(Higher-order) Clustering in the SDSS Bob Nichol (Portsmouth) Gauri Kulkarni (CMU) SDSS collaboration

3pt primer r qr Q(r,q, Peebles Hierarchical Ansatz dP 12 = n 2 dV 1 dV 2 [1 + (r)] dP 123 =n 3 dV 1 dV 2 dV 3 [1+ 23 (r)+ 13 (r)+ 12 (r)+ 123 (r)] dV 1 dV 2 s

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 Q galaxy ~ Q matter /b 1 + b 2 /b 1 2 Gaztanaga & Frieman 1994 Only works in real-space, complex in redshift-space 1.Work in real space: convert observations 2.Work in projected space 3.Work in redshift-space: convert theory Harder theoretically Harder observationally The 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

N1N1 d max d min Usually binned into annuli r min < r < r max Thus, for each r transverse both trees and prune pairs of nodes No count d min < r max or d max < r min N 1 x N 2 r min > d min and r max < d max N2N2 Therefore, only need to calculate pairs cutting the boundaries. Scales as O(XlogX) 1.3 Also running on TeraGrid NPT:Dual Tree Algorithm

Nichol et al Fair samples & binning 2dFGRS Baugh et al Croton et al

Eisenstein et al ,700 LRGs over 3816 deg 2 and 0.16<z< h -3 Gpc detection SDSS LRG

Detected U-shape dependence on large scales Read off biasing (b 1 =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, N(M) = exp(-M min /M) [1+(M/M 1 Fit a grid of HOD models 1.Match N and 2pt 2.Degeneracy between M 1 and 3.Top 30 models cluster into 3 solutions 4.Limited sensitivity to M min

Errors from 30 mocks

Note errors again Excellent agreement in 3pt Hierarchical Ansatz works

Whats 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

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