1. January 25, 2006 NCW, Nice 1 1 Caustics in Dark Matter Halos Sergei Shandarin, University of Kansas (collaboration with Roya Mohayaee, IAP) Nonlinear Cosmology Program: Nice-Marseille-Paris Sergei Shandarin, University of Kansas (collaboration with Roya Mohayaee, IAP) Nonlinear Cosmology Program: Nice-Marseille-Paris

2. January 25, 2006 NCW, Nice 2 2 Outline  LCDM and LWDM models  Introduction to caustics: 1D and 2D cases  3D universe  Summary 1  What kills caustics?  Summary 2  LCDM and LWDM models  Introduction to caustics: 1D and 2D cases  3D universe  Summary 1  What kills caustics?  Summary 2

3. January 25, 2006 NCW, Nice 3 3 A big question: what is the dark matter? DIRECT DETECTION INDIRECT DETECTION Annihilation of self-annihilated axions and neutralinos produces gamma-rays HESS, GLAST experiments Aharonian et al 2005, Science Weak lensing e.g. Gavazzi, Mohayee, Fort 2005 e.g. Sikivie, Ipser 1992 Sikivie, Tkachev, Wang 1997: role of internal and external caustics

4. January 25, 2006 NCW, Nice 4 4 Unresolved problems in LCDM  Reduction of satellite halos  Kauffmann et al 1993; Klypin et al 1999; Moore et al 1999; Willman et al 2004  Reduction of galaxies in voids  Peebles 2001; Bode et al 2001  Low concentration of DM in galaxies  Dalcanton & Hogan 2001; van den Bosch & Swaters 2001; Zentner & Bullock 2002; Abazajian et al 2005  Angular momentum problem and formation of disk galaxies  Dolgov & Sommer-Larson 2001 ; Governato et al 2004; Kormendy & Fisher 2005 Possible solution: Warm Dark Matter

5. January 25, 2006 NCW, Nice 5 5 Lamda Warm Dark Matter (LWDM) Abazajian 2005 1.7 keV < m < 8.2 keV

6. January 25, 2006 NCW, Nice 6 6 Why caustics? Saichev 1976 For 100 GeV SUSY neutralino (LCDM) For a few keV sterile neutrino or gravitino (LWDM) Galaxy formation is not hierarchical or only marginally hierarchical! ( only a few mergers results in the halo of galactic size)

7. January 25, 2006 NCW, Nice 7 7 Caustics in geometric optics

8. January 25, 2006 NCW, Nice 8 8 Generic singularities in 1D Points at a generic instant of time Points at particular instants of time Arnol’d, Shandarin, Zel’dovich 1982

9. January 25, 2006 NCW, Nice 9 9 Collisionless DM and collisional baryons Shandarin, Zel’dovich 1989 Dark matter Baryons

10. January 25, 2006 NCW, Nice 10 Zel’dovich Approximation in comoving coordinates potential perturbations Density are eigen values of is a symmetric tensor Density becomes

11. January 25, 2006 NCW, Nice 11 Generic singularities in 2D Lines (1D) at a generic instant of time Points (0D) at a generic instant of time Points (0D) at particular instants of time Arnol’d, Shandarin, Zel’dovich 1982

12. January 25, 2006NCW, Nice12 Zel’dovich Approximation (2D) N-body simulations (2D) versus

13. January 25, 2006 NCW, Nice 13 2D N-body simulations (discreteness effect) Melott, Shandarin 1989

14. January 25, 2006 NCW, Nice 14 Caustics in high resolution 2D Simulation s

15. January 25, 2006 NCW, Nice 15 2D vs 3D 2D simulations 3D simulations Melott, Shandarin 1989Shirokov, Bertschinger 2005

16. January 25, 2006 NCW, Nice 16 Shirokov, Bertschinger 2005

17. January 25, 2006 NCW, Nice 17 Complexity of caustics (2D simulations) Melott, Shandarin 1989

18. January 25, 2006 NCW, Nice 18 Outline  LCDM and LWDM models  Introduction to caustics: 1D and 2D cases  3D universe  Summary 1  What kills caustics?  Summary 2  LCDM and LWDM models  Introduction to caustics: 1D and 2D cases  3D universe  Summary 1  What kills caustics?  Summary 2

19. z=153 z=7.2 z=86 z=115 z=0z=1 LCDM simulation (Diemand et al 2005)

20. January 25, 2006 NCW, Nice 20 * Hierarchical clustering * Smallest halos

21. January 25, 2006 NCW, Nice 21 LWDM simulation s m_x = 1.2 h^(5/4)) keV Gotz & Sommer-Larson 2003

22. January 25, 2006 NCW, Nice 22 Generic singularities in 3D Lines (1D) at a generic instant of time Surfaces (2D) at a generic instant of time Points (0D) at a generic instant of time Points (0D) at particular instants of time Arnol’d, Shandarin, Zel’dovich 1982

23. January 25, 2006 NCW, Nice 23 Caustics in hot systems Colombi, Touma 2005

24. January 25, 2006NCW, Nice24 Summary 1  Formation of caustics in dark matter halos (structures) is a more universal phenomenon than many cosmologists thought before.  Caustics have a complex geometry.  The generic caustics can be  Surfaceses (2D)  Lines (1D)  Points (0D) at generic time  Points (0D) at particular times  Exiting prospect: testing particle physics using caustics in DM halos.  Formation of caustics in dark matter halos (structures) is a more universal phenomenon than many cosmologists thought before.  Caustics have a complex geometry.  The generic caustics can be  Surfaceses (2D)  Lines (1D)  Points (0D) at generic time  Points (0D) at particular times  Exiting prospect: testing particle physics using caustics in DM halos.

25. January 25, 2006 NCW, Nice 25 Three things that destroy caustics. Discreteness (numerical, not physical) Phase-space becomes too fine-grained eventually reaching the physical discreatness (physical) Thermal velocity dispersion (physical)

26. January 25, 2006 NCW, Nice 26 2D N-body simulations (discreteness effect)

27. January 25, 2006 NCW, Nice 27 Phase space becomes too fine- grained Colombi, Touma 2005

28. January 25, 2006 NCW, Nice 28 Self-similar spherically symmetric solution Fillmore & Goldreich 1984; Bertschinger 1985 Equation of motion

29. January 25, 2006 NCW, Nice 29 Nondimensional Equation Initial condition

30. January 25, 2006 NCW, Nice 30 Function Bertschinger 1985 At constant q: trajectory of particle At constant \tau: positions of particles Two interpretations

31. January 25, 2006 NCW, Nice 31 Density near caustics

32. January 25, 2006 NCW, Nice 32 Density (cold medium)

33. January 25, 2006 NCW, Nice 33 Density near caustics Tully 2005 NGC 5846

34. January 25, 2006 NCW, Nice 34 Effect of thermal velocity dispersion Initial condition in cold medium

35. January 25, 2006 NCW, Nice 35 Effect of thermal velocity dispersion Distance of the caustic in stream v from the caustic in stream v=0

36. January 25, 2006 NCW, Nice 36 Universal density profiles in the vicinity of caustics

37. January 25, 2006 NCW, Nice 37 Gravitational cooling Mohayaee, Shandarin 2005

38. January 25, 2006NCW, Nice38 Summary 2  Spherical (self-similar) model can be used as a guideline  More realistic models are badly needed  Other singularities may be more interesting for annihilation detection provided that they can be resolved  Evolution in phase space needs to be studied in more detail  Spherical (self-similar) model can be used as a guideline  More realistic models are badly needed  Other singularities may be more interesting for annihilation detection provided that they can be resolved  Evolution in phase space needs to be studied in more detail