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

Outline

Motivations Solar wakes Axion signal modulation WIMP signal modulation Conclusions

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

Solar wakes

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

b

Impact parameter vs. polar angle

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

Flows velocity modulation (on Earth)

Flows velocity modulationDistortion near the spike

Flow 4+

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

Flow density modulation (on Earth)

Flow 10+

Axion Signal Modulation

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

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

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

WIMP Signal Modulation

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

The function T(E)

June

December

Isothermal

Cold static

F

1

v

2Fv

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).

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

...

T(E) in the caustic ring halo model

Predicted event rate modulation @ DAMA in the range 2 – 6 keV

50m GeV

120m GeV 35m GeV

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.

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