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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!