(Higher-order) Clustering in the SDSS

Bob Nichol (Portsmouth)

Gauri Kulkarni (CMU)

SDSS collaboration

3pt primer

r

qr

Q(r,q,

23 + 23

+ 121

2

3

Peebles “Hierarchical Ansatz”

dP12 = n2 dV1 dV2 [1 + (r)]

dP123=n3dV1dV2dV3[1+23(r)+13(r)+12(r)+123(r)]

dV1

dV2s

Credit: Alex Szalay

Same 2pt, different 3pt

Why Bother?Non-gaussianity

Careful comparing things using just 1D & 2D statistics (LF, 2pt)

Why Bother again?Biasing

Qgalaxy ~ Qmatter/b1 + b2/b12

Gaztanaga & Frieman 1994

Only works in real-space, complex in redshift-space

1. Work in real space: convert observations2. Work in projected space3. Work in redshift-space: convert theory

Hard

er

theore

tica

llyH

ard

er o

bse

rvatio

nallyThe last one is emerging as favourite because of diverse

range of mock catalogues (thanks GAVO)

Today, we talk about the HOD (Kravtsov talk)

Gaztanaga & Scoccimarro 2005

N1 dmax

dmin

Usually binned into annuli

rmin< r < rmax

Thus, for each r transverse both trees and prune pairs of nodes

No count

dmin < rmax or dmax < rmin

N1 x N2

rmin > dmin and rmax< dmax

N2

Therefore, only need to calculate pairs cutting the boundaries.

Scales as O(XlogX)1.3

Also running on TeraGrid

NPT:Dual Tree AlgorithmNPT:Dual Tree Algorithm

Nichol et al. 2006Fair samples & binning

2dFGRSBaugh et alCroton et al

Eisenstein et al. 200546,700 LRGs over 3816 deg2

and 0.16<z<0.470.72h-3Gpc3

3.4 detection

SDSS LRG

Detected U-shape dependence on large scales

Read off biasing (b1=1.5)

Errors well-behaved (jk)

r

qr

Modeling: Nbody + HOD 30 DM halo catalogs with m=0.27, =0.73, h=0.72, 8=0.9, 512Mpc/h, 256 3

N(M) = exp(-Mmin/M) [1+(M/M1

Fit a grid of HOD models 1. Match N and 2pt2. Degeneracy between M1

and 3. Top 30 models cluster into

3 solutions4. Limited sensitivity to Mmin

Errors from 30 mocks

Note errors again

Excellent agreement in 3pt“Hierarchical Ansatz” works

What’s happening with the errors?

As increases, this simulation becomes more important: like

the jk errors

Summary

• The higher order statistics have come of age: we have the mocks, the data and the algorithms

• However, need “fair samples” which does demand large datasets (SDSSII)

• Beware of fitting just to lower order statistics

• Measure biasing

• With the right HOD, 3pt function is just a simple product of the 2pt i.e. gaussian conditions

WMAP new results are now available