The axion-photon interaction andgamma ray signals of dark matter
Juan Barranco Monarca
DCI Universidad de Guanajuato
In collaboration with David Delepine and Alba Carrillo
PASCOS, Merida Yucatan, Mexico. June 5,2012
The axion-photon interaction and gamma ray signals of dark matter– p. 1
Outline
Dark matter detection
A couple of new proposal for indirect dark matterdetection
UHE neutrino flux suppression
Gamma rays and the axion-photon mixing1. A galactic halo made of collisionless ensemble of
axion stars?2. A possible flux of high energy photons from the
Sun?
Conclusions
The axion-photon interaction and gamma ray signals of dark matter– p. 2
Motivation
The axion-photon interaction and gamma ray signals of dark matter– p. 3
Dark matter detection
No Dark matter candidate has been detected so far (?)
The axion-photon interaction and gamma ray signals of dark matter– p. 4
Indirect DM searches
The axion-photon interaction and gamma ray signals of dark matter– p. 5
Indirect DM searches
The axion-photon interaction and gamma ray signals of dark matter– p. 6
Does it exist alternative ways?
The axion-photon interaction and gamma ray signals of dark matter– p. 7
Does it exist alternative ways?
If cosmic rays (i.e. ν’s or photons) interact with DMthere could be some effect
The axion-photon interaction and gamma ray signals of dark matter– p. 7
Possible suppression
The mean free path
λmfp = (nσ)−1 =mDM
ρDMσ,
where n is the DM density and σ
is the elastic cross section ν-DM,and mDM is the mass of the DMparticle.
There will be a ν’s UHE fluxsuppression given by
F (L) = F0e−L/λmfp
,
where F (L) is the suppressed fluxand F0 is the flux at the source. 10
-3210
-2410
-1610
-810
0
mDM
(eV)
10-60
10-48
10-36
σ ν-D
M(c
m2 )
Induces 95% flu
x suppres
sion
The axion-photon interaction and gamma ray signals of dark matter– p. 8
SFDM as a viable model for DM
The Scalar Field Dark Matter model (SFDM)The Dark Matter is modeled by a scalar field with a ultra-light associated particle.(m ∼ 10−23eV)
At cosmological scales it behaves as cold dark matterT. Matos, L.A. Urena-Lopez, Class. Quant. Grav. 17 L75 (2000),V. Sahni and L.M. Wang, Phys. Rev D 62, 103517 (2000).
At galactic scales, it does not have its problems: neither a cuspy profile, nor aover-density of satellite galaxies.A. Bernal, T. Matos, D. Nuñez, Rev. Mex. A.A. 44, 149 (2008)T. Matos, L.A. Urena-Lopez, Phys. Rev. D 63, 063506 (2001)
The axion-photon interaction and gamma ray signals of dark matter– p. 9
Could it be possible that we have already observed this interaction?
ICECUBE limit on ν’s from GRBs
[PRL 106 (2011) 141101]
Auger limit
[PRL 100 (2008) 211101]
The axion-photon interaction and gamma ray signals of dark matter– p. 10
The cross section
Assume ν − φ interaction as in [D. Hooper et al. PRL 93 (2004) 161302, C. Boehm et al.
PRL 92 (2004) 101301 C. Boehm and P. Fayet NPB 683 (2004) 219]
If mν ∼ 1eV and Eν ∼ 1018 eV, the cross section is valid for mφ >> O (10−18) eV.Furthermore, in the limit s, u ≪ MI and integrating over solid angle
σ ≃(
gνφ
MI
)4 m2ν
16π.
useful limit for ultra-high-energetic neutrinos
λ = 16π × 10−6
(
MI/gνφ
GeV
)4 ( eV
mν
)2(
GeV/cm3
ρφ
)
( mφ
10−15eV
)
GeV2cm3
≃ L0
(
MI/gνφ
GeV
)4 ( eV
mν
)2(
GeV/cm3
ρφ
)
( mφ
10−18eV
)
,
where L0 ≃ 42 pc.
The axion-photon interaction and gamma ray signals of dark matter– p. 11
Possible suppression
F (L) = F0e−L/λmfp
,
gνφ
MI&
[
ln
(
F0
F
)
L0mφ
ρφm2νL
] 1
4
.
L = 5 × 102 Mpc, mν ∼ 1 eV andρDM = 1,2× 10−6 GeV/cm3
J. Barranco, O. G. Miranda, C. A. Moura,T. I. Rashba, F. Rossi-TorresJCAP 1110 (2011) 007arXiv:1012.2476 [astro-ph.CO].
1e-20 1e-19 1e-18 1e-17 1e-16 1e-15mφ[eV]
0.2
1
5
(gνφ
/MI)[
GeV
-1]
ρφ = ρDM
ρφ = 0.1 ρDM
The axion-photon interaction and gamma ray signals of dark matter– p. 12
Axion
Axion was originally proposed to solve strong CP problem
There is a remnant γ − a interaction
L =1
2(∂µφ∂µφ−m2φ2)− 1
4
φ
MFµν F
µν − 1
4FµνF
µν
The axion-photon interaction and gamma ray signals of dark matter– p. 13
Self-gravitating axion
Axion properties
1010GeV ≤ fa ≤ 1012GeV
10−5eV ≤ m ≤ 10−3eV
At late times in the evolution of the universe, the energy density potential of the axion is
V (φ) = m2f2a
[
1− cos(
φ
fa
)]
, ,
which can be expanded as
V (φ) ∼ 1
2m2φ2 − 1
4!m2 φ
4
f2a
+1
6!m2 φ
6
f4a
− ...
with the identification λ = m2/6f2a : Hence, we can estimate (incorrectly)
Mmax ∼ 1027√λM⊙ ≈ 104M⊙!
F.E. Shunck and W. Mielke. Class. Quantum Grav. 20 (2003)
The axion-photon interaction and gamma ray signals of dark matter– p. 14
Axion stars
V (φ) = m2f2a
[
1− cos(
φ
fa
)]
V (φ) ∼ 1
2m2φ2 − 1
4!
(
m
fa
)
φ4 +1
6!
m2
f4a
φ6 − ...
V (φ) → 〈Q|V (φ)|Q〉
φ = µ+R(r)e−iE1t + µ−R(r)e+iE1t
µ|Q〉 = 0
〈Q|φ2|Q〉 = R2
〈Q|φ4|Q〉 = 2R4
〈Q|φ6|Q〉 = 5R6
The axion-photon interaction and gamma ray signals of dark matter– p. 15
Axion star
R =fa√m
σ , r =mp
fa
√
m
4πx , α =
4πf2a
m2pm
A(x) = 1− a(x)
a′ +a(1 + a)
x+ (1− a)2x
[(
1
B+ 1
)
m2σ2 − mσ4
4+ α
σ′2
(1− a)+
σ6
72
]
= 0 ,
B′ +aB
x− (1− a)Bx
[(
1
B− 1
)
m2σ2 +mσ4
4+ α
σ′2
(1− a)− σ6
72
]
= 0 ,
σ′′ +
(
2
x+
B′
2B+
a′
2(1− a)
)
σ′ + (1− a)
[(
1
B− 1
)
m2σ +mσ3
3− σ5
24
]
= 0
The axion-photon interaction and gamma ray signals of dark matter– p. 16
Axion star
0
1×10-4
2×10-4
3×10-4
4×10-4
5×10-4
σ(x)
σ(0)=5x10-4
σ(0)=3x10-4
σ(0)=1x10-4
0 500 1000 1500 2000x
-7e-14
-6e-14
-5e-14
-4e-14
-3e-14
-2e-14
-1e-14
0
a(x)
r =mp
fa
√
m
4πx
σ(0) Mass (Kg) R99 (meters) density ρ (Kg/m3)
5× 10−4 3,90× 1013 1,83 6,3× 1012
3× 10−4 6,48× 1013 2,86 2,7× 1012
1× 10−4 1,94× 1014 8,54 3,1× 1011
[J. Barranco, A. Bernal, PRD83, 043525 (2011)]
The axion-photon interaction and gamma ray signals of dark matter– p. 17
Galactic halo as a collisionless ensemble of DM machos
0
5
10
15
20
25
30
-8 -6 -4 -2 0 2 4 6
t = 13.7 Gyr
log10 t/ys
log10 m/Mo
Mini MACHOS
Forbidden because ofMACHO Microlensing
Forbiddenbecause ofdynamical instability
Rich Cluster 1015 Mo
Large Galaxy 1012 MoDwarf Galaxy 108 Mo
Forbidden because of arguments on massive BHs
Forbidden because of gravothermal instability
X. Hernandez, T. Matos, R. A. Sussman and Y. Verbin,Phys. Rev. D 70, 043537 (2004)
The axion-photon interaction and gamma ray signals of dark matter– p. 18
Possible γ signal?
Consider the galactic halo as an ensemble of axion stars
0.01 0.1 1 10 100r [Kpc]
1e+12
1e+13
1e+14
1e+15
1e+16
1e+17
1e+18
Axi
on s
tars
/pc3
KratsovNavarro Frenk WhiteMooreIsothermal
Remember
L =1
2(∂µa∂µa−m2a2)− 1
4
a
MFµν F
µν − 1
4FµνF
µν
It is possible axion transform to photons in presence of an external magnetic field!
The axion-photon interaction and gamma ray signals of dark matter– p. 19
Possible γ signal?
Strong magnetic fields → NS > 108 Gauss.
∼ 109 NS in the galaxy
Does axion stars collision with Neutron Stars produce a visible effect?
Start with
Laγγ =cα
fPQπa ~E · ~B
Obtain “modified” Gauss law:
∂ ~E =−cα
fPQπ~∂ · (a ~B)
Energy dissipated in the magnetized conducting media, with averange σ electricconductivity (Ohm’s law)
W =
∫
ABSσE2
ad3x = 4c2 × 1054erg/s
σ
1026/s× M
10−4M⊙
B2
(108G)2
YES! there could be a signal
The axion-photon interaction and gamma ray signals of dark matter– p. 20
HE Gamma rays from the Sun?
Remember the Lagrangian
L =1
2(∂µφ∂µφ−m2φ2)− 1
4
φ
MFµν F
µν − 1
4FµνF
µν
If the magnetic field changes on length scales larger than the wavelength of theparticles, the equation of motion will be
i∂zΨ = −(ω +M)Ψ ; Ψ = (Ax, Ay , φ)
M =
∆p 0 ∆Mx
0 ∆p ∆My
∆Mx∆My
∆m
.
∆Mi=
Bi
2M= 1,755× 10−11
(
Bi
1G
)(
105GeV
M
)
cm−1
∆m =m2
2ω= 2,534× 10−11
( m
10−3eV
)
(
1GeV
ω
)
cm−1
∆p =ω2p
2ω= 3,494× 10−11
( ne
1015cm−3
)
(
1GeV
ω
)
cm−1
(1)The axion-photon interaction and gamma ray signals of dark matter– p. 21
HE Gamma rays from the sun?
P =4B2ω2
M2(ω2p−m2)2 + 4B2ω2
sin2(
πz
losc
)
losc =4πωM
√
M2(ω2p−m2)2 + 4B2ω2
The axion-photon interaction and gamma ray signals of dark matter– p. 22
HE Gamma rays from the sun?
The axion-photon interaction and gamma ray signals of dark matter– p. 23
Conclusions
Dark matter detection
A couple of new proposal for indirect dark matterdetection
UHE neutrino flux suppression
Gamma rays and the axion-photon mixing1. A galactic halo made of collisionless ensemble of
axion stars?2. A possible flux of high energy photons from the
Sun?
The axion-photon interaction and gamma ray signals of dark matter– p. 24