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
The GC gamma-ray excess Map of the residual Diffusion of electrons and positrons from DM Fits with prompt emission only Fitting the Fermi-LAT GeV excess with the leptonic channels 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
The GC gamma-ray excess Map of the residual Diffusion of electrons and positrons from DM Fits with prompt emission only Fitting the Fermi-LAT GeV excess with the leptonic channels Diffusion must be taken into account Gordon & Macias 2013 Thomas Lacroix Fermi-LAT GeV excess & DM: importance of electron propagation
The GC gamma-ray excess Map of the residual Diffusion of electrons and positrons from DM Fits with prompt emission only Fitting the Fermi-LAT GeV excess with the leptonic channels Diffusion must be taken into account Best fit a priori for prompt emission only for b ¯ b ρ ∝ r − 1.2 , � σ v � ∼ 2 × 10 − 26 cm 3 s − 1 m DM =30 GeV , b prompt only γ dn / dE γ (GeV cm − 2 s − 1 ) -7 10 E 2 -1 0 1 10 10 10 E γ (GeV) Data points from Gordon & Macias 2013 Thomas Lacroix Fermi-LAT GeV excess & DM: importance of electron propagation
The GC gamma-ray excess Map of the residual Diffusion of electrons and positrons from DM Fits with prompt emission only Fitting the Fermi-LAT GeV excess with the leptonic channels Diffusion must be taken into account Relatively good fit with mixture of leptons and b quarks m DM =10 GeV , l +b prompt only γ dn / dE γ (GeV cm − 2 s − 1 ) -7 10 E 2 -1 1 0 10 10 10 E γ (GeV) Thomas Lacroix Fermi-LAT GeV excess & DM: importance of electron propagation
The GC gamma-ray excess Map of the residual Diffusion of electrons and positrons from DM Fits with prompt emission only Fitting the Fermi-LAT GeV excess with the leptonic channels Diffusion must be taken into account But we’re nowhere near a priori with leptons only... m DM =10 GeV , leptons prompt only γ dn / dE γ (GeV cm − 2 s − 1 ) -7 10 E 2 -1 0 1 10 10 10 E γ (GeV) Thomas Lacroix Fermi-LAT GeV excess & DM: importance of electron propagation
The GC gamma-ray excess Map of the residual Diffusion of electrons and positrons from DM Fits with prompt emission only Fitting the Fermi-LAT GeV excess with the leptonic channels 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
The GC gamma-ray excess Semi-analytical method Diffusion of electrons and positrons from DM Resolution: halo function Fitting the Fermi-LAT GeV excess with the leptonic channels 2 L R gal = 20 kpc Thomas Lacroix Fermi-LAT GeV excess & DM: importance of electron propagation
The GC gamma-ray excess Semi-analytical method Diffusion of electrons and positrons from DM Resolution: halo function Fitting the Fermi-LAT GeV excess with the leptonic channels Diffusion-loss equation K ∇ 2 ψ + ∂ ∂ E ( b tot ψ ) + q = 0 (1) ψ ( � x , E ) cosmic-ray spectrum after propagation � E � δ K diffusion coefficient: K ( E ) = K 0 with E 0 = 1 GeV E 0 b tot ( E ) total energy loss rate (IC, synchrotron, Bremsstrahlung...) x , E ) source term ∝ ρ 2 for DM annihilations q ( � Thomas Lacroix Fermi-LAT GeV excess & DM: importance of electron propagation
The GC gamma-ray excess Semi-analytical method Diffusion of electrons and positrons from DM Resolution: halo function Fitting the Fermi-LAT GeV excess with the leptonic channels Spectrum of e − and e + after propagation � ∞ κ x ( λ D ( E , E S )) d n ˜ ψ ( � x , E ) = I d E ( E S ) d E S (2) � b tot ( E ) E κ normalization factor ∝ annihilation cross section b tot ( E ) total energy loss rate ˜ x halo function − → fundamental quantity for diffusion I � λ D ( E , E S ) diffusion length d n d E injection spectrum Thomas Lacroix Fermi-LAT GeV excess & DM: importance of electron propagation
The GC gamma-ray excess Semi-analytical method Diffusion of electrons and positrons from DM Resolution: halo function Fitting the Fermi-LAT GeV excess with the leptonic channels Computing ˜ I with Green’s functions � 2 � ρ ( � x S ) � ˜ I x ( λ D ( E , E S )) = DZ d � x S G ( � x , E ; � x S , E S ) (3) � ρ ⊙ G ( � x , E ; � x S , E S ) ≡ G ( � x , � x S , λ D ( E , E S )) Green’s function Trick for steepness of ρ : logarithmic steps G becomes infinitely peaked for λ D → 0 (i.e. E → E S ) = ⇒ 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
The GC gamma-ray excess Contributions from diffusion Diffusion of electrons and positrons from DM Total spectrum Fitting the Fermi-LAT GeV excess with the leptonic channels Morphology All contributions of the same order of magnitude m DM =10 GeV , B =3 µ G , n gas =3 cm − 3 , leptons prompt bremsstrahlung IC prompt +IC +brem γ dn / dE γ (GeV cm − 2 s − 1 ) -7 10 E 2 -1 0 1 10 10 10 E γ (GeV) TL, C. Bœhm, J. Silk, arXiv:1403.1987 Thomas Lacroix Fermi-LAT GeV excess & DM: importance of electron propagation
The GC gamma-ray excess Contributions from diffusion Diffusion of electrons and positrons from DM Total spectrum Fitting the Fermi-LAT GeV excess with the leptonic channels Morphology Best fit for democratic annihilation into leptons! � σ v � = 0.86 × 10 − 26 cm 3 s − 1 m DM =10 GeV , B =3 µ G , n gas =3 cm − 3 , leptons prompt only prompt +IC +brem γ dn / dE γ (GeV cm − 2 s − 1 ) -7 10 E 2 -1 0 1 10 10 10 E γ (GeV) TL, C. Bœhm, J. Silk, arXiv:1403.1987 Thomas Lacroix Fermi-LAT GeV excess & DM: importance of electron propagation
The GC gamma-ray excess Contributions from diffusion Diffusion of electrons and positrons from DM Total spectrum Fitting the Fermi-LAT GeV excess with the leptonic channels Morphology Fit for b ¯ b only slightly affected m DM =30 GeV , B =3 µ G , n gas =3 cm − 3 , b prompt only prompt +IC +brem γ dn / dE γ (GeV cm − 2 s − 1 ) -7 10 E 2 -1 0 1 10 10 10 E γ (GeV) TL, C. Bœhm, J. Silk, arXiv:1403.1987 Thomas Lacroix Fermi-LAT GeV excess & DM: importance of electron propagation
The GC gamma-ray excess Contributions from diffusion Diffusion of electrons and positrons from DM Total spectrum Fitting the Fermi-LAT GeV excess with the leptonic channels 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) m DM =10 GeV , B =3 µ G , n gas =3 cm − 3 , 2 / 3mu +1 / 3tau prompt only prompt +IC +brem γ dn / dE γ (GeV cm − 2 s − 1 ) -7 10 E 2 -1 0 1 10 10 10 E γ (GeV) Thomas Lacroix Fermi-LAT GeV excess & DM: importance of electron propagation
The GC gamma-ray excess Contributions from diffusion Diffusion of electrons and positrons from DM Total spectrum Fitting the Fermi-LAT GeV excess with the leptonic channels Morphology Less good fit with BR into µ + µ − of 0.25 (Bringmann et al. 2014) m DM =10 GeV , B =3 µ G , n gas =3 cm − 3 , 1 / 4mu +3 / 4tau prompt only prompt +IC +brem γ dn / dE γ (GeV cm − 2 s − 1 ) -7 10 E 2 -1 0 1 10 10 10 E γ (GeV) Thomas Lacroix Fermi-LAT GeV excess & DM: importance of electron propagation
The GC gamma-ray excess Contributions from diffusion Diffusion of electrons and positrons from DM Total spectrum Fitting the Fermi-LAT GeV excess with the leptonic channels Morphology At low energy possible tension between signal from diffusion and morphology in the literature between 0.1 ◦ and 1 ◦ m DM =10 GeV , B =3 µ G , n gas =3 cm − 3 , E γ =0 . 1 GeV -2 10 prompt -3 10 prompt +IC +brem dE γ dΩ (GeV cm − 2 s − 1 sr − 1 ) -4 10 -5 10 -6 10 -7 10 dn -8 E 2 γ 10 -9 10 -2 -1 0 1 2 10 10 10 10 10 b (deg) TL, C. Bœhm, J. Silk, arXiv:1403.1987 Thomas Lacroix Fermi-LAT GeV excess & DM: importance of electron propagation
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