1. DARK MATTER ON DEPARTMENT SCALE Daniele Fantin (M. Merrifield, A. Green) (M. Merrifield, A. Green) University of Nottingham Bologna, 2 April 2009

2. Summary Dark Matter Candidates Dark Matter Detection State of art of N-body simulations Alternative approaches (My research) Daniele Fantin, University of Nottingham

3. Dark Matter Evidence Daniele Fantin, University of Nottingham Universe Energy Budget

4. Potential dark matter candidate Optically dark: does not couple strongly with photons Electrically neutral Non-relativistic Collisionless: in order to form extended halos Stable: doesn’t decay on timescale shorter than age of the Universe Daniele Fantin, University of Nottingham

5. Cold Dark Matter – Candidates Non-baryonic matter WIMPs WIMPs (Weakly Interactive Massive Particles) (Lee & Weinberg, 77; Gunn et al, 78) Neutralino (lightest supersymmetric particle ) Axions Axions (Peccei & Quinn, 77; Weinberg, 78) Daniele Fantin, University of Nottingham

6. Why WIMPs? Any stable WIMP in thermal equilibrium in the early Universe will have the right density at the present day to be the DM Daniele Fantin, University of Nottingham χ + χ ↔ U + Ū 132 1.High T: Efficient Creation/destruction 2.Destruction 3.Creation in overdense regions

7. Lightest Super-symmetric particle Stable (conservation of R-parity) Not completely collisionless Small cross section M = 10 GeV ÷ few TeV (Bertone, 2004) Why neutralinos? Daniele Fantin, University of Nottingham

8. Particle Colliders (LHC) How can we detect WIMPs?. Generic signal: missing energy/momentum Won’t demonstrate the existence of DM Daniele Fantin, University of Nottingham

9. Via products of annihilations (e.g. γ-rays, positrons, anti- protons,neutrinos) in high density regions. Indirectly Daniele Fantin, University of Nottingham

10. γ-rays: FERMI, HESS, MAGIC, VERITAS Anti-matter: PAMELA,ATIC Neutrinos: IceCube, ANTARES Dependence of signals on local dark matter distribution Daniele Fantin, University of Nottingham

11. Via elastic scattering on detector nuclei in the lab. χ+N Solutions: go underground (mines) Detect recoil energy via ionisation, scintillation and/or heat. Problem: radioactivity Directly Daniele Fantin, University of Nottingham

12. ZEPLIN III CDMSII DAMA Daniele Fantin, University of Nottingham

13. The event rates in direct detection experiments depend on the DM density (and in some cases velocity) distribution. Why is the DM Distribution important? WIMP cross-section on proton dR/dE ≈ σ p ρ χ ∫ f(v)/v dv v min ∞ Differential event rate (per kg/day/KeV): minimum WIMP speed which can cause a recoil of energy E. WIMP speed distribution in rest frame of detector local WIMP density Daniele Fantin, University of Nottingham

14. To confirm the existence of DM we need to detect it. WIMPs are a good dark matter candidate They can be detected: directly via elastic scattering in the lab signals depend on ultra-local dark matter density and speed distribution indirectly via annihilation products signals depend on Milky Way density distribution in high density regions Intro-Summary Daniele Fantin, University of Nottingham

15. Event rate depends on dark matter distribution The standard halo model: assumes Milky Way halo as isotropic, isothermal sphere velocity distribution is then Maxwellian BUT “observed” and simulated halos are triaxial, anisotropic and contain substructure. Halo Modelling Daniele Fantin, University of Nottingham

16. Actual predictions about f(v) based on very simple assumptions: Maxwellian (Freese et al. 1988) Multivariate Gaussian (Evans et al. 2000, Helmi et al. 2002) Probably NOT valid in reality!! Dark Matter Distribution Daniele Fantin, University of Nottingham

17. How good is the assumption of a Maxwellian speed distribution? Depends on the ultra-local (sub-mpc) WIMP distribution. Which depends on how well-mixed the tidal debris from disrupted sub-halos is. i) Ultra-local WIMP distribution is smooth, consisting of large number of streams. [Helmi, White & Springel,02; Vogelsberger et al,08] ii) Ultra-local WIMP distribution consists of a finite number of streams [Stiff & Widrow,01 ; Moore et al., 04; Fantin, Merrifield & Green,08] Daniele Fantin, University of Nottingham

18. Choose input cosmological parameters Calculate linear power spectrum Carry out large volume parent N-body simulation Select Milky Way like halos Re-simulate using lower mass particles in region that forms halo of interest Carry out convergence tests Simulating Milky Way-like Halos Daniele Fantin, University of Nottingham

19. Collisionless N-body simulation High resolution DM only Very simple physics: Gravity Bad approx. in center of big galaxies, where baryons dominates Good for dwarfs and sub-units Dark Matter Simulations Daniele Fantin, University of Nottingham

20. Mass profiles are nearly universal Density profiles are cuspy no convergence in the centre Clumpy Triaxial DM Halos: Main Results Daniele Fantin, University of Nottingham

21. First cosmological simulation able to resolve the building bricks of massive MW-like DM halo (10¹²M ⊙ ) at z=0 Presence in the Phase S of underdense elongated streams formed by material removed from accreted subhalos Substructures: Via Lactea - GHALO Diemand et al, 08 800 kpc 40 kpc Daniele Fantin, University of Nottingham

22. Observed in: Motion of nearby halo stars Outer regions of Galactic Halo (Helmi,1999) Traces in solar neighborhood: Series of peaks in velocity DF Otherwise smooth Gaussian distribution Stream Observation Daniele Fantin, University of Nottingham

23. Substructures mass function Halo density/mass profile Subhalos density profile Number fraction of subhalos Total mass fraction in subhalos Detectablility of subhalos Important Aspects Daniele Fantin, University of Nottingham

24. 4 generations of substructures Smooth emission from the main halo Smooth emission from the subhalos Substructures: AQUARIUS Springel et al, 08 Daniele Fantin, University of Nottingham

25. Recent simulations of Milky Way-like halos Daniele Fantin, University of Nottingham

26. Substructures Distribution Abundance Mass Profile Annihilation signal Phase-space distribution of DM DM Halos: Open Questions Daniele Fantin, University of Nottingham

27. Slope of the central cusp Substructures Distribution/Abundance Mass Profile Annihilation signal Phase-space distribution of DM DM Halos: Open Questions Daniele Fantin, University of Nottingham

28. Via Lactea, Aquarius resolutions are 8 orders of magnitude off 8 orders of magnitude off the minimum required to perform such scales that observations are looking for!!! Daniele Fantin, University of Nottingham

29.  The smallest halos resolved in sim are close to 10⁵ M ⊙, while the mass of the smallest WIMP microhalos 10⁻⁶ M ⊙ (Green et al., 2004)  Resolution in simulations ~ 100 pc, while the expected scales probed by direct detection experiments are 0.1-1 mpc NEW APPROACHES REQUIRED!!! Sim-Summary/Conclusions Daniele Fantin, University of Nottingham

30. No consensus on whether local DM distribution is smooth: Stiff & Widrow, 01: reverse simulations, finite number of streams in solar neighbourhood Helmi, White et al (02,07): 10⁵ streams in solar neighbourhood (from time dependence of density of a single stream) Daniele Fantin, University of Nottingham

31. Method based on reverse integration process AIM: look at DM ultra-fine structure DM distribution in the solar neighbourhood characterized by discrete peaks Stiff & Widrow Approach Daniele Fantin, University of Nottingham

32. Work backwards in time Resolve DM ultra-fine structure in the PS Realistic Ф describing MW Stiff & Widrow Approach Daniele Fantin, University of Nottingham

33. Softening length: Approximation not good (20 Kpc >> 8.5 Kpc) Cusp problem: the potential is “smooth”, so it covers the effect due to the cusp present in the centre of the galaxy Stiff & Widrow: weeknesses Daniele Fantin, University of Nottingham

34. Method based on reverse integration process Collision head-on between unbound system of particles and a galaxy No numerical integration First model of the ultra-fine structure of the DM halo in the solar neighbourhood My Research Daniele Fantin, University of Nottingham

35. Realistic gravity Results in a single timestep Orbits history can be calculated analytically No numerical integration: quick Exploration of parameter space with very high resolution Positive Aspects Daniele Fantin, University of Nottingham

36. No detailed quantitative/realistic comparison with Milky Way Isochrone potential Negative Aspects Negative Aspects Daniele Fantin, University of Nottingham

37. Dynamics for isochrone trivial Hamiltonian does NOT change too quickly in time → analytic analysis of system’s evolution N-dim action space faithful representation of 2N-dim phase-space Action Angle Variables Daniele Fantin, University of Nottingham

38. i. Set the IC for the satellite and the time in the past t 0 at which it was at that location ii. Set the present-day PS coordinates of the detector location iii. Evolve analytically these coords. backwards in time iv. Assume for the merging halo a Gaussian distribution v. Evaluate the initial PS density due to the satellite for this PS location vi. Repeat for a grid of v to map out the full velocity distribution within the detector Main Steps Daniele Fantin, University of Nottingham

39. Set initial conditions Hamiltonian (H) in Cartesian Coord Transformation in Action Angle variables Integration of H backwards in time Revert to Cartesian configuration Computation of velocity DF Main Steps Daniele Fantin, University of Nottingham

40. Evolution at t = 1.23 Gyr Look at the difference in resolution!!! Results Daniele Fantin, University of Nottingham fxfx vxvx fxfx vxvx

41. fxfx vxvx t =13.6 Gyr (MW’s age): Single Merger: Distribution Function  Halo perturbed  Whole series of peaks Daniele Fantin, University of Nottingham

42. Distribution Function Evolution Daniele Fantin, University of Nottingham Fantin et al, 08

43. cosθ v Diagnostic for Directional Detectors Cos θ = vy/v Smooth background + Evident features Daniele Fantin, University of Nottingham Fantin et al, 08

44.  Many mergers at each timestep  Add to each merger a signal  Analysis of the final signal Multiple Merger cosθ v Daniele Fantin, University of Nottingham

45. Merger Tree Merger tree of a MW-like halo Add f(v) at different z Look for the final velocity/angle distribution Daniele Fantin, University of Nottingham

46. Multiple Merger: Angle Distribution Daniele Fantin, University of Nottingham M(M ⊙ ) Time(Gyr) 10⁶ 10⁸ 10¹⁰ 13.61.367.35136

47. Merger Tree Daniele Fantin, University of Nottingham 1 3 2 1.Relations between velocity components 2.Presence of shell structure 3.Presence of escape velocity Fantin et al, in prep.

48. Event rate in direct detection of DM depends on the Ultra-local spatial(velocity) distribution In this case N-body simulation cannot help us New approaches are necessary to investigate Presence of “features” in the velocity distribution coming from merging events Work is still ongoing Final Summary Daniele Fantin, University of Nottingham

49. Any Question? Daniele Fantin, University of Nottingham