Caustics in Dark Matter HalosSergei Shandarin, University of Kansas

(collaboration with Roya Mohayaee, IAP)Nonlinear Cosmology Program: Nice-Marseille-Paris

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Outline

LCDM and LWDM models Introduction to caustics: 1D and 2D cases 3D universe Summary 1 What kills caustics? Summary 2

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A big question: what is the dark matter?DIRECT DETECTIONINDIRECT DETECTIONAnnihilation of self-annihilatedaxions and neutralinos producesgamma-raysHESS, GLAST experimentsAharonian et al 2005, Science

Weak lensinge.g. Gavazzi, Mohayee, Fort 2005e.g. Sikivie, Ipser 1992Sikivie, Tkachev, Wang 1997: role of internal and external caustics

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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 2005Possible solution: Warm Dark Matter

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Lamda Warm Dark Matter (LWDM)Abazajian 20051.7 keV < m < 8.2 keV

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Why caustics?Saichev 1976For 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)

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Caustics in geometric optics

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Generic singularities in 1DPoints at a generic instant of timePoints at particular instants of timeArnold, Shandarin, Zeldovich 1982

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Collisionless DM and collisional baryonsShandarin, Zeldovich 1989Dark matterBaryons

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Zeldovich Approximationin comoving coordinatespotential perturbationsDensityare eigen values ofis a symmetric tensorDensity becomes

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Generic singularities in 2DLines (1D) at a generic instant of timePoints (0D) at a generic instant of timePoints (0D) at particular instants of timePoints (0D) at particular instants of timeArnold, Shandarin, Zeldovich 1982

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ZeldovichApproximation (2D) N-body simulations (2D)versus

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2D N-body simulations (discreteness effect)Melott, Shandarin 1989

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Caustics in high resolution 2D Simulations

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2D vs 3D2D simulations3D simulationsMelott, Shandarin 1989Shirokov, Bertschinger 2005

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Shirokov, Bertschinger 2005

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Complexity of caustics(2D simulations) Melott, Shandarin 1989

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Outline

LCDM and LWDM models Introduction to caustics: 1D and 2D cases 3D universe Summary 1 What kills caustics? Summary 2

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

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* Hierarchical clustering

* Smallest halos

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LWDM simulationsm_x = 1.2 h^(5/4)) keVGotz & Sommer-Larson 2003

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Generic singularities in 3DLines (1D) at a generic instant of timeSurfaces (2D) at a generic instant of timePoints (0D) at a generic instant of timePoints (0D) at a generic instant of timePoints (0D) at particular instants of timePoints (0D) at particular instants of timeArnold, Shandarin, Zeldovich 1982

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Caustics in hot systemsColombi, Touma 2005

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Summary 1Formation 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 timePoints (0D) at particular timesExiting prospect: testing particle physics using caustics in DM halos.

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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)

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2D N-body simulations (discreteness effect)

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Phase space becomes too fine-grainedColombi, Touma 2005

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Self-similar spherically symmetric solutionFillmore & Goldreich 1984; Bertschinger 1985Equation of motion

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Nondimensional EquationInitial condition

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Function Bertschinger 1985At constant q:trajectory of particleAt constant \tau:positions of particlesTwo interpretations

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Density near caustics

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Density (cold medium)

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Density near causticsTully 2005NGC 5846

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Effect of thermal velocity dispersionInitial condition in coldmedium

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Effect of thermal velocity dispersion Distance of the caustic in stream v from the caustic in stream v=0

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Universal density profiles in the vicinity of caustics

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Gravitational coolingMohayaee, Shandarin 2005

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Summary 2Spherical (self-similar) model can be used as a guidelineMore realistic models are badly neededOther 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

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Caustics are lines of infinite brightness -> caustics are surfaces, lines, or point of infinite density of dark matterScales > wavelength