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Detecting galactic structure via the Detecting galactic structure via the annual modulation signal of WIMPsannual modulation signal of WIMPs

Christopher M. SavageFine Theoretical Physics Institute

University of Minnesota

Katie Freese (University of Michigan)

Paolo Gondolo (University of Utah)

PRD 74, 043531 (2006)

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Overview

Galactic dark matter halo

Early collapse of of dark matter

virialized smooth/diffuse halo (position & velocity space)

Turbulent; late accretion streams (“cold” flow) Clumps Tidal streams Caustics

WIMP direct detection signatures Energy Time (annual modulation)

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Halo

Galaxy formationgravitational collapse

Standard Halo Model Isothermal sphere Non-rotating

D. Dixon, cosmographica.com

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Halo Substructure Tidal streams

Dwarf galaxies Sagittarius Stream

Clumps Hierarchical clustering

Caustics

D. Martinez-Delgado & G. Perez

Newberg et al. (2003)Freese, Gondolo & Newberg (2003)

Klypin et al. (1999); Moore et al. (1999)Stiff, Widrow & Frieman (2001)

V. Springer

Gunn & Gott (1972)Sikivie, Tkachev & Wang (1995,1997)

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Halo Smooth halo component (dominant?)

+ streams / “cold” flows

Local DM density: <> ~ 0.3 GeV/cm3

Typical velocities: v ~ 100’s km/s

Local velocity distribution:

Mean inverse velocity:

min

),(1

),( 3min vv

tfv

vdtv v

),( tf v

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Halo Velocity distribution ),( tf v

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Halo Mean inverse velocity

min

),(1

),( 3

vvtf

vvdtE v

2min

22 vE m

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Direct Detection

Elastic scattering of WIMP off detector nuclei

Rate:

CDMS, CRESST, DRIFT, EDELWEISS, NAIAD, PICASSO,SIMPLE, XENON, ZEPLIN, etc.

DetectorWIMP

WIMPScatter

),()(2

1),(),(

2tEq

mtE

dE

dRtE

Goodman & Witten (1985)

particle physicsastrophysics

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Annual Modulation

Earth’s motion With disk (June)

Against disk (December)

DAMA/NaI (R. Bernabei et al., 2003)

Modulation amplitude: 0.0200 ± 0.0032 /kg/day/keVee (2-6 keVee) DAMA/LIBRA

30 km/s

~300 km/s

WIMP Halo Wind

Drukier, Freese & Spergel (1986)

),()(),( ave tEEtE m

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Standard Halo Model (SHM)

Non-rotating, isothermal spherev = 270 km/s

0 = 0.3 GeV/cm3

( )

Detector velocity:

vdet(t) = vŸ + V(t)

Sun’s velocity vŸ (disk rotation ~220 km/s)

Earth’s orbital velocity V(t)

Characteristic time tc: vobs maximum (June 1 for SHM)

Freese, Frieman & Gould (1988)

e vt

vtf

2/])([3 2det2/3

23 )(),(

uvu

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Mean Inverse Speed: SHM ),(),( tEtE

Phase reversal

Small modulation amplitude

(few percent)

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Modulation: SHM

Characteristic time tc

(June 1)

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…Add a Stream

Sagittarius (Sgr) streamYanni et al (2003)

Sagittarius-like stream(for illustration) Direction & speed (~340 km/s) Dispersion: v = 25 km/s

Density: Sgr = 0.05 SHM

Sgr stream: 0.3-25% Freese, Gondolo & Newberg (2003)

Clumps: 1-5% Stiff, Widrow & Frieman (2001)

Caustic ring model: ~75% Sikivie, Tkachev & Wang (1995)

APOD 9/30/03 (Martinez-Delgado & Perez)

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Mean Inverse Speed: SHM + Stream no dispersion (v = 0)

Cutoff Energy Eco(t)

Characteristic EnergyEc = <Eco(t)> (39 keV)

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Mean Inverse Speed: SHM + Stream with dispersion (v > 0)

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Modulation: SHM + Stream

5% Stream!!!

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Modulation: Recoil Energy

Sgr stream modulation

Characteristic time tc

(Dec 28)

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Modulation: Recoil Energy

Total modulation

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Modulation: Recoil Energy Binning

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Modulation: Stream Density

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General Streams / Cold Flows

Phase of modulation (tc) independent of SHM

Rapid dropoff in count rate near some characteristic energy Ec

Small, cosine-like modulation below Ec

Large O(1) modulation near Ec (not cosine-like)

Ec, tc differ from Sagittarius stream

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Extracting Parameters

Characteristic energy Ec cold flow speed

Characteristic time tc cold flow direction (1 component)

Modulation amplitude relative densities (Str / SHM)

More difficult: cold flow dispersion 2nd direction component

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Summary

Local Halo: presence of streams / cold flows Small component

Annual modulation Mild effect …except near some characteristic energy:

Relatively large effect Not cosine-like

Modulation detection: probe structure of halo …sooner!