The cosmic-ray positron excess from a local Dark Matter over-density Andi Hektor,1, 2 Martti Raidal,1, 3 Alessandro Strumia,1, 4 and Elmo Tempel1, 5 1National Institute of Chemical Physics and Biophysics, Ravala 10, 10143 Tallinn, Estonia 2Helsinki Institute of Physics, P.O. Box 64, FI-00014, Helsinki, Finland 3Institute of Physics, University of Tartu, Estonia 4Dipartimento di Fisica dell’Universit`adi Pisa and INFN, Italia 5Tartu Observatory, Observatooriumi 1, 61602 Toravere, Estonia (Dated: September 15, 2021) We show that the cosmic-ray positron excess measured by PAMELA and AMS could be induced by Dark Matter annihilations in a local over-density. In such a context leptophilic DM is not needed and good fits to positron data, in agreement with antiproton and gamma-ray measurements, are obtained for DM annihilations to WW , hh, ZZ, tt¯, b¯b, qq¯ channels. The classic Dark Matter candidates, such as the pure supersymmetric Wino with standard thermal annihilation cross-section, can fit the positron excess, without invoking any additional assumption on Dark Matter properties. Introduction. The new AMS02 measurement [1, In this paper we propose a solution to the positron 2] of the cosmic ray positron energy spectrum up anomaly that does not require additional ad hoc assump- to 350 GeV confirms with better precision the ear- tions on DM properties. The idea is that the positron lier claim by PAMELA [3] and FERMI [4] of a rising anomaly is a local effect arising from DM annihilations positron/electron fraction. Such a spectral feature de- in a local DM over-density. DM density fluctuations, that mands either non-conventional models of the astrophysi- are not gravitationally bound, are predicted to occur and cal background [5] or new sources, such as pulsars [6{11] disappear continuously everywhere in our Galaxy by the or annihilations of weakly interacting Dark Matter (DM). cold DM paradigm. The measured positron excess could then originate from such a local over-density even with DM can explain the positron excess compatibly with the standard thermal annihilation cross-section.1 the absence of a similar excess in the antiproton flux This implies observable energy spectra of e±; p;¯ γ dif- provided that the DM of the main Milky Way halo an- ferent from the standard case where DM annihilates in nihilates predominantly into the Standard Model (SM) all the Galaxy. Our most important result is that DM leptons with a cross-section 2 − 3 orders of magnitude annihilations into the usual theoretically favoured chan- larger than the annihilation cross-section predicted by nels, the hypothesis that DM is a thermal relic [12{14]. Such a large cross-section today may result from a Sommer- W W; ZZ; hh; qq;¯ b¯b; tt;¯ : : : ; feld enhancement [12], maybe mediated by new hypo- thetical GeV scale vectors [13]. However, this scenario is can now reproduce the energy spectrum of the positron severely constrained by the absence of associated gamma- excess, while purely leptonic channels become dis- rays from the galactic center, from dwarf galaxies and in favoured. This is because positron energy losses can now the diffuse background [15{20]. Additional constraints be neglected, such that a more shallow energy spectrum arise from observations of the cosmic microwave back- at production is needed to fit the positron excess. This re- ground (CMB) [18, 21{23]. Such constraints challenge sult implies that the conventional WIMP DM models are various aspects of current DM theories | DM origin as preferred by data without invoking additional assump- a thermal relic, early cosmology, simulations of the Milky tions. We will show that constraints fromp ¯ and γ are arXiv:1307.2561v2 [hep-ph] 12 Jul 2013 Way DM halo density profile, as well as particle physics satisfied. models of the DM. Additional information that may discriminate between DM models is provided by DM direct detection experi- Furthermore, even DM annihilations into leptons are ments. If the local DM over-density exists today around challenged, because the final state e± loose almost all us, the DM coupling to nuclei must be suppressed. This of their energy through inverse Compton scattering on favours, for example, pure Wino DM or Minimal Dark galactic star-light and CMB, producing a secondary flux Matter scenarios, where DM couples to matter only via of energetic photons. Such Inverse Compton photons can be compatible with gamma-ray observations pro- vided that DM in the Milky Way has a cored (such as an isothermal) density profile [24{31]. 1 Various past articles considered the possibility of interpreting the The non-observation of such Inverse Compton photons positron excess in terms of enhanced DM matter annihilations from a variety of different kinds of nearby DM sub-structures, favors the possibility that the positron excess is local, such as clumped sub-haloes [32], black holes [34], dark stars [33], rather than present in all the Milky Way. a dark disk [35]. 2 a W -boson loop. If, instead, the DM over-density has 0.50 Bpart =1 already disappeared, and today we observe a remnant R=0.5 kpc Diffusion: MIN position excess trapped by the Galactic magnetic fields, 0.20 é é é í é typical WIMP DM model are viable candidates. é é í é é é 0.10 éééééé éé L í ééé - í é e ééééé F é é é ééééé í + éíé íé ééíéé + éíé é í í íééé é The local DM over-density. N-body simulations e 0.05 íé é ééíéééééé F H + e of cold DM structure formation predict a wide spectrum F í PAMELA of density and velocity fluctuations in any DM halo such 0.02 é AMS02 as our Galaxy [36]. Only a very small fraction of the den- cc®bb 1893 GeV, 45r cc® r 0.01 WW 1194 GeV, 41 sity fluctuations develop high enough over-density, a few cc®hh 2124 GeV, 50r H L Background hundred times over the local average, to become gravi- H L tationally bound sub-halos. A fluctuation with density ρ 10 H 50L 100 500 1000 5000 Energy GeV and radius R is gravitationally bound provided that the escape velocity from it is smaller than the typical local FIG. 1: Best fits of the positronH fractionL from DM annihila- DM velocity dispersion, tions to WW , hh, ¯bb for parameters indicated in the figure. Over-densities are indicated as ρloc and given relative to the r 8π average density ρ0. v = G R2ρ 10−3; (1) esc 3 N i.e. for ρ/ρ 200×(kpc=R)2, where ρ = 0:4 GeV=cm3 0 0 To compute the diffusion effects we assume the is the average DM density around the Sun. Those dense MIN/MED/MAX diffusion models of [39], as described fluctuations collapse gravitationally and develop cuspy in [38]. The number densities f(~x;t; E) of e+ and their NFW or Einasto like profile similarly to the main halo. fluxes Φ + = cf=4π are well approximated by neglecting However, the vast majority of fluctuations just occur e the energy loss term in the time-independent diffusion and disappear continuously without affecting large scale equation, that becomes simply structure formation. Those over-density regions have 2 shallow profiles, such as Gaussians, since they are not dNe+ 1 ρ dNe+ − K(E)r2f = Q = hσvi ; (2) gravitationally bound. dE 2 M 2 dE In this work we assume that there exists, or there ex- where K(E) is approximatively given by the Larmor isted not long time ago, a local DM over-density with radius in the local turbulent Milky Way magnetic a radius of few hundred pc. Such an assumption is in field. Analyses of cosmic ray data suggest K(E) = δ agreement with the determination of local DM density K0(E=GeV) with δ = 0:85 − 0:46 and K0 = (0:016 − at the distance of Sun. The latter is measured by the 0:0765) kpc2=Myr [39]. movement of stars in a cylinder of radius 1 kpc extend- Assuming, for simplicity, that we live at the center ing ±4 kpc in both directions around the Galactic disc. of a spherical excess with constant local density ρ and A local over-density with radius R = 100 pc forms just radius R, and neglecting DM annihilations outside it, 1/6000 of this volume, not affecting the average result. the solution is In fact, several over- and under-density fluctuations are 3Γ dNe+ expected to occur in such a big volume. Furthermore, a Φ + = ; (3) e 32π2K(E)R dE moderate local over-density is compatible with solar sys- tem gravitational measurements that imply a local DM where Γ is the total DM annihilation rate in the local density smaller than ρ/ρ0 < 15000 [37]. over-density: Z 4πR3 1 ρ2 Γ = dV Q = hσvi : (4) Explaining the positron excess. We now try to 3 2 M 2 interpret the measured positron excess as due to DM an- nihilations in a local DM over-density. As a result, we The shape and location of the local excess only affect the obtain the size and density of such a fluctuation from overall numerical factor in eq. (3), leaving unaffected the the AMS and PAMELA data. This will allow us to later main feature: the positron energy spectrum at detection predict the associated gamma-ray and antiproton fluxes. is given by the positron energy spectrum at production In our exploration we follow the model independent ap- over the diffusion factor K(E). proach introduced in [12, 38]. We allow DM to annihilate The boost factor B that enhances the positron DM flux into all possible two-body SM final states with the stan- with respect to the standard scenario can be expressed dard thermal relic cross-section hσvi ≈ 3 · 10−26 cm2: as The energy spectra of the various stable SM particles + (e ; p;¯ γ; ν; : : :) are computed with PYTHIA8.