• (very brief) Review of evidence for dark matter

• Dark matter candidates

• WIMPs (motivation and detection)

WIMP hunting: searching for dark matterAnne Green

University of Nottingham

Observational evidence for dark matter

Lots of evidence for (non-baryonic cold) dark matter from diverse astronomical and cosmological observations

[galaxy rotation curves, galaxy clusters (galaxy velocities, X-ray gas, lensing), galaxy red-shift surveys, Cosmic Microwave Background]

assuming Newtonian gravity/GR is correct.

Could the observations be explained by modified gravity instead?

MOdified Newtonian DynamicsAn empirical modification to Newton’s 2nd law at low accelerations proposed by Milgrom, designed to explain galaxy rotation curves without invoking dark matter.

Tensor Vector Scalar gravityRelativistic theory proposed by Bekenstein in 2004. Reduces to general relativity and MOND in relevant limits.Could, c.2006, (broadly) reproduce CMB anisotropies and galaxy clustering (with cosmological constant and massive neutrinos). [Skordis et al.]

Could the observations be explained by modified gravity instead?

MOdified Newtonian DynamicsAn empirical modification to Newton’s 2nd law at low accelerations proposed by Milgrom designed to explain galaxy rotation curves without invoking dark matter.

Tensor Vector Scalar gravityRelativistic theory proposed by Bekenstein in 2004. Reduces to general relativity and MOND in relevant limits.Could, c. 2006, (broadly) reproduce CMB anisotropies and galaxy clustering (with cosmological constant and massive neutrinos). [Skordis et al.]

The bullet cluster

Separation of gravitational potential (reconstructed from lensing obs) and dominant baryonic mass component (hot gas, X-ray emission detected by Chandra).

A big challenge for modified gravity theories.

[Clowe et al.]

Dark matter candidates

Weakly Interacting Massive ParticlesMore later

Axions consequence of Pecci-Quinn symmetry proposed to solve strong CP problem (“why is the electric dipole moment of the neutron so small?”).

very light and very weakly interacting (never in thermal equilibrium in the early Universe, microphysics very different from WIMPs).

constraints on mass from cosmology, lab searches and from cooling of stars and supernovae.

Raffelt

NeutrinosThey exist, and have mass (neutrino oscillations) but can’t have high enough phase space density to be galactic dark matter (Pauli exclusion principle) and are relativistic and hence wash out structure on small scales.

Primordial Black HolesMay be formed in the early Universe from large overdensities, but fine tuning required to produce interesting abundance?

‘Exotica’Wimpzillas, solitons (Q-balls, B-balls),

More dark matter candidates

WIMPs

Any Weakly Interacting Massive Particle in thermal equilibrium in the early Universe will have an interesting density today.

χ+χ⇔X+X_

x

ΩWIMP ≡ρWIMP

ρc∼ 0.2

(m/Tf o)/25< σannv > /1pb

Supersymmetry

Every standard model particle has a supersymmetric partner. (Bosons have a fermion spartner and vice versa)

Motivations: Gauge hierarchy problem (MW ~100 GeV << MPl ~ 1019 GeV) Unification of coupling constants String theory

In most models the Lightest Supersymmetric Particle (which is usually the lightest neutralino, a mixture of the susy partners of the photon, the Z and the Higgs) is stable (R parity is conserved) and is a good CDM candidate.

Kazakov

How to detect WIMPs?

Particle Colliders (LHC)

In theory ‘generic’ signal: missing energy/momentum.

In practice not quite that simple.....

In SUSY models characteristic event: decay of gluinos and squarks into energetic quarks and leptons and invisible WIMPs

Collider production and detection of a WIMP-like particle would be very exciting, but wouldn’t demonstrate that the particles produced have lifetime greater than the age of the Universe and are the dark matter.

Current status: waiting......

Indirect detection

Via products of annihilations, gamma-rays, positrons and anti-protons

Particles produced in WIMP annihilations

WIMP spatial (density) distribution

(for charged particles) propagation of annihilation products

+

+

predicted signals

Particle physics

Astrophysics (with some particle input)

Indirect detection

Via products of annihilations, gamma-rays, positrons and anti-protons

Event rates depend on WIMP distribution . Enhancement of rate w.r.t that produced by smooth halo, parameterised by boost factor.

Different species probe different scales/regions (and often on scales far smaller than those directly resolved by numerical simulations). Boost factor species dependent and not accurately known.

Often need to distinguish WIMP annihilation from astrophysical backgrounds.

∝ ρ2

Particles produced in WIMP annihilations

WIMP spatial (density) distribution

(for charged particles) propagation of annihilation products

+

+

predicted signals

Particle physics

Astrophysics (with some particle input)

Current status:

Gamma-rays:

Fermi (aka GLAST): launched June 08, data taking underway

Air Cherenkov Telescopes (HESS, MAGIC, VERITAS): have observed Galactic centre and several dwarf galaxies, (weak) constraints on annihilation cross-section

Current status:

Gamma-rays:

Fermi (aka GLAST): launched June 08, data taking underway

Air Cherenkov Telescopes (HESS, MAGIC, VERITAS): have observed Galactic centre and several dwarf galaxies, (weak) constraints on annihilation cross-section

Anti-particles:

PAMELA: recently published excess in positron fraction between 10 and 100 GeV (confirming and extending earlier observations by HEAT, AMS1) no excess in anti-protons

Interpretation? Could be produced by nearby pulsars. Significant uncertainties in flux of secondary positrons (produced by interactions between cosmic rays and interstellar gas) [Delahaye et al.] IF due to DM annihilation need: i) large enhancement in annihilation rate (clumpy DM within ~kpc, or Sommerfeld enhancement) ii) to not overproduce anti-protons

Other claimed signals:

EGRET excess: [de Boer et al.] After subtracting backgrounds, excess of diffuse gamma-rays remains. Could be produced by annihilation of ~50-100 GeV WIMPs BUT i) requires very strange DM distribution (massive rings of DM in Galactic plane) ii) would probably produce too many anti-protons iii) large uncertainties in backgrounds

WMAP ‘haze’: [Finkbeiner et al.] After subtraction of foregrounds ‘haze’ remains around Galactic centre. Could be produced by synchrotron emission by relativistic electrons and positrons produced by DM annihilation.

INTEGRAL 511 keV line: [Boehm et al.] Large flux of 511 keV photons from Galactic bulge. Could be produced by annihilation of MeV DM particles or ‘exciting’ DM. Latest data show distribution is asymmetric (and similar to the distribution of low mass X-ray binaries).

(IMHO...) nothing convincing observed yet, but stay tuned.

positrons and electronsproduced can’t gave energy greater than a few MeV or else line would be wider than observed.

Direct detection

Via elastic scattering on detector nuclei in the lab.

Detect recoil energy via ionisation, scintillation and/or heat.

χ+N⇒χ+N

Solutions: go underground, use shielding and radiopure detector components.

Experimental issues: event rate and recoil energies very small, backgrounds(electron recoils due to αs and γs and nuclear recoils due to neutrons fromcosmic rays or local radioactivity)

WIMP smoking guns

Earth’s orbit

annual modulationand

direction dependence

Spergel fig. by Ben MorganDrukier, Freese & Spergel

Current experimental status: i) null-results

CDMS Xenon10

Edelweiss Zeplin

WARP CRESST

CoGENT TEXONO

Ge, 150 kg-days,E

R=5/10 keV

ionisation & heat

CaWO4, 20 kg-days,

ER=10 keV

scintillation & heat

Ge, 60 kg-days,E

R=13 keV

ionisation & heat

liquid Xe, 230 kg-days,E

M = 5 keV

scintillation & ionisation

Assuming ‘standard’ halo model(Maxwellian speed distribution

local density 0.3 GeV/cm-3)

2-phase Xe, 140 kg-days,E

R = 4.5 keV

scintillation & ionisation

Ar, 96.5 kg-days,E

R=55 keV

scintillation & ionisation

Ge, 0.337 kg-days,E

M=0.23 keV

ionisation

Ge, 8.4 kg-days,E

M= 0.23 keV

ionisation

WIMP Mass [GeV/c2]

Cro

ss-s

ecti

on

[cm

2]

(no

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ised

to

nu

cleo

n)

080924203200

http://dmtools.brown.edu/ Gaitskell,Mandic,Filippini

100

101

102

103

10-48

10-46

10-44

10-42

10-40

10-38

WIMP Mass [GeV/c2]

Cro

ss-s

ecti

on [

cm2]

(norm

alis

ed t

o n

ucl

eon)

080924152900

http://dmtools.brown.edu/ Gaitskell,Mandic,Filippini

100

101

102

103

10-48

10-46

10-44

10-42

10-40

10-38

ii) DAMA signal

Annual modulation in scintillation pulses in NaI crystals first reported by DAMA in 1998.

New experiment, by same collaboration, DAMA/LIBRA confirms observation of annual modulation at 8.2 sigma, total exposure: 299 000 kg-day.

Is this a WIMP signal?Is it compatible with exclusion limits from other experiments?

Bernabeitime

totalrate

Independent analysis by Savage et al.:

If channeling occurs, interpretation of DAMA signal in terms of light, but otherwise standard, WIMPs is just barely compatible with exclusion limits from

other experiments.

Channeling: recoils along crystal axes cause deposit larger fraction of energy to electrons(and recoil energy otherwise over estimated).

Dependence on the dark matter distribution

Standard halo model: isotropic Maxwellian velocity distribution

BUT “observed” and simulated halos are triaxial, anisotropic and contain substructure.

dRdE

∝ σρZ ∞

vmin

f (v)v

dv

Via Lactea II, Diemand et al.

Halo modelling

Results:

Time averaged event rate: Shape of energy spectrum doesn’t change significantly. -> small change in exclusion limits, small systematic uncertainty in measurement of WIMP mass. Main uncertainty is factor of 2 uncertainty in local WIMP density. -> similar uncertainty in measurements of/constraints on cross-section.

Annual modulation: Phase can change by tens of days, and amplitude by an order of magnitude. -> region of WIMP mass-cross-section parameter space consistent with an observed signal can vary significantly.

Directional signal: Detailed angular signal can change significantly (but would need huge quantity of data to measure this). Rear-front assymmetry robust.

Use analytic models which are solutions of the collisionless Boltzmann equation (i.e. assume the phase space distribution function has reached a steady state).

Issue

Has the local phase space distribution reached a steady state? Galaxy halos form heirarchically and at least some substructure survives.

(very) Small scale structure

WIMP direct detection probes the dark matter distribution on sub-mpc scales (c.f. ~100 pc resolution of Galaxy simulations, ~100 kpc radius of Milky Way).

Indirect detection signals enhanced by clumping.

How clumpy is the small scale dark matter distribution?

This depends on the structure and evolution of the first generation of DM halos to form, which in turn depends on the nature of the dark matter and its interactions

WIMP microphysics

After freeze-out (chemical decoupling) WIMPS carry on interacting kinetically with radiation.

χ+χ⇔ X + X χ+ X ⇒χ+ X

Energy transfer erases v. small scale density perturbations (collisional damping).

x

After kinetic decoupling WIMPs free-stream, erasing perturbations on slightly larger scales.

Perturbations on (comoving) scalessmaller than 1pc are erased.

(work with Stefan Hofmann and Dominik Schwarz)

Power spectrum at z=500 Red-shift at which typical 1-sigma fluctuations go non-linear and form bound structures.

Estimates of properties (using spherical top-hat collapse model): radius ~ 0.02 pc, mass ~ 10-6 Msun,

Present day overdensity (assuming they survive....) ~106

For a 100 GeV WIMP and a scale invariant, WMAP normalised, primordial power spectrum:

∆ =ρ− ρ

ρ P∆(k) =k3

2π2 〈|∆k|2〉

Numerical simulations

‘Earth-mass dark-matter haloes as the first structures in the early Universe’J Diemand, B. Moore & J. Stadel

Re-simulate a small region starting at z=350 (when the fluctuations are still linear) up until z=26 (when the high resolution region begins to merge with surrounding low resolution regions).

Numerical simulations

‘Earth-mass dark-matter haloes as the first structures in the early Universe’J Diemand, B. Moore & J. Stadel

Re-simulate a small region starting at z=350 (when the fluctuations are still linear) up until z=26 (when the high resolution region begins to merge with surrounding low resolution regions).

density profiles of3 sample halos (at z=26) mass function

Open questions and implications

i) What happens to the micro-halos between z=26 and the present day?

Lose mass due to interactions with stars and tidal stripping by gravitational field of parent halo.

Earth mass micro-halos in the solar neighbourhood will typically lose most of their mass on a time scale of order the age of the MW.

BUT

Even if most of mass is lost inner high density ‘cusp’ can remain relatively intact.

For individual micro-halos, mass loss depends on orbit (in particular stellar distribution along orbit) and initial density contrast.

(slightly?) more massive micro-halos can retain most of their mass.

Summary of results of Zhao et al., Green & Goodwin, Goerdt et al. and Angus & Zhao:

If some fraction of micro-halos retain a significant fraction of their mass: will enhance diffuse gamma-ray flux expected due to WIMP annihilation in the Milky Way may be detectable by GLAST as gamma-ray point sources

ii) What happens to the matter which is stripped from the micro-halos [what isthe ultra-local DM (velocity and density) distribution]?

No consensus:

Stiff & Widrow: reverse simulations, finite number of streams in solar neighbourhood

Vogelsberger, White, Helmi, White & Springel: 105 streams in solar neighbourhood (divide local mean density by time evolved density in a single stream)

Fantin, Merrifield & Green: preliminary results (from evolution of single sub-halo in isochrone potential) at least some features remain in phase space distribution

Measuring the WIMP properties (using direct detection data, if a signal is detected)

For the standard halo model (Maxwellian/Gaussian speed distribution) the energyspectrum is close to exponential:

∝ m2χ

- - - - neglecting Earth’s motion

_____ with Earth’s motion, for Eth=10 keV

_ _ _ asymptotic limits

characteristic energy scalefor Ge target

dR

dE(E) ≈

(dR

dE

)

0

F 2(E) exp(− E

ER

)ER =

2µ2Aχv2cmA

∝ const

3x102 kg day 3x103 kg day

3x104 kg day 3x105 kg day

σp = 10−7 pbmχ = 100GeV

λ= 7.8

For a SuperCDMS like Ge detector:

Fractional mass limits as a function of input mass:

Difficult to measure the mass of heavy or very light WIMPs:

For heavy (>> mA) WIMPs characteristic energy scale varies weakly with energy.

For light WIMPs [ < O(25 GeV)] the number of events above the threshold energy is small.

σp = 10−8 pb

Exposures:

3x103,3x10

4 and 3x10

5 kg day.

Solid (dotted) lines 95% (68%) confidence limits.

Varying the WIMP distribution

What if the speed distribution isn’t Maxwellian?

Uncertainty in the local circular speed (and hence the mean WIMP kinetic energy) leads to a systematic uncertainty in the WIMP mass determination:

i) smooth ultra-local WIMP distribution

vc = 220±20kms−1Δmχ

mχ=

[1+(mχ/mA)

] Δvcvc

Uncertainty in shape of WIMP speed distribution leads to a small systematic uncertainty in the WIMP mass determination (since the mean energy spectrum depends only weakly on the detailed shape of the WIMP speed distribution Kamionkowski & Kinkhabwala; Donato, Fornego & Scopel)

ii) ultra-local WIMP distribution consists of a finite number of streams

Energy spectrum would consist of a number of (sloping) steps.

Positions of steps would depend on WIMP mass, target nuclei mass and the (unknown) streamspeeds.Heights of steps would depends on WIMP cross-section and the (unknown) stream densities.

With multiple targets could (in principle) measure WIMP mass without makingany assumptions about the WIMP speed distribution Drees & Shan.

Summary

Galaxy halos (and the Universe as a whole….) contain significant amounts of non-baryonic dark matter (assuming Newtonian gravity/GR is correct).

WIMPs generically have the right sort of present day density and supersymmetry provides us with a concrete candidate, the neutralino.

Direct and indirect detection experiments have the sensitivity required to detect WIMPs (depending on their interaction cross-section) and are complementary to colliders.

Detection signals depend on the small scale dark matter distribution (which depends on the fate of the first dark matter halos to form).