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(Higher-order) Clustering in the SDSS

(Higher-order) Clustering in the SDSS. Bob Nichol (Portsmouth) Gauri Kulkarni (CMU) SDSS collaboration. 3pt primer. 3. r. dP 12 = n 2 dV 1 dV 2 [1 + x (r)]. . dV 2. 2. dV 1. s. qr. dP 123 =n 3 dV 1 dV 2 dV 3 [1+ x 23 (r)+ x 13 (r)+ x 12 (r)+ x 123 (r)].

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(Higher-order) Clustering in the SDSS

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

  2. 3pt primer 3 r dP12 = n2 dV1 dV2 [1 + x(r)]  dV2 2 dV1 s qr dP123=n3dV1dV2dV3[1+x23(r)+x13(r)+x12(r)+x123(r)] Peebles “Hierarchical Ansatz” Q(r,q,   1 23+ 23+ 12

  3. Why Bother? Non-gaussianity Credit: Alex Szalay Same 2pt, different 3pt Careful comparing things using just 1D & 2D statistics (LF, 2pt)

  4. Why Bother again?Biasing Qgalaxy ~ Qmatter/b1 + b2/b12 Gaztanaga & Frieman 1994 Today, we talk about the HOD (Kravtsov talk) Only works in real-space, complex in redshift-space Work in real space: convert observations Work in projected space 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)

  5. Gaztanaga & Scoccimarro 2005

  6. NPT:Dual Tree Algorithm N1 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 dmax dmin N2 Therefore, only need to calculate pairs cutting the boundaries. Scales as O(XlogX)1.3 Also running on TeraGrid

  7. 2dFGRS Baugh et al Croton et al Fair samples & binning Nichol et al. 2006

  8. 3.4 detection Eisenstein et al. 2005 46,700 LRGs over 3816 deg2 and 0.16<z<0.47 0.72h-3Gpc3 SDSS LRG

  9. Detected U-shape dependence on large scales Read off biasing (b1=1.5) Errors well-behaved (jk) r  qr

  10. 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 Match N and 2pt Degeneracy between M1 and  Top 30 models cluster into 3 solutions Limited sensitivity to Mmin

  11. Errors from 30 mocks

  12. Excellent agreement in 3pt “Hierarchical Ansatz” works Note errors again

  13. What’s happening with the errors? As  increases, this simulation becomes more important: like the jk errors

  14. 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

  15. WMAP new results are now available

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