(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