WIMP direct detection: Intro WIMP direct detection: halo modelling and small scale structure Anne Green Astro-Particle Theory and Cosmology Group University of Sheffield Halo properties Halo modelling Effect on signals Small scale structure Intro AMG PRD66 083003 (2002), astro-ph/0207366 AMG PRD68 023004 (2003), astro-ph/0304446 AMG, Stefan Hofmann & Dominik Schwarz to appear in MNRAS, astro-ph/0309621 and JCAP in preparation

WIMP direct detection WIMP direct detection c + N c + N via elastic scattering in lab: c + N c + N Detect energy deposited via ionisation, scintillation and/or heat. f(v): WIMP speed dist in detector rest frame s: WIMP elastic scattering cross-section r: local WIMP density vmin: minimum WIMP velocity that can produce a scattering of energy E

WIMP signals WIMP signals Earth’s motion -> annual modulation and direction dependence Spergel Drukier, Freese & Spergel; Freese, Frieman & Gould (see Ben Morgan’s talk) Time and angular dependence of WIMP flux mc = 100 GeV, r = 0.3 GeV/cm3

Current experimental status Theory v. expt briefly Current experimental status Constraints on the spin independent elastic scattering cross-section, assuming the “standard” halo model (Maxwellian velocity distribution).

Halo properties Halo properties Standard Halo Model: spherical and isotropic, r ~ 1/r2 Observations: Of other galaxies: b/a > 0.8 0.2 < c/a < 1.0 (e.g. Sackett & Merrifield reviews) Milky Way: c/a ~ 0.7-0.9 (Olling & Merrifield) Probed by Sgr stream (see Amina Helmi’s talk) Simulations: Triaxiality and anisotropy vary significantly between halos and also as a function of radius (closer to spherical and isotropic in the inner regions). (e.g. Moore et al. and many others) Simulations with gas cooling produce more spherical halos. (Kazantzidis et al.) Preference for radial orbits. (e.g. Moore et al.)

Halo modelling Halo modelling Logarithmic Ellipsoidal model (e.g. Binney and Tremaine `Galactic Dynamics’) Steady-state phase space distribution of a collection of collisionless particles is given by the solution of the collisionless Boltzmann equation. For spherical and istropic systems there is a unique relationship: r(r) -> f(v) Triaxial and anisotropic systems are far more complicated; assumptions have to be made about the form of the anisotropy or velocity distribution. Logarithmic Ellipsoidal model (Evans, Carollo & de Zeeuw) Simplest, triaxial generalisation of the isothermal sphere, f(v) is a multi-variate gaussian in conical co-ordinates. Triaxiality and anisotropy independent of radius. Osipkov-Merritt (Osipkov; Merritt) Spherically symmetric models, anisiotropy increases with radius.

Effect on signals Effect on signals Exclusion limits (Donato et al.; Kamionkowski & Kinkhabwala; Green) f(v) for OM and LGE models Differential event rate for OM model (for a Ge detector): mc = 50 GeV = 10-5 pb r = 0.3 GeV/cm3

Exclusion limits for: IGEX, OM halo model; IGEX, LGE halo model; HM OM halo model Exclusion limits change by of order tens of per-cent and change shape. Change depends on experiment and halo model used.

Effect of uncertainty in the local circular velocity: f(v) for vc= 200 km/s (dotted) 220 km/s (solid) 240 km/s (dashed) Differential event rates for a Ge detector. mc = 50 GeV = 10-5 pb r = 0.3 GeV/cm3 CDMS exclusion limit

Annual modulation: f(v) in Winter and Summer T(vmin) in Winter and Summer Amplitude of T(vmin) (Summer max +ve)

Amplitude and phase of signal can change significantly. (Brhlik & Roszkowski; Vergados; Belli et al.; Ullio & Kamionkowski; Green; Gelmini & Gondolo; Copi & Krauss; Fornengo & Scopel; Ling, Sikivie & Wick) Amplitude and phase of signal can change significantly. Vc=200 km/s Vc=220 km/s Vc=240 km/s Phase v. amplitude (vmin=100, 300, 500 km/s) for the LGE model for parameters which produce stable halos (dots), and for parameters which produce halos (roughly) consistent with observations and simulations (crosses). If only the component of the Earth’s velocity parallel to the Galactic plane is used, the phase shift is missed.

Comparing Experiments Is non-trivial…….. Na I Ge

Small scale structure Small scale structure Simulation of MW size (r ~ 200 kpc) halo. (Ben Moore) Is the DM distribution smooth on sub-milli pc scales? Equivalently, has the phase space distribution function reached a steady state?

At solar radius in simulations: smooth background + high velocity particles from late accreted sub-halos. (90% of the mass was already in place 10 Gyr ago.) (Helmi, White and Springel) [Debris from the Sagittarius dwarf galaxy passes close to the solar neighbourhood. (Freese, Gondolo, Newberg and Lewis, but see Amina Helmi’s talk)] BUT resolution of simulations ~ 100 pc (>> mpc) DM distribution on small scales depends on the structure (and hence fate) of the first generation of DM halos to form. (Moore et al.) Velocity distribution at a single point in a simulated halo consists of a number of peaks? (Stiff and Widrow) Need to know the CDM power spectrum on small scales = primordial power spectrum + microphysics of CDM particles (talks by Stefan Hofmann and Vyacheslav Dokuchaev)

summary Summary Sub-structure on sub-pc scales? The Milky Way halo is unlikely to be perfectly spherical and isotropic. Halo modelling is a tricky business. Different models with the same macroscopic properties can have very different velocity distributions. For halo models with parameters chosen to reproduce the range of properties of simulated and observed halos: Exclusion limits vary by of order tens of per-cent (change in shape is experiment and halo model dependent). The amplitude and phase of the annual modulation signal change significantly. The WIMP distribution is unlikely to be completely smooth: Streams of high velocity particles from late accreted sub-halos. Sub-structure on sub-pc scales?