1. Reporter: Haijun Tian Alex Szalay, Mark Neyrinck, Tamas Budavari arXiv:1011.2481

2.  Background  Redshift Space  in Linear Theory  Measurement from simulations  Measurement from SDSS  Quantifying the redshift space features  Conclusion

3.  Acoustic Oscillations: the competition between the photon pressure and the baryons gravitational collapse prior to the epoch of recombination  The Redshift Space Distortion: Due to the peculiar velocity Smaller Scale: dominated by nonlinear (FoG’s) Larger Scale: present as compression effect along LOS It is relative to Real Space

4. From 2DF ProjectFrom SDSS Project

5.  Eisenstein et al (2005) – LRG

6.  Main Galaxies 800K galaxies, high sampling density, but not too deep Volume ~ 0.12 Gpc 3  Luminous Red Galaxies(“Sweet Spot”) 100K galaxies, color and flux selected m_r < 19.5, 0.15 < z < 0.45, close to volume-limited Lower density, Volume > 2 Gpc 3 Good balance of volume and sampling  Quasars 20K QSOs, cover huge volume, but too sparse

7. Gaztanaga et al(2009) Kazin(2010)

8.  Mixing of  0,  2 and  4  Along the line of sight

9.  Nearby the LOS, the distortions sharpen the “bumpy” feature, and much weaker, much further from the LOS.  Overall smoothly shifts towards negative along the LOS, and towards positive in the transverse.

10.  The basis of CAT-SCAN

11.   _3D   _2D   _1D (LOS)  P(k)_3D  P(k)_2D   _2D   _1D  Slice sample(2D)   _2D  average    _1D  Slice sample(2D)  P(k)_2D  average P(k)   _2D   _1D  Principally, all the cases will contain the same  _LOS, nevertheless the covariance between the  bins estimated in different ways will be somewhat different.

12.  Millennium Simulation(MS) Size: 500 h -1 Mpc a bit small, 256 3 Grid R-mag: < -20 (absolute) Mean density: 0.02 (h -1 Mpc) -3  Particle-Mesh(PM) dark-matter Simulations Size: 1024 h -1 Mpc, 100 256 3 particles  1400 Gaussian Simulations Size: 768 h -1 Mpc, 16 h -1 Mpc thickness(at 370 h -1 Mpc)

13.  MS is divided into 3 x 64 slices, 8 h -1 Mpc  For Redshift Space:

14.  Real Space: 3 orientations, 8 h -1 Mpc  Redshift Space: 6 orientations(3 possible LOS axes, times 2 slice orientations contain LOS)

15.  Linear-theory distortions in 2D sharpen the baryon bump relative to the real space.  While fingers of god(non-linear) degrade all features, even away from LOS.  Error bars for the LOS BAO bump are slightly reduced compared with the angle-averaged bump.  Even in 3D,  in redshift space have a sharper BAO bump than in 2D.  Redshift-space distortions tend to amplify the bump sharpness, especially along the LOS.

16.  SDSS DR7 MGS, Stripes 9 through 37, Northern cap  0.001 0.9, Z_err<0.1  Remove all the objects in the incomplete areas  About 527K objects.  From 0 to 165deg, 15deg increments,12 angular orientations, 2.5deg thickness, 20deg<width<80deg, 660slices  17M random galaxies  Spatial weighting

17.  Estimator:  Done on an GPU(NVIDIA’s CUDA) 400 trillions galaxy/random pairs  Brute force massively parallel code much (hundreds of times) faster than tree-code  All done inside the JHU SDSS database  Based on the Buffon’s needle(Buffon 1777), figure out the number slices on average that enter the LOS.

18. Average  ( ,  ) of the 660 2.5deg slices of SDSS galaxies(left),and the full 3D  (right) 100Mpc/h<dist<750Mpc/h 300 Mpc/h <dist<750 Mpc/h

19. 1D  for low-resolution PM, MS, SDSS sample, angle-average (top), and LOS(6deg)

20. The Bump at160Mpc/h 300 Mpc/h <dist<750 Mpc/h 50<dist<300 Mpc/h

21. The S/N of the wavelet transform. S/N, 1400 Gaussian simulations, box_size:768Mpc/h, cell_size:2Mpc/h. The S/N for the SDSS real sample

22. [top left] The linear theory redshift space  ( ,  ), [middle] The mean MS redshift space  ( ,  ), [top right] The mean PM redshift space  ( ,  ), [bottom] The mean SDSS redshift space  ( ,  ),

23. S/N Frequency 1400 Gaussian simulations, SDSS-like Volume, ~40% of the simulations: S/N 2.2-sigma, LOS ~ 70%, S/N 4-sigma, flat weighting.

24. 12 orientations DOF: 12/9.3 = 1.3(LOS) 12/1.7 = 7 (flat) S/N: 9.0 +/- 7.9 (LOS) 5.2 +/- 2. (flat)

25. Strong Non-Linear Infall (55Mpc) Distribution of 1D wavelet coefficients over the 660 slices, Mexican Hat  Centered at 55 h -1 Mpc, 25 h -1 Mpc wide,

26. Far Side Infall (140Mpc/h)  Centered on 140 h -1 Mpc, width 25 h -1 Mpc  Still shows some skewness

27.  Redshift space distortions amplify and sharpen features along the line of sight  4  detection of BAO in SDSS DR7 MGS at around 110 h -1 Mpc, potentially constraining the equation of state at low z  Trough at 55 h -1 Mpc indicates effects of nonlinear infall on these scales

28.  M = 0.279  L = 0.721  K = 0.0 h = 0.701 w 0 = -1