1. DARK MATTER IN THE MILKY WAY ALEXEY GLADYSHEV (JINR, DUBNA & ITEP, MOSCOW)

2. 2 Outlook  Introduction.  Evidence for Dark Matter. Types of Dark Matter. Direct searches for the Dark Matter.  EGRET data: an excess of the diffuse gamma ray flux  Dark matter distribution in the Milky Way. Halo density profile. Halo substructure. The Milky Way rotation curve.  Positrons and antiprotons in the cosmic rays  WMAP and EGRET constraints in Constrained Minimal Supersymmetric Standard Model  Conclusions

3. 3 WMAP  WMAP mission has provided the first detailed full-sky map of the microwave background radiation in the Universe

4. 4

5. 5 Composition of the Universe Heavy elements 0.03 % Massive neutrino0.3 % Luminous stars0.5 % H and He3.5 % Dark Matter23 % Dark Energy73 %

6. 6 WMAP  Results of WMAP Combination with other cosmic experiments gives

7. 7 Evidence for the Dark Matter  First evidence for the dark matter – motion of galaxies within clusters (F.Zwicky, 1933)  The most direct evidence for the existence of large amount of the dark matter are the flat rotation curves of spiral galaxies (the dependence of the linear velocity of stars on the distance to the galactic center)  Spiral galaxies consist of a rather thin disc and a spherical bulb in the galactic center

8. 8 Evidence for the Dark Matter  From the equality of forces one gets  Assuming spherical distribution of mass in the core one gets inner part outer part Solar system rotation curve

9. 9 Evidence for the Dark Matter  Observation tell us that for large radii r which means linear distribution of mass This points to the existence of the huge amount of dark matter surrounding the visible part of the galaxy Contribution of the dark matter halo alone Contribution of the disc (visible stars) alone

10. 10 Evidence for the Dark Matter  Nowadays, thousands of galactic rotation curves are known, and they all suggest the existence of about ten times more mass in the halos than in the stars of the disc Elliptic galaxies and cluster of galaxies also contain a large amount of the dark matter

11. 11 Evidence for the Dark Matter  The Milky Way rotation curve has been measured and confirms the usual picture  Measurements of velocities of Magellanic Clouds tells that the Milky Way has very large and massive halo  VIRGOHI21 object – a galaxy, consisting only of dark matter

12. 12 Matter content of the Universe  The matter content of the Universe is determined by the mass density parameter  M. the possible contributions are The luminous baryonic matter (stars in galaxies) The dark baryonic matter (MAssive Compact Halo Objects - MACHOs ? ) The hot dark matter (massive neutrinos ? ) The cold dark matter (Weakly Interacting Massive Particles - WIMPs - neutralinos ? )

13. 13 Matter content of the Universe  All the luminous matter in the Universe from galaxies, clusters of galaxies, etc. is and is very far from the critical density  Deuterium from the primordial nucleosynthesis provides a good test for the matter density (Large density - Fast interactions - Lower abundance) Observation of primordial deuterium abundance gives  Thus, besides luminous matter there exist invisible baryonic matter, with a mass more than ten times larger.

14. 14 Dark Matter candidates  Baryonic Dark Matter (MACHOs – MAssive Compact Halo Objects)  Normal stars No, since they would be luminous  Hot gas No, since it would shine  Burnt-out stellar remnants seems implausible, since they would arise from a population of normal stars of which there is no trace in the halo  Neutron stars No, since they would arise from supernova explosions and thus eject heavy elements into the galaxy

15. 15 Dark Matter candidates  Baryonic Dark Matter (MACHOs – MAssive Compact Halo Objects)  White dwarfs (stars with a mass which is not enough to reach the supernova phase): possible, since white dwarfs are known to exist and to be plentiful. Maybe they could be plentiful enough to explain the Dark Matter if young galaxies that produced white dwarfs cool more rapidly than present theory predicts. But the production of large numbers of white dwarfs implies the production of a large amount of helium, which is not observed

16. 16 Dark Matter candidates  Baryonic Dark Matter (MACHOs – MAssive Compact Halo Objects)  Brown dwarfs (stars ten times lighter than the Sun) possible Astronomers have found some objects that are either brown dwarf stars or very large planets. However, there is no evidence that brown dwarfs are anywhere near as abundant as they would have to be to account for the Dark Matter in our galaxy

17. 17 Dark Matter candidates  Non-baryonic “hot” dark matter  Massive neutrinos Today we have a convincing evidence of neutrino oscillations. This means that neutrinos have a mass. The measurable quantity – mass- squared difference. If neutrino mass is as large as, their contribution to the total density of the Universe is comparable to the contribution of the luminous baryonic matter!

18. 18 Dark Matter candidates  Non-baryonic “cold” dark matter The most reasonable explanation – weakly interacting massive particles (WIMP’s) WIMP’s could have been produced in the Big Bang origin of the Universe in the right amounts and with the right properties to explain the Dark Matter BUT: we do not know WHAT the WIMP IS

19. 19 Direct searches for the Dark Matter  Optical observations from the Earth (EROS, MACHO, … )  Underground searches (DAMA, EDELWEISS, CDMS, … )  Underwater searches (ANTARES, … )  Searches in space (AMS, … )

20. 20 Direct searches for the Dark Matter  EROS experiment (Expérience pour la Recherche d'Objets Sombres)  Location - La Silla mountain, Atacama desert, Chile  Main goal - search and the study of dark stellar bodies, so-called "brown dwarfs" or "MACHOs“  Signature - occasional amplification of the light by the gravitational lens effect

21. 21 Direct searches for the Dark Matter  MACHO experiment (MAssive Compact Halo Object)  Location - Mount Stromlo Observatory, Canberra, Australia  Main goal - search for objects like brown dwarfs or planets (Massive Compact Halo Objects - MACHOs)  Signature - occasional amplification of the light by the gravitational lens effect

22. 22 Direct searches for the Dark Matter  The effect is large and easily detectable: the amplification could be as large as 0.75m  The phenomenon has a very symmetric light curve, characterized by only 3 parameters (brightness in the maximum, time and duration of the light amplification)  The amplification is the same for all wavelenghts  For the particular star the effect can take place only once

23. 23 Direct searches for the Dark Matter  Different collaborations have seen the signal (1993-1996) OGLE 18 candidates in the direction to the galactic centre MACHO 120 DUO 10 Gravitional lens effect has been detected also in the direction to the Large Magellanic Cloud MACHO 8 EROS 2 The most probable mass of the lens However, MACHOs can only account for less than ~ 50 % of the halo

24. 24 Direct searches for the Dark Matter  DAMA experiment (DArk MAtter)  Location - Gran Sasso National Laboratory of I.N.F.N.  Main goal - search for dark matter particles: WIMPs  Main process – WIMP elastic scattering on the target nuclei  Measured quantity - nuclear recoil energy in the keV range

25. 25 Direct searches for the Dark Matter  Positive evidence for a WIMP signal could arise from the kinematics of the Earth withing non-rotating WIMP halo. The sun is orbiting about the galactic centre with a velocity of ~ 220 km/s. The Earth is orbiting about the Sun with a velocity of ~ 30 km/s.  The resulting relative Earth-halo velocity is modulated, thus the WIMP flux is also modulated which should lead to the modulation of the count rate.

26. 26 Direct searches for the Dark Matter  DAMA group claim they do observe the modulation of their count rate (results of 4 years running - 57986 kg  d)

27. 27 Direct searches for the Dark Matter  This result is compatible with a signal from WIMPs with a mass and a WIMP-nucleon cross section of

28. 28 Direct searches for the Dark Matter  Severe criticism has arisen in the community, ascribing the observed annual modulation rater to systematics than to a WIMP signature. DAMA insists on their model-independent analysis:  presence of annual modulation with the proper features;  neither systematics nor side reactions able to mimic the signature

29. 29 Direct searches for the Dark Matter  EDELWEISS experiment  Location - Laboratoire Souterrain de Modane (LSM), France (1700 m underground)  Main goal - search for dark matter particles: WIMPs  Main process – WIMP elastic scattering on the target nuclei (EDELWEISS uses Ge detector)  Measured quantity - nuclear recoil energy in the keV range

30. 30 Direct searches for the Dark Matter  1 st data taking: Fall 2000 2 nd data taking: 1 st semester 2002 3 rd data taking :October 2002 - March 2003  EDELWEISS new limits  DAMA best fit exclusion at > 99.8 % C.L confirmed with 3 new detectors and extended exposure  Exclusion limits are astrophysical model independent

31. 31 Direct searches for the Dark Matter  EDELWEISS II  New run started : improved energy threshold  Expect further factor > 2 in exposure with improved sensitivity  September 2003 : EDELWEISS I stops and EDELWEISS II installation begins with 21×320g Ge  Sensitivity will be improved by a factor of 100

32. 32 Searches for the Dark Matter  AMS-02 experiment (AntiMatter in Space)  Location - International Space Station (Hopes it’ll be launched in 2007, scheduled to be launched 15 Oct 2005, planned 4 Sep 2003)  Main Goal - search for dark matter, missing matter & antimatter in space

33. Indirect searches for the Dark Matter

34. 34 EGRET Excess  EGRET Data on diffuse Gamma Rays show excess in all sky directions with the same energy spectrum from monoenergetic quarks  9 yrs of data taken (1991-2000)  Main purpose: sky map of point sources above diffuse background.

35. 35 EGRET Excess A: Inner Galaxy (l=±30 0, |b|<5 0 ) B: Galactic plane avoiding A (30-330 0 ) C: Outer Galaxy (90-270 0 ) D: Low latitude (10-20 0 ) E: Intermediate lat. (20-60 0 ) F: Galactic poles (60-90 0 ) Excess has the same shape implying the same source everywhere in the galaxy

36. 36 EGRET Excess A: Inner Galaxy (l=±30 0, |b|<5 0 ) B: Galactic plane avoiding A (30-330 0 ) C: Outer Galaxy (90-270 0 ) D: Low latitude (10-20 0 ) E: Intermediate lat. (20-60 0 ) F: Galactic poles (60-90 0 ) Excess has the same shape implying the same source everywhere in the galaxy EGRET gamma excess above extrapolated background from data below 0.5 GeV

37. 37 EGRET Excess A: Inner Galaxy (l=±30 0, |b|<5 0 ) B: Galactic plane avoiding A C: Outer Galaxy D: Low latitude (10-20 0 ) E: Intermediate lat. (20-60 0 ) F: Galactic poles (60-90 0 )

38. 38 EGRET Excess vs WIMP annihilation  The excess of diffuse gamma rays is compatible with WIMP mass of 50 -100 GeV  Region A: inner Galaxy (l=±30 0, |b|<5 0 ) Background WIMP contribution

39. 39 EGRET Excess vs WIMP annihilation A: inner Galaxy (l=±30 0, |b|<5 0 ) B: Galactic plane avoiding A C: Outer Galaxy D: low latitude (10-20 0 ) E: intermediate lat. (20-60 0 ) F: Galactic poles (60-90 0 )

40. 40 EGRET Excess vs WIMP annihilation  3 components (galactic background + extragalactic background + DM annihilation) fitted simultaneously with same WIMP mass and DM normalization in all directions.  Blue: uncertainty from WIMP mass WIMP mass 50 - 100 GeV 65 100 WIMPS 00

41. 41 Determination of halo profile  The differential gamma flux in a direction forming an angle ψ with the direction of the galactic center is given by: WIMP annihilation cross section branching ratio into the tree-level annihilation final state f differential photon yield for the final state f Dark matter mass density BoostfactorWIMP mass

42. 42 Determination of halo profile  A survey of the optical rotation curves of 400 galaxies shows that the halo distributions of most of them can be fitted either with the Navarro-Frank-White (NFW) or the pseudo-isothermal profile. The halo profiles can be parametrized as follows: a is a scale radius, define behaviour at r ≈ a, r >> a and r << a

43. 43 Determination of halo profile  Navarro-Frank-White profile (1,3,1)very cuspy  Moore profile (1.5,0,1.5)very cuspy  Isotermal profile (2,2,0) less cuspy β=2 implies flat rotation curve

44. 44 Determination of halo profile  The spherical profile can be flattened in two directions to form a triaxial halo. N-body simulations suggest the ratio of the short (intermediate) axis to the major axis is typically above 0.5-0.7  It is not clear if the dark matter is homogeneously distributed or has a clumpy character. Clumps can enhance the annihilation rate. This enhancement (boostfactor) can be determined from a fit to the data.

46. 46 Determination of halo profile  The possible enhancement of DM density in the disc was parametrized by a set of Gaussian rings in the galactic plane in addition to the expected triaxial profile for the DM halo. At least two rings should be envisaged: one “outer” ring and one “inner” ring. Parameters of the rings can be determined from a fit to the data. =2  1/r 2 2 Gaussian ovals

47. 47 Determination of halo profile  Spiral structure  Caustic rings

48. 48 Determination of halo profile  Parameters in halo profile fitted by requiring minimal difference between boostfactors of various regions.  If clustering is similar in all directions (same boostfactors everywhere), then the excess of diffuse gamma rays is ~ 2 along the line of sight.  is determined by the halo profile, which is normalized to the local dark matter density ρ 0.  ρ 0 can be estimated from the rotation curve to be 0.3 GeV/cm 3 for a spherical profile and R 0 = 8.5 kpc. For a non-spherical one the density has to be rescaled.

49. 49 Determination of halo profile  Energy spectrum of diffuse gamma rays is well described by background + WIMP annihilation  Longitude and lattitude distributions (different sky directions!) of gammas are used for determination of halo and substructure (rings) parameters

50. 50 Gammas below 0.5 GeV (EGRET) Longitude: azimuthal angle Latitude: angle out of the plane

51. 51 Gammas above 0.5 GeV (EGRET) Longitude: azimuthal angle Latitude: angle out of the plane

52. 52 Fits for 1/r 2 profile with/without rings WITHOUT rings DISC 5 0 <b<10 0 10 0 <b<20 0 20 0 <b<90 0 WITH 2 rings DISC 5 0 <b<10 0 20 0 <b<90 0 10 0 <b<20 0

53. 53 Fit results for halo profile Fit results of halo parameters Enhancement of rings over 1/r 2 profile 2 and 7, respectively. Mass in rings 1.6% and 0.3% of total Dark Matter

54. 54 Determination of halo profile H2H2 H R[kpc] 4  14 kpc coincides with ring of stars at 14-18 kpc due to infall of dwarf galaxy (Yanny, Ibata, ….., 2003)  4 kpc coincides with ring of neutral hydrogen molecules!

55. 55 The Milky Way rotation curve  Contributions to the rotation curve of the Milky Way from  Visible bulge  Visible disk  Dark halo  Inner dark ring  Outer dark ring Outer Ring Inner Ring bulge totalDM 1/r 2 halo disk Rotation Curve

56. 56 Halo density at 300 kpc Cored isothermal halo profile. Total mass: 3×10 12 solar masses SideviewTopview

57. 57 Halo density at 30 kpc Ring halo substructure. R ~ 4 and 14 kpc. SideviewTopview

59. 59 Possible origin of rings  In 1994 Cambridge astronomers discovered a highly distorted dwarf galaxy in the Sagittarius constellation. The galaxy falls towards the Milky Way spreading out stars along its pass.  In 2003 Canis Major dwarf galaxy was discovered  In 2003 a giant stellar structure surrounding the Galaxy was discovered (possibly the remnant of a galaxy “eaten” by Milky Way very long ago)

61. 61 Positrons and antiprotons in cosmic rays  SAME halo and WIMP parameters as for gamma rays

62. WEAKLY INTERACTIVE MASSIVE PARTICLES WHERE ARE THEY ? WHAT ARE THEY ?

63. 63 Supersymmetry FERMIONS (s=1/2)BOSONS (s=0,1) Quarks Electron, Muon, Tau Neutrinos Photon Z-boson W-boson Higgs

64. 64 Supersymmetry FERMIONS (s=1/2)BOSONS (s=0,1) QuarksSquarks Electron, Muon, TauSleptons Neutrinos Sneutrinos PhotinoPhoton ZinoZ-boson WinoCharginosW-boson Neutralnos Higgsino 1Higgs 1 Higgsino 2Higgs 2

65. 65 Neutralino – SUSY dark matter  Still we know nothing about WIMP  Supersymmetry helps again

66. 66 Neutralino – SUSY dark matter  Lagrangian of the Minimal Supersymmetric Standard Model:  Yukawa interactions

67. 67  Supersymmetry is a broken symmetry.  Breaking takes place in a hidden sector. Messengers to the visible sector can be gravitino, gauge bosons, gauginos, …  Breaking must be soft (dimension of soft SUSY breaking operators  3)  In total one has about a hundred parameters Neutralino – SUSY dark matter

68. 68 Neutralino – SUSY dark matter  Main uncertainties come from soft supersymmetry breaking parameters.  Universality hypothesis: soft supersymmetry breaking parameters unify at the scale of Grand Unification  As a result one has only 5 free parameters (4 + one sign)  Common scalar mass m 0  Common gaugino mass m 1/2  Common soft SUSY breaking parameter A 0  tan  = v 2 / v 1

69. 69 Neutralino – SUSY dark matter  Neutralino – a mixture of superpartners of photon, Z-boson and neutral Higgs bosons  Neutral (no electric chaege, no colour)  Weakly interacting (due to supersymmetry)  The lightest supersymmetric particle  Stable (!) if R-parity is conserved  Perfect candidate for dark matter particle (WIMP) photino zino higgsino higgsino

70. 70 Neutralino – SUSY dark matter  Limits on neutralino mass  Heavy enough to account for cold non- baryonic dark matter in the Universe  Annihilation cross sections are known (at least we know how to calculate them)

71. 71 Neutralino – SUSY dark matter  Main diagrams for neutralino annihilation  Dominant diagram for WMAP cross section:

72. 72 Neutralino – SUSY dark matter  B-fragmentation well studied at LEP! Yield and spectra of positrons, gammas and antiprotons well known!  Galaxy = SUPER-B-factory with luminosity some 40 orders of magnitude above man-made B-factories

73. 73 Neutralino – SUSY dark matter  Annihilation cross sections in m 0 -m 1/2 plane (μ > 0, A 0 =0) tanβ=5 tanβ=50  For WMAP cross section of  2×10 -26 cm 3 /s one needs large tanβ bb t

74. 74 Favoured regions of parameter space  Pre-WMAP allowed regions in the parameter space. Fit to all constraints tanβ=50 Fit to Dark matter constraint

75. 75 Favoured regions of parameter space  WMAP data leave only very small allowed region as shown by the thin blue line which give acceptable neutralino relic density  Excluded by LSP  Excluded by Higgs searches at LEP2  Excluded by REWSB

76. 76 Favoured regions of parameter space  The region compatible with all electroweak constraints as well as with WMAP and EGRET constraints are rather small  It corresponds to the best fit values of parameters tanβ = 51 m 0 = 1400 GeV m 1/2 = 180 GeV A 0 = 0.5 m 0

77. 77 Favoured regions of parameter space  Superparticle spectrum for m 0 =1400 GeV, m 1/2 =180 GeV  Squarks/sleptons are in TeV range  Charginos and neutralinos are light  LSP is largely Bino  Dark Matter may be supersymmetric partner of Cosmic Microwave Background

78. 78 Comparison with direct DM searches Spin-independentSpin-dependent Prediction from EGRET data assuming supersymmetry DAMA CDMS ZEPLIN Edelweiss Projections

79. 79 Summary: input  Astronomy  Dark matter in clusters of galaxies and galaxies itself  Rotation curve of the Milky Way  Astrophysics  Gamma ray flux from the sky (EGRET)  Positrons and antiprotons in cosmic rays  Cosmology  Amount of the dark matter (~23%)  Particle physics  Annihilation cross sections  Spectrum of gamma quanta from quarks/antiquarks

80. 80 Summary: physics questions & answers  Astrophysicists: What is the origin of “GeV excess” of diffuse galactic gamma rays? What is the origin of “7 GeV excess” of positrons in cosmic rays? What is the origin of “GeV excess” of antiprotons in cosmic rays? Answer: Dark matter annihilation

81. 81 Summary: physics questions & answers  Astronomers: Why a change of slope in the Milky Way rotation curve at R 0 =8.3 kpc? Answer: Dark matter substructure Why ring of stars at 14 kpc so stable? Why ring of molecular hydrogen at 4 kpc so stable?

82. 82 Summary: physics questions & answers  Cosmologists: How is Cold Dark Matter distributed? Answer: 1/r 2 profile + substructure (two rings)  Particle physicists: Is DM annihilating as expected in Supersymmetry? Answer: Cross sections are perfectly consistent with SUSY

83. THE END