2. Galaxy and Mass Power Spectra Shaun Cole ICC, University of Durham Main Contributors: Ariel Sanchez (Cordoba) Steve Wilkins (Cambridge) Imperial College London Outstanding Questions for the Standard Cosmological Model March 2007 Photograph by Malcolm Crowthers

3. Outstanding Question: Do uncertainties in modelling non-linearity and galaxy bias compromise constraints on cosmological parameters coming from measurements of the galaxy power spectrum?

4. Subsidiary Questions: Do analysis techniques effect the results? Do differences in sample selection and completeness effect the results?

5. Outline Motivation for comparing 2dF and SDSS Methods for parallel Analysis of 2dFGRS and SDSS DR5 –Modelling the selection functions (Comparison in the overlap region) Comparison of Power Spectra –Understanding the differences –Model Fits and Cosmological Parameters Conclusions and Future Prospects

6. The Shape of 2dF and SDSS P(k) differ on large scales Resulting parameter constraints 2dF: (Cole et al 2005) SDSS: (Tegmark et al 2004)

7. Combined with CMB Sanchez et al 2006

8. Combined with CMB Sanchez et al 2006

9. Methods Use equivalent methods and modelling for both 2dF and SDSS so that direct comparisons can be made.

10. 2dFGRS data and selection function 2dFGRS final data release Completeness and magnitude limit masks from Cole et al 2005 using methods of Norberg et al 2002 Selection function modelled via the luminosity function Data, modelling and methods identical to Cole et al 2005

11. 2dF Random Catalogue

12. SDSS data and selection function DR5 public data (500k redshifts)DR5 public data (500k redshifts) Completeness and magnitude limit masks retaining 450k redshiftsCompleteness and magnitude limit masks retaining 450k redshifts Assign a redshift, magnitude and other properties byAssign a redshift, magnitude and other properties by 1.Selecting an object at random from the r=17.77 sample 2.Keep/reject according to apparent magnitude limit map

13. SDSS data and selection function DR5 public data (500k redshifts)DR5 public data (500k redshifts) Completeness and magnitude limit masks retaining 450k redshiftsCompleteness and magnitude limit masks retaining 450k redshifts Assign a redshift, magnitude and other properties byAssign a redshift, magnitude and other properties by 1.Selecting an object at random from the r=17.77 sample 2.Keep/reject according to apparent magnitude limit map

15. SDSS data and selection function DR5 public data (500k redshifts)DR5 public data (500k redshifts) Completeness and magnitude limit masks retaining 450k redshiftsCompleteness and magnitude limit masks retaining 450k redshifts Assign a redshift, magnitude and other properties byAssign a redshift, magnitude and other properties by 1.Selecting an object at random from the r=17.77 sample 2.Keep/reject according to apparent magnitude limit map

16. SDSS Random Catalogue

17. Real and random redshift slices ?????

18. 2dFGRS and SDSS comparison

20. 2dF SDSS overlap

22. Power Spectrum Estimation Weight galaxies as in Cole et al 2005 using PVP method Assign galaxies onto a grid and use FFTs Determine the spherically averaged power in bins of log(k)

23. Optimum Weighting

24. Optimum weight with bias

25. (Percival, Verde & Peacock 2004) Optimum weight with bias

26. Adopted Colour and Luminosity dependent bias relations Convert SDSS magnitudes to 2dF bands and then apply simple k-correction from Cole et al 2005 Split at restframe colour of 1.07 and adopt the bias relations:

27. Determining Statistical Errors Log-Normal Random catalogues –Realizations of random fields with log-normal density distributions, luminosity dependent clustering and realistic P(k). –Used to determine statistical errors –Used to test ability to recover input P(k)

28. oPower Spectrum from 1000 LN mocks compared to the input P(k) convolved with the window function

29. Window Function The window function is computed directly from the random catalogue and the spherically averaged The window function is computed directly from the random catalogue and the spherically averaged

30. 2dF and SDSS P(k) Full samples Differing window functions Good match at high k

31. 2dF and SDSS P(k) Full samples “Deconvolved” Good match at high k Less large scale power in SDSS? Robust to selection cuts, mask details, incompleteness corrections

32. 2dF and SDSS P(k) Full samples “Deconvolved” Good match at high k Less large scale power in SDSS? Robust to selection cuts, mask details, incompleteness corrections Very similar P(k) from Tegmark et al (2006)

33. Parameter Constraints Direct comparison of 2dFGRS and SDSS Tegmark et al 2004

34. Parameter Constraints Direct comparison of 2dFGRS and SDSS But SDSS are red and 2dF blue selected

35. All galaxies

36. Blue Galaxies

37. Red galaxies

38. Power Spectra of the red and blue galaxies in the same volume of space The errors on the ratio take account of the correlation this induces To first order they have a very similar shape and only differ in amplitude Only the shape differences on small scales are statistically significant Cole et al 2005

39. 2dF and SDSS P(k) Red galaxies “Deconvolved”

40. Evolution of the mass power spectrum z=0 z=1 z=2 z=3 z=4 z=5 linear growth non-linear evolution z=0 z=1 z=2 z=3 z=4 z=5 large scale power is lost as fluctuations move to smaller scales

41. Non-linearity, scale dependent bias and redshift space distortions Angulo et al 2007

42. Non-linearity, scale dependent bias and redshift space distortions Tegmark et al 2006

43. Model P(k) Red galaxies are more strongly clustered and have a larger value of Q. Our assumed linear bias matches the amplitude around k=0.1 h/Mpc

44. Parameter Constraints Red galaxies only

45. Conclusions I 2dFGRS and SDSS DR5 galaxy power spectra differ in shape at the 2 to  level. This is due to scale dependent bias which is largest for red (and more luminous) galaxies. It is an even larger effect for the SDSS LRG survey. A simple empirical model of the distortion appears to be robust. When marginalized over the distortion parameter Q, 2dFGRS, SDSS and SDSS-LRG constraints agree within the statistical noise.

46. Conclusions II Galaxy surveys give robust constraints on the linear mass power spectrum Important for constraining the parameters of the standard model More important still for constraining non- standard models