Indirect signatures of Gravitino Dark Matter

Indirect signatures ofGravitino Dark Matter

Alejandro Ibarra

DESY

In collaboration with

W. Buchmuller, L. Covi, K. Hamaguchi and T. Yanagida (JHEP 0703:037, 2007)

G . Bertone, W. Buchmuller, L. Covi (JCAP11(2007)003)

D. Tran (Phys.Rev.Lett.100,061301 (2008) and arXiv:0804.4596)

Planck’08Barcelona20th May 2008

Alejandro Ibarra (DESY) Gravitino Dark Matter – p.1/33

IntroductionMany evidences of dark matter at different scales







The main features of any dark matter candidate are:

⋆ weakly interacting

⋆ cold (may be warm)

⋆ long lived (not necessarily stable)!

lifetime > age of the Universe (∼ 1017s)


Candidates for dark matterMany! Some interesting candidates are:

Massive SM neutrinos (now excluded)

Axions

Heavy sterile neutrinos




Axions


Neutralinos (requires R-parity conservation)

Gravitinos




Axions



Gravitinos

Axinos




Axions



Gravitinos

Axinos

Lightest Kaluza-Klein particles (B1, KK graviton), scalarsinglets, Q-balls, branons, WIMPzillas, mini-black holes,cryptons, monopoles...


Why the gravitino?


Gravitino dark matterThe gravitino is present in any theory with local supersymmetry. When thegravitino is the lightest supersymmetric particle, it constitutes a veryinteresting (and promising!) candidate for the dark matter of the Universe.

Gravitinos are thermally produced in the early Universe by QCDprocesses. For example:

+

ga

gb gc

Ggc

+

ga

gb gc

G

ga +

ga

gb gc

G

gb

ga

gb gc

G

Also produced by non-thermal processes (inflaton decay, NLSP decay)

The existence of relic gravitinos is unavoidable. Whether they constitutethe dark matter or not is just a quantitative question.


From M. Bolz

The interactions of the gravitino with the MSSM particles are fixed bythe symmetries



The relic abundance is calculable in terms of very few parameters

Ω3/2h2≃ 0.27

(TR

1010 GeV

) (100GeV

m3/2

) ( meg

1 TeV

)2

NICELY COMPATIBLE WITH LEPTOGENESIS!

(TR >∼

109GeV)



The relic abundance is calculable in terms of very few parameters

Ω3/2h2≃ 0.27

(TR

1010 GeV

) (100GeV

m3/2

) ( meg

1 TeV

)2

NICELY COMPATIBLE WITH LEPTOGENESIS!

(TR >∼

109GeV)

However, it is undetectable in dark matter searches (direct and indirect)This is a disadvantage rather than a problem.


The ultimate goal would be to construct a consistent thermal history ofthe Universe.

There seems to be a conflict between these three paradigms:

⋆ Supersymmetric dark matter

⋆ Big Bang Nucleosynthesis

⋆ Leptogenesis (TR >∼

109 GeV)

The extremely weak interactions of the gravitino can be veryproblematic in the early Universe


If R-parity is conserved, the NLSP can only decay into gravitinos andSM particles, with a decay rate suppressed by MP :

ΓNLSP ≃m5

NLSP

48πm23/2M

2P

=⇒ very long lifetimes.


If R-parity is conserved, the NLSP can only decay into gravitinos andSM particles, with a decay rate suppressed by MP :

ΓNLSP ≃m5

NLSP

48πm23/2M

2P

=⇒ very long lifetimes.

The leptogenesis constraint TR >∼

109 GeV requires for gravitino darkmatter m3/2 >∼ 5 GeV. Then,

τNLSP ≃ 2 days( m3/2

5 GeV

)2(

150GeV

mNLSP

)5

The NLSP is present during and after BBN. The decays couldjeopardize the abundances of primordial elements.


Summary of the implications of a high reheat temperature (TR >∼

109 GeV)for gravitino dark matter:

gravitino LSPSee talk by Kazunori Kohri

neutralino NLSP RH stau NLSP other candidates

?

HH

HH

HHj

? ? ?

χ01 → ψ3/2 hadrons Catalytic production

of 6LiHadrodissociation ofprimordial elements

stopLH sneutrinoRH sneutrino

Conflict with BBN Conflict with BBN


Summary of the implications of a high reheat temperature (TR >∼

109 GeV)for gravitino dark matter:

gravitino LSPSee talk by Kazunori Kohri

neutralino NLSP RH stau NLSP other candidates

?

HH

HH

HHj

? ? ?

χ01 → ψ3/2 hadrons Catalytic production

of 6LiHadrodissociation ofprimordial elements

stopLH sneutrinoRH sneutrino

Conflict with BBN Conflict with BBN

BBN is the Achilles’ heel of gravitino dark matter

Root of all the problems: the NLSP is very long lived.

Simple solution: get rid of the NLSP before BBN −→ R-parity violation


Gravitino DM with broken R-parity⋆ When R-parity is broken, the superpotential reads:

W = WRp + µi(HuLi) + 12λijk(LiLj)e

ck + λ′

ijk(QiLj)dck + λ

′′

ijk(ucidcjdck)

The coupling λijk induces the decay of the right-handed stau. For example,

eτR → µ ντ with lifetime:

τeτ ≃ 103s`

λ10−14

´−2 ` meτ100 GeV

´−1

Even with a tiny amount of R-parity violation (λ >∼

10−14)

the stau will decay before the time of BBN.


Gravitino DM with broken R-parity⋆ When R-parity is broken, the superpotential reads:

W = WRp + µi(HuLi) + 12λijk(LiLj)e

ck + λ′

ijk(QiLj)dck + λ

′′

ijk(ucidcjdck)

The coupling λijk induces the decay of the right-handed stau. For example,

eτR → µ ντ with lifetime:

τeτ ≃ 103s`

λ10−14

´−2 ` meτ100 GeV

´−1

Even with a tiny amount of R-parity violation (λ >∼

10−14)

the stau will decay before the time of BBN.

⋆ The lepton/baryon number violating couplings λ, λ′, λ′′ can erase thelepton/baryon asymmetry. The requirement that an existing baryon asymmetry is

not erased before the electroweak transition implies:Campbell, Davidson, Ellis, OliveFischler, Giudice, Leigh, PabanDreiner, Ross

λ, λ′ <∼ 10−7

Plenty of room! 10−14 <∼ λ, λ′ <∼ 10−7. In this range leptogenesis is unaffected.


⋆ Interestingly, even though the gravitino is no longer stable, it still constitutes aviable dark matter candidate. It decays for example ψ3/2 → νγ, with lifetime:

τ3/2 ∼ 1026s`

λ10−7

´−2“

m3/2

10 GeV

”−3

(Remember: age of the Universe ∼ 1017s)

Stable enough to constitute the dark matter of the Universe. Takayama, Yamaguchi



τ3/2 ∼ 1026s`

λ10−7

´−2“

m3/2

10 GeV

”−3



In summary: A scenario with the gravitino as LSP with a mass in the range

5-300 GeV, and a small amount of R-parity violation, 10−14 <∼ λ, λ′ <∼ 10−7,

provides a good candidate for dark matter and provides a consistent thermalhistory of the Universe (allows leptogenesis and successful BBN).



τ3/2 ∼ 1026s`

λ10−7

´−2“

m3/2

10 GeV

”−3



In summary: A scenario with the gravitino as LSP with a mass in the range

5-300 GeV, and a small amount of R-parity violation, 10−14 <∼ λ, λ′ <∼ 10−7,

provides a good candidate for dark matter and provides a consistent thermalhistory of the Universe (allows leptogenesis and successful BBN).

The gravitino is still undetectable in direct dark matter searches. But the R-parity

violating decay of the gravitino into photons, positrons, antiprotons and neutrinosopens the possibility of the indirect detection.


DATA!Gamma rays

Gravitinos with a mass of several GeV decay producing photons in theGeV range −→ gamma rays.

EGRET measured gamma rays with energies between 30 MeV and 100 GeV.

The first analysis from Sreekumar et al. gave an extragalactic fluxdescribed by the power law

E2 dJdE = 1.37 × 10−6

(E

1 GeV

)−0.1

(cm2str s)−1GeV, for 50 MeV<∼ E <∼ 10 GeV

Close to the prediction for the γ- ray flux from gravitino decay when λ ≃ 10−7!!


The more recent analysis by Strong, Moskalenko and Reimer (’04) shows a power law

behaviour between 50 MeV and 2 GeV, but a clear excess between 2 GeV and 50GeV!!

10-1 100 101 102 103 104 105 106 107 108 109

Photon Energy (keV)

0.1

1.0

10.0

100.0

E2 d

J/dE

(ke

V2 /(

cm2 -s

-keV

-sr)

HEAO A2,A4(LED)

ASCA HEAO-A4 (MED)

COMPTEL

v

EGRET

The photon flux from the decay of gravitinos may be hidden in this excess.

Still, many open questions:

⋆ Extraction of the signal from the galactic foreground

⋆ Is the signal isotropic/anisotropic?

⋆ Precise shape of the energy spectrum?

GLAST will clarify these issues.


Positrons

The HEAT collaboration has reported an excess of positrons at energies >∼ 7 GeV.

Same energies as the EGRET excess!

0.01

0.1

1 10 100 1000

Pos

itron

frac

tion

e+/(

e++

e− )

T [GeV]

Background only

HEAT 94/95/00


Positrons

The HEAT collaboration has reported an excess of positrons at energies >∼ 7 GeV.

Same energies as the EGRET excess!

0.01

0.1

1 10 100 1000

Pos

itron

frac

tion

e+/(

e++

e− )

T [GeV]

Background only

HEAT 94/95/00AMS-01 98

CAPRICE 94MASS 91

PAMELA will provide an accurate measurement of the positron fraction.


Antiprotons

10-3

10-2

10-1

10-1

1 10

Kinetic Energy (GeV)

p– fl

ux (

m-2

sr-1

sec-1

GeV

-1)

1

1

Bottino2

2

Bergstrom3

3

Biebar4

4Mitsui λ(R,β)

55

Mitsui λ(R)

BESS(95+97)BESS(93)IMAXCAPRICE

Cosmic Ray P–

The antiproton flux is consistent with the astrophysical mod els


Gravitino decay channelsψ3/2

γ

γν

Light gravitino m3/2 <∼MW

ψ3/2 → γν

Γ(ψ3/2 → γν) =1

32π|Uγν |2

m33/2

M2P



γ

γν

ψ3/2

Z

Z

ν

ψ3/2

W

W

l


ψ3/2 → γν

Γ(ψ3/2 → γν) =1

32π|Uγν |2

m33/2

M2P

“not-so-light” gravitino 100 GeV <∼m3/2 <∼ 300 GeV

ψ3/2 → Z0ν

Γ(ψ3/2 → Z0ν) =1

32π|UZν |

2m33/2

M2P

f

M2Z

m23/2

!

ψ3/2 →W±ℓ∓

Γ(ψ3/2 →W±ℓ∓) =2

32π|UWℓ|

2m3

3/2

M2P

f

M2W

m23/2

!



γ

γν

ψ3/2

Z

Z

ν

ψ3/2

W

W

l

γ’s

γ’s


ψ3/2 → γν

Γ(ψ3/2 → γν) =1

32π|Uγν |2

m33/2

M2P

“not-so-light” gravitino 100 GeV <∼m3/2 <∼ 300 GeV

ψ3/2 → Z0ν

Γ(ψ3/2 → Z0ν) =1

32π|UZν |

2m33/2

M2P

f

M2Z

m23/2

!

ψ3/2 →W±ℓ∓

Γ(ψ3/2 →W±ℓ∓) =2

32π|UWℓ|

2m3

3/2

M2P

f

M2W

m23/2

!


Gamma-ray flux from gravitino decayThe energy spectrum of photons from gravitino decay is

dNγ

dE≃ BR(ψ3/2 → γν) δ

“

E −m3/2

2

”

+ BR(ψ3/2 →Wℓ)dNW

γ

dE+ BR(ψ3/2 → Z0ν)

dNZγ

dE



dNγ


“

E −m3/2

2

”


γ

dE+ BR(ψ3/2 → Z0ν)

dNZγ

dE

The branching ratios are determined by the relative size of the mixing parameters

|Ueγν | ≃»(M2 −M1)sW cWM1c2W +M2s2W

–|U eZν |

|UfWℓ| ≃√

2cWM1s

2W +M2c

2W

M2|U eZν |

Assuming gaugino mass universality at the Grand Unified Scale,

|Ueγν | : |U eZν | : |UfWℓ| ≃ 1 : 3.2 : 3.5

m3/2 BR(ψ3/2 → γν) BR(ψ3/2 → Wℓ) BR(ψ3/2 → Z0ν)

10 GeV 1 0 0

85 GeV 0.66 0.34 0

100 GeV 0.16 0.76 0.08

150 GeV 0.05 0.71 0.24

250 GeV 0.03 0.69 0.28



dNγ


“

E −m3/2

2

”


γ

dE+ BR(ψ3/2 → Z0ν)

dNZγ

dE

0.01 0.1 1 10 100E (GeV)

0.01

0.1

1

10

E2 dN

/dE

m3/2

=10 GeV

γ

0.01 0.1 1 10 100E (GeV)

0.01

0.1

1

10

E2 d

N/d

E

m3/2

=150 GeV

W

Zγ


Gamma ray spectrumIf gravitinos decay, we expect a diffuse background of gamma rays withtwo different sources.

The decay at cosmological distances gives rise to a perfectly isotropic

extragalactic diffuse gamma-ray flux.The decay of the gravitinos in the Milky Way halo gives rise to an anisotropic γray flux

The precise value of the flux depends on the halo profile. Averaging over allsky, one finds typically Dγ/Cγ ∼ O(1) −→ the halo contribution dominates


Gamma ray spectrumIf gravitinos decay, we expect a diffuse background of gamma rays withtwo different sources.

The decay at cosmological distances gives rise to a perfectly isotropic

extragalactic diffuse gamma-ray flux.The decay of the gravitinos in the Milky Way halo gives rise to an anisotropic γray flux

The precise value of the flux depends on the halo profile. Averaging over allsky, one finds typically Dγ/Cγ ∼ O(1) −→ the halo contribution dominates


γ ray spectrum for light gravitinos m3/2 <∼MW

Bertone, Buchmüller, Covi, AI

10-7

10-6

0.1 1 10

E2 d

J/d

E (

GeV

(cm

2 s

str

)-1)

E (GeV)

energy resolutionof EGRET: 15%

extgal

halo

m3/2 = 10 GeV, τ3/2 = 1027 s

The energy spectrum from gravitino decay is just a delta function: dNγ

dE= δ

“

E −m3/2

2

”


γ ray spectrum for “not-so-light” gravitinos 100 GeV <∼m3/2 <∼ 300 GeV

The total flux receives contribution from different sources.

AI, Tran

|Ueγν | : |U eZν| : |UfWℓ

| ≃ 1 : 3.2 : 3.5

10-7

10-6

0.1 1 10 100

E2 d

J/dE

[GeV

cm

-2 s

-1 s

r-1]

E [GeV]

Gamma-ray spectrum for m3/2 = 150 GeV




AI, Tran


| ≃ 1 : 3.2 : 3.5

10-7

10-6

0.1 1 10 100

E2 d

J/dE

[GeV

cm

-2 s

-1 s

r-1]

E [GeV]


W -halo

W -extgal




AI, Tran


| ≃ 1 : 3.2 : 3.5

10-7

10-6

0.1 1 10 100

E2 d

J/dE

[GeV

cm

-2 s

-1 s

r-1]

E [GeV]


Z-halo

Z-extgal




AI, Tran


| ≃ 1 : 3.2 : 3.5

10-7

10-6

0.1 1 10 100

E2 d

J/dE

[GeV

cm

-2 s

-1 s

r-1]

E [GeV]


γ-halo

γ-extgal




AI, Tran


| ≃ 1 : 3.2 : 3.5

10-7

10-6

0.1 1 10 100

E2 d

J/dE

[GeV

cm

-2 s

-1 s

r-1]

E [GeV]


background




AI, Tran


| ≃ 1 : 3.2 : 3.5

10-7

10-6

0.1 1 10 100

E2 d

J/dE

[GeV

cm

-2 s

-1 s

r-1]

E [GeV]


total

τ3/2 = 1.3 × 1026s =⇒ |Ueγν | ≃ 2 × 10−10

See also talk by Koji Ishiwata


Positron fractionThe fragmentation of the W and Z bosons produces positrons.

The positrons travel under the influence of the tangled magnetic field ofthe galaxy and lose energy −→ Complicated propagation equation

The computation of the positron fraction requires inputs from particlephysics and from astrophysics. The EGRET anomaly fixes m3/2 ≃ 150

GeV and τ3/2 ≃ 1.3 × 1026s −→ no uncertainties from particle physics.However, there are many uncertainties from astrophysics: halo model?propagation model?


0.01

0.1

1 10 100 1000

Pos

itron

frac

tion

e+/(

e++

e− )

T [GeV]

Background only

HEAT 94/95/00AMS-01 98

CAPRICE 94MASS 91


Fix M2 propagation model. Different halo models

AI, Tran

0.01

0.1

1 10 100 1000

Pos

itron

frac

tion

e+/(

e++

e− )

T [GeV]

Background only

Isothermal

NFW

Moore et al.

HEAT 94/95/00AMS-01 98

CAPRICE 94MASS 91


Fix M2 propagation model. Different halo models

AI, Tran

0.01

0.1

1 10 100 1000

Pos

itron

frac

tion

e+/(

e++

e− )

T [GeV]

Isothermal

Moore et al.

NFW

Background only

HEAT 94/95/00AMS-01 98

CAPRICE 94MASS 91

The scenario of decaying gravitino dark matter predicts a bump

in the right energy range, independently of the halo model

See also talk by Koji Ishiwata


AI, Tran

0.01

0.1

1 10 100 1000

Pos

itron

frac

tion

e+/(

e++

e− )

T [GeV]

M1, MED

M2

Background only

HEAT 94/95/00AMS-01 98

CAPRICE 94MASS 91

Fix NFW halo model. Different propagation model

The scenario of decaying gravitino dark matter predicts a bump

in the right energy range, independently of the propagation model


An intriguing coincidence...The anomalies in the extragalactic gamma-ray flux and in the positronfraction can be simultaneously explained in this framework.

10-7

10-6

0.1 1 10 100

E2 d

J/dE

[GeV

cm

-2 s

-1 s

r-1]

E [GeV]


0.01

0.1

1 10 100 1000

Pos

itron

frac

tion

e+/(

e++

e− )

T [GeV]

Isothermal

Moore et al.

NFW

Background only

HEAT 94/95/00AMS-01 98

CAPRICE 94MASS 91

⋆ Recall that the scenario of decaying gravitino dark matter was initially proposednot to explain these anomalies, but to reconcile the paradigms of SUSY dark

matter, leptogenesis and BBN!⋆ This result also applies to any scenario of decaying dark matter with lifetime

∼ 1026 s which decays predominantly into Z0 or W± with momentum ∼ 50 GeV.Alejandro Ibarra (DESY) Gravitino Dark Matter – p.24/33

Antiproton fluxPropagation mechanism more complicated than for the positrons. Weneglect in our analysis reacceleration and tertiary contributions.

The predicted flux suffers from huge uncertainties due to degeneraciesin the determination of the propagation parameters.


Antiproton fluxPropagation mechanism more complicated than for the positrons. Weneglect in our analysis reacceleration and tertiary contributions.

The predicted flux suffers from huge uncertainties due to degeneraciesin the determination of the propagation parameters.

m3/2 ≃ 150 GeV and τ3/2 ≃ 1.3 × 1026s. NFW halo model

AI, Tran

10-4

10-3

10-2

10-1

100

101

0.1 1 10 100

Ant

ipro

ton

flux

[GeV

-1 m

-2 s

-1 s

r-1]

T [GeV]

MIN

MED

MAX

Φ = 500 MV

BESS 95+97BESS 95IMAX 92

CAPRICE 94CAPRICE 98

The MAX and MED model are probably excluded (despite the uncertainties)


The MIN case:m3/2 ≃ 150 GeV and τ3/2 ≃ 1.3 × 1026s. NFW halo model

AI, Tran

10-3

10-2

10-1

100

0.1 1 10

Ant

ipro

ton

flux

[GeV

-1 m

-2 s

-1 s

r-1]

T [GeV]

Signal

BackgroundTotal

Φ = 500 MV

BESS 95+97BESS 95IMAX 92

CAPRICE 94CAPRICE 98

Together with the background, the total flux is a factor ∼ 2 too large

In the view of all the uncertainties in the propagation, it might bepremature to rule out the scenario of decaying gravitino dark matter onthe basis of this small excess.


Wish listWhat will make me believe in decaying gravitino dark matter

1– No positive signal from direct dark matter search experiments.




2– GLAST confirms the EGRET anomaly in the extragalactic gamma rayflux.





3– The angular distribution of gamma raysat 1 GeV <

∼E <

∼100 GeV is consistent with

decaying gravitino dark matter.





3– The angular distribution of gamma raysat 1 GeV <

∼E <

∼100 GeV is consistent with

decaying gravitino dark matter.

4– The energy spectrum of gamma rays isconsistent with decaying gravitino dark matter−→ m

(γ)3/2, τ (γ)

3/2.10-7

10-6

0.1 1 10 100

E2 d

J/dE

[GeV

cm

-2 s

-1 s

r-1]

E [GeV]



5– PAMELA confirms the anomaly in the positron fraction.



6– The positron fraction as a function of thepositron energy is consistent with decaying

gravitino dark matter. −→ m(e+)3/2 , τ (e+)

3/2

0.01

0.1

1 10 100 1000

Pos

itron

frac

tion

e+/(

e++

e− )

T [GeV]

Isothermal

Moore et al.

NFW

Background only

HEAT 94/95/00AMS-01 98

CAPRICE 94MASS 91



6– The positron fraction as a function of thepositron energy is consistent with decaying

gravitino dark matter. −→ m(e+)3/2 , τ (e+)

3/2

0.01

0.1

1 10 100 1000

Pos

itron

frac

tion

e+/(

e++

e− )

T [GeV]

Isothermal

Moore et al.

NFW

Background only

HEAT 94/95/00AMS-01 98

CAPRICE 94MASS 91

7– m(γ)3/2 ≃ m

(e+)3/2

τ(γ)3/2 ≃ τ

(e+)3/2 .


8– Low energy supersymmetry is discovered at the LHC.


8– Low energy supersymmetry is discovered at the LHC.9– If the stau is the NLSP, the main decay is τR → τ νµ, µ ντ (through λLLec)

cτlepτ ∼ 15 cm

(mτ

400GeV

)−1 (

λ323

10−8

)−2

Long heavily ionizing charged track followed by a muon track or a jet.A very spectacular signal at colliders!The determination of the R-parity violating coupling would lead to arelation of the gravitino lifetime and the gravitino mass:

τ3/2 ∼ 1026s( m3/2

150GeV

)−3 (

meτ

400GeV

) (τeτ

10−8s

)


Gamma rays as a thermometer of the Universe?If the scenario of decaying dark matter turns out to be correct, there mightbe a chance of measuring the temperature of the early Universe.

10-7

10-6

0.1 1 10 100

E2 d

J/dE

[GeV

cm

-2 s

-1 s

r-1]

E [GeV]


m3/2/2

The thermal relic abundance of gravitinos is given by

Ω3/2h2≃ 0.27

(TR

1010 GeV

)(100 GeV

m3/2

) ( meg

1 TeV

)2



10-7

10-6

0.1 1 10 100

E2 d

J/dE

[GeV

cm

-2 s

-1 s

r-1]

E [GeV]


m3/2/2

If there is only thermal production

TR ≃ 2 × 1010GeV

(Ω3/2h

2

0.1

) ( m3/2

150GeV

) ( meg

500 GeV

)−2



10-7

10-6

0.1 1 10 100

E2 d

J/dE

[GeV

cm

-2 s

-1 s

r-1]

E [GeV]


m3/2/2

In general

TR <∼

2 × 1010GeV

(Ω3/2h

2

0.1

)( m3/2

150GeV

)( meg

500 GeV

)−2


ConclusionsGravitino dark matter is a very interesting scenario.

Gravitino dark matter with R-parity violation is even more interesting.The potential conflict of BBN and leptogenesis is automatically solved,while preserving the nice features of the gravitino as dark matter. Also,indirect detection might be possible!

The anomalies observed in the extragalactic gamma-ray flux (EGRET)and the positron fraction (HEAT) can be simultaneously explained bythe decay of the gravitino.

Future experiments (GLAST, PAMELA, LHC, XENON, CDMS...) willprovide in the near future indications for this scenario or evidencesagainst it.


Isotropy of the signal

energy (MeV) 10 210 310 410 510

MeV

-1

s-1

sr

-2. i

nten

sity

, cm

2E

-310

V Strong, Moskalenko, Reimer


l b Intensity 0.1-10 GeV Description

0–360 < −10, > +10 11.10 ± 0.12 N+S hemispheres

0–360 < −10 11.70 ± 0.15 N hemisphere

0–360 > +10 9.28 ± 0.21 S hemisphere

270–90 < −10, > +10 11.90 ± 0.17 Inner Galaxy N+S

90–270 < −10, > +10 9.75 ± 0.17 Outer Galaxy N+S

0–180 < −10, > +10 10.80 ± 0.17 Positive longitudes N+S

180–360 < −10, > +10 11.60 ± 0.16 Negative longitude N+S

270–90 > +10 13.00 ± 0.22 Inner Galaxy N

270–90 < −10 9.14 ± 0.32 Inner Galaxy S

90–270 > +10 10.60 ± 0.22 Outer Galaxy N

90–270 < −10 8.18 ± 0.34 Outer Galaxy S


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Indirect signatures of Gravitino Dark Matter