Gamma rays from
WIMP annihilations
around the Sun
Sofia Sivertsson
In collaboration with Joakim Edsjö
Partikeldagarna 2007, Göteborg
The Milky Way WIMP halo
The Milky Way has a halo of Dark Matter which the
Sun moves in.
The Milky Way WIMP halo is assumed to have a
Maxwell-Boltzmann distribution.
The halo is assumed to be isotropic, also in the
Sun’s reference system.
Gamma rays from WIMP annihilations around the Sun, Sofia Sivertsson, Partikeldagarna 2007
Illustration of the WIMP capture process
1
3
2
Gamma rays from WIMP annihilations around the Sun, Sofia Sivertsson, Partikeldagarna 2007
Gamma ray production
In the capture process the bound WIMPs produce an
overdensity of WIMPs around the Sun.
WIMP annihilations within this halo around the Sun
produces gamma rays.
This signal has low background since the Sun itself does
not produce gamma rays.
Such gamma rays can be detected by Cherenkov
telescopes such as the Milagro detector.
Gamma rays from WIMP annihilations around the Sun, Sofia Sivertsson, Partikeldagarna 2007
Previous work
The gamma radiation from the Sun’s WIMP halo has been
estimated previously by Strausz and Hooper.
Strausz comes to the conclusion that the gamma ray signal
should be measurable or constrain unknown parameters of
the WIMP model.
Hooper comes to the conclusion that the gamma ray signal is
too weak to be detected.
The aim of this project was to make a more accurate
calculation of this gamma ray signal.
Gamma rays from WIMP annihilations around the Sun, Sofia Sivertsson, Partikeldagarna 2007
The WIMP capture process
The WIMP-nucleus cross
section is given by a spin
dependent and a spin
independent cross section.
The spin dependent cross
section here only couples to
hydrogen, this cross section is
also less constrained.
If a 100 GeV WIMP scatters only
off hydrogen it has to scatter at
least some 40 times before it is
buried inside the Sun.
1
3
2
18
x/(sqrt((4-x)*x-1))
16
14
12
10
8
6
4
2
0
0
0.5
1
1.5
2
2.5
r
Gamma rays from WIMP annihilations around the Sun, Sofia Sivertsson, Partikeldagarna 2007
3
3.5
4
The WIMPs’ distribution after their first scatter
in the Sun
45000
1e+07
8e+06
6e+06
4e+06
2e+06
0
-5e+10
’sunscattersi.dat’
’sunscattersd.dat’
number of scattered WIMPs per unit time, energy and radius
number of scattered WIMPs per unit time, energy and radius
1.2e+07
0
5e+10
1e+11
reduced energy
1.5e+11
2e+11
2.5e+11
40000
35000
30000
25000
20000
15000
10000
5000
0
-6e+11
-5e+11
-4e+11
-3e+11
-2e+11
-1e+11
0
1e+11
2e+11
reduced energy
The energy distribution of WIMPs after their first scatter in the Sun. The
different lines shows the distribution of WIMPs which have scattered at
different shells in the Sun, with radius 10%, 20%,…, 60% of the Sun’s
radius. Here M=100 GeV.
Gamma rays from WIMP annihilations around the Sun, Sofia Sivertsson, Partikeldagarna 2007
3e+11
Monte Carlo simulation
The WIMP density in the Sun’s WIMP halo is calculated
through constructing a Monte Carlo.
The Monte Carlo picks WIMPs randomly according to the
previously shown distribution and then simulates the
WIMPs life until complete capture inside the Sun.
Uses the average orbit life time.
The WIMP orbit is not entirely elliptical inside the Sun,
which affects the scatter probability.
The cross section for scatter off heavier nuclei depends
on the energy loss.
Gamma rays from WIMP annihilations around the Sun, Sofia Sivertsson, Partikeldagarna 2007
Monte Carlo simulation
The line number density of WIMPs around the Sun is
then calculated for different configurations of the cross
sections and WIMP mass.
2e+23
The line density fits a
curve proportional to
1
r
The WIMP density is
independent of the
scale of the cross
sections.
1.8e+23
1.6e+23
WIMP line number density [1/m]
’mon23hundra.dat’
1.76e23/sqrt(x)
1.4e+23
1.2e+23
1e+23
8e+22
6e+22
4e+22
2e+22
0
0
20
40
60
80
solar radii
100
120
Gamma rays from WIMP annihilations around the Sun, Sofia Sivertsson, Partikeldagarna 2007
140
The gamma ray flux at earth
Knowing the WIMP density distribution, the gamma ray
flux profile from the WIMP halo can be calculated.
5e-69
’gamma_flux.dat’
4.5e-69
4e-69
3.5e-69
flux at earth per steradian
3e-69
2.5e-69
2e-69
1.5e-69
1e-69
5e-70
0
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0.016
0.018
0.02
angle of sight, theta
Gamma rays from WIMP annihilations around the Sun, Sofia Sivertsson, Partikeldagarna 2007
Result
The total gamma ray flux at earth from the WIMP halo
around the Sun can then be calculated.
The flux at earth per square meter per second for different
Nγ = 20
WIMP mass and cross section: σ v = 10−32 m3s−1
M = 102 m p
M = 103 m p
M = 104 m p
σ sd = 10−3 pb, σ sd = 0
5.3 ⋅ 10−19
6.8 ⋅ 10−21
3.2 ⋅ 10−23
σ sd = 0, σ si = 10−5 pb
1.1 ⋅ 10−19
3.7 ⋅ 10−21
5.5 ⋅ 10−23
Gamma rays from WIMP annihilations around the Sun, Sofia Sivertsson, Partikeldagarna 2007
The End
Gamma rays from WIMP annihilations around the Sun, Sofia Sivertsson, Partikeldagarna 2007