Redshift -Space Enhancement of LOS Baryon Acoustic Oscillations in the SDSS-MGS

1. Redshift-Space Enhancement of LOS Baryon Acoustic Oscillations in the SDSS-MGS Reporter: Haijun Tian Alex Szalay, Mark Neyrinck, Tamas Budavari arXiv:1011.2481

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

3. Definition • 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. Redshift Distortion From SDSS Project From 2DF Project

5. Detect BAO for the First time • Eisenstein et al (2005) – LRG

6. SDSS Redshift Samples • Main Galaxies 800K galaxies, high sampling density, but not too deep Volume ~ 0.12 Gpc3 • 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 Gpc3 Good balance of volume and sampling • Quasars 20K QSOs, cover huge volume, but too sparse

7. A Recent Controversy on Bump_LOS Kazin(2010) Gaztanaga et al(2009)

8. (r) from linear theory + BAO • Mixing of 0 , 2 and 4 • Along the line of sight

9. What can predict • 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. Projection and Slicing Theorem • The basis of CAT-SCAN

11. Methods to estimate lower Dimensional  • _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. Measurement From Simulation • Millennium Simulation(MS) Size: 500 h-1Mpc a bit small, 2563 Grid R-mag: < -20 (absolute) Mean density: 0.02 (h-1Mpc)-3 • Particle-Mesh(PM) dark-matter Simulations Size: 1024 h-1Mpc, 100 2563 particles • 1400 Gaussian Simulations Size: 768 h-1Mpc, 16 h-1Mpc thickness(at 370 h-1Mpc)

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

14. Correlation function from100 PMs • Real Space: 3 orientations, 8 h-1Mpc • Redshift Space: 6 orientations(3 possible LOS axes, times 2 slice orientations contain LOS)

15. What can we find from simulations • 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. Measurement from SDSS • SDSS DR7 MGS, Stripes 9 through 37, Northern cap • 0.001<z<0.18, Z_conf>0.9, Z_err<0.1 • Remove all the objects in the incomplete areas • About 527K objects. • 17M random galaxies • Spatial weighting • From 0 to 165deg, 15deg increments,12 angular orientations, 2.5deg thickness, 20deg<width<80deg, 660slices

17. Computing and Correlations • 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. Contour of  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. Angle-average and LOS  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. S/N of wavelet transform 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 (,), [top right] The mean PM redshift space (,), [middle] The mean MS 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-1Mpc, 25 h-1Mpc wide,

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

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

28. Cosmology used M = 0.279 L = 0.721 K = 0.0 h= 0.701 w0 = -1