Diurnal and Annual Modulation of Cold Dark Matter Signals Ling Fu-Sin IDM2004, Edinburgh, Sept. 8th...
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![Page 1: Diurnal and Annual Modulation of Cold Dark Matter Signals Ling Fu-Sin IDM2004, Edinburgh, Sept. 8th 2004 in collaboration with Pierre Sikivie & Stuart.](https://reader036.fdocuments.us/reader036/viewer/2022062511/551ac3cf55034656628b5abf/html5/thumbnails/1.jpg)
Diurnal and Annual Modulation of Cold Dark Matter Signals
Ling Fu-Sin IDM2004, Edinburgh, Sept. 8th 2004
in collaboration with Pierre Sikivie & Stuart Wick,
Phys. Rev. D66, 023504 (2002) (astro-ph/0203448)astro-ph/0405231
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Outline
Motivations Solar wakes Axion signal modulation WIMP signal modulation Conclusions
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Motivations Quest for DM: we need an accurate
description of the potential signature. DM is characterized by two essential
properties: It is collisionless It has negligible velocity dispersion
Axions
WIMPs
5
0
5 26 317 10
v ( ) 3 10a
a
teV
m tt c
1 22 3
12 0100v ( ) 10W
W
tGeVt c
m t
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Solar wakes
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Effect of the Sun’s gravity on the structure of cold DM flows
Solar wakes: 1 flow upstream, 3 flows downstream
Appearance of caustics: Spike: line caustic on the axis of
symmetry, downstream Skirt: conical surface near with opening
close to the maximum scattering angle
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b
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Impact parameter vs. polar angle
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Flows velocity From energy and angular momentum
conservation
with
2
0 02
2 ˆˆv ( ) v 1 vi ii
b bar r
r r r
1,2 2
4 ( )( , ) 1 1
2
a r zb z
( ) ( ) ( )i s i
Rb b
r O
20v
GMa
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Flows velocity modulation (on Earth)
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Flows velocity modulationDistortion near the spike
Flow 4+
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Flows density
01,2
11 2
4 1
dd Y
Y
02
( )
( )
1sin
s i
s i
i
R
r
db
d
bdd
r
O
22
2
4 2( )
sin
a aY r z
r
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Flow density modulation (on Earth)
Flow 10+
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Axion Signal Modulation
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Axion detection Principle: Photoconversion in a strong magnetic field
Photon energy:
Frequency resolution of ADMX detector @ LLNL (in search mode) for Cavity bandwidth set by the quality factor
of the cavity. If one octave is to be covered in one year, the time spent at each frequency is about 100 sec.
2
2
2
v1
a
c
m c
2 4
2 4
1 v 3 v1
2 8afc c
510Q /f Q
2
2a
a
m c
10 mHzf 1110a
f
&
10 eVam µ
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Frequency modulation
Relativistic effects Jupiter & other planets Earth’s gravity Earth’s rotation
Earth’s orbital rotation
Earth’s eccentricity Frequency shift on the measurement time scale
102
7 10GMf
f c R
2 4
2 4
1 v 3 v1
2 8afc c
1210
orb rotv v v ( ) v ( ) vi i it t
122
10J
J
GMf
f c R
rotv 0.465 / coskm s l 2
12 2rot2
v10 cos
2
fl
f c 9rot
2
v v10 cos
2
fl
f c
orbv 30 /km s2
9orb2 2
v5 10
2 2
GMf
f c a c
8
210
GMf
f c a
7orb2
v v10
2if
f c
0.0167e
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Density modulation Away from spike
Near spike
Near skirt
0
5
4
2
1 0 2 0
2
300 /
v
12.4 10
sin
km sd d d d
3 2d d
1 2 0 2 2
1
2( )
ad d d
a 5
3 010d d
6
max
2 3 0
1.5 10d d d
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WIMP Signal Modulation
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WIMP direct detection formulas Detection by elastic scattering with nuclei
Differential event rate
Total rate
with , ,
Cold flow
with ,
min
0
2
2
v
(v)
v2v
rr
qfd
m m
dRF d
dE
2
1
r
r
E
E
dRdE
dER
N
N
r
m m
m mm
2 N rm Eq
min
2v
r
q
m
F(v)= (v-v )f
2 max 1 max
0
2
F
min{ , } min{ , }2 v
( ) ( )F
r
E E E Ed
m mR
F F
2
0
( ) r
E
F q dEE F
2 2
Fmax
2 vr
N
m
mE
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The function T(E)
June
December
Isothermal
Cold static
F
1
v
2Fv
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The WIMP Signal modulation for the Caustic ring halo model and the DAMA result
Caustic ring halo model: self similar infall halo model with a large number of flows corresponding to particles falling in and out for the nth time
P. Sikivie et al., PRD56(1997)1863.P. Sikivie, PLB567(2003).
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List of flowsn v
(km/s)v_X
(km/s)v_Y
(km/s)v_Z
(km/s)d
(10^-26 gr/cm^3)
1+ 620 480 20 -395 0.3
1- 605 -570 20 210 0.3
2+ 520 450 10 -255 0.8
2-3+3-4+4-5+5-6+6-7+7-8+8-...
505435420350340265255300280330310330315...
-440415-310350-1651301201007570355520...
10~0~0-10-1085
-120230-245300-305320-310
...
250-130285~0295210195160120110508020...
0.81.41.43.43.4
15 or 170170 or 153.4 or 6.56.5 or 3.41.3 or 4.14.1 or 1.31.1 or 2.02.0 or 1.1
...
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T(E) in the caustic ring halo model
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Predicted event rate modulation @ DAMA in the range 2 – 6 keV
50m GeV
120m GeV 35m GeV
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Conclusions DM is collisionless and has negligible
velocity dispersion. These features determine the shape of its signal in a detector. Axion: narrow peak in frequency WIMP: plateau in the differential event
rate The presence of caustics is potentially
crucial for DM discovery.
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Axions: Diurnal modulation enables to reconstruct the velocity of the DM flow. It is therefore crucial to include all effects to a precision .
WIMPs: Event rate modulation is very sensitive to thresholds, and can therefore be different with different targets. Caustic ring halo model not incompatible with DAMA: large WIMP masses are favored.
510v / c