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