to CDM
Bright galaxies today were assembled from fragments at high redshift
Nonlinear evolution and bias
Linear
NL
Benson et al. (2000):
galaxies tend to be antibiased on small scales in
numerical simulations
= autocorrelation = FT (power spectrum)
Results from the 2dF Galaxy Redshift Survey
Target: 250,000 redshifts to B<19.45
(median z = 0.11)
250 nights AAT 4m time
1997-2002
The 2dFGRS Team Australia
Joss Bland-Hawthorn Terry Bridges Russell Cannon Matthew Colless Warrick Couch Kathryn Deeley Roberto De Propris Karl Glazebrook Carole Jackson Ian Lewis Bruce Peterson Ian Price Keith Taylor
Britain Carlton Baugh Shaun Cole Chris Collins Nick Cross Gavin Dalton Simon Driver George Efstathiou Richard Ellis Carlos Frenk Ofer Lahav Stuart Lumsden Darren Madgwick Steve Maddox
Stephen Moody Peder Norberg John Peacock Will Percival Mark Seaborne Will Sutherland Helen Tadros
33 people at 11
institutions
2dFGRS input catalogue Galaxies: bJ 19.45 from revised APM
Total area on sky ~ 2000 deg2
250,000 galaxies in total, 93% sampling rate Mean redshift <z> ~ 0.1, almost all with z < 0.3
2dFGRS geometry
NGP
SGP
NGP 75x7.5 SGP 75x15 Random 100x2Ø ~70,000 ~140,000 ~40,000
~2000 sq.deg.250,000 galaxies
Strips+random fields ~ 1x108 h-3 Mpc3
Volume in strips ~ 3x107 h-3 Mpc3
The 2dF site
Prime Focus
2dF on the AAT
Final 2dFGRS Sky Coverage
NGP
SGP
Final redshift total: 221,283
2dFGRS Redshift distribution
N(z) Still shows significant clustering at z < 0.1
The median redshift of the survey is <z> = 0.11
Almost all objects have z < 0.3.
Cone diagram: 4-degree wedge
Fine detail: 2-deg NGP slices (1-deg steps)
2dFGRS: bJ < 19.45
SDSS: r < 17.8
2dFGRS power-spectrum results
Dimensionless power:
d (fractional variance in density) / d ln k
Percival et al. MNRAS 327, 1279 (2001)
2dFGRS power spectrum - detail
Ratio to h=0.25CDM model (zero baryons)
nonlinearities, fingers of God, scale-dependent bias ...
CDM Model fitting
Essential to include window convolution and full data covariance matrix
Confidence limits
‘Prior’:
h = 0.7 ± 10%
&
n = 1
mh = 0.20 ± 0.03
Baryon fraction = 0.15 ± 0.07
Consistency with other constraints
Cluster baryon fraction
Nucleo-synthesis
Comparison with other data
All-sky PSCz: = 0.20 0.05 SDSS EDR: = 0.19 0.04
2dFGRS: = 0.16 0.03
Power spectrum: Feb 2001 vs ‘final’
Model fits: Feb 2001 vs ‘final’
mh = 0.20 ± 0.03
Baryon fraction = 0.15 ± 0.07
mh = 0.18 ± 0.02
Baryon fraction = 0.17 ± 0.06
(if n = 1)
Initial conclusions
• Lack of oscillations. Must have collisionless component
• CDM models work
• Low density if n=1 and h=0.7 apply
• possibilities for error:
• Isocurvature?
• =1 plus extra ‘radiation’?
• Massive neutrinos?
• Scale-dependent bias? (assumed gals mass)
Power spectrum and galaxy type
shape independent of galaxy type
Relation to CMB results
Combining LSS & CMB breaks degeneracies:
LSS measures mh only if power index n is known
CMB measures n and mh3 (only if curvature is known)
curvature
total density
baryons
2dFGRS + CMB: Flatness
CMB alone has a geometrical degeneracy: large curvature is not ruled out
Adding 2dFGRS power spectrum forces flatness:
| 1 - tot | < 0.04
Efstathiou et al. MNRAS 330, L29 (2002)
The CMB peak degeneracy
Detailed constraints
for flat models
(CMB + 2dFGRS only: no priors)
Preferred model is scalar-dominated and very nearly scale-invariant
Percival et al. MNRAS 337, 1068 (2002)
The tensor CMB degeneracy
Degeneracy: compensate for high tensors with high n and high baryon density
scalar
plus tensors
tilt to n = 1.2
raise b to 0.03
Effect of neutrinos
Free-stream length: 80 (M/eV)-1 Mpc
(m h2 = M / 93.5 eV)
M ~ 1 eV causes lower power at
almost all scales, or a bump at the largest
scales
=0.05
Neutrino mass limit
Elgaroy et al. PRL 89, 061301 (2002)
Degeneracy: higher neutrino mass resembles lower h, so true h can be higher
Needs a prior:
for < 0.5, limit is f< 0.13, or
M < 1.8 eV (sum of
eigenvalues)
Vacuum equation of state (P = w c2)
w shifts present horizon, so different m
needed to keep CMB peak
location for given h
w < -0.54
similar limit from
Supernovae: w < -0.8 overall
2dFGRS
Extra relativistic components?
Matter-radiation horizon scale depends on matter density (mh2) and relativistic density (=1.68 CMB for 3 light neutrinos).
Suppose rel = X (1.68 CMB ) so apparent mh = mh X-1/2 and m=1 h=0.5 works if X=8
But extra radiation affects CMB too. Maintaining peak location needs h=0.5X1/2 if m=1
If w=-1, 2dFGRS+CMB measure h X-1/2 = 0.71 +- 5% with HST h = 0.72 +- 11%, hence
1.68X = 1.70 +- 0.24 (3.1 +- 1.1 neutrinos)
Summary >10 Mpc clustering in good accord with CDM
– power spectrum favours m h= 0.18 & 17% baryons
CMB + 2dFGRS implies flatness– CMB + Flatness measures m h3.4 = 0.078
– hence h = 0.71 ± 5%, m = 0.26 ± 0.04
No evidence for tilt (n = 0.96 +- 0.04) or tensors– But large tensor fractions not yet strongly excluded
Neutrino mass <1.8 eV if m =1 excluded
w < -0.54 by adding HST data on h (agrees with SN) Boosted relativistic density cannot save m =1
– Neutrino background detected if w=-1
And 2dFGRS has much to say about galaxy formation