1. 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 PRD (2002), astro-ph/
AMG PRD (2003), astro-ph/
AMG, Stefan Hofmann & Dominik Schwarz
to appear in MNRAS, astro-ph/ and JCAP in preparation

2. 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

3. 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

4. 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).

5. Halo properties Halo properties
Standard Halo Model: spherical and isotropic, r ~ 1/r2
Observations:
Of other galaxies:
b/a > < c/a < 1.0
(e.g. Sackett & Merrifield reviews)
Milky Way:
c/a ~ (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.)

6. 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.

7. 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
= pb
r = 0.3 GeV/cm3

8. 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.

9. 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
= pb
r = 0.3 GeV/cm3
CDMS exclusion limit

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

11. 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.

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

13. 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?

14. 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)

15. 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?