The axion-photon interaction andgamma ray signals of dark matter

Juan Barranco Monarca

DCI Universidad de Guanajuato

In collaboration with A.Bernal, D. Delepine and A. Carrillo

Essential Cosmology for the Next Generation. Los Cabos San Lucas, Mexico 2014

The axion-photon interaction and gamma ray signals of dark matter– p. 1

Two fantastic news!

Higgs discovery.

1. Confirms the Standard Modelof elementary particles.

2. First élementary’scalarparticle found in nature

Is there somenthing else? Any other fun-damental scalar?

The axion-photon interaction and gamma ray signals of dark matter– p. 2

Axion

The strong CP problem.

Axion was originallyproposed to solve strongCP 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. 3

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) = m2f2

a

[

1− cos(

φ

fa

)]

, ,

which can be expanded as

V (φ) ∼ 1

2m2φ2 − 1

4!m2

φ4

f2a

+1

6!m2

φ6

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. 4

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. 5

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)

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. 6

Galactic halo as a collisionless ensemble of DM machos

0 2e+11 4e+11 6e+11

ρ(0)[Kg/m3]

2e-21

4e-21

6e-21

8e-21

M [

Sola

r m

asse

s]

0 3e+10 6e+10 9e+10

ρ(0)[Kg/m3]

0

1e-15

2e-15

3e-15

4e-15

5e-15

[J. Barranco, A. Carrillo, D. Delepine, PRD87 (2013) 10301183]

The axion-photon interaction and gamma ray signals of dark matter– p. 7

Galactic halo as an ensemble of DM mini-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 andY. Verbin,“Scalar field mini-MACHOs: A new explanation for

galactic dark matter,” Phys. Rev. D 70, 043537 (2004)

Axions may form such scalar fieldmini-MACHOS. Maxion star <

10−15M⊙ J. Barranco, A. Bernal,Phys. Rev. D 83 (2011) 043525

The axion-photon interaction and gamma ray signals of dark matter– p. 8

Galactic halo as an ensemble of DM mini-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 andY. Verbin,“Scalar field mini-MACHOs: A new explanation for

galactic dark matter,” Phys. Rev. D 70, 043537 (2004)

Axions may form such scalar fieldmini-MACHOS. Maxion star <

10−15M⊙ J. Barranco, A. Bernal,Phys. Rev. D 83 (2011) 043525

Clumpy neutralino dark matterMneutralino star ∼ 10−7M⊙. J. Ren, X. Li, H.Shen, Commun.Theor.Phys. 49 (2008) 212-216

Formation of dark matter clumps:

Axion minicluster:The evolution of the axion fieldat the QCD transition epoch may producegravitationally bound miniclusters of axionsSuch minicluster, due to collisional 2a → 2a

process, it may relax to a selfgravitatingsystem. [Kolb and Tkachev PRL 71 (1993)3051-3054]

Neutralino clumps: At the phase transition from aquark-gluon plasma to a hadron gas, thespectrum of density perturbations may developpeaks and dips produced by the growth ofhadronic bubbles. → Kinematically decoupledCDM falls into the gravitational potential wellsprovided from those peaks leading theformation of dark matter clumps with masses< 10−10M⊙. [Schmid PRD 59 (1999) 043517]

The axion-photon interaction and gamma ray signals of dark matter– p. 8

Possible γ signal?

Consider the galactic halo as an ensemble of axion stars

0.01 0.1 1 10r [Kpc]

1010

1012

1014

1016

Axi

on s

tars

/pc3

MooreNavarro-Frenk-WhiteKratsovIsothermal

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. 9

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. 10

Possible γ signal?

The number of collisions per pc3 per second will be

Rc = nAS(r)× ρNS(r)× S × v ,

nAS is the number of AS per pc3,

ρNS is the probability to find a Neutron Star at that point

0.01 0.1 1 10 100r [Kpc]

10-22

10-20

10-18

10-16

10-14

Col

lisio

ns p

er y

ear

MooreNavarro-Frenk-WhiteKratsovIsothermalSalucci et al.

10-8

10-6

10-4

10-2

The axion-photon interaction and gamma ray signals of dark matter– p. 11

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

The axion-photon interaction and gamma ray signals of dark matter– p. 12

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. 13

HE Gamma rays from the sun?

The axion-photon interaction and gamma ray signals of dark matter– p. 14

Conclusions

Axions are good candidates for DM

They may form mini-clumps i.e. axion stars

Galaxies may be a collisionless ensemble of such axion stars

The axion-photon conversion is an interesting tool for indirect detection of axion

The axion-photon interaction and gamma ray signals of dark matter– p. 15