1. An Analytic Model for the Tidal Effect on Cosmic Voids Jounghun Lee & Daeseong Park Seoul National University Lee & Park 2006, ApJ, 652, 1 Park & Lee 2006, astro-ph/0610520

2. Table of Contents Introduction & Motivation Analytic Model  Key concepts & basic assumptions  Mathematical framework  Main results & implications Numerical Test  Voids from the Millennium Run simulation  Comparison: numerical vs. analytical Summary & Future work

3. Collection of bubble-like voids separated by filaments and sheets Voids occupy 40 % of cosmic volume Voids have very low density Introduction – The Universe on the Largest Scale Hoyle & Vogeley 2004 void regions

4. Introduction – Origin & Properties of Cosmic Voids Originated from the local minima of the initial density field

5. Expansion only – spherical shape void galaxies void

6. Motivation Come on! voids are not spherical at all … Shandarin et al. 2004

7. Motivation Why? well, it should be because of the tidal force … Why? well, it should be because of the tidal force … Shandarin et al. 2006

8. Strong tidal effect – non spherical shape

9. Spherical caseNonspherical case

10. Key Concept Void spin angular momentum, J :  m  : the mass of a void galaxy  x  : the position of a void galaxy  v  : the velocity of a void galaxy

11. Mathematical Framework The Tidal Torque Theory (Peebles 1969, Doroshekvich 1970, White 1984)  T ij : the local tidal shear tensor  I ij : the inertia momentum tensor

12. Basic Assumption For the case of voids, the principal axes of the inertia momentum and the tidal shear tensors are maximally misaligned with each other: preferential alignment of J with the intermediate principal axis of T ij

13. Mathematical Framework Alignment of void spins with local shears Lee & Pen (2000, 2001)

14. 1 2 3 r strong spatial correlations between neighbor void spins Intrinsic correlation Intrinsic correlation Spatial correlation

15. Main Prediction Void spin-spin correlation function  R  r tt he two-point correlations of the density field smoothed on the void scale, R

16. Numerical Test Millennium Run Galaxy Catalog (Springel et al. 2005)   CDM cosmology (  m =0.25,n s =1,  8 =0.9,h=0.73)  A cubic box of linear size 500 h -1 Mpc  809848723 galaxies at z=0 Void-Finder Algorithm (Hoyle & Vogeley 2002)  The number of voids identified: 24037  The mean effective radius: 10.45 Mpc/h  13507 voids with more than 30 galaxies

17. Numerical Test (Lee & Park 2006)

21. Summary A new concept of the void spin angular momentum introduced to quantify the tidal effect on voids. The linear tidal torque theory used to derive analytically the void spin-spin correlations. The analytic prediction agrees excellently with the Millennium Run numerical data points.

22. Key Concept Void ellipticity where

23. Basic Assumption Void ellipticity is related to the eigenvalues of the tidal tensor as Void forms in the local minima of the initial density field:

24. Mathematical Framework

25. The distribution of { 1, 2, 3 } (Doroshkevich 1970)

26. Main Prediction The void ellipticity distribution

27. Park & Lee 2006 Astro-ph/0610520 WMAP 3 rd year WMAP 1 st year

28. Numerical Test (Park & Lee 2006, astro-ph/0610520)

29. Projected Images of Voids

30. (Park & Lee 2006, astro-ph/0610520)

31. Summary The Zel’dovich approximation used to derive analytically the void ellipticity distribution. The void ellipticity distribution depends sensitively on the values of the key cosmological parameters. The analytic prediction agrees excellently with the numerical result from the Millennium Run simulation.

32. Ongoing & Future Works Application to observational data  SDSS void catalogs Evolution of the void ellipticity distribution as a probe of dark energy equation of state  (Lee 2007, in preparation) Void-supercluster alignment connection as a new clue to the filamentary cosmic web  (Park & Lee 2007, in preparation)