Fitting the Fermi-LAT GeV excess: on the importance of the - - PowerPoint PPT Presentation

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Fitting the Fermi-LAT GeV excess: on the importance of the - - PowerPoint PPT Presentation

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The GC gamma-ray excess Diffusion of electrons and positrons from DM Fitting the Fermi-LAT GeV excess with the leptonic channels Fitting the Fermi-LAT GeV excess: on the importance of the propagation of electrons from dark matter Thomas

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The GC gamma-ray excess Diffusion of electrons and positrons from DM Fitting the Fermi-LAT GeV excess with the leptonic channels

Fitting the Fermi-LAT GeV excess: on the importance of the propagation of electrons from dark matter

Thomas Lacroix (IAP)

Supervisors: Joseph Silk (IAP) & Céline Bœhm (IPPP)

FFP 2014 15 July 2014

Thomas Lacroix Fermi-LAT GeV excess & DM: importance of electron propagation

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The GC gamma-ray excess Diffusion of electrons and positrons from DM Fitting the Fermi-LAT GeV excess with the leptonic channels Map of the residual Fits with prompt emission only Diffusion must be taken into account

GC excess in γ-rays between 0.1 and 10 GeV in Fermi data Fermi-LAT collaboration 2009 Hooper & Linden 2011 Gordon & Macias 2013 Abazajian et al. 2014 Daylan et al. 2014 Within region smaller than 10◦ × 10◦ around the GC Spherically symmetric Obtained by subtracting known sources and using Fermi models for diffuse emission Background modelling debated Variety of possible astrophysical explanations for the excess, but DM interpretation possible

Thomas Lacroix Fermi-LAT GeV excess & DM: importance of electron propagation

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The GC gamma-ray excess Diffusion of electrons and positrons from DM Fitting the Fermi-LAT GeV excess with the leptonic channels Map of the residual Fits with prompt emission only Diffusion must be taken into account

Gordon & Macias 2013

Thomas Lacroix Fermi-LAT GeV excess & DM: importance of electron propagation

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The GC gamma-ray excess Diffusion of electrons and positrons from DM Fitting the Fermi-LAT GeV excess with the leptonic channels Map of the residual Fits with prompt emission only Diffusion must be taken into account

Best fit a priori for prompt emission only for b¯ b ρ ∝ r−1.2, σv ∼ 2 × 10−26 cm3 s−1

10

  • 1

10 10

1

Eγ (GeV) 10

  • 7

E2

γ dn/dEγ (GeV cm−2 s−1 )

mDM =30 GeV, b

prompt only

Data points from Gordon & Macias 2013

Thomas Lacroix Fermi-LAT GeV excess & DM: importance of electron propagation

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The GC gamma-ray excess Diffusion of electrons and positrons from DM Fitting the Fermi-LAT GeV excess with the leptonic channels Map of the residual Fits with prompt emission only Diffusion must be taken into account

Relatively good fit with mixture of leptons and b quarks

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  • 1

10 10

1

Eγ (GeV) 10

  • 7

E2

γ dn/dEγ (GeV cm−2 s−1 )

mDM =10 GeV, l +b

prompt only

Thomas Lacroix Fermi-LAT GeV excess & DM: importance of electron propagation

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The GC gamma-ray excess Diffusion of electrons and positrons from DM Fitting the Fermi-LAT GeV excess with the leptonic channels Map of the residual Fits with prompt emission only Diffusion must be taken into account

But we’re nowhere near a priori with leptons only...

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10 10

1

Eγ (GeV) 10

  • 7

E2

γ dn/dEγ (GeV cm−2 s−1 )

mDM =10 GeV, leptons

prompt only

Thomas Lacroix Fermi-LAT GeV excess & DM: importance of electron propagation

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The GC gamma-ray excess Diffusion of electrons and positrons from DM Fitting the Fermi-LAT GeV excess with the leptonic channels Map of the residual Fits with prompt emission only Diffusion must be taken into account

But this is for prompt emission only Electrons also by-products of DM annihilations Inverse Compton and Bremsstrahlung emissions from e+ and e− produced in DM annihilations shouldn’t be neglected (Ackermann et al. 2013, Cirelli et al. 2013) − → corrections Diffusion must be included to model these emissions = ⇒ totally changes the interpretation of the data!

Thomas Lacroix Fermi-LAT GeV excess & DM: importance of electron propagation

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The GC gamma-ray excess Diffusion of electrons and positrons from DM Fitting the Fermi-LAT GeV excess with the leptonic channels Semi-analytical method Resolution: halo function

Rgal = 20 kpc 2L

Thomas Lacroix Fermi-LAT GeV excess & DM: importance of electron propagation

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The GC gamma-ray excess Diffusion of electrons and positrons from DM Fitting the Fermi-LAT GeV excess with the leptonic channels Semi-analytical method Resolution: halo function

Diffusion-loss equation K∇2ψ + ∂ ∂E(btotψ) + q = 0 (1) ψ( x, E) cosmic-ray spectrum after propagation K diffusion coefficient: K(E) = K0 E E0 δ with E0 = 1 GeV btot(E) total energy loss rate (IC, synchrotron, Bremsstrahlung...) q( x, E) source term ∝ ρ2 for DM annihilations

Thomas Lacroix Fermi-LAT GeV excess & DM: importance of electron propagation

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The GC gamma-ray excess Diffusion of electrons and positrons from DM Fitting the Fermi-LAT GeV excess with the leptonic channels Semi-analytical method Resolution: halo function

Spectrum of e− and e+ after propagation ψ( x, E) = κ btot(E)

∞

E

˜ I

  • x(λD(E, ES)) dn

dE(ES) dES (2) κ normalization factor ∝ annihilation cross section btot(E) total energy loss rate ˜ I

  • x halo function −

→ fundamental quantity for diffusion λD(E, ES) diffusion length dn dE injection spectrum

Thomas Lacroix Fermi-LAT GeV excess & DM: importance of electron propagation

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The GC gamma-ray excess Diffusion of electrons and positrons from DM Fitting the Fermi-LAT GeV excess with the leptonic channels Semi-analytical method Resolution: halo function

Computing ˜ I with Green’s functions ˜ I

  • x(λD(E, ES)) =
  • DZd
  • xS G(

x, E; xS, ES) ρ( xS) ρ⊙ 2 (3) G( x, E; xS, ES) ≡ G( x, xS, λD(E, ES)) Green’s function Trick for steepness of ρ: logarithmic steps G becomes infinitely peaked for λD → 0 (i.e. E → ES) = ⇒ trick: defining different regimes for G (TL, C. Bœhm, J. Silk, arXiv:1311.0139)

Thomas Lacroix Fermi-LAT GeV excess & DM: importance of electron propagation

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The GC gamma-ray excess Diffusion of electrons and positrons from DM Fitting the Fermi-LAT GeV excess with the leptonic channels Contributions from diffusion Total spectrum Morphology

All contributions of the same order of magnitude

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1

Eγ (GeV) 10

  • 7

E2

γ dn/dEγ (GeV cm−2 s−1 )

mDM =10 GeV, B =3 µG, ngas =3 cm−3 , leptons

prompt bremsstrahlung IC prompt +IC +brem

TL, C. Bœhm, J. Silk, arXiv:1403.1987

Thomas Lacroix Fermi-LAT GeV excess & DM: importance of electron propagation

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The GC gamma-ray excess Diffusion of electrons and positrons from DM Fitting the Fermi-LAT GeV excess with the leptonic channels Contributions from diffusion Total spectrum Morphology

Best fit for democratic annihilation into leptons! σv = 0.86 × 10−26 cm3 s−1

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  • 1

10 10

1

Eγ (GeV) 10

  • 7

E2

γ dn/dEγ (GeV cm−2 s−1 )

mDM =10 GeV, B =3 µG, ngas =3 cm−3 , leptons

prompt only prompt +IC +brem

TL, C. Bœhm, J. Silk, arXiv:1403.1987

Thomas Lacroix Fermi-LAT GeV excess & DM: importance of electron propagation

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The GC gamma-ray excess Diffusion of electrons and positrons from DM Fitting the Fermi-LAT GeV excess with the leptonic channels Contributions from diffusion Total spectrum Morphology

Fit for b¯ b only slightly affected

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  • 1

10 10

1

Eγ (GeV) 10

  • 7

E2

γ dn/dEγ (GeV cm−2 s−1 )

mDM =30 GeV, B =3 µG, ngas =3 cm−3 , b

prompt only prompt +IC +brem

TL, C. Bœhm, J. Silk, arXiv:1403.1987

Thomas Lacroix Fermi-LAT GeV excess & DM: importance of electron propagation

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The GC gamma-ray excess Diffusion of electrons and positrons from DM Fitting the Fermi-LAT GeV excess with the leptonic channels Contributions from diffusion Total spectrum Morphology

Very good fit with only muons (2/3) and taus (cf. AMS limits on e+e−, Bergström et al. 2013, Ibarra et al. 2014, Bringmann et al. 2014)

10

  • 1

10 10

1

Eγ (GeV) 10

  • 7

E2

γ dn/dEγ (GeV cm−2 s−1 )

mDM =10 GeV, B =3 µG, ngas =3 cm−3 , 2/3mu +1/3tau

prompt only prompt +IC +brem

Thomas Lacroix Fermi-LAT GeV excess & DM: importance of electron propagation

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The GC gamma-ray excess Diffusion of electrons and positrons from DM Fitting the Fermi-LAT GeV excess with the leptonic channels Contributions from diffusion Total spectrum Morphology

Less good fit with BR into µ+µ− of 0.25 (Bringmann et al. 2014)

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  • 1

10 10

1

Eγ (GeV) 10

  • 7

E2

γ dn/dEγ (GeV cm−2 s−1 )

mDM =10 GeV, B =3 µG, ngas =3 cm−3 , 1/4mu +3/4tau

prompt only prompt +IC +brem

Thomas Lacroix Fermi-LAT GeV excess & DM: importance of electron propagation

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The GC gamma-ray excess Diffusion of electrons and positrons from DM Fitting the Fermi-LAT GeV excess with the leptonic channels Contributions from diffusion Total spectrum Morphology

At low energy possible tension between signal from diffusion and morphology in the literature between 0.1◦ and 1◦

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  • 2

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γ dn dEγdΩ (GeV cm−2 s−1 sr−1 )

mDM =10 GeV, B =3 µG, ngas =3 cm−3 , Eγ =0.1 GeV

prompt prompt +IC +brem

TL, C. Bœhm, J. Silk, arXiv:1403.1987

Thomas Lacroix Fermi-LAT GeV excess & DM: importance of electron propagation

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The GC gamma-ray excess Diffusion of electrons and positrons from DM Fitting the Fermi-LAT GeV excess with the leptonic channels Contributions from diffusion Total spectrum Morphology

Morphology closer to the literature at 1 GeV

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b (deg) 10

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  • 3

10

  • 2

E2

γ dn dEγdΩ (GeV cm−2 s−1 sr−1 )

mDM =10 GeV, B =3 µG, ngas =3 cm−3 , Eγ =1.0 GeV

prompt prompt +IC +brem

TL, C. Bœhm, J. Silk, arXiv:1403.1987

Thomas Lacroix Fermi-LAT GeV excess & DM: importance of electron propagation

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The GC gamma-ray excess Diffusion of electrons and positrons from DM Fitting the Fermi-LAT GeV excess with the leptonic channels

Conclusion Strong case for DM b¯ b and prompt emission simplest set-up a priori But very important to include all relevant emission processes and diffusion b¯ b and 30 GeV is not the only possibility: DM can be 10 GeV and annihilate into leptons Including emissions of diffused electrons drastically changes interpretation of the excess in terms of DM Morphology below ∼ 1◦ at low energies can help to discriminate between leptonic and b¯ b channels

Thomas Lacroix Fermi-LAT GeV excess & DM: importance of electron propagation

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The GC gamma-ray excess Diffusion of electrons and positrons from DM Fitting the Fermi-LAT GeV excess with the leptonic channels

Thank you for your attention!

Thomas Lacroix Fermi-LAT GeV excess & DM: importance of electron propagation