Download Positrons from dark matter annihilation in the galactic

Positrons from dark matter annihilation in the
galactic halo: Theoretical uncertainties
Roberto A. Lineros R.
Università degli studi di Torino
Based on:
T. Delahaye, R.L, F. Donato, N. Fornengo and P. Salati.
Phys. Rev. D 77, 063527 (2008)
ISCRA’08 – p.1/17
Motivation
⋆ To study positron/electron Cosmic Rays (CR) signals and its
potential to reveal new exotic signals.
⋆ To study indirect searches of galactic Cold Dark Matter (CDM)
⋆ To study uncertainties related to particle and astrophysics, for
disentangle new signals from background.
ISCRA’08 – p.2/17
Outline
•
Dark Matter indirect signals
* Dark Matter annihilations.
•
Positron/Electron CRs
* Two–Zone Propagation Model.
* Transport Equation (TE), Halo Function.
* Fluxes, Positron fraction.
•
Conclusions
ISCRA’08 – p.3/17
(Mathis et al 2002)
DM indirect signals
Many candidates from
BSM theories:
The nature of DM
is not clear.
Neutralinos, KK particles . . .
Structure formation:
DM overdensities.
DM present in galaxies
may annihilate and act as
exotic CR sources.
Experiments:
HEAT, CAPRICE, AMS,
PAMELA, MASS . . .
ISCRA’08 – p.4/17
0.10
Positron fraction
+
+
−
e / (e +e )
CR: positron/electron
0.01
Background
Heat 2000
AMS Run 1
AMS Run 2
MASS−91
CAPRICE94
0
10
1
10
Positron energy [GeV]
2
10
ISCRA’08 – p.5/17
CR: propagation overview
ISCRA’08 – p.6/17
Two–Zone Propagation Model
The CR propagation is modeled in a cylinder where all physical
processes happen (Maurin et al. 2001).
It is composed by two zones:
i) A cylinder Lz , which defines a
zone where CR propagates.
ii) A thin disk models the galactic
plane, sources and interactions
among CRs and ISM.
Rg = 20kpc , hz ∼ 100pc , Lz = 1, 20kpc
CR close to the boundaries may escape. This implies that CR
density vanishes in the boundaries.
ISCRA’08 – p.7/17
Transport Equation
In a steady–state regime, the TE for positrons and electrons is:
2 ǫ
−K0 ǫδ ∇2 ψ − ∂ǫ
ψ =q
τE
(analytically solvable)
It describes the number density per unit energy evolution.
TE is composed by:
* Diffusion term
* Energy-loss term
* Source term (we will see in a few slides)
ISCRA’08 – p.8/17
Transport Equation: parameters
Those are constrained with observation on other CR species
L [kpc]
Iso-χ2 contours for B/C (χ2< 40)
δ = 0.46
0.6
0.7
0.85
b
0.5
K0 /L [kpc Myr ]
-1
f(δ) × K0 /L [kpc Myr ]
-1
(Maurin et al.
2001)
From B/C analysis:
K0 = 0.0112 kpc2 /Myr
δ = 0.7
Lz = 4 kpc
ISCRA’08 – p.9/17
Transport Equation: solution
For source terms with the form :
q(x, ǫ) = f (x) × g(ǫ)
We define the Halo Function:
ak =
˜ D) =
I(λ
X
ak χk (x⊙ ) exp (−4k 2 λ2D )
Z
dx χ†k (x)f (x)
1−δ − ǫ1−δ
ǫ
S
λ2D = 4 K0
1−δ
k
τE
ψ(x⊙ , E) = 2
ǫ
Z
∞
˜ D ) g(ǫs )
dǫs I(λ
ǫ
ISCRA’08 – p.10/17
DM as positron source
The source term for case of DM annihilation is:
ρ2⊙ dn
q(x, E) = α hσann vi 2
(E)
mχ dE
ρ2 (x)
ρ2⊙
Thermally av. cross section
Annihilation distribution
WMAP, particle model
Isothermal, NFW, Moore
Multiplicity distribution
decays, hadronization, (PYTHIA)
ISCRA’08 – p.11/17
Halo function for CDM distributions
The Halo Function encodes the information about CDM distribution.
ISCRA’08 – p.12/17
Positron flux
The positron flux is obtained from the density:
βc
βc
φe+ (E) =
ψ(x⊙ , E) =
4π
4π
τE
ǫ2
Z
∞
˜ D ) g(ǫs )
dǫs I(λ
ǫ
For a generic DM particle,
mχ = 100, 500 [GeV]
hσann vi = 2.1 × 10−26 [cm3 /sec]
with specific annihilation channels:
e+ e−
bb̄
+
⇒
e
χχ ⇒
W +W − τ +τ −
ISCRA’08 – p.13/17
Positron flux
T. Delahaye, R. Lineros, N. Fornengo, F. Donato & P.Salati (2007)
10−5
E2 Φe+ [GeV cm−2 s−1 sr−1]
E2 Φe+ [GeV cm−2 s−1 sr−1]
B/C best fit
M1 flux
M2 flux
uncer. band
B/C best fit
Background
B/C best fit (no mod)
10−4
10−5
10−6
−
Direct production
bb channel
NFW Halo profile (rs = 20 kpc)
E2 Φe+ [GeV cm−2 s−1 sr−1]
<σv> = 2.1 × 10−26 cm3 s−1
mχ = 100 GeV
−
Direct production
bb channel
Boost factor = 300
Boost factor = 250
Heat 94+95
MASS−91
CAPRICE94
NFW Halo profile (rs = 20 kpc)
10−3
−26
3 −1
<σv> = 2.1 × 10
cm s
mχ = 500 GeV
Bkg. factor = 1.1
E2 Φe+ [GeV cm−2 s−1 sr−1]
10−5
10−4
10−6
10−5
10−6
+
10−7
Heat 94+95
AMS Run 1
AMS Run 2
10−3
10−6
10−7
T. Delahaye, R. Lineros, N. Fornengo, F. Donato & P.Salati (2007)
−
+ −
τ τ channel
W W channel
100
101
Positron energy [GeV]
102
100
101
Positron energy [GeV]
mχ = 100 GeV
+
−
+ −
τ τ channel
W W channel
Boost factor = 300
102
100
Boost factor = 400
101
102
Positron energy [GeV]
100
101
102
Positron energy [GeV]
mχ = 500 GeV
Also astrophysical uncertainties play an important role.
ISCRA’08 – p.14/17
Positron Fraction
T. Delahaye, R. Lineros, N. Fornengo, F. Donato & P.Salati (2007)
e+/ (e++e−)
B/C best fit
uncer. band
background
<σv> = 2.1 × 10−26 cm3 s−1
mχ = 100 GeV
Bkg. factor = 1.1
−
Direct prod.
bb channel
Boost factor = 10
Boost factor = 50
0.10
0.01
Heat 2000
MASS−91
CAPRICE94
−
τ τ channel
Boost factor = 30
Boost factor = 40
+ −
101
Positron energy [GeV]
102
100
101
Positron energy [GeV]
mχ = 100 GeV
Boost factor = 50
<σv> = 2.1 × 10−26 cm3 s−1
mχ = 100 GeV
Bkg. factor = 1.1
0.10
0.01
0.01
100
Boost factor = 10
−
bb channel
Positron fraction
0.10
W W channel
Direct production
NFW Halo profile (rs = 20 kpc)
e+/ (e++e−)
Heat 2000
AMS Run 1
AMS Run 2
Positron fraction
e+/ (e++e−)
0.01
+
B/C best fit
M1 flux
M2 flux
backg.
Expected measurement for PAMELA
(3 years)
Positron fraction
0.10
Positron fraction
e+/ (e++e−)
NFW Halo profile (rs = 20 kpc)
T. Delahaye, R. Lineros, N. Fornengo, F. Donato & P.Salati (2007)
102
+
−
W W channel
Boost factor = 30
100
101
102
Positron energy [GeV]
+ −
τ τ channel
Boost factor = 40
100
101
102
Positron energy [GeV]
Expected measurement for PAMELA
ISCRA’08 – p.15/17
Conclusions
• Astrophysical uncertainties can not be neglected, specially in
the context of the identification of a possible exotic signal.
• We obtained CDM scenarios where positron signal related to
CDM annihilation can be disentangled from the background.
• Experiments as PAMELA and AMS02 will provide new
information in the energy range above previous experiments,
and will confirm/reject the excess seen by HEAT.
ISCRA’08 – p.16/17
Thanks
ISCRA’08 – p.17/17