1. The Filament-Void Network and the Scale of Homogeneity in the Universe Suketu P. Bhavsar University of Kentucky Graduate Student Seminar, 2005

2. Outline A brief history of filamentary structure Sky surveys and redshift surveys Are the filaments real? Analysis of the Las Campanas Redshift Survey Is there a largest scale for physical filaments? Conclusions: Homogeneity - for L > 80Mpc

3. The Lick galaxy counts North Galactic Cap – Seldner et al.

4. 1 st a rock group “The Filaments 2 nd 3 rd 4 th 5 th structure in the Universe “Filaments”

6. The Lick counts – southern galactic cap 'grey scale' matters for what the eye tells the brain South Galactic Cap – Seldner et al.

7. The “stick man” - Slice from the CfA2 redshift survey – a bubbly universe angular position and radial velocity are plotted for each galaxy

9. ● ●Note: data permuting technique = SHUFFLE

10. the “wall” CfA2 six slices superposed – angular position and radial velocity are plotted for each galaxy

11. How do we get this - CfA North and South slices

12. ...........From this?

13. Actually.......... from this? Microwave sky image from WMAP

14. Famous Cosmological Problems

15. ●T he formation and description of structure remains a crucial problem in cosmology

17. Comparison of redshift surveys ●1D, 2D and 3D surveys

18. The Las Campanas Redshift Survey ●Six slices through space

19. What are the scales of the largest real filamentary features in the LCRS? Collaborators – Somnath Bharadwaj (IIT Kh) – Jatush V. Sheth (IUCAA)

20. LCRS: -3 o slice

21. Method Identifying filamentary structure Embed a 1 h -1 Mpc x 1 h -1 Mpc rectangular grid on each slice. Generate “coarse grained” map by filling neighboring cells of occupied cells. This creates larger structure, as the filling factor, FF, increases for a slice. Use “friends of friends” to define features for at each value of the FF.

22. Smoothing ●FF = filling factor

23. “Friends of friends” (Turner & Gott 1977) define clusters ● Shown are 4 levels of smoothing, note how clusters grow (clockwise) with FF ● Colors represent separate clusters

24. Filamentarity In 2D the shape of an object can be characterised by: perimeter (L) and area (S). A dimensionless Shapefinder statistic, filamentarity, F (0 ≤ F ≤ 1), can be constructed out of L and S. Extremes:F = 0...... circle F = 1...... a line Use Shapefinders to obtain average filamentarity, F 2, of the features as a function of FF. (Bharadwaj et al. 2000).

25. Shuffling – A procedure for randomising structure larger than some scale and keeping it intact below that scale.

28. Shuffling: an experiment with a Poisson distribution of points Creating a “Glass pattern”

31. Consequences of Shuffling – Large scale structures that are real, break, and do not re-form when Shuffled – Large scale structures that are visual, i.e. due to chance, are formed again and again due to statistical chance.

32. The -3 o slice Shuffled at L = 70 and 80 Mpc ●Top: original LCRS slice and a Poisson distribution ●Bottom: Shuffled slices

33. Determining the number of real filaments at various values of L Plot F 2 versus FF for the original data and the Shuffled slices for L from 10 Mpc to 100 Mpc The excess of F 2 in the LCRS above its values for Shuffled slices gives the REAL filamentarity through the range of FF for each slice.

35. Conclusions The scale of the largest real structures in the LCRS are ~80 h -1 Mpc The filament void network is statistically repeated on scales > 80 -1 Mpc. This is the scale on which the universe is statistically homogeneous

36. Future Projects The Sloan Digital Sky Survey The 2dF survey N-body simulations