1. Mapping the Mass with Galaxy Redshift-Distance Surveys Martin Hendry, Dept of Physics and Astronomy University of Glasgow, UK “Mapping the Mass”: Birmingham, 1 – 2 Aug 2002

2. Cosmic Velocity Fields: Paris, July 1993

4. “Mapping the Mass”: Birmingham, 1 – 2 Aug 2002 Overview Review of (recent) history:-  Distance indicators and datasets  Peculiar velocities as cosmological probes  Statistical bias  Cosmological bias  Conclusions

5. “Mapping the Mass”: Birmingham, 1 – 2 Aug 2002 Distance Indicators and Datasets Tully-Fisher Mark III, SFI, SCI, SCII, Shellflow Fundamental Plane Mark III, SMAC, ENEAR, EFAR SBF Tonry et al. Type Ia SN Riess et al.

6. “Mapping the Mass”: Birmingham, 1 – 2 Aug 2002 Distance Indicators and Datasets Tully-Fisher Mark III, SFI, SCI, SCII, Shellflow Fundamental Plane Mark III, SMAC, ENEAR, EFAR SBF Tonry et al. Type Ia SNe Riess et al. Shellflow TF relation From Courteau et al. (2000)

7. “Mapping the Mass”: Birmingham, 1 – 2 Aug 2002 Distance Indicators and Datasets Tully-Fisher Mark III, SFI, SCI, SCII, Shellflow Fundamental Plane Mark III, SMAC, ENEAR, EFAR SBF Tonry et al. Type Ia SNe Riess et al. From Colless et al. (2001) EFAR FP relation

8. “Mapping the Mass”: Birmingham, 1 – 2 Aug 2002 Distance Indicators and Datasets Tully-Fisher Mark III, SFI, SCI, SCII, Shellflow Fundamental Plane Mark III, SMAC, ENEAR, EFAR SBF Tonry et al. Type Ia SNe Riess et al. Individual distance errors of 20 – 30%; O(10 3 ) galaxies Individual distance errors of ~10%; O(10 2 ) galaxies

9. “Mapping the Mass”: Birmingham, 1 – 2 Aug 2002 We can constrain the matter distribution with peculiar velocities via:-  Bulk flow statistics  Velocity correlations  Velocity-density reconstructions POTENT VELMOD / ITF Peculiar Velocities as Cosmological Probes

10. “Mapping the Mass”: Birmingham, 1 – 2 Aug 2002 Bulk Flow Statistics Bulk flows are sensitive to the power spectrum on larger scales than the density field Model and fit by minimising parameters of distance indicator Compare with theoretical predictions

11. “Mapping the Mass”: Birmingham, 1 – 2 Aug 2002 Bulk Flow Statistics Convergence to the CMB dipole seen by a number of authors on scales above ~ 6000 kms -1

12. “Mapping the Mass”: Birmingham, 1 – 2 Aug 2002 Bulk Flow Statistics Convergence to the CMB dipole seen by a number of authors on scales above ~ 6000 kms -1 Shellflow (Courteau et al.)

13. “Mapping the Mass”: Birmingham, 1 – 2 Aug 2002 Bulk Flow Statistics Convergence to the CMB dipole seen by a number of authors on scales above ~ 6000 kms -1 Larger-scale bulk flows detected by some surveys (e.g. Lauer & Postman, LP10K, SMAC) but not at high statistical significance From Colless et al (2001)

14. “Mapping the Mass”: Birmingham, 1 – 2 Aug 2002 Velocity Correlation Statistics 2-point velocity correlation tensor In linear theory (Gorski 1988) and,,

15. “Mapping the Mass”: Birmingham, 1 – 2 Aug 2002 Velocity Correlation Statistics From Bridle et al. (2001) Combined with CMBR, SN

16. We can compare observed peculiar velocities with the reconstructed density and velocity field from all-sky redshift surveys, via linear theory relations:- “Mapping the Mass”: Birmingham, 1 – 2 Aug 2002 Velocity – Density Reconstructions  density-density comparisons  velocity-velocity comparisons

17. “Mapping the Mass”: Birmingham, 1 – 2 Aug 2002 Archetype is POTENT ( Bertschinger & Dekel 1988; Dekel et al 1999 ) Density – density comparisons Need only radial components, but everywhere! Interpolate u(r) on a regular grid x Smoothing window

18. Compare v pec with e.g. IRAS  -field. Assume linear biasing: “Mapping the Mass”: Birmingham, 1 – 2 Aug 2002 Density – density comparisons versus has slope Sigad et al. (1998) Archetype is POTENT ( Bertschinger & Dekel 1988; Dekel et al 1999 )

19. “Mapping the Mass”: Birmingham, 1 – 2 Aug 2002 Density – density comparisons POTENT is vulnerable to a number of statistical biases:- See e.g. Strauss & Willick (1995), Hendry & Simmons (1995), Hendry (2001)  Calibration bias  Inhomogeneous Malmquist bias  Tensor window bias  Sampling gradient bias

20. “Mapping the Mass”: Birmingham, 1 – 2 Aug 2002 Density – density comparisons POTENT is vulnerable to a number of statistical biases:- See e.g. Strauss & Willick (1995), Hendry & Simmons (1995), Hendry (2001)  Calibration bias  Inhomogeneous Malmquist bias  Tensor window bias  Sampling gradient bias

21. “Mapping the Mass”: Birmingham, 1 – 2 Aug 2002 Inhomogeneous Malmquist bias Line of sight o d u est cz Interpolate u(r) on a real space grid

22. “Mapping the Mass”: Birmingham, 1 – 2 Aug 2002 Inhomogeneous Malmquist bias Line of sight o d u est cz r u true Interpolate u(r) on a real space grid

23. “Mapping the Mass”: Birmingham, 1 – 2 Aug 2002 Inhomogeneous Malmquist bias Line of sight o d u est cz r u true In general Interpolate u(r) on a real space grid Bias correction depends on

24. “Mapping the Mass”: Birmingham, 1 – 2 Aug 2002 Archetype is VELMOD ( Willick & Strauss 1997, Willick et al 1998 ) Velocity – velocity comparisons Maximise likelihood of observing Tully-Fisher data, given a velocity field and TF model ‘Forward’ VELMOD ‘Inverse’ VELMOD = parameters of TF relation and velocity model VELMOD also requires a parametric model for

25. “Mapping the Mass”: Birmingham, 1 – 2 Aug 2002 Velocity – velocity comparisons VELMOD also requires a parametric model for Strauss & Willick (1995) Triple-value regions

26. “Mapping the Mass”: Birmingham, 1 – 2 Aug 2002 VELMOD Results Willick et al 1998: Mark III + IRAS 1.2Jy predicted v-field

27. “Mapping the Mass”: Birmingham, 1 – 2 Aug 2002 VELMOD Results Branchini et al. 2001 SFI + PSCz v-field Nusser et al. 2001 ENEAR + PSCz v-field

28. “Mapping the Mass”: Birmingham, 1 – 2 Aug 2002 VELMOD Results Consistent picture of    Good agreement with results of ITF method, but significantly discrepant with POTENT results What is the origin of this discrepancy?… c.f. Berlind et al. 2001,  estimation in non-linear local biasing schemes Rauzy & Hendry (2000) – robust approach

29. Assumption: luminosity function is Universal Selection effects Spatial distribution Luminosity function Null hypothesis (see Rauzy 2001) Step function Angular and radial Selection function Robust Method “Mapping the Mass”: Birmingham, 1 – 2 Aug 2002

30. Define:- Can show:- P1: P2: and are independent Robust Method “Mapping the Mass”: Birmingham, 1 – 2 Aug 2002 Assuming define Can show:- P3: and are independent

31. Also (see Efron & Petrosian 1992) Robust Method “Mapping the Mass”: Birmingham, 1 – 2 Aug 2002 Estimate  via

32. Robust Method “Mapping the Mass”: Birmingham, 1 – 2 Aug 2002 From Rauzy & Hendry 2000 MarkIII MAT + IRAS 1.2Jy v-field Non-parametric: independent of LF, spatial distribution. Insensitive to Malmquist bias. Very conservative use of TF information. Monte Carlo error estimates straightforward – permutation test. Rejection test on values of 

33. Robust Method “Mapping the Mass”: Birmingham, 1 – 2 Aug 2002 Rauzy & Hendry 2000 MarkIII MAT + IRAS 1.2Jy v-field Strength: Robust support for VELMOD analysis: validity of Malmquist corrections Weakness: Completeness requirement restricts sample size and depth (c.f. SFI + PSCz) Scale dependent biasing?….

34. Zaroubi (2002) Assume + prior model for power spectrum Unbiased minimal variance estimator Consistency at last?…. “Mapping the Mass”: Birmingham, 1 – 2 Aug 2002

35. Zaroubi et al. (2002): ENEAR + SFI vs PSCz (astro-ph/0207356) Consistency at last?…. “Mapping the Mass”: Birmingham, 1 – 2 Aug 2002

36. Conclusions  Peculiar velocities useful cosmological probes – parameter constraints from bulk flows, correlations  Major issues of sparseness, noise and bias still affect their calibration and use – handle with care!  (Finally!) consensus emerging on    ~ 0.5 from velocity-velocity and density-density comparisons  No realistic prospect to extend beyond linear bias – not competitive with e.g. 2dF  Are peculiar velocities’ best days behind them?….