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Caustics in Dark Matter Halos

Caustics in Dark Matter Halos. Sergei Shandarin, University of Kansas (collaboration with Roya Mohayaee, IAP) Nonlinear Cosmology Program: Nice-Marseille-Paris. Outline. LCDM and LWDM models Introduction to caustics: 1D and 2D cases 3D universe Summary 1 What kills caustics?

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Caustics in Dark Matter Halos

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

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

  3. 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 A big question: what is the dark matter? e.g. Sikivie, Ipser 1992 Sikivie, Tkachev, Wang 1997: role of internal and external caustics NCW, Nice

  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 NCW, Nice

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

  6. For 100 GeV SUSY neutralino (LCDM) Why caustics? Saichev 1976 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) NCW, Nice

  7. Caustics in geometric optics NCW, Nice

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

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

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

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

  12. Zel’dovich Approximation (2D) N-body simulations (2D) versus NCW, Nice

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

  14. Caustics in high resolution 2D Simulations NCW, Nice

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

  16. Shirokov, Bertschinger 2005 NCW, Nice

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

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

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

  20. * Hierarchical clustering* Smallest halos NCW, Nice

  21. LWDM simulations m_x = 1.2 h^(5/4)) keV Gotz & Sommer-Larson 2003 NCW, Nice

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

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

  24. 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. NCW, Nice

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

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

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

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

  29. Nondimensional Equation Initial condition NCW, Nice

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

  31. Density near caustics NCW, Nice

  32. Density (cold medium) NCW, Nice

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

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

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

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

  37. Gravitational cooling Mohayaee, Shandarin 2005 NCW, Nice

  38. 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 NCW, Nice

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