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