January 25, 2006 NCW, Nice 1 Caustics in Dark Matter Halos Sergei Shandarin, University of Kansas (collaboration with Roya Mohayaee, IAP) Nonlinear Cosmology Program: Nice-Marseille-Paris
January 25, 2006 NCW, Nice 1 1 Caustics in Dark Matter Halos Sergei Shandarin, University of Kansas (collaboration with Roya Mohayaee, IAP) Nonlinear Cosmology.
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January 25, 2006January 25, 2006 NCW, NiceNCW, Nice 11
Caustics in Dark Matter Halos
Caustics in Dark Matter HalosSergei 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
January 25, 2006January 25, 2006 NCW, NiceNCW, Nice 22
OutlineOutline
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
January 25, 2006January 25, 2006 NCW, NiceNCW, Nice 33
A big question: what is the dark matter?
A big question: what is the dark matter?
DIRECT DETECTIONINDIRECT DETECTION
Annihilation of self-annihilatedaxions and neutralinos producesgamma-raysHESS, GLAST experimentsAharonian et al 2005, Science
Weak lensinge.g. Gavazzi, Mohayee, Fort 2005
e.g. Sikivie, Ipser 1992Sikivie, Tkachev, Wang 1997: role of internal and external caustics
January 25, 2006January 25, 2006 NCW, NiceNCW, Nice 44
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
January 25, 2006January 25, 2006 NCW, NiceNCW, Nice 55
Lamda Warm Dark Matter
(LWDM)
Lamda Warm Dark Matter
(LWDM)
Abazajian 20051.7 keV < m < 8.2 keV
January 25, 2006January 25, 2006 NCW, NiceNCW, Nice 66
Why caustics?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)
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Caustics in geometric optics
Caustics in geometric optics
January 25, 2006January 25, 2006 NCW, NiceNCW, Nice 88
Generic singularities in 1DGeneric singularities in 1D
Points at a generic instant of time
Points at particular instants of time
Arnol’d, Shandarin, Zel’dovich 1982
January 25, 2006January 25, 2006 NCW, NiceNCW, Nice 99
Collisionless DM and collisional baryons
Collisionless DM and collisional baryons
Shandarin, Zel’dovich 1989
Dark matter
Baryons
January 25, 2006January 25, 2006 NCW, NiceNCW, Nice 1010
Zel’dovich ApproximationZel’dovich Approximation
in comoving coordinates
potential perturbations
Density
are eigen values of
is a symmetric tensor
Density becomes
January 25, 2006January 25, 2006 NCW, NiceNCW, Nice 1111
Generic singularities in 2DGeneric 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
Points (0D) at particular instants of time
Arnol’d, Shandarin, Zel’dovich 1982
January 25, 2006January 25, 2006 NCW, NiceNCW, Nice 1212
Zel’dovichApproximation (2D)
N-body simulations (2D)
versus
January 25, 2006January 25, 2006 NCW, NiceNCW, Nice 1313
2D N-body simulations (discreteness effect)
2D N-body simulations (discreteness effect)
Melott, Shandarin 1989
January 25, 2006January 25, 2006 NCW, NiceNCW, Nice 1414
Caustics in high
resolution
2D Simulatio
ns
Caustics in high
resolution
2D Simulatio
ns
January 25, 2006January 25, 2006 NCW, NiceNCW, Nice 1515
2D vs 3D2D vs 3D
2D simulations 3D simulations
Melott, Shandarin 1989 Shirokov, Bertschinger 2005
January 25, 2006January 25, 2006 NCW, NiceNCW, Nice 1616
QuickTime™ and aYUV420 codec decompressor
are needed to see this picture.
QuickTime™ and aYUV420 codec decompressor
are needed to see this picture.
Shirokov, Bertschinger 2005
January 25, 2006January 25, 2006 NCW, NiceNCW, Nice 1717
Complexity of caustics(2D simulations)
Complexity of caustics(2D simulations)
Melott, Shandarin 1989
January 25, 2006January 25, 2006 NCW, NiceNCW, Nice 1818
OutlineOutline
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
z=153
z=7.2
z=86z=115
z=0z=1
LCDM simulation (Diemand et al 2005)
January 25, 2006January 25, 2006 NCW, NiceNCW, Nice 2020
* Hierarchical clustering
* Smallest halos
* Hierarchical clustering
* Smallest halos
January 25, 2006January 25, 2006 NCW, NiceNCW, Nice 2121
LWDM simulations
m_x = 1.2 h^(5/4)) keV
Gotz & Sommer-Larson 2003
January 25, 2006January 25, 2006 NCW, NiceNCW, Nice 2222
Generic singularities in 3DGeneric 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 a generic instant of time
Points (0D) at particular instants of time
Points (0D) at particular instants of time
Arnol’d, Shandarin, Zel’dovich 1982
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Caustics in hot systems
Caustics in hot systems
Colombi, Touma 2005
January 25, 2006January 25, 2006 NCW, NiceNCW, Nice 2424
Summary 1Summary 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.
January 25, 2006January 25, 2006 NCW, NiceNCW, Nice 2525
Three things that destroy caustics.
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)
January 25, 2006January 25, 2006 NCW, NiceNCW, Nice 2626
2D N-body simulations (discreteness effect)
2D N-body simulations (discreteness effect)
January 25, 2006January 25, 2006 NCW, NiceNCW, Nice 2727
Phase space becomes too fine-
grained
Phase space becomes too fine-
grained
Colombi, Touma 2005
January 25, 2006January 25, 2006 NCW, NiceNCW, Nice 2828
Self-similar spherically symmetric solution
Self-similar spherically symmetric solution
Fillmore & Goldreich 1984; Bertschinger 1985
Equation of motion
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Nondimensional EquationNondimensional Equation
Initial condition
January 25, 2006January 25, 2006 NCW, NiceNCW, Nice 3030
Function
Function
Bertschinger 1985
At constant q:trajectory of particle
At constant \tau:positions of particles
Two interpretations
January 25, 2006January 25, 2006 NCW, NiceNCW, Nice 3131
Density near caustics
Density near caustics
January 25, 2006January 25, 2006 NCW, NiceNCW, Nice 3232
Density (cold medium)Density (cold medium)
January 25, 2006January 25, 2006 NCW, NiceNCW, Nice 3333
Density near caustics
Density near caustics
Tully 2005
NGC 5846
January 25, 2006January 25, 2006 NCW, NiceNCW, Nice 3434
Effect of thermal velocity dispersion
Effect of thermal velocity dispersion
Initial condition in coldmedium
January 25, 2006January 25, 2006 NCW, NiceNCW, Nice 3535
Effect of thermal velocity dispersion
Effect of thermal velocity dispersion
Distance of the caustic in stream Distance of the caustic in stream v from the caustic in stream v=0v from the caustic in stream v=0
January 25, 2006January 25, 2006 NCW, NiceNCW, Nice 3636
Universal density profiles in the vicinity of caustics
Universal density profiles in the vicinity of caustics
January 25, 2006January 25, 2006 NCW, NiceNCW, Nice 3737
Gravitational cooling
Mohayaee, Shandarin 2005
January 25, 2006January 25, 2006 NCW, NiceNCW, Nice 3838
Summary 2Summary 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
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