1. Small Scale Structure in Voids Danny Pan Advisor: Michael Vogeley

2. Motivation/Goal  -CDM models show small scale structure in voids  -CDM models show small scale structure in voids Goal is to verify the small scale structure of voids Goal is to verify the small scale structure of voids Possible results? Possible results? Structure exists, agree with models Structure exists, agree with models Structure does not exist, models may not tell the whole story Structure does not exist, models may not tell the whole story

3. Millenium Run Simulation

4. Simulated Universe Gottlober (2003) Gottlober (2003)

5. Outline Introduction Introduction Research in Voids Research in Voids VoidFinder (finds voids!) VoidFinder (finds voids!) Methods of Analysis Methods of Analysis Void Statistics Void Statistics Correlation Function Correlation Function ShapeFinder ShapeFinder Conclusion/Results Conclusion/Results Future Work Future Work

6. Introduction The Universe contains objects, but it is mostly empty The Universe contains objects, but it is mostly empty Modern cosmology tells us that evolution of the Universe causes clumpiness Modern cosmology tells us that evolution of the Universe causes clumpiness Dense regions stay dense and grow asymmetrically Dense regions stay dense and grow asymmetrically Underdense regions stay underdense and grow symmetrically Underdense regions stay underdense and grow symmetrically Result is spherical voids with dense walls in the Universe Result is spherical voids with dense walls in the Universe

7. Research in Voids Gregory and Tifft (1976) first looked at structure in Coma Supercluster Gregory and Tifft (1976) first looked at structure in Coma Supercluster Found regions that seemed very empty Found regions that seemed very empty Kirshner et al (1982) found a 1,000,000 cu Mpc region in Bootes that was empty Kirshner et al (1982) found a 1,000,000 cu Mpc region in Bootes that was empty Interest in voids grew Interest in voids grew Rojas et al. (2004) observed differences in void and wall galaxies Rojas et al. (2004) observed differences in void and wall galaxies

8. VoidFinder Used to determine sample of Void regions and Void galaxies Used to determine sample of Void regions and Void galaxies Volume limited sample from SDSS Volume limited sample from SDSS 4783 square degrees of the sky 4783 square degrees of the sky magnitude cut of 17.5 magnitude cut of 17.5 approximately L * at furthest distance approximately L * at furthest distance radial cut of 100 and 300 h -1 Mpc radial cut of 100 and 300 h -1 Mpc 61,000 galaxies 61,000 galaxies

9. Galaxies

10. 3 Nearest Neighbors

11. Potential Void Galaxies

12. Walls Only

13. Maximal Spheres

14. Void Galaxies

15. VoidFinder Results Results 527 void regions 527 void regions 3369 void galaxies 3369 void galaxies 40% of the volume are voids 40% of the volume are voids

16. Picture of VoidFinder

17. Methods of Analysis Void Statistics Void Statistics Correlation Function Correlation Function ShapeFinder ShapeFinder

18. Void Statistics

23. Correlation Function Probability of two points separated by a distance r is: Probability of two points separated by a distance r is:

24. Correlation Function Landy-Szalay (1993) equation Landy-Szalay (1993) equation Correlation depends on data points as well as random points Correlation depends on data points as well as random points

25. Correlation Function

26. ShapeFinder Defined by Sahni et al. (1998) to assess shapes of objects Defined by Sahni et al. (1998) to assess shapes of objects Uses Minkowski Functionals to help determine shapes Uses Minkowski Functionals to help determine shapes Volume (V) Volume (V) Surface Area (S) Surface Area (S) Integrated Mean Curvature (C) Integrated Mean Curvature (C) Gaussian Curvature (G) Gaussian Curvature (G)

27. ShapeFinder Can determine 3 phase space lengths Can determine 3 phase space lengths L1 = V/S L1 = V/S L2 = S/C L2 = S/C L3 = C L3 = C L1=L2<L3 Filament L1=L2<L3 Filament L1<L2=L3 Pancake L1<L2=L3 Pancake 2 ShapeFinder statistics 2 ShapeFinder statistics K1 = (L2-L1)/(L2+L1) K1 = (L2-L1)/(L2+L1) K2 = (L3-L2)/(L3+L2) K2 = (L3-L2)/(L3+L2) K1=0, K2=0 Sphere K1=0, K2=0 Sphere K1=1, K2=0 Pancake K1=1, K2=0 Pancake K1=0, K2=1 Filament K1=0, K2=1 Filament

28. ShapeFinder Images

29. ShapeFinder Results TABLE OF SHAPEFINDER RESULTS ON LARGEST VOIDS TABLE OF SHAPEFINDER RESULTS ON LARGEST VOIDS

30. Conclusions Void Statistics match other observational results as well as theoretical models Void Statistics match other observational results as well as theoretical models Radial density profiles match very well with expected results, validates VoidFinder Radial density profiles match very well with expected results, validates VoidFinder 2 Point Correlation Function matches various other samples 2 Point Correlation Function matches various other samples Implies correlation of underdense regions mimic that of the entire sample Implies correlation of underdense regions mimic that of the entire sample

31. Future Work ShapeFinder needs to be expanded to accommodate for multiple “objects” within each void region ShapeFinder needs to be expanded to accommodate for multiple “objects” within each void region Analysis needs to be done on the Millenium Run sample or another Lambda CDM model to compare results Analysis needs to be done on the Millenium Run sample or another Lambda CDM model to compare results

32. Acknowledgements Thank you Thank you Dr. Michael Vogeley Dr. Michael Vogeley Dr. Fiona Hoyle Dr. Fiona Hoyle Committee Committee Dr. Avijit Ghosh Dr. Avijit Ghosh Dr. Dave Goldberg Dr. Dave Goldberg Dr. Bhuvnesh Jain Dr. Bhuvnesh Jain Dr. Gordon Richards Dr. Gordon Richards