BAO and Tomography of the SDSS

Alex SzalayHaijun Tian

Tamas BudavariMark Neyrinck

SDSS Redshift Samples

Main Galaxies◦ 800K galaxies, high sampling density, but

not too deep◦ Volume is about 0.12 Gpc3

Luminous Red Galaxies◦ 100K galaxies, color and flux selected◦ mr < 19.5, 0.15 < z < 0.45, close to

volume-limitedQuasars

◦ 20K QSOs, cover huge volume, but too sparse

Finding the Bumps – DR4Eisenstein et al (2005) – LRG

sample

Primordial Sound Waves in SDSSPower Spectrum(Percival et al 2006, 2007)SDSS DR6+2dF

SDSS DR5

800K galaxies

(r) from linear theory + BAOMixing of 0 , 2 and 4

◦Along the line of sight)()(

21)(

0

22 kPkrjkdkr nn

)(35

8)(7

43

4)(53

21)( 4

2

2

2

0

2)( rrrrs

r

2D SymmetryThere is a planar symmetry:

◦Observer+ 2 galaxiesThus 2D correlation of a slice is

the sameWe usually average over cosVery little weight along the

axis:◦Sharp of features go away

Tomography of SDSSSDSS DR7 Main Galaxy Sample

◦Limit distances to 100<r<750 h-1 Mpc

Cut 3D data into thin angular slices◦Project down to plane (only 2D info)◦Different widths (2.5, 5, 10 deg)◦Rotate slicing direction by 15

degreesAnalyze 2D correlation function (,)

Average over angle for 1-D correlations

Why correlation function?For a homogeneous isotropic process,

the correlation function in a lower dimsubset is identical

There are subtleties:◦With redshift space distortions the process is

not fully homogeneous and isotropicRedshift space distortions and ‘bumps’

◦Distortions already increase the ‘bumps’◦Any effects from the ‘slicing’?

Projection and Slicing Theorem

Nmmm FSPF

The basis of CAT-SCAN / Radon xform

Slices of finite thicknessProject redshift-space power

spectrum with a corresponding window function

sinc(kzR)Anisotropic power spectrum

◦There is a thickness-dependent effect

◦Thinner slices give bigger boost

Millennium 64Mpc

Millennium 16Mpc

Millennium 4Mpc

Millennium 1Mpc

2.5 deg slices (702 total)

5 deg slices

10 deg slices

10 deg, in 3D

Full 3D correlation function

Full 3D no Great Wall

2.5 deg slices (702 total)

(r) along the line of sight

0 20 40 60 80 100 120 140 160 180 200-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0.05

Average of all 2.5 degree slices

3D along the line

No Great Wall

(r) along the line of sightThe correlation function along a

1D line:◦Pencilbeam

Corresponding power spectrum◦Projection of P(s)(k) onto a single axis

Computations on GPUsGenerated 16M randoms with

correctradial and angular selection for SDSS-N

Done on an NVIDIA GeForce 260 card

400 trillion galaxy/random pairsBrute force massively parallel

code muchfaster than tree-code

All done inside the JHU SDSS database

2D correlation function is now DB utility

SummaryRedshift space distortions amplify featuresLower dimensional subsets provide further

amplification of ‘bumps’ at 107-110h-1MpcBoost much stronger along the line of sightUsing these techniques we have strong

detection of BAO in SDSS DR7 MGSEffect previously mostly seen in LRGsTrough at 55h-1Mpc is a harmonic,

sharpness indicates effects of nonlinear infall

Bump at 165h-1Mpc puzzling

Millennium galaxies

Cosmology usedM = 0.279L = 0.721K = 0.0h = 0.701w0 = -1