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Wiener Reconstruction of the Wiener Reconstruction of the Galaxy Redshift SurveysGalaxy Redshift Surveys
Pirin Erdogdu, Ofer Pirin Erdogdu, Ofer Lahav, Saleem Lahav, Saleem Zaroubi and the Zaroubi and the 2dFGRS Team 2dFGRS Team
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We assign The Reconstructed Density Field of 2dFGRS in Declination Strips
Pirin Erdogdu and 2dFGRS Team, 2003, in preparation
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MotivationMotivation Statistical Uncertainties due to Shot NoiseStatistical Uncertainties due to Shot Noise
Incomplete Sky CoverageIncomplete Sky Coverage
Incomplete Galaxy SamplingIncomplete Galaxy Sampling
Recovering one field from anotherRecovering one field from another
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Wiener FilterWiener Filter
≡d ns +=
≡≡n
s Underlying Signal (ΛCDM)
)( NNoise
(For details see Zaroubi et al 1995, ApJ, 449, 446)
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⇒ βαβα dWFs WF =
where the matrix WF is chosen such that the residual:
22
ααα ssr WF −= is minimised.
Hence:
1−= TT dddsWF βγγααβ
~ prior/(prior + noise)WF⇒
⇒ βαβα dWFs WF =
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( ) γαγα
αγγα
α γ
ξ dVdVrVV
CssCell Cell
sT
∫ ∫==1
TTT nnssdd γαγαγα +=
( ) ( )βα zdzs T =
Density Reconstruction in Redshift Space :
Density Reconstruction in Real Space:
)()(
51
32
1
31
1)()(
2βαβα
ββ
βzszszdrs TT
++
+=
Data –Data Correlation Matrix:
Signal –Data Cross-Correlation Matrix:
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PixelisationPixelisation Application to 2df
Survey
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EACH GALAXY IS ASSIGNED THE WEIGHT:
( ) ( ) ( )gali zMgalw
φΩ=
1
So the data vectoris written as:
( )
i
i
iN
gali
Vn
Vngalw
d
gal
−
=∑ )(
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2dFGRS SGP
SCGP01 VSGP02VSGP01
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Density Threshold as A Function of Redshift
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2dFGRS NGP
VNGP26SCNGP16 SCNGP18 SCNGP19 SCNGP17VNGP25
VNGP27
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2dFGRS SGP
SCSGP 21 SCSGP22
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Are these structures real?
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)()()()()()(1
ββαβαα rururururvrv TTWF −=
Large Scale Reconstruction from Peculiar Velocities
≡)(ru ε+⋅= rrv ˆ)(
And assuming vf ⋅∇Ω= −v
1)(δ
)()()()()()(1
ββαβαα δδ rururururr TTWF −=
FUTURE WORK
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Zaroubi, Hoffman & Dekel 1999 ApJ,520, 412
Reconstruction from Mark III data.
Top Right panel : Mark III dataTop Left Panel: IRAS data
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WORK IN PROGRESS
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ConclusionsConclusions
WF is applied to the density WF is applied to the density reconstruction of 2dFGRSreconstruction of 2dFGRS
Major superclusters and voids are Major superclusters and voids are identified.identified.
WF can be used to reconstruct the WF can be used to reconstruct the density and velocity fields of 6dFGRS.density and velocity fields of 6dFGRS.
The reconstructed density fields can The reconstructed density fields can be used as an input to different be used as an input to different analyses.analyses.