Measuring large-scale structure in the universe with the 2dF Galaxy Redshift Survey John Peacock Garching December 2001
Jan 05, 2016
Measuring large-scale structure in the universe with the 2dF Galaxy Redshift Survey
John Peacock Garching December 2001
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’
Las Campanas Redshift Survey~25000 z’s
CfA Survey~15000 z’s
Redshift surveys: v = cz = H0 d d = z x 3000 h-1 Mpc
h = H0 / 100 km s-1 Mpc -1
Inflationary origin of
structure?
Assume early universe dominated by scalar-field V() at GUT energies
Predicts small fluctuations in metric. Scalar fluctuations (= Newtonian potential) have nearly flat spectrum
- also expect tensor modes (gravity waves)
Gravitational instability:
hierarchical collapse
generates ever larger structures
Nonlinear predictions
of theory
Bright galaxies today were assembled from fragments at high redshift
Results from the 2dF Galaxy Redshift Survey
Target: 250,000 redshifts to B<19.45
(median z = 0.11)
Current total: 213,000
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
Tiling strategy‘2dF’ = ‘two-degree field’ = 400 spectra
Efficient sky coverage, but variable completeness
High completeness through adaptive tiling: multiple coverage of high-density regions
The 2dF site
Prime Focus
2dF on the AAT
Survey Progress
45% of nights allocated were usable
Current rate 1000 redshifts per allocated night
Survey will end in Jan 2002 after 250 nights total
Expected final size: 230,000
Now: 213000 z’s
62% of fields were observed up to July 2001 Final strips will be trimmed to finish early 2002.
Sky Coverage of Survey
NGP
SGP
Redshift distribution N(z) for 156000
galaxies.
Still shows significant clustering.
The median redshift of the survey is <z>=0.11
Almost all objects have z < 0.3.
Survey mask
NGP
SGP
Cutouts are bright stars and satellite
trails.
Sampling & Uniformity Adaptive tiling efficient, uniform sampling… when done.
At current stage of survey, sampling is highly variable.
This limits applications requiring large contiguous volumes.
Cone diagram: 4-degree wedge
Fine detail: 2-deg NGP slices (1-deg steps)
2dFGRS: bJ < 19.45
SDSS: r < 17.8
The CDM power
spectrum
growth:
aa f([a])
Break scale relates to (density in units of critical density):
In practice, get shape parameter almost = h
2dFGRS power-spectrum results
APM deprojection: real space
2df: redshift space
result robust with respect to inclusion of random fields
Dimensionless power:
d (fractional variance in density) / d ln k
Effects of baryons
2dFGRS power spectrum - detail
Ratio to h=0.25CDM model (zero baryons)
nonlinearities, fingers of God, scale-dependent bias ...
Power spectrum and survey window
Window sets power resolution and maximum scale probed:
Pobs(k) = P(k) * |W(k)|2
Full survey more isotropic, compact window function.
Gain x2.3 in P(k) range
Model fitting
Essential to include window convolution and full data covariance matrix
Confidence limits
‘Prior’:
h = 0.7 ± 10%
mh = 0.20 ± 0.03
Baryon fraction = 0.15 ± 0.07
Relation to CMB results
Geometrical degeneracy: need a value for h, even with no tensors
curvature
total density
baryons
Consistency with other constraints
Cluster baryon fraction
Nucleo-synthesis
CMB
Scalar fit to 2dFGRS + CMB
Joint likelihood removes need to assume parameters: mh2 from CMB and mh from LSS gives both m & h:
m = 0.27 ± 0.05
Redshift-space distortions (Kaiser 1987)
zobs = ztrue +v / c v prop. to 0.6 0.6 b-1
n/n
Apparent shape from below
linear nonlinear
(bias)
Redshift-space clustering
z-space distortions due to peculiar velocities are quantified by correlation fn (,).
Two effects visible:– Small separations
on sky: ‘Finger-of-God’;
– Large separations on sky: flattening along line of sight
r
and Fit quadrupole/monopole ratio of
(,) as a function of r with model having 0.6/b and p (pairwise velocity dispersion) as parameters.
Best fit for r > 8 h-1 Mpc (allowing
for correlated errors) gives:
= 0.6/b = 0.43 0.07 p = 385 50 km s-1
Applies at z = 0.17, L =1.9 L* (significant corrections)
Full survey will reduce random errors in to 0.03.
Model fits to z-space distortions
= 0.3,0.4,0.5; p= 400
= 0.4, p= 300,500
99%
Measuring bias - 1: CMB
The problem: do galaxies trace mass? n/n = b r/r
Take mass 8 from CMB (scalar fit) and apparent (redshift-space) 8 from 2dFGRS P(k):
b(1.9L*) = (1.00 ± 0.09) exp[- + 0.5(n-1)]
Measuring bias - 2: Bispectrum(with Verde, Heavens, Matarrese)
1
2
1
2
3
Two-point correlations:
< 1 2 > = : FT = P(k) power spectrum
Three-point correlations:
< 1 2 3 > = : FT = B(k1,k2,k3) bispectrum
= 0 for Gaussian field. Measure of gravitational nonlinearity
Bispectrum resultsAssume local nonlinear bias: g = b1 m + b2 (m)2
Nonlinear bias can mimic some aspects of gravitational evolution (e.g. skewness) - but full bispectrum contains shape information: bias doesn’t form filaments
CDM
CDM
Results for NGP + SGP: b1 b2 (for L=1.9L*)
+ result m = 0.27 - entirely internal to 2dFGRS
data match unbiased predictions
Clustering as f(L)
Clustering increases at high luminosity:
b(L) / b(L*) = 0.85 + 0.15(L/L*)
suggests << L* galaxies are slightly antibiased
- and IRAS g’s even more so: b = 0.8
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
Constraining tensors with Dimensionless power:
d (fractional variance in density) / d ln k
Scalar only: 8 = 0.75.
Predicts (L*) = 0.39
High tensor: 8 = 0.64.
Predicts (L*) = 0.29
(also fails to match cluster abundance)
Summary
>10 Mpc clustering in good accord with LCDM– power spectrum favours m h= 0.20 & 15% baryons
• With h = 0.7 ± 10%, gives m = 0.27 ± 0.05
No significant large-scale bias (3 arguments):– redshift-space distortions with m from P(k)
– comparing CMB 8 with P(k) amplitude
– direct internal bispectrum analysis Matches no-tilt no-tensor vanilla CMB
– tensor-dominated models excluded
See http://www.mso.anu.edu.au/2dFGRS/ for 100,000 redshift 2dFGRS data release