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

We assign The Reconstructed Density Field of 2dFGRS in Declination Strips

Pirin Erdogdu and 2dFGRS Team, 2003, in preparation

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

Wiener FilterWiener Filter

≡d ns +=

≡≡n

s Underlying Signal (ΛCDM)

)( NNoise

(For details see Zaroubi et al 1995, ApJ, 449, 446)

⇒ 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 =

( ) 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:

PixelisationPixelisation Application to 2df

Survey

EACH GALAXY IS ASSIGNED THE WEIGHT:

( ) ( ) ( )gali zMgalw

φΩ=

1

So the data vectoris written as:

( )

i

i

iN

gali

Vn

Vngalw

d

gal

−

=∑ )(

2dFGRS SGP

SCGP01 VSGP02VSGP01

Density Threshold as A Function of Redshift

2dFGRS NGP

VNGP26SCNGP16 SCNGP18 SCNGP19 SCNGP17VNGP25

VNGP27

2dFGRS SGP

SCSGP 21 SCSGP22

Are these structures real?

)()()()()()(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

Zaroubi, Hoffman & Dekel 1999 ApJ,520, 412

Reconstruction from Mark III data.

Top Right panel : Mark III dataTop Left Panel: IRAS data

WORK IN PROGRESS

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.