Updated cosmic-ray and radio constraints on light dark matter:Implications for the GeV gamma-ray excess at the Galactic center

Torsten Bringmann,1, ∗ Martin Vollmann,2, † and Christoph Weniger3, ‡

1Department of Physics, University of Oslo, Box 1048 NO-0316 Oslo, Norway2II. Institute for Theoretical Physics, University of Hamburg,

Luruper Chaussee 149, 22761 Hamburg, Germany3GRAPPA, University of Amsterdam, Science Park 904, 1090 GL Amsterdam, Netherlands

The apparent gamma-ray excess in the Galactic center region and inner Galaxy has attractedconsiderable interest, notably because both its spectrum and radial distribution are consistent withan interpretation in terms of annihilating dark matter particles with a mass of about 10− 40 GeV.We confront such an interpretation with an updated compilation of various indirect dark matterdetection bounds, which we adapt to the specific form required by the observed signal. We find thatcosmic-ray positron data strongly rule out dark matter annihilating to light leptons, or ’democrati-cally’ to all leptons, as an explanation of the signal. Cosmic-ray antiprotons, for which we presentindependent and significantly improved limits with respect to previous estimates, are already inconsiderable tension with DM annihilation to any combination of quark final states; the first set ofAMS-02 data will thus be able to rule out or confirm the DM hypothesis with high confidence. Forreasonable assumptions about the magnetic field in the Galactic center region, radio observationsindependently put very severe constraints on a DM interpretation of the excess, in particular for allleptonic annihilation channels.

I. INTRODUCTION

Because of the high expected dark matter (DM) den-sity, the inner part of the Galaxy is one of the primetargets for indirect searches for particle DM (for recentreviews, see Refs. [1–3]). Indeed, indications for DMsignals from the Galactic center (GC) region have re-peatedly appeared in the past – in particular in gammarays [4–10], but also in microwaves [11] and the anni-hilation radiation from positrons [12]. This part of theGalaxy, however, is also an astrophysically very rich en-vironment. Unless one can identify a distinct spectralsignature [13, 14], this generally makes disentangling anypotential DM signal from astrophysical backgrounds aformidable task. In fact, more refined analyses and newdata have so far always tended to disfavour the DM hy-potheses previously put forward [15–19]. The field hasmatured significantly in recent years however, concern-ing both the understanding of astrophysical backgroundsand the statistical analysis of potential signals, not theleast because of the unprecedented wealth of high-qualitydata that now are at our disposal. At the same time,many theoretical models predict signals just below cur-rent exclusion limits. This implies both that more signalclaims should be expected in the near future, and thatthose should not be dismissed too easily.

An example for such a sophisticated analysis is the re-cent discussion of the GeV gamma-ray excess in Fermi-LAT [20] data of the GC and inner Galaxy [21], whichreconfirms corresponding earlier findings [22–29] with a

∗ Torsten.Bringmann@fys.uio.no† Martin.Vollmann@desy.de‡ C.Weniger@uva.nl

high level of detail (see also Ref. [30] for a review). Thespectrum of the excess seen at the GC can be well de-scribed by the annihilation of 10 − 40 GeV DM parti-cles into quarks, or leptons, which then produce sec-ondary photons during their fragmentation and decay.Indeed, the signal normalization is consistent with thatexpected for thermally produced DM. The observed spec-trum, however, does not contain the type of sharp fea-tures that would unambiguously point to a DM origin. Itis thus arguably even more interesting that the signal isspherically symmetric and that it is claimed to extend toat least 1.5 kpc away from the GC [28], where astrophys-ical backgrounds with a similar morphology are expectedto be strongly suppressed. Last but not least, the excessemission decreases with galactocentric distance in a waythat is consistent with the wide range of expectations forannihilating DM. Not surprisingly, the most recent analy-sis of this excess [21] has already triggered a considerableactivity in concrete model-building attempts [31–42].

If the excess can indeed be attributed to annihilatingDM particles, this will also leave traces in other cosmic-ray fluxes. In fact, a confirmation of the DM hypothesisessentially requires to find corroborating evidence froma different type of experiment, and observations usingother cosmic-ray messengers or photons at other wave-lengths seem to be a particularly natural choice to lookfor such a second signal (while the translation to expectedrates in direct detection experiments or at colliders ismuch more model-dependent). Given the renewed inter-est in the GC gamma-ray excess, we thus present herean updated collection of constraints deriving from indi-rect DM searches. In particular, we point out that theobserved radial distribution of the gamma-ray signal es-sentially fixes the DM distribution in the inner Galaxy,thereby significantly reducing the astrophysical uncer-tainties typically associated with such limits. This al-

arX

iv:1

406.

6027

v2 [

astr

o-ph

.HE

] 2

Dec

201

4

2

lows to reliably constrain the DM interpretation of thesignal, almost independent of the DM profile and muchless model-dependent than corresponding constraints de-rived from DM searches at colliders or in direct detectionexperiments [43–47].

This article is organized as follows. We start in SectionII by reviewing the current situation of the GeV excess,with an emphasis on the possibility that it is inducedby annihilating DM. In Section III we present updatedbounds on this interpretation from other indirect searchesfor DM, in particular using cosmic-ray antiprotons andpositrons, as well as radio observations. We provide amore detailed discussion of systematic uncertainties forthe most relevant limits in Section IV, and a summary interms of the main possible DM annihilation channels incontext of the GC GeV excess in Section V. In SectionVI, finally, we conclude.

II. CHARACTERISTICS OF THE GEV EXCESS

The DM interpretation of the excess emission at theGC is suggestive in a number of ways: The extendedemission appears to peak relatively sharply at energiesaround 1–3 GeV, is rotationally symmetric around theGC, and roughly follows a ∝ r−2.5 emission profile,compatible with the annihilation signal from a standardcuspy – if slightly contracted – DM distribution [23]. Fur-thermore, the same spectral signature was claimed to ex-tend to much higher Galactic latitudes, |b| & 10 [28] (seealso Ref. [29]). Indeed, a signal from DM annihilationis in general expected to extend to high latitudes, andcan even be visible at the Galactic poles if the substruc-ture enhancement of the annihilation signal is significantat cosmological distances. Astrophysical explanations interms of milli-second pulsars (MSPs), bremsstrahlung orneutral pion decay close to the GC are not yet excluded,but would all face serious challenges if – despite the size-able systematic uncertainties [48] – the extension of theGeV excess to Galactic latitudes of |b| > O(10) is con-firmed. It should in fact be stressed that the nominalstatistical significance of the excess is extremely high(e.g. at the level of ∼ 40σ in the inner Galaxy analy-sis of Ref. [21]), and that by now background modelinguncertainties are the main limiting factor in characteriz-ing its properties.

First claims that the gamma-ray emission from the GCas seen by Fermi LAT suggests a DM annihilation sig-nal were put forward in Ref. [22], using a simple power-law model for the spectrum of Galactic diffuse emission.The authors found that annihilation into bb final states, aDM mass around 25–30 GeV and an annihilation cross-section close to the thermal value are compatible withthe data. In Ref. [23] the same authors found that thedominant part of the emission comes from the inner 1.25

around the GC, with a volume emissivity that scales like∼ r−2.5, and discussed possible astrophysical interpreta-tions in terms of MSPs (first mentioned in Ref. [49]; see

also Ref. [50] for a much earlier discussion in the contextof EGRET measurements) and neutral pion decay fromcosmic-ray interactions. Ref. [24] presented an updatedanalysis, using three years of Pass 7 Fermi LAT data, andarriving at similar conclusions. Ref. [51] pointed out theimportance of a proper treatment of point sources closeto the GC.

In an independent analysis, Ref. [25] confirmed the ex-istence of a significant extended emission at the GC, andfound it well compatible with the spectrum of knownMSPs. Alternative scenarios discussed in the literatureare bremsstrahlung of electrons on molecular gas [52]within the inner few hundred pc, or proton-proton in-teraction within the inner few pc of the super-massiveblack hole (SMBH) [53]. In Ref. [54], the authors studysome of the systematic uncertainties related to standardemission models for the diffuse backgrounds at the Galac-tic center, and find that – after marginalizing over pointsources and diffuse background uncertainties – both DMannihilation and a population of at least ∼ 1000–2000MSPs are compatible with the excess emission from theGalactic center.

The latest analyses of the GC excess emission werepresented in Ref. [27], discussing in some detail back-ground modeling systematics related to point sources,molecular gas and generic extended diffuse emission, andin Ref. [21], which updates previous analyses by using asubset of Fermi LAT data with improved angular resolu-tion (based on a cut on CTBCORE [55]). For definiteness,we will mostly base the discussion in this paper on theresults obtained in Ref. [21].

A. DM interpretation

Focussing on the DM interpretation of the GeV ex-cess, let us first have a detailed look at what the ob-servations would tell us about the annihilating particles.For definiteness, we will do this for a number of bench-mark scenarios – based on the results from Ref. [21], butadditionally including uncertainties related to the DMdistribution.

The differential intensity of photons from DM annihi-lation as observed at Earth can be calculated via

dφ

dEdΩ=

1

4π

∫l.o.s.

ds〈σv〉2m2

χ

dNγdE

ρ(r)2

︸ ︷︷ ︸≡Q(r,E)

, (1)

where 〈σv〉 is the average velocity-weighted annihila-tion cross-section, mχ denotes the DM mass, dNγ/dEthe energy spectrum of prompt photons produced inthe annihilation, and ρ(r) is the DM density as func-tion of the galactocentric radius r. The integral runsover the line-of-sight parameter s, and r is given byr =

√(R − s cosψ)2 + (s sinψ)2, where R = 8.5 kpc

is the distance between Sun and GC, and ψ the angleto the GC. Lastly, we defined Q(r, E) as the differentialinjection rate of gamma rays from DM annihilation.

3

When extrapolating the excess emission observed atthe GC to other points in the Galaxy, the main unknownis the shape of the Galactic DM halo and the distributionof DM substructures. The infall of baryons onto the cen-tral regions during galaxy formation can cause adiabaticcontraction of the DM halo [56]. The exact strength ofthis effect is unknown, and we will here use a generalizedNavarro-Frenk-White (NFW) profile [57], given by

ρ(r) = ρ

(r

R

)−Γ(r + rsR + rs

)Γ−3

, (2)

where Γ is the inner slope of the DM halo, and ρ theDM density at the position of the Solar system. Observa-tional constraints from microlensing and rotation curvesof stars or gas [58] on the slope of the DM halo in theinner few kpc of the Galaxy remain relatively weak andallow values up to Γ ∼ 1.5. Throughout, we will useρ = 0.3 GeV cm−3 and rs = 20 kpc as reference values.Note that we are eventually only interested in the ratio ofvarious constraints to the putative signal, implying thatthe local DM density ρ drops out and thus can be fixedto any value simply as a matter of convention. In thatcase, the variation of the annihilation rate at the Sun’sposition corresponds to a variation of the annihilationcross-section itself.

In Ref. [21], the authors find slopes Γ ' 1.26±0.05 (at3σ CL) from an analysis of the inner Galaxy (excludingthe inner one degree above and below the Galactic disc),and a value of Γ ' 1.04–1.24 from an analysis of theGC source. We will quote our main results using thecentral value of the inner Galaxy analysis, Γ = 1.26, andwill comment on the impact of shallower profiles whennecessary. Note that throughout the analysis, we willneglect the effect of substructure in the DM halo. Due totidal forces, the associated boost at the GC is in generalexpected to be negligible; at kpc distances it can howeverlead to O(1) enhancements of the effective annihilationrate (see e.g. Ref. [59]). Neglecting these effects rendersour constraints conservative.

We show in Fig. 1 the radial dependence of the DMannihilation rate per volume for different values of Γ. Therates are normalized to yield an identical projected signalflux from the inner 1–3 around the GC, taking 〈σv〉 =1.7× 10−26 cm3s−1 into bb, mχ = 35 GeV and Γ = 1.26as benchmark.1 For slopes Γ compatible with the GeVexcess, and assuming a scale radius of rs = 20 kpc, theannihilation rate can vary by about a factor of ∼ 3.3(namely, when taking Γ = 1.24 as reference, 2.9 up and1.1 down).

Considering possible variations in the scale radius inthe range rs = 20+15

−10 kpc, as suggested by DM-only sim-ulations on the one and dynamical observations on the

1 We checked that normalizing instead in the range 1–2 (1–5)would change the fluxes corresponding to Γ = 1.04 at most by+10% (−15%).

10−2 10−1 100 101 102

r [kpc]

10−30

10−29

10−28

10−27

10−26

1 2〈σv〉(ρ

(r)/m

χ)2·r

3[kpc3cm

−3s−

1] Γ = 1.26

Γ = 1.24

Γ = 1.04

FIG. 1. DM annihilation rate per volume as function of thegalactocentric radius r, for different values of the inner slopeΓ. The normalization is fixed to produce a signal emission inan annulus of 1–3 around the GC that is compatible withthe values quoted in Ref. [21] (see text for details). At theposition of the Sun (vertical line) the annihilation rate canvary by a factor of 3.3, as indicatd by the black lines. Thisregion is extended as shown by the gray lines when allowingfor variations in the scale radius of the DM profile, leading toan additional factor two uncertainty in both directions. Wemultiplied the annihilation rate by r3 for visual convenience.

other hand (see discussion in Ref. [58]) allows for an ad-ditional change of up to a factor of two in the DM an-nihilation rate at the position of the Sun (see Fig. 1).Adopting the proceedure discussed in Ref. [60] and re-quiring that a given DM profile with fixed ρ and Γ canreproduce the SDSS mass constraint M(r = 60 kpc) =4.7 × 1011M [61], we find that rs = 24(34) kpc forΓ = 1.0(1.26) if ρ = 0.3 GeV/cm3, and rs = 15(18) kpcif ρ = 0.4 GeV/cm3. Interestingly, these values favourthe upper range of the above uncertainty band. Notethat uncertainties in R lead to variations in the anni-hilation rate at the Sun’s position of at most a few 10%,which can be neglected in the present discussion.

Finally, Fig. 1 demonstrates that steepening the pro-file, by increasing Γ, makes local messengers (likepositrons) a weaker probe of the GeV excess – while mes-sengers originating from very small galactocentric dis-tances (like radio signals) will lead to increasingly tighterconstraints – and vice versa. Furthermore, constraints onthe GC GeV excess derived from observations at galacto-centric distances of . 100 pc (like our radio constraints)are practically independent of rs. Combining informa-tion from indirect DM searches with different messengersthus allows to test the DM hypothesis in a way that iseven more independent of the assumed DM distributionthan what can be inferred from gamma-ray observationsalone.

The energy spectrum of the excess emission as derivedfrom the inner Galaxy analysis of Ref. [21] can be wellfitted with secondary photons from DM annihilation into

4

5 10 20 50mχ [GeV]

10−26

10−25

〈σv〉[cm

3s−

1]

bb

cc

charge

dem

mass

qq

ss

τ+τ−(80%)

FIG. 2. The ellipses show the preferred values of the DMannihilation cross-sections and mass from the inner Galaxyanalysis of Ref. [21], where we include the uncertainties com-ing from the DM profile slope in quadrature (Γ = 1.26± 0.05at 3σ); see also Tab. I. The error-bars indicate the annihila-tion cross-section preferred for the values Γ = 1.04–1.24, asfound from the GC analysis in Ref. [21].

hadronic final states. Fits with the harder photon spec-tra from annihilation into leptonic final states (caused byfinal state radiation and, in the case of τ leptons, the de-cay of energetic neutral pions) are however disfavouredon purely statistical grounds with high significance. Incase of annihilation into τ+τ− final states, this discrep-ancy can be alleviated by adding a bb component of atleast 20% (in which case the resulting ∆χ2 is still worseby ∼ 20 than a pure bb fit). An alternative can be addi-tional photons from bremsstrahlung and Inverse Comp-ton scattering [62] – though a sizeable effect requires verylarge branching ratios into e± or µ± final states, as e.g. inthe case of democratic annihilation to all leptons.

In Fig. 2, we show the values of the DM annihi-lation cross-section and DM mass that are consistentwith the GeV excess, based on the findings of Ref. [21].We increased the size of the confidence regions to in-clude the uncertainty in the DM profile slope – ∆Γ '0.05 as inferred from the inner Galaxy analysis – inquadrature; this translates into a relative uncertainty of∆〈σv〉/〈σv〉 ' 22 %. These numbers are also summarizedin Tab. I for convenience, and will be used as benchmarksin our subsequent study of implications for charged cos-mic rays and radio emission. Furthermore, the verticalerror bars indicate the range that is preferred by the GCanalysis [21], which is in general higher than the rangeinferred from the inner Galaxy analysis.

B. Astrophysical scenarios

For completeness, we will here briefly sketch astrophys-ical scenarios that might account for the excess emissionseen at the GC. The arguably most plausible explana-

Channel Mass mχ Cross-section 〈σv〉[GeV] [10−26cm3s−1]

bb 35.5± 4.2 1.7± 0.3

cc 27.0± 3.3 1.2± 0.22

qq 18.5± 2.1 0.72± 0.13

τ+τ−(80%) 9.3± 0.8 0.7± 0.12

mass 33.3± 3.9 1.6± 0.29

dem 21.9± 3.1 1.1± 0.2

ss 21.4± 2.9 0.93± 0.16

charge 18.7± 2.3 1.3± 0.23

TABLE I. List of benchmark annihilation channels that weconsider in this work. Annihilation rates refer to a gener-alized NFW profile with central values Γ = 1.26 and localdensity ρ = 0.3 GeV/cm3, using results from Ref. [21] (seethere for a definition of final states). The errors are from thestatistical fit (95% CL) and include additional uncertaintiesin Γ = 1.26 ± 0.05 (3σ CL) in quadrature. Taking into ac-count the larger uncertainties in the slope Γ as inferred fromthe GC analysis (see Fig. 1) can furthermore change the val-ues as indicated in Fig. 2; for Γ = 1.04, e.g., the best-fit valueof 〈σv〉 given in the table must be multiplied by 3.3.

tion for at least part of the observed excess emission atand close to the GC is the emission from a large number(∼ 1000) of MSPs below the point-source sensitivity ofFermi LAT [49]. Up to now, more than 40 MSPs havebeen observed in gamma rays by the Fermi LAT [63],with spectra that are compatible with the spectrum ofthe extended source at the GC [54] (unless the spectrumof the GC excess below 1 GeV is confirmed to be ex-tremely hard [21]). MSPs remain gamma-ray emittersfor billions of years, and it was argued that with kickvelocities of the order of ∼ 40 km/s they have the rightproperties to in principle account for the steepness as wellas the extension of the observed gamma-ray excess [24].The main argument against a significant contribution ofMSPs to the GC excess is that it appears to be non-trivialto find plausible source distributions that completely re-main below the Fermi LAT point source threshold [64–66], while still being compatible with the emission prop-erties of the pulsar population that is observed locally.

The emission of TeV gamma rays in the Galactic ridgeregion as observed by H.E.S.S. (in the inner |b| < 0.3

and |`| < 0.8) is well correlated with the distributionof molecular clouds that are observed in the inner 200pc around the GC by means of radio observations [67].This strongly suggests that the diffuse TeV gamma-ray emission is due to a hard population of cosmic-rayelectrons or protons, producing gamma rays either viabremsstrahlung or proton–proton interactions. It is plau-sible that the same populations also contribute to theGC emission at GeV energies. In the context of cosmic-ray electrons, Ref. [52] showed that the bremsstrahlungfrom an electron population compatible with the ob-served synchrotron emission at the GC could indeed pro-

5

duce the characteristic peaked GeV excess emission. Themain argument against the interpretation in terms of cos-mic rays is the apparent extension of the GeV excess to∼kpc distances from the GC as well as its spherical sym-metry, which does not resemble the distribution of de-tected gas (see e.g. Ref. [27]). Recent counter exampleswhich go beyond the typical assumptions of static cosmic-ray equilibrium at the Galactic center were presented inRefs. [68, 69]. In both papers, the authors discuss recentburst events (up to about one million years ago) that in-jected either high-energy electrons [68] or protons [69] atthe Galactic center, giving after a diffusion period rise toa quasi-spherical excess emission around the GC.

III. CONSTRAINTS FROM OTHER INDIRECTDETECTION CHANNELS

We now turn to a discussion of other messengers forthe indirect detection of DM than gamma rays. In allthese cases the source function is given by the differ-ential injection rate of particles from DM annihilation,Q(r, E) = 1

2 〈σv〉dN/dE (ρχ/mχ)2, that was already in-troduced in Eq. (1) in the context of gamma rays. Asstressed in the previous Section, cf. Figs. 1 and 2, thisquantity is rather tightly constrained if the GeV excessis indeed explained by DM. In consequence, the intrinsi-cally large uncertainties due to the DM distribution thatlimits from indirect detection are typically hampered byare greatly reduced in our case. In particular, they donot depend on the overall normalization of the DM den-sity profile (conventionally expressed in terms of the localDM density ρ).

The spectrum of the DM signal is determined bydN/dE, i.e. the differential number of a given species ofcosmic-ray particles that are produced per annihilation.We obtain these functions from DarkSUSY 5.1.1 [70],which provides tabulated fragmentation functions forvarious possible annihilation channels based on the eventgenerator PYTHIA 6.414 [71] (for light quarks q = u, d, s,we take instead the spectra provided in Ref. [60] as thoseare currently not implemented in DarkSUSY).

A. Antiprotons

Final state quarks from DM annihilation in the Galaxywill fragment and produce antiprotons [72]. Unlikegamma rays, those are deflected by stochastically dis-tributed inhomogeneities in the galactic magnetic fieldsuch that the resulting propagation can be modelled bya diffusion process [73]. On the other hand, there areno primary but only secondary sources of astrophysicalantiprotons: these are produced through the collisionsof cosmic rays, in particular protons, with the interstel-lar medium. This astrophysical background is extremelywell understood and can nicely be described in relativelysimple semi-analytical diffusion models with cylindrical

symmetry [74, 75]. Fitting the parameters of those mod-els to other cosmic-ray data, in particular other observedsecondary to primary ratios like the boron over carbonratio B/C [76], results in a prediction for the antiprotonbackground that is both tightly constrained and providesa very good fit to the data.

The main uncertainty in the background prediction de-rives from the range of propagation parameters compati-ble with B/C and from uncertainties in the nuclear crosssections for the production of antiprotons. For the en-ergy range we are interested in here, both effects can in-dependently affect the flux by up to about 30% [73]. Forrecent studies that find similar values, and offer more de-tailed discussions about the underlying systematics, seeRefs. [77, 78]. In our analysis, we will take into accountthe full range of uncertainty in the background predic-tion by two independent parameters αprop, αnuc ∈ [0, 1]that interpolate linearly between the minimal and max-imal predictions for the secondary flux due to these twoeffects (for which we use the results from Refs. [74] and[75], respectively). Low-energy antiprotons are further-more affected by local effects like adiabatic energy lossesin the expanding solar wind and diffusion in the solarmagnetic field, often collectively referred to as solar mod-ulation (see e.g. Ref. [79] for a recent discussion). For theenergies of interest to our analysis this is extremely welldescribed by the force-field approximation [80, 81], seediscussion in section IV A, implying that a single param-eter – the Fisk potential φF – is sufficient to relate thelocal interstellar (LIS) antiproton flux to the one mea-sured at the top of the atmosphere (TOA).

For our analysis we use the newest release of PAMELAdata that result from measurements between June 2006and January 2010 [82], featuring significantly reduced er-ror bars with respect to any previous antiproton data.2

These data agree remarkably well with the much olderpredictions [74] for the antiproton background we aretesting against: with the three free parameters describedabove, we find χ2/d.o.f. = 10.1/(23 − 3) = 0.51 for thebest fit point. Clearly, this provides an important testfor the underlying diffusion model. In Fig. 3 we plotthis best-fit prediction for the background as a solid line,along with the PAMELA data points. The yellow band inthat figure corresponds to a choice of nuclear cross sectionparameterization that minimizes the flux (as adopted inRef. [74], this corresponds to setting αnuc = 0 in ouranalysis), while the orange band corresponds to a choicethat maximizes the flux (as in Ref. [75], corresponding toour αnuc = 1). In both cases, the width of these bands isgiven by the uncertainty in the propagation parametersthat results from the B/C analysis (which corresponds tovarying our parameter αprop from 0 to 1).

2 Note that the error bars stated in that data release are statisticalonly. Systematical error bars are expected to be of the same orderas in the first release [83] of PAMELA data [84]. In our analysis,we thus add those in quadrature.

6

FIG. 3. PAMELA antiproton data [82] as measured on top ofthe atmosphere (TOA). The coloured bands show the predic-tion for the astrophysical background (BG), with the width ofeach band deriving from uncertainties in the propagation pa-rameters left from the B/C analysis. The two different bandsbracket the uncertainty from nuclear cross sections, where themaximal (minimal) flux corresponds to the analysis performedin Ref. [75] ([74]). The best-fit BG model is given by the solidline. For comparison, the dotted and dashed lines also showthe case of a fiducial WIMP with mass 34 GeV, annihilatingto bb with a rate barely allowed at 95%CL (see Fig. 4).

The contribution to the antiproton flux from DM anni-hilation [72] is subject to much larger theoretical uncer-tainties than what is illustrated by the coloured bandsin Fig. 3 for the astrophysical background [85]. Themain reason for this is that DM annihilation is very effi-cient in a rather large part of the halo, implying thatit probes a much larger volume of the diffusion zonethan the B/C analysis that is restricted to sources in theGalactic disk. In particular, the antiproton flux fromDM is mostly sensitive to the thickness L of the dif-fusion zone perpendicular to the Galactic plane, whileB/C essentially only constrains the ratio of L and thediffusion coefficient D [86]. While the B/C analysis inprinciple allows a diffusion zone as small as L ∼ 1 kpc,a vertical extension of L ∼ 10 kpc is preferred when tak-ing into account radioactive isotopes [87], with similarresults obtained when adding gamma rays [88, 89] andcosmic-ray electrons [90, 91] to the analysis. Also ra-dio [92, 93] and low-energy cosmic-ray positron [94] datahave been shown to be clearly inconsistent with a halosize as small as ∼ 1 kpc. With this in mind, we will in thefollowing mainly use the recommended reference model,’KRA’, of the recent comprehensive analysis presentedin Ref. [95], which features L = 4 kpc (and is very simi-

FIG. 4. Limits on the annihilation rate of DM into quark finalstates from our analysis of the PAMELA antiproton data.Solid lines refer to the generalized NFW profile of Eq. (2)with Γ = 1.04 and are essentially indistinguishable from thestandard NFW (Γ = 1) case; dotted lines show the case forΓ = 1.26.

lar to the best-fit model of Ref. [86]). For the propaga-tion of primary antiprotons we use DarkSUSY [70], whichimplements the semi-analytical solution of the diffusionequation described in Refs. [95, 96].

We use the likelihood ratio test [97] to determine lim-its on a possible DM contribution to the antiproton fluxmeasured by PAMELA. For the likelihood function, weadopt a product of normal distributions over each databin i,

L = ΠiN(fi|µi, σi) , (3)

where fi is the measured value, µi the total antiprotonflux predicted by the model and σi its variance. For agiven mass and annihilation channel, the DM contribu-tion enters with a single degree of freedom that parame-terizes the non-negative signal normalization (and whichwe will always express in terms of the annihilation rate).95%CL upper limits on 〈σv〉 are thus derived by increas-ing the signal normalization from its best-fit value until−2 lnL has changed by 2.71, while re-fitting (’profilingover’) the parameters (αprop, αnuc, φF ) of the backgroundmodel.

In Fig. 4, we show the resulting limits on 〈σv〉 as afunction of the DM mass mχ, for all quark final statesand two representative values of the Γ-parameter of thegeneralized NFW profile of Eq. (2). Limits for the stan-dard NFW profile (Γ = 1) are essentially indistinguish-able from the Γ = 1.04 case displayed here. These limitsare one of our main results and rather strong, exclud-ing the cross section 〈σv〉therm ≡ 3 · 10−26cm3s−1 typi-cally favoured by thermally produced DM up to massesof mχ ∼ 35− 55 GeV for an NFW profile (depending onthe channel). There are two main reasons why we couldimprove previous limits [79, 95, 98, 99] by a factor ofroughly 2–5 at the DM masses of interest here (while thelimits presented in Ref. [100] are actually slightly stronger

7

FIG. 5. Reference p limits (thick line) and effects of varyingthe propagation scenario for bb final states. As in Fig. 4, thearea above the lines is excluded at 95%CL. For comparison,also the signal region for a DM interpretation of the gamma-ray excess in the inner Galaxy [21] is plotted, rescaled toΓ = 1.04.

than ours): i) we use the only recently published updateof PAMELA data [82] rather than the first public release[83] and ii) we employ an improved statistical treatmentof the background uncertainties (see Section IV A for amore detailed discussion).3 When comparing these re-sults to Fig. 2, we find that any interpretation of thegamma-ray excess as being due to DM annihilating intoquark final states is in strong tension with the cosmic-rayantiproton data.

Let us, finally, comment on the impact of differentpropagation scenarios on our limits. Conventionally, thecorresponding uncertainty is bracketed by two sets ofpropagation parameters, ’MIN’ and ’MAX’, that are con-sistent with the B/C analysis and, respectively, minimizeand maximize the primary antiproton flux from DM anni-hilation [85]. As we have stressed before, however, thereare several additional observations that constrain theseparameters much better than the B/C analysis alone,such that the range of allowed fluxes spanned by MINand MAX must be considered unrealistically large. Inorder to give a conservative indication of the involved as-trophysical uncertainties, and in order to follow the typ-ically adopted procedure, we still show in Fig. 5 how ourlimits change when varying the propagation parameterswithin these ranges.4 As can be seen from this figure,

3 Below mχ ∼ 50 GeV, the limits presented in Ref. [99] becomefurthermore significantly weaker due to the deliberate choice ofnot including data with T < 10 GeV.

4 Given that L = 1 kpc as featured by the MIN model proposed inRef. [85] has in the meantime been firmly ruled out, however, weused instead a MIN’ model with the same parameters as MINbut with L = 2 kpc and a diffusion coefficient of D0 = 9.65 ·1026 cm2s−1. This takes into account the lower bound of L ≥2 kpc from radio observations [92, 93] and the fact that B/C onlyis sensitive to L/D0 [76, 86]. Note that even L = 2 kpc is very

10−2 10−1 100

BR(χχ → e+e−)/BR(χχ → ℓ+ℓ−)

10−2

10−1

100

BR(χχ→

µ+µ−)/BR(χχ→

ℓ+ℓ−

)

AMS-02 e+e−

AMS-02 µ+µ−

democratic

BR(χχ → ℓ+ℓ−) = 1− BR(χχ → bb)=1; mχ = 9.2 GeV

FIG. 6. Upper limits (95% CL) on the relative branchingratios into leptonic two-body final states, as derived froma spectral analysis [104] of AMS-02 positrons. We assume100% annihilation into leptonic final states. For each point,we determine the DM mass and cross-section by a fit to thegamma-ray spectrum of the inner Galaxy excess [21], assum-ing Γ = 1.26. The green regions are excluded, while the grayregion shows where the spectral fit to the GeV excess worsenssignificantly (see text for details). The white area shows theremaining allowed parameter space, corresponding to an al-most pure τ+τ− final state. Note, however, that this gives afit to the data that is still much worse (by about ∆χ2 ∼ 130)than a fit with a bb final state.

the DM interpretation of the excess becomes compatiblewith limits from the PAMELA antiproton data only inthe most unfavourable case of propagation parameters –at least within the cylindrical two-zone diffusion modelthat is commonly considered. Antiproton data from theAMS-02 experiment on board of the international spacestation may improve limits on a DM contribution by asmuch as one order of magnitude with respect to the cur-rent PAMELA data [79, 95, 99]. Expected to be pub-lished in less than a year from now, AMS-02 data willthus either show an excess also in antiprotons or allowto rule out the DM hypothesis with rather high confi-dence. Similar conclusions apply more generally to otherquark annihilation channels and DM profiles than whatis shown explicitly in Fig. 5 (i.e. bb and Γ = 1.04).

B. Positrons

The energy spectrum of cosmic-ray positrons as wellas the positron fraction (the fraction of positrons in thetotal electron and positron flux) was recently measuredwith unprecedented precision by the AMS-02 [101] exper-iment, in the energy range 0.5 to 350 GeV. AMS-02 con-

conservative in light of the recent analysis of low-energy positrondata [94].

8

10−2 10−1 100

BR(χχ → e+e−)/BR(χχ → ℓ+ℓ−)

10−2

10−1

100BR(χχ→

µ+µ−)/BR(χχ→

ℓ+ℓ−

)

AMS-02 e+e−

AMS-02 µ+µ−democratic

BR(χχ → ℓ+ℓ−) = 1− BR(χχ → bb)=0.8; mχ = 9.3 GeV

10−2 10−1 100

BR(χχ → e+e−)/BR(χχ → ℓ+ℓ−)

10−2

10−1

100

BR(χχ→

µ+µ−)/BR(χχ→

ℓ+ℓ−

)

AMS-02 e+e−

democratic

BR(χχ → ℓ+ℓ−) = 1− BR(χχ → bb)=0.2; mχ = 30.1 GeV

FIG. 7. Same as Fig. 6, but for non-zero branching ratios into bb final states. The magenta line in the left (right) panel indicateswhere the best-fit DM mass exceeds 14 (34) GeV.

firmed the rise in the positron fraction at energies above10 GeV that was previously observed by PAMELA [102]and Fermi LAT [103], but with significantly smaller sta-tistical and systematical errors. This allowed for the firsttime a dedicated spectral search for signals from light(mχ . 350 GeV) DM particles annihilating into leptonicfinal states [104, 105], in a way that is largely indepen-dent of the origin of the rise in the positron fraction itself.For DM masses around 10 GeV, the limits on the annihi-lation cross-section into e+e− (µ+µ−) are very tight andaround 1.2× 10−28 cm3s−1 (1.3× 10−27 cm3s−1) [104].

The AMS-02 measurements of the positron fractionhave important consequences for the DM interpretationof the GeV excess. We will here consider the option thatthe GeV excess is dominantly caused by annihilation intoleptonic two-body final states, with a possible admixtureof bb. This scenario is described by the branching ra-tios into the three charged lepton families (e+e−, µ+µ−

and τ+τ− final states) as well as bb. For a given setof branching ratios, we calculate the prompt gamma-rayemission using DarkSUSY [70]. We refit the energy spec-trum of the GC excess emission (Fig. 5 in Ref. [21]) toobtain the total annihilation cross-section and DM mass,assuming a DM profile with Γ = 1.26. During the fit,we constrain the DM mass to be larger than 9.2 GeV toapproximately account for the fact that bremsstrahlungand inverse Compton emission can potentially contributeat low energies to reconcile the spectra of mixed leptonicfinal states with the measurements [62] (though this ar-guments only works in case of sizeable branching ratiosto e+e− final states, as is the case for the democraticscenario that Ref. [62] considers).

For a given set of branching ratios and the impliedDM mass and total cross-section, we adopt the AMS-02 limits from Ref. [104] to decide whether a scenario isexcluded. We use here the central values of the limitsfrom Ref. [104]; uncertainties in the local radiation fieldallow these limits to weaken by maximally a factor of

two. We use a reference value of Γ = 1.26 throughout.Note that a shallower profile would strengthen the AMS-02 limits, which mostly depend on the annihilation rateat the Sun’s position, by a factor of ∼ 3; variations inthe scale radius rs allow for an additional factor two upor down in the annihilation rate (cp. Fig. 1).

The results of this procedure are shown in Figs. 6and 7: In Fig. 6 we consider the purely leptonic case,i.e. BR(χχ → bb) = 0. In this figure, the best-fit DMmass always stays close to the imposed lower limit of 9.2GeV. The white areas are allowed and the green areas ex-cluded by limits on e+e− or µ+µ− final states at 95% CL;the gray area indicates where the formal fit to the databecomes worse by ∆χ2 & 25. In Fig. 7 we show the samesituation, but assume that 20% (left panel) or 80% (rightpanel) go into bb final states. In each case, we indicate inthe figure header the best-fit mass that we obtain in thelimit BR(χχ → e+e−) = BR(χχ → µ+µ−) = 0. As onecan see from these plots, the democratic case, featuringequal leptonic branching ratios, is clearly excluded fromAMS-02 cosmic-ray positron data.

Let us stress again that leptons alone do not featurea spectral shape consistent with that of the GeV ex-cess. This holds not only for the extremely hard spec-trum associated with light lepton final states, but alsofor the slightly softer spectrum from tau leptons. Dueto the strong AMS-02 constraints on the contributionfrom µ± and e± final states for BR(χχ → bb) . 0.2, wefind that this conclusion cannot be changed by includingthe effect of inverse Compton and bremsstrahlung pro-cesses, as suggested in Ref. [62]. Note that this holdseven if annihilation is assumed to happen dominantlyinto µ± and τ±, thereby evading the extremely strongconstraints for e± final states: In order to produce areasonable fit to the data, one would in that case needBR(χχ→ µ+µ−) 0.25 [62], which we identify in Fig. 6as being excluded by AMS-02 data.

9

C. Radio signals

Electrons and positrons from DM annihilation (hence-forth collectively referred to as electrons) are expectedto emit synchrotron radiation when propagating throughthe Galactic magnetic fields. Here, we shall focus on cor-responding radio signals from the GC. In particular, wewill use the Jodrell Bank upper flux limit of 50 mJy fromthis region [106], obtained for a frequency of 408 MHz, toconstrain the DM annihilation rate. As has been noticedbefore [107–115], the resulting constraints are typicallyrather strong. In this subsection we will derive our base-line constraints and defer a critical discussion of the stepsto Section IV C.

The arguably most critical – yet, as we shall see, re-alistic – assumption that enters our analysis is that theelectrons in the GC region lose their energy essentially insitu, via synchrotron radiation, implying that both free-streaming and diffusion effects can be neglected. Thisis motivated by the fact that one expects a much largerturbulent magnetic field at O(1 pc) distances from theGC [116] than the average Galactic value of ∼ 6µG[117]. In order to get a quantitative idea of the mag-netic field strength that is required, we will here assumethat diffusion at . 1 pc from the GC is well described byBohm diffusion (see Ref. [108] for a similar treatment);in Section IV C we will argue that this assumption canin fact be relaxed by several orders of magnitude. Incase of Bohm diffusion, the scattering length of the dif-fusion process is given by the gyroradius rg, leading toa diffusion constant DBohm = 1

3rgc = Eec/3eB. The

length scale ldiff ' (DBohmtloss)1/2 over which relativistic

electrons propagate during their synchrotron energy losstime, tloss ≈ E/b(r, E) = 3m4

ec7/2e4B2E where b(r, E)

is the loss rate, should then be significantly smaller thanthe DM density scale height lχ ≡ |ρχ(r)/ρ′χ(r)|, i.e. [115]

ldiff

lχ' m2

ec4

√2e5/2lχB3/2

. 1 . (4)

For the generalized NFW profile that we consider here,see Eq. (2), this implies a lower limit on the magneticfield strength of

B(r) & 4 Γ2/3(pc

r

)2/3

µG (5)

for the diffusion of electrons from DM annihilation at theGC to be negligible. Once this condition is satisfied, theresulting limits will actually decrease with increasing B(while the opposite is true in the regime where diffusioncannot be neglected, see e.g. Ref. [118]).

Observationally, the magnetic field in the Galaxy canbe inferred only indirectly via the Faraday effect. Theresulting rotation of polarized radio waves with wave-length λ is given by β = λ2 × RM, where the rotationmeasure RM is proportional to the integral over the line-of-sight magnetic field B(r) and the electron density n(r),RM ∝

∫B(r)n(r).

&&

&&

diffusion not negligible

PSR J1745-2900

G=1.26

G=1.04

core

0.01 0.05 0.10 0.50 1.00 5.00 10.0010

-7

10-6

10-5

10-4

0.001

0.01

0.1

r @pcD

B@G

D

FIG. 8. Solid line: Simplified model for the magnetic fieldprofile close to the GC black hole [111], assuming energyequipartition inside the accretion volume and magnetic fluxconservation outside. The gray area defines the domain whereBohm diffusion can no longer be neglected (as assumed in ouranalysis, cf. Eq. (5)). Lower limits (in red) refer to ultra-conservative and realistic field values, respectively, inferredfrom multi-wavelength observations of the recently discoveredmagnetar PSR J1745-2900 [119]. Horizontal arrows indicatethe ranges of galactocentric distances that, depending on theprofile, contribute ∼ 95% of the annihilation signal flux at408 MHz in the 4” cone observed in Ref. [106] (see text fordetails). For our actual limits, we conservatively take onlyradio fluxes from the inner 1 pc around the GC into account.

At the distances that are of interest for our radio dis-cussion, ∼ 0.1 pc, Ref. [119] infers the magnetic field frommulti-wavelength observations of the recently discoveredmagnetar PSR J1745-2900, which has a rotation mea-sure of RM ∼ 7× 104 rad m−2 at a projected distance of0.12 pc from the central black hole, Sagittarius A∗ (SgrA∗).5 Together with an observed dispersion measure of∼ 1.8× 103 cm−3 pc, which determines the column den-sity of electrons towards the pulsar, this allows to derivea very conservative lower limit on the magnetic field of50 µG (assuming that all electrons along the line-of-sightare localized close to the Galactic center, and that noturbulent field components and/or field reversals reducethe RM). A more realistic estimate gives a much largerlower limit of about 8 mG [119], but it is interesting tonote that already the extremely conservative limit satis-fies Eq. (5) if Bohm diffusion is realized.

For definiteness, we follow the often adopted assump-tion [116] that the magnetic field near the galactic centeris mainly powered by the central SMBH. Concretely, thismeans that we assume an approximate equipartition ofmagnetic, kinetic and gravitational energy inside the ac-cretion zone, i.e. B ∝ r−5/4 for r < Racc. = 0.04 pc (see

5 For comparison, the highest RM of any Galactic source,∼ 5× 105 rad m−2, is associated with the radio emission of SgrA∗ itself [120].

10

10 pc

5 pc

2 pc

1 pc

0.5 pc

0.2 pc

0.1 pc

no core

G = 1.2680 % Τ

+Τ

-

10 20 3015

10-30

10-29

10-28

10-27

10-26

mΧ@GeVD

Σv@

cm3

sD

10 pc

5 pc

2 pc

1 pc

0.5 pc

0.2 pc

0.1 pc

no core

G = 1.0480 % Τ

+Τ

-

10 20 3015

10-28

10-27

10-26

10-25

mΧ@GeVD

Σv@

cm3

sD

FIG. 9. Left panel: Limits from radio observations on the annihilation rate of DM particles into 80% τ+τ− and 20% bb, fora generalized NFW profile with an inner slope of 1.26 (lowest line). The other curves show the same limits when adding anartificial core to the DM profile with a core size rc as indicated (i.e. assuming a constant profile for galactocentric distancessmaller than what is stated next to the respective curve). Right panel: same as left panel but with an inner slope of Γ = 1.04.

also Refs. [121, 122]). For r > Racc., which is the regionmost relevant for our limits, magnetic flux conservationleads to B ∝ r−2. In Fig. 8, we plot this magnetic fieldprofile [111] along with the condition given in Eq. (5) andthe observationally infered lower limits.

If energy losses are dominated by synchrotron radi-ation, and the effect of diffusion can be neglected, thetransport equation can be solved analytically. The totalsynchrotron flux density is then given by [108, 111, 115]

Fν '〈σv〉

8πνR2m

2χ

∫Eρ2

χ(r)Ne(E) dV , (6)

where Ne(E) denotes the number of electrons (orpositrons) per annihilation, with energy larger than E.In arriving at this expression, the monochromatic ap-proximation for synchrotron radiation was used,

E =

(4πm3

eν

eB

) 12

= 0.46( ν

GHz

) 12

(B

mG

)− 12

GeV , (7)

which we checked affects our limits by less than 30% forthe masses of interest here. The integration volume inEq. (6) is a cone corresponding to the 4′′ region (∼ 0.32 pcof diameter at the GC) observed at Jodrell Bank [106].We restrict the integration to a region r < rmax = 1 pcwhere diffusion can be safely neglected, see Fig. 8, thusignoring the synchrotron emission of electrons created inregions where diffusion effects are not clearly negligible.While this restriction has no significant effect on our lim-its for the case of a generalized NFW profile, it rendersour limits in the presence of a core, as discussed below,rather conservative.

In Fig. 9 we show the results from confronting the DMhypothesis with the 408 MHz Jodrell Bank upper limit

in the case where the annihilation of DM particles oc-curs with a branching ratio of 80% into τ+τ− and with20% into bb. Besides limits for a generalized NFW profilewith Γ = 1.26 (left panel) and Γ = 1.04 (right panel), wealso show limits for these profiles if an ad hoc cutoff at agalactocentric distance rc is introduced in the DM den-sity profile. Below this, the DM density is assumed tostay constant, i.e. ρχ(r<rc) = ρχ(rc) while ρχ(r>rc) isgiven by Eq. (2). At much smaller scales than consideredhere, such a DM density plateau is expected to resultfrom the large DM annihilation rate [123] (in extremecases, also dynamical effects like the off-center formationof the SMBH [124] or major SMBH merger events [125]could significantly reduce the DM density at r . 1 pc,though this would not result in a complete flattening ofthe profile). Here, the postulated flattening at r < rcrather serves as a phenomenological parameterization ofthe maximal effect that uncertainties in the DM distribu-tion at small scales may have on our limits. Let us stressthat the DM interpretation of the GeV excess fixes theform of the density profile down to roughly 10 pc [21],and that there is no particular reason to expect a cutoff atonly slightly smaller scales. GC radio observations thusplace extremely tight constraints on annihilating DM forthe steep density profiles considered here, at least if ex-tending down to r > rc ∼ 1 pc.6 In fact, as we willdiscuss in more detail in Section IV C, these limits gen-erally depend much more strongly on the DM profile –

6 It is worth stressing that for such large core sizes, rc & 1 pc,the limits shown in Fig. 9 are rather strongly affected by ourconservative choice of restricting the volume for which we con-sider synchrotron integration. Changing the integration range inEq. (6) from r<rmax = 1 pc to rmax = 4 pc inside the 4” cone,for example, the constraints depicted for the rc = 10 pc casewould tighten by a factor of up to a few for mχ = O(10) GeV.

11

bb

cc

qq

80% Τ+

Τ-

G=1.04rc =2pc

10 20 3015

10-26

2

3

5

mΧ@GeVD

Σv@

cm3

sD

FIG. 10. Constraints from GC radio observations for variousannihilation channels, along with the corresponding contourscharacterizing the DM interpretation of the GeV excess ingamma rays [21]. These constraints assume an ad hoc corein the DM density profile at galactocentric distances smallerthan rc = 2 pc, i.e. only slightly below the O(10) pc distancedown to which the signal profile is observed in gamma rays(see Fig. 9 for an indication of how limits improve if the profileis assumed to continue to smaller scales).

which is fixed once we accept the DM interpretation ofthe GeV excess – than on the strength of the magneticfield.

In Fig. 10, we finally compare our radio limits directlyto the gamma-ray signal claims [21] for various annihi-lation channels. Assuming that the observed profile ex-tends down to a moderate rc . 2 pc, indeed, we findthat all channels are excluded as an explanation of thesignal. Here, we used an inner slope of the DM profileof Γ = 1.04; increasing this to Γ = 1.26 would tightenthe limits by roughly one order of magnitude for the DMmasses that best describe the excess.

For completeness, let us mention that a standard NFWprofile (Γ = 1) without a core, or a core at galacto-centricdistances less than 0.1 pc, leads to limits that are lessthan a factor of 3 weaker than for the case of Γ = 1.04considered above. This implies that for such a profilethermal cross sections are excluded for DM masses belowroughly 120 GeV (400 GeV) for τ+τ− (bb) final states.For an Einasto profile, on the other hand, we find con-straints that are weaker by more than 2 orders of mag-nitude below mχ ∼ 100 GeV, thus not probing thermalcross sections even for dark matter masses as small asa GeV. This large difference is easily understood by ob-serving that for the small distance scales r ∼ 1 pc thatare most relevant in setting the limits, c.f. Fig. 8, theEinasto profile is already much shallower than the NFWprofile.

D. Further constraints

Strong and robust constraints on light annihilating DMparticles are in principle also provided by measurementsof the cosmic microwave background [126–131]. However,even projected limits from Planck data [130] for lightlepton final states are much less constraining than theAMS-02 positron limits discussed above (and somewhatweaker for τ lepton final states). For quark final states,it will be possible to probe the thermal annihilation crosssection up to masses of ∼ 25 GeV. While this provides in-teresting and completely complementary limits comparedto the ones derived from cosmic-ray antiproton observa-tions, this only barely starts to constrain the assumedGeV signal region for DM annihilation into light quarks(cf. Fig. 2).

Gamma-ray observations of dwarf spheroidal galaxiesof the Milky Way are a further powerful and robust probefor the annihilation of DM. As practically background-free targets, and with a DM content that is well con-strained from observations of member stars, they wereused by several groups to perform DM searches bothwith space- and ground-based telescopes [132–138]. Forlight DM, the most recent study was based on a com-bined analysis of Fermi LAT observations of 15 dwarfspheroidal galaxies [133]. Only upper limits on the an-nihilation cross-section of DM could be found, and incase of e.g. χχ → bb these are consistent with the DMinterpretation of the GeV excess at the Galactic center.Interestingly, however, for DM masses around mχ = 10–25 GeV the current analysis indicates a slight preferencefor a signal at ∼ 2.3σ (after the typical fluctuation level ofthe extragalactic gamma-ray background has been takeninto account). Data collected by the Fermi LAT over theupcoming years will help to sort out whether this is asignal or merely a fluctuation.

Constraints from galaxy clusters [139–142] or the ex-tragalactic gamma-ray background [143, 144], are lessstringent, since they rely heavily on the distribution ofsubstructures in DM halos. However, a cross-correlationbetween the distribution of DM in the local Universe andthe unresolved gamma-ray sky can be a promising venueto confirm the GeV excess at higher latitudes [145–149].In passing, let us mention that previous constraints de-rived from GC observations [100, 150] are actually some-what in tension with the observed GeV excess and itsinterpretation in terms of DM annihilation.

Radio searches for DM annihilation have recently beenperformed also for other targets than the GC that wehave discussed at length above. The goal is usually notto identify a DM signal – which is extremely hard dueto the large modeling uncertainties of signals and back-grounds – but to put upper limits on the DM annihilationrate. In contrast to the constraints derived in the presentwork, which only depend weakly on the magnetic field,above a certain threshold, most other constraints crit-ically depend on the assumptions about magnetic fieldand cosmic-ray diffusion. Limits and prospective con-

12

G=1.04, 100% bb

PAMELA 2010 @reference; full data setDPAMELA 2010, only Tp

TOA > 1.2 GeV

PAMELA 2010, only TpTOA < 11 GeV

PAMELA 2008

BESSpolar

10 1005020 3015 70

1 ´10-27

5 ´10-27

1 ´10-26

5 ´10-26

1 ´10-25

5 ´10-25

mΧ @GeVD

<Σ

v>

@cm

3s

-1

D

FIG. 11. Reference p limits and dependence on energy cutsand/or different data sets (assuming an NFW-like profile,with Γ = 1.04, and annihilation into bb). For comparison,we also show the claimed signal region for a DM interpreta-tion of the GC GeV excess in this channel [21].

straints from the inner Galaxy (a few degrees off theGC) were discussed in Refs. [113, 114, 151–153]. Themost recent analysis of Galaxy clusters was presentedin Ref. [154], leading to limits that are stronger thancorresponding cluster constraints from gamma-ray ob-servations. Radio searches in dwarf spheroidal galax-ies suffer from the basically unknown magnetic field indwarfs [155, 156].

The Andromeda galaxy (M31), on the other hand, hascurrently a lower star formation rate than the MilkyWay, making it particularly suited for radio searchesfor DM. For realistic assumptions about the magneticfield, recent searches in M31 lead to very competitiveconstraints [157]. Depending also on the assumed halomodel of M31, these are in some tension with the DMinterpretation of the GeV excess.

IV. DISCUSSION

In the previous Section we have seen that indirectsearches using other messengers than gamma rays placevery strong constraints on light annihilating DM, essen-tially for every possible fermionic annihilation channel(with the exception of neutrinos, which we have not dis-cussed here). These constraints, if taken at face value,have far-reaching implications for a possible DM inter-pretation of the GeV gamma-ray excess. In this Section,we will therefore re-assess their validity and discuss sys-tematic uncertainties not addressed so far.

A. Antiprotons

As we have stressed earlier, one of the main reasons forwhy we could improve previous antiproton limits is the

statistical analysis we have adopted. In particular, wetook into account that nuclear uncertainties are not un-correlated in energy (as was done e.g. in Ref. [79]), whilestill allowing in our fits for the whole range of both nu-clear and propagation uncertainties typically accountedfor in the literature. Even though one might in princi-ple still worry that these uncertainties may in reality belarger, in particular when considering more complicatedpropagation models, it is worthwhile to emphasize againthat our simple 3-parameter background model providesan extremely good fit to the data. Despite a certain de-generacy in these three parameters, in fact, the data con-strain the shape of the background flux extremely tightly– which is the reason why we can derive strong limits inparticular for light DM contributions, which feature asomewhat different spectral shape of the antiproton fluxat low energies (for a given value of the Fisk potential).

As demonstrated in Fig. 11, it is indeed almost the fulldata range that is responsible for setting the limits, notonly the lowest data bins. Even though the DM contribu-tion is negligible at higher energies, e.g., all data pointsbelow about 20 GeV contribute significantly to fixing allparameters (αprop, αnuc, φF ). As a consequence, the DMcontribution at these energies cannot easily be compen-sated by a change in those parameters. In fact, evenneglecting data points below Tp ∼ 1 GeV in the analy-sis allows to set stringent limits due to the very smallerror bars in the data at intermediate energies (unless,obviously, one considers very low DM masses).

In the same figure, we show for comparison also lim-its obtained with the older PAMELA data [82] and thedata taken by the BESS-Polar experiment [158]. Inter-estingly, the updated PAMELA analysis allows to placesignificantly stronger limits on a DM contribution ex-actly in the range of masses relevant for the GC GeVexcess (in particular for the bb channel, for lighter quarksthe difference is less pronounced). Notably, this is notmainly due to the longer observation time but due to anoptimized ’spillover’ analysis [82] that results in a some-what different shape of the best-fit background model:in contrast to the old data, the new PAMELA data [82]favour the maximal possible flux contribution that canbe attributed to nuclear and propagation uncertainties(i.e. αprop = αnuc = 1), which is compensated by a sig-nificantly larger best-fit value for the Fisk potential φF(769 MV rather than 496 MV). Despite smaller error bars,this improves the total χ2 of the best-fit model by morethan 2. In view of these relatively large differences, itis comforting to see that an analysis of the BESS-Polardata results in limits that are comparable to the onesobtained with the newer PAMELA data.7

7 BESS-Polar only measured antiproton energies up to 4.7 GeV,which limits the possibility to constrain large DM masses if theFisk potential is left as a completely unconstrained parameterin the analysis. We thus imposed the very conservative [159]restriction of φF < 1.5 GV in our fits, which starts to affect

13

100 101

T [GeV]

10−5

10−4

10−3

10−2

10−1

100φ[1/m

2ssr

GeV

]

MED

MAXχχ → bbmχ = 30 GeV

LIS

TOA, Fornengo et al. 2014 (using HelioProp)

TOA, force-field approximation, φF = 550 MeV

FIG. 12. Comparison of the force-field approximation to so-lar modulation with numerical results using HelioProp [160].The dotted black line shows the local interstellar flux as func-tion of the antiproton kinetic energy; the dashed and solidlines show the top-of-atmosphere flux obtained from the force-field approximation and the numerical results from Ref. [79].We adopt here as two exemplary LIS fluxes the antiproton sig-nals from χχ→ bb with thermal cross-section, mχ = 30 GeV,and using the MED and MAX cosmic-ray propagation sce-narios [85], respectively.

Another potential systematic limitation of our analysisis our treatment of solar modulation. The full 4D propa-gation equations, including the diffusion and drift motionalong the large scale gradients of the spiralling solar mag-netic field, the heliospheric current sheet, and the radiallyexpanding solar wind, were recently implemented in thenumerical code HelioProp [160]. Ref. [79] employedthis code to analyse in detail the effect of solar modu-lation on cosmic-ray antiprotons from DM annihilation.On the other hand, a well-known analytic solution to theeffect of the heliosphere on the flux of cosmic rays – theforce-field approximation [80, 81] – is obtained under thesimplifying assumption of spherical symmetry and con-stant diffusion. It relates the LIS to the TOA flux with asingle modulation parameter, the Fisk potential φF , via(see Refs. [161, 162] for a derivation and discussion)

ΦTOA(TTOA)

ΦLIS(TLIS)=p2TOA

p2LIS

=TTOA(TTOA + 2mp)

TLIS(TLIS + 2mp), (8)

with kinetic energies related by TTOA = TLIS − φF .In Fig. 12, we compare the numerical results from

Ref. [79] that were obtained with HelioProp for twospecific sets of propagation parameters with the resultsthat we find by simply applying the force-field approxi-mation, Eq. (8), like we did in our analysis. As bench-mark scenarios we adopt one of the channels that well

limits from BESS-Polar for mχ & 30 GeV, but has no effect onany of the other limits shown in Fig. 11 or elsewhere.

reproduce the gamma-ray GeV excess, χχ → bb withmχ = 30 GeV, assuming a thermal annihilation cross-section, and the MED and MAX scenarios [85] for theantiproton propagation in the Galaxy. We find that,when adopting a Fisk potential of φF = 500 MeV,the force-field approximation reproduces the numericalresults remarkably well. Though a detailed compari-son between the force-field approximation and a largeset of heliospheric propagation parameters is still lack-ing, we conclude that the force-field approximation isvery well suited to study the impact of solar modula-tion on DM searches with antiprotons for kinetic ener-gies Tp & 0.1 GeV. In particular, uncertainties relatedto heliospheric propagation appear negligible w.r.t. un-certainties coming from cosmic-ray propagation in theGalaxy.

Finally, let us remark that in the above analysis, wefollowed the common approach of adding statistical andsystematic error bars in quadrature to obtain an esti-mate for the overall flux uncertainty. This step neglectspossible bin-to-bin correlations between the systematicerrors, which in the case of the PAMELA data may beoverly optimistic [84]. A correct treatment of systematicuncertainties would require knowledge about the covari-ance matrix of the systematic errors, which is howevernot available. The impact on our results would then, inprinciple, critically depend on the spectral similarity be-tween the principal components of the covariance matrixand the shape of signal and background fluxes.

While we leave a more detailed study to future work,let us here briefly illustrate the possible impact of cor-related systematical errors on our results for a few sim-ple toy scenarios. Firstly, we allow the normalizationof the measured flux to vary by ±5%, correspondingto the typical error stated for the PAMELA 2010 data.We implement this in the fit as a constrained rescalingfactor, αs ∈ [0.95, 1.05], for the measured fluxes. Sec-ondly, we allow the spectral index of the measured fluxto vary. This is implemented as an energy-dependentprefactor αt(E) = 1 + κ log(E/

√EmnEmin), where |κ| ≤

0.05/ log(Emax/Emin). The logic is here that the max-imal deviation that we obtain at the end-points of themeasured spectrum deviates by up to 5% from the nom-inal value. Accounting for correlated systematics in thisway, we find that our limits would be weakened by barelymore than a factor of 2, thus not affecting our conclusionsfor the reference propagation model.

B. Positron limits

Systematic uncertainties that play a role when con-straining DM annihilation into leptonic final states withthe positron flux measurements of AMS-02 were dis-cussed in detail in Ref. [104]. Here, we briefly summarizethe main aspects.

The propagation of cosmic-ray electrons (andpositrons) is dominated by energy losses rather than

14

by diffusion, namely by efficient synchrotron radiationon the Galactic magnetic field and by inverse Comptonscattering on starlight, thermal dust radiation and theCMB. As a consequence, positrons are a much more localprobe of DM annihilation than the other messengersthat we have considered here. In case of the channelthat is most constrained by AMS-02 data, annihilationinto electron-positron pairs, the resulting spectrum afterpropagation has a sharp step-like cutoff at energiesEe± = mχ, with a long tail towards lower energies. Theelectron flux at this energy, and hence the height of thestep, depends almost exclusively on the local energy-lossrate, and hence on the local radiation field, which can beestimated to within 50%. The details of the propagationscenario (height of diffusive halo etc) play on the otherhand only a marginal role for the step-like signal.

Solar modulation will affect the TOA flux of cosmic-ray electrons at energies below 5–10 GeV. For DM massesaround mχ ≈ 10 GeV, this is not relevant for e+e− andµ+µ− final states, where the relevant peak of the signalis close to the DM mass, but it can slightly affect limitsin case of the broader τ+τ− spectrum.

Lastly, the discreteness of astrophysical sources thatmight cause the rise in the positron fraction can poten-tially lead to small variations in the measured energyspectrum. This is currently not observed, but can leadto a variation of the limits on e+e− final states by up toa factor of about three.

C. Radio limits

Our limits in the radio band are essentially based onthree main assumptions: (i) diffusion, advection effectsand energy losses other than those due to synchrotronemission can be neglected, (ii) energy equipartition inthe accretion zone, i.e. at galactocentric distances smallerthan ∼ 0.04 pc, and magnetic flux conservation outside,(iii) the monochromatic approximation for synchrotronemission. As already discussed, however, a strong mag-netic field as adopted in our model is observationally wellsupported [119], and our limits are rather insensitive tothe monochromatic approximation; we will hence mostlyconcentrate on a discussion of (i).

In deriving Eq. (5) as a condition for (i) to be sat-isfied, we made use of the fact that for sufficiently largemagnetic fields and turbulent conditions the diffusion co-efficient approaches the critical (i.e. minimum possible)value of D ∼ DBohm = rgc/3. Deviations from the as-sumption of Bohm diffusion will lead to less frequent scat-tering and more efficient transport, D = κDBohm, wherewe introduced a free parameter κ ≥ 1 to account forthis possibility. Importantly, even allowing κ 1 thecondition for the neglection of diffusion in Eq. (5) scalesonly with a factor of κ1/3 on the right-hand side (at leastfor constant B). This has profound consequences for therobustness of our radio limits: The bulk of the radiosignal of interest comes from a relatively small range of

G=1.04rc =2pc

10 20 3015

10-26

2

3

5

mΧ@GeVD

Σv@

cm3

sD

FIG. 13. Same as Fig. 9, but for constant magnetic fields ofstrength B = 50µG (dot-dashed lines), B = 8 mG (dottedlines), and our baseline magnetic field model (solide lines).The constant values correspond to the recently obtained lowerlimits at a galactocentric distance of ∼ 0.1 pc [119].

distances from the Galactic center, around r ∼ 0.1 pc,depending on the shape of the DM profile (see Fig. 8).Observations give a lower limit on the magnetic field thatis around 8 mG [119] at these scales. We thus find that atr ' 0.1 pc diffusion can be neglected even if the diffusionconstant is ∼ 107 times larger than the Bohm value.

Since the requirement of in situ energy loss is very wellsatisfied, our limits depend much more on the DM profilethan on the magnetic field strength. This is visualizedin Fig. 9, but also directly apparent from Eq. (6) whereρχ enters squared and gives a particularly large contribu-tion to the volume integration for singular profiles. Theproduct ENe(E), on the other hand, determines the de-pendence on B (implying in fact slightly stronger limitsfor weaker magnetic fields). In the limit of E mχ,corresponding to large magnetic field values, Ne(E) ap-proaches a constant and the synchrotron flux scales asE ∝ B−1/2. In general, Ne(E) is a monotonically de-creasing function of E, which implies that the actual B-dependence of Eq. (6) will in practice be smaller. Anintuitive way to understand this relatively weak depen-dence of the flux density for a given frequency is that, inthe limit of synchrotron losses happening in situ as dis-cussed above, the value of B does not affect anymore thetotal power radiated away but merely the frequency atwhich this happens. Note also that for larger magneticfields B, we do not need to follow the super-conservativeapproach of only integrating up to 1 pc (see Fig. 8). Thisimplies that – in case of cored profiles – limits will real-istically weaken even less with increased magnetic fieldvalues.

To illustrate the scaling of the limits withB, we presentin Fig. 13 the cases where the magnetic field takes theconstant values B = 50 µG and B = 8 mG, as mo-tivated by the recently obtained lower limits [119] dis-

15

cussed above, and compare the resulting limits with thoseshown for our baseline magnetic field model in Fig. 10.Interestingly, the case of a constant magnetic field ofB = 50 µG leads indeed to very similar limits. At DMmasses mχ 50 GeV, limits weaken as expected with a

factor of (8 mG/50µG)1/2 ∼ 13 when instead adoptingthe much larger constant field of B = 8 mG. At lowmasses, they may however even strengthen due to theNe(E) dependence discussed above. In both cases, wesee that DM annihilation into 80% τ+τ− + 20% bb leadsto limits that exclude the interpretation of the excessin terms of such annihilations, whereas a large magneticfield of B = 8 mG would require a slightly smaller coresize in the profile, rc . 2 pc, to fully exclude also thepossibility of bb final states.

Let us conclude this Section by mentioning a very re-cent analysis [163] which revisited radio constraints onDM annihilation in the GC. In particular, this analy-sis challenges the standard assumption of in situ energylosses of the emitted electrons due to synchrotron radia-tion when taking into account inverse Compton scatter-ing (ICS), or strong convective winds in the inner Galaxy.For the magnetic field model that we have adopted, e.g.,the limits are claimed to weaken by more than two ordersof magnitude when including ICS off the dense interstel-lar radiation field close to the GC (but note that the ac-tual B-field is likely stronger, as discussed above, whichwould make ICS less important in proportion). Togetherwith the assumption of a very strong convective windthat blows electrons away from the galactic disk with avelocity of vc ∼ 1000 km/s, this would result in a weak-ening of our limits by less than 4 orders of magnitude intotal. For a steep profile with Γ = 1.26, however, eventhis extreme case is not sufficient to make the GC excesscompatible with radio observations unless one introducesan artificial cutoff at rc & 0.1 pc.

V. SUMMARY

In Fig. 14 we present a summary of the constraintson DM annihilation that we derived from antiproton,positron and radio observations, and confront them withrepresentative benchmark scenarios that can explain theGC GeV excess observed with Fermi LAT. Since the an-nihilation cross-section that best reproduces the gamma-ray signal depends on the assumption on the DM pro-file, in particular the inner slope Γ and the local DMdensity, in Fig. 14 we normalize the annihilation cross-section to the values that best reproduce the GeV excess(cp. Tab. I). In this way, we collapse the best-fit regionsinto one single region, which is per construction centeredonto one. The limits change then according to the slopeΓ (and the scale radius rs, which we will comment on be-low), whereas the overall normalization of the DM pro-file drops out (as do symmetry factors in the annihilationrate related to whether or not the DM particles are theirown antiparticles).

In case of DM annihilation into bb final states, as shownin the upper left panel of Fig. 14, limits from existingobservations of antiprotons firmly exclude the DM in-terpretation of the GeV excess by almost one order ofmagnitude, if our benchmark KRA scenario is adoptedfor the propagation of Galactic cosmic rays. These lim-its weaken by about a factor of two if Γ increases fromΓ = 1.04 to Γ = 1.26. Note that, as shown in Fig. 1,variations in the scale radius rs introduce another uncer-tainty in the local annihilation rate that can be as large asa factor of two, which in case of very cuspy profiles (likeΓ = 1.26) will typically tend to increase the annihilationsignal when mass constraints on the Milky Way are takeninto account. However, we checked explicitly that theantiproton limits – which probe a relatively large annihi-lation volume – are only strengthened by 24 % (weakenedby 39 %) when changing our references value of rs from20 kpc to 35 kpc (10 kpc). As shown in Fig. 5, in caseof the very conservative MIN’ propagation scenario thelimits can weaken by an additional factor of 7–8. Only inthis extreme propagation setting, the GeV excess wouldstill be marginally consistent with current antiproton ob-servations – implying that AMS-02 will either observe acorresponding excess in antiprotons or rule out even thisremaining possibility.

We also show limits obtained from 408 MHz JodrellBank radio observations of the inner 4” centered on theGC. As discussed above, these limits are rather robustconcerning assumptions on the magnetic field, but theycritically depend on the adopted DM profile. Most im-portantly, in case of the gamma-ray excess, the DM pro-file is fixed to a large extent, allowing to make muchmore precise signal predictions. For a profile that re-mains cuspy all the way down to . 0.1 pc, all channelsthat could explain the GeV excess are ruled out by sev-eral orders of magnitude (cp. Fig. 9) – though these limitsbecome much less severe when allowing for strong convec-tive winds or ICS to dominate over synchrotron emission[163]. In Fig. 14, we show limits that are obtained for anad hoc flattening of the generalized NFW profile at radiibelow 2 pc. Even with such an artificial core, in case ofthe cuspy Γ = 1.26 the limits still exclude the DM inter-pretation of the GeV excess by more than one order ofmagnitude. Note that GC radio observations only probethe innermost region of the DM halo. The resulting lim-its thus do not depend on the scale radius rs, see Fig. 1.For the same reason, steeper profiles imply much strongerradio constraints in the context of the GeV excess, whilethey imply slightly weaker constraints for antiprotons. Incase of DM annihilation into cc or light quarks qq (upperright and lower left panel of Fig. 14), the limits obtainedfrom radio and antiproton observations are quantitativelyvery similar to the case of bb.

In the lower right panel of Fig. 14, we finally show lim-its on the mixed final state τ+τ− (80%) plus bb (20%),which was motivated in Ref. [21] by a spectral fit to theexcess seen in the inner Galaxy (see also the discussionin Section II A). In this case, antiproton constraints only

16

FIG. 14. Summary of our limits for various annihilation channels, expressed in terms of the ratio of the corresponding limiton 〈σv〉 and the best-fit DM signal interpretation. For convenience, we also show the corresponding 1σ, 2σ and 3σ regionsdescribing the signal from the inner Galaxy analysis [21] (see also Fig. 2). Dashed lines show limits for a generalized NFWprofile with slope Γ = 1.26 and solid lines show the corresponding limits for Γ = 1.04 (note that the limits presented this wayare independent of any overall normalization of the DM profile, e.g. in terms of the local DM density ρ = 0.3 GeV cm−3). Inall panels, antiproton limits are displayed in green, positron limits in blue and radio limits in red. Radio constraints assumethat the DM profile flattens out at radii below 2 pc from the GC. See text for further details.

lead to an exclusion by a factor of roughly 2 in case of theKRA propagation scenario (and no exclusion if the MIN’model is adopted). However, radio limits firmly excludethis channel for a DM profile that remains cuspy down toat least 2 pc. Additional robust constraints derive fromthe shape analysis [104] of the flux of cosmic-ray positronsas measured by AMS-02, which again marginally ex-cludes the interpretation of the gamma-ray GeV excessin terms of DM annihilation into τ+τ− final states fora cuspy profile with Γ = 1.26 (as preferred by the in-ner galaxy analysis of Ref. [21]). As discussed above (seeFigs. 6 and 7), these limits are much stronger in case ofother leptonic final states, and exclude branching ratiosinto e+e− down to about ∼ 2.3 × 10−2, and down to∼ 2.5× 10−1 in case of µ+µ− final states. Note that un-certainties related to the scale radius rs of the DM profileare larger than for antiprotons and can in principle be aslarge as a factor of two; for Γ = 1.26, however, they tendto increase the local annihilation signal.

We recall that a larger contribution of ττ final statesthan 80% results in a spectrum that no longer provides areasonable fit to the observed GeV excess, even when tak-ing into account the contribution from bremsstrahlungand inverse Compton scattering. A smaller contribu-tion, on the other hand, necessarily implies a larger bb(or lighter quark) contribution in view of the strongAMS-02 limits on light leptons as annihilation products.While a mixed final state with a smaller τ± componentcould evade AMS-02 bounds, the antiproton bounds fromPAMELA would thus become even more severe.

In summary, we find that the DM interpretation of theGeV excess in terms of hadronic or leptonic final states isstrongly constrained by our analysis of existing antipro-ton, positron and radio data. A way to make these limitseven more robust would be to study diffusion parameters,in particular the truly minimal diffusion zone height, inlight of existing radio, gamma-ray and cosmic-ray obser-vations in a combined analysis. For the case of antiproton

17

limits, the most important next step would then be tosystematically improve on the nuclear uncertainties con-nected to secondary antiproton production. For positronlimits on τ+τ− final states, on the other hand, a dedi-cated study of the effects of solar modulation on the spec-trum of DM induced positrons below energies of ∼ 5 GeVwould be more warranted. Avoiding the radio limits wehave presented requires a dedicated discussion of whatmechanisms could give rise to a DM profile that is cuspyin the inner Galaxy, down to O(10) pc scales, but has acore with an extension of a few pc at its center. Lastbut not least, it will certainly help to get a better handleon the systematics connected to the determination of theDM profile slope Γ, as well as the scale radius rs, fromgamma-ray and dynamical observations.

While all those possible directions of further investi-gation clearly lie beyond the scope of the present study,they certainly indicate that there is room to make indi-rect DM searches even more competitive – especially forlight DM models, but independently of the concrete ap-plication of the GeV gamma-ray excess currently claimedat the GC and inner Galaxy.

VI. CONCLUSIONS

In this article, we have revisited current bounds fromindirect searches for DM and identified the messengersand targets that are most relevant for light DM, i.e. formasses roughly below 100 GeV:

• For DM annihilation into light charged leptons,positrons provide the most stringent and robustbounds [104, 105]. This constrains the ’thermal’annihilation rate of 〈σv〉 = 3 · 10−26cm3s−1 formasses of roughly mχ . 200 GeV (mχ . 100 GeV)assuming dominant annihilation to e+e− (µ+µ−)final states.

• As has been pointed out earlier, antiprotons providea very efficient means of constraining light DM an-nihilating into quarks [95, 164–166]. Here, we havederived new bounds that constrain the thermal an-nihilation rate for mχ . 55 GeV in the case of bbfinal states, and for mχ . 35 GeV if annihilationinto light quarks dominates.

• Null-searches for 408 MHz radio signals from a 4”region around the GC, finally, provide extremelystringent constraints [107–115]. We revisited thosebounds and discussed that the dependence on as-sumptions about the magnetic field is typicallymuch smaller than that related to the DM den-sity at pc scales away from the GC. For a cuspyprofile (like NFW) that extends down to at least0.1 pc, thermal cross sections are excluded for DMmasses below roughly 120 GeV (for τ+τ−) or even400 GeV (for bb).

As an application, we have discussed at length thatthese findings are particularly relevant for a possible DMinterpretation of the much-debated excess in GeV gammarays from the GC and inner Galaxy [21–27]. In fact, suchan interpretation requires a well-defined and highly con-strained region both in the 〈σv〉 vs. mχ plane and in therange of possible DM density profiles. This implies thatconstraints from other indirect detection methods can di-rectly be applied and are subject to much less severe un-certainties than in the absence of a signal indication. Forexample, these constraints become independent of theoverall normalization of the annihilation rate and thus,e.g., of the DM production mechanism. In fact, probingthe same annihilation mechanism, such constraints aremuch more model-independent than constraints derivedfrom collider or direct searches [43–47].

For reasonable benchmark scenarios for cosmic-raypropagation and a DM density profile consistent withthe observed excess, we basically find that all annihila-tion channels that were considered in Ref. [21] are ruledout (the same holds for purely leptonic annihilation chan-nels, which were suggested in Ref. [62]). The tensioncan be somewhat alleviated by (a) assuming a borderlinepropagation scenario with minimal diffusion zone height(our MIN’) and (b) assuming that the DM profile cutsoff at radii of at least ∼ 5 pc from the Galactic cen-ter (while keeping its Γ = 1.26 slope observed at largerradii r & 10 pc). On the model-building side, the tensioncould also be made somewhat less severe by consideringcascade decays [36, 39, 167] rather than the direct decayinto two SM particle final states that we have consideredhere. While a thorough investigation of this possibilitylies beyond the scope of this work, we do not expect ourconclusions to change qualitatively.

A confirmation of the DM interpretation of the GeVexcess clearly requires corroborating evidence from multi-ple observations. While this could also come from collideror direct probes, indirect searches arguably provide themost model-independent way of testing the signal. Eventhough the excess is already in rather strong tension withthese searches, it is conceivable that the individual uncer-tainties of the respective limits (as discussed in SectionIV and summarized in Section V) conspire such that asignal interpretation would still be viable. In this case,an independent confirmation of the GeV excess as a DMsignal – if indeed true – is likely to be just around thecorner.

ACKNOWLEDGMENTS

We would like to thank Lars Bergstrom, Celine Boehm,Mirko Boezio, Carmelo Evoli, Dan Hooper, Tim Linden,Meng Su, Jacco Vink, and Wei Xue for very useful dis-cussions. TB acknowledges support from the GermanResearch Foundation (DFG) through the Emmy Noether

18

grant BR 3954/1-1. TB and CW thank NORDITA forgenerous support and an inspiring atmosphere in the con-text of the programme “What is Dark Matter?”, wherepart of this work was completed. MV acknowledgessupport from the Forschungs- und WissenschaftsstiftungHamburg through the program “Astroparticle Physicswith Multiple Messengers”. This work makes use ofSciPy [168], Minuit [169] and Matplotlib [170].

Note added. After the submission of this work, an-other comprehensive analysis of antiproton constraintson the GeV excess appeared on the arXiv [171], adopt-ing a somewhat different background parameterizationand statistical method.

[1] M. Cirelli, “Indirect Searches for Dark Matter: a sta-tus review,” Pramana 79, 1021 (2012) [arXiv:1202.1454[hep-ph]].

[2] J. Lavalle and P. Salati, “Dark Matter Indirect Sig-natures,” Comptes Rendus Physique 13, 740 (2012)[arXiv:1205.1004 [astro-ph.HE]].

[3] T. Bringmann and C. Weniger, “Gamma Ray Signalsfrom Dark Matter: Concepts, Status and Prospects,”Phys. Dark Univ. 1, 194 (2012) [arXiv:1208.5481 [hep-ph]].

[4] A. Cesarini, F. Fucito, A. Lionetto, A. Morselli andP. Ullio, “The Galactic center as a dark matter gamma-ray source,” Astropart. Phys. 21, 267 (2004) [astro-ph/0305075].

[5] D. Horns, “TeV gamma-radiation from dark matter an-nihilation in the Galactic center,” Phys. Lett. B 607,225 (2005) [Erratum-ibid. B 611, 297 (2005)] [astro-ph/0408192].

[6] L. Bergstrom, T. Bringmann, M. Eriksson andM. Gustafsson, “Gamma rays from Kaluza-Klein darkmatter,” Phys. Rev. Lett. 94, 131301 (2005) [astro-ph/0410359].

[7] T. Bringmann, X. Huang, A. Ibarra, S. Vogland C. Weniger, “Fermi LAT Search for InternalBremsstrahlung Signatures from Dark Matter Annihi-lation,” JCAP 1207, 054 (2012) [arXiv:1203.1312 [hep-ph]].

[8] C. Weniger, “A Tentative Gamma-Ray Line from DarkMatter Annihilation at the Fermi Large Area Tele-scope,” JCAP 1208, 007 (2012) [arXiv:1204.2797 [hep-ph]].

[9] M. Su and D. P. Finkbeiner, “Strong Evidence forGamma-ray Line Emission from the Inner Galaxy,”arXiv:1206.1616 [astro-ph.HE].

[10] A. V. Belikov, G. Zaharijas and J. Silk, “Study of theGamma-ray Spectrum from the Galactic Center in viewof Multi-TeV Dark Matter Candidates,” Phys. Rev. D86, 083516 (2012) [arXiv:1207.2412 [astro-ph.HE]].

[11] D. Hooper, D. P. Finkbeiner and G. Dobler, “Possibleevidence for dark matter annihilations from the excessmicrowave emission around the center of the Galaxyseen by the Wilkinson Microwave Anisotropy Probe,”Phys. Rev. D 76, 083012 (2007) [arXiv:0705.3655 [astro-ph]].

[12] C. Boehm, D. Hooper, J. Silk, M. Casse and J. Paul,“MeV dark matter: Has it been detected?,” Phys. Rev.Lett. 92, 101301 (2004) [astro-ph/0309686].

[13] L. Bergstrom, P. Ullio and J. H. Buckley, “Observabil-ity of gamma-rays from dark matter neutralino annihi-lations in the Milky Way halo,” Astropart. Phys. 9, 137(1998) [astro-ph/9712318].

[14] T. Bringmann, F. Calore, G. Vertongen and C. Weniger,“On the Relevance of Sharp Gamma-Ray Features forIndirect Dark Matter Searches,” Phys. Rev. D 84,103525 (2011) [arXiv:1106.1874 [hep-ph]].

[15] R. E. Lingenfelter, J. C. Higdon and R. E. Rothschild,“Is There a Dark Matter Signal in the Galactic PositronAnnihilation Radiation?,” Phys. Rev. Lett. 103, 031301(2009) [arXiv:0904.1025 [astro-ph.HE]].

[16] D. T. Cumberbatch, J. Zuntz, H. K. K. Eriksen andJ. Silk, “Can the WMAP Haze really be a signature ofannihilating neutralino dark matter?,” arXiv:0902.0039[astro-ph.GA].

[17] F. Aharonian et al. [H.E.S.S. Collaboration], “H.E.S.S.observations of the Galactic Center region and their pos-sible dark matter interpretation,” Phys. Rev. Lett. 97,221102 (2006) [Erratum-ibid. 97, 249901 (2006)] [astro-ph/0610509].

[18] F. W. Stecker, S. D. Hunter and D. A. Kniffen,“The Likely Cause of the EGRET GeV Anomalyand its Implications,” Astropart. Phys. 29, 25 (2008)[arXiv:0705.4311 [astro-ph]].

[19] M. Ackermann et al. [Fermi-LAT Collaboration],“Search for Gamma-ray Spectral Lines with the FermiLarge Area Telescope and Dark Matter Implications,”Phys. Rev. D 88, 082002 (2013) [arXiv:1305.5597 [astro-ph.HE]].

[20] See http://fermi.gsfc.nasa.gov/ssc/.

[21] T. Daylan, D. P. Finkbeiner, D. Hooper, T. Linden,S. K. N. Portillo, N. L. Rodd and T. R. Slatyer, “TheCharacterization of the Gamma-Ray Signal from theCentral Milky Way: A Compelling Case for Annihilat-ing Dark Matter,” arXiv:1402.6703 [astro-ph.HE].

[22] L. Goodenough and D. Hooper, “Possible EvidenceFor Dark Matter Annihilation In The Inner MilkyWay From The Fermi Gamma Ray Space Telescope,”arXiv:0910.2998 [hep-ph].

[23] D. Hooper and L. Goodenough, “Dark Matter Anni-hilation in The Galactic Center As Seen by the FermiGamma Ray Space Telescope,” Phys. Lett. B 697, 412(2011) [arXiv:1010.2752 [hep-ph]].

[24] D. Hooper and T. Linden, “On The Origin Of TheGamma Rays From The Galactic Center,” Phys. Rev.D 84, 123005 (2011) [arXiv:1110.0006 [astro-ph.HE]].

19

[25] K. N. Abazajian and M. Kaplinghat, “Detection of aGamma-Ray Source in the Galactic Center Consistentwith Extended Emission from Dark Matter Annihilationand Concentrated Astrophysical Emission,” Phys. Rev.D 86, 083511 (2012) [arXiv:1207.6047 [astro-ph.HE]].

[26] O. Macias and C. Gordon, “The Contribution of CosmicRays Interacting With Molecular Clouds to the GalacticCenter Gamma-Ray Excess,” Phys. Rev. D 89, 063515(2014) [arXiv:1312.6671 [astro-ph.HE]].

[27] K. N. Abazajian, N. Canac, S. Horiuchi and M. Kapling-hat, “Astrophysical and Dark Matter Interpretations ofExtended Gamma-Ray Emission from the Galactic Cen-ter,” Phys. Rev. D 90, 023526 (2014) [arXiv:1402.4090[astro-ph.HE]].

[28] D. Hooper and T. R. Slatyer, “Two Emission Mecha-nisms in the Fermi Bubbles: A Possible Signal of Anni-hilating Dark Matter,” Phys. Dark Univ. 2, 118 (2013)[arXiv:1302.6589 [astro-ph.HE]].

[29] W. -C. Huang, A. Urbano and W. Xue, “Fermi Bub-bles under Dark Matter Scrutiny. Part I: AstrophysicalAnalysis,” arXiv:1307.6862 [hep-ph].

[30] D. Hooper, “The Empirical Case For 10 GeV Dark Mat-ter,” Phys. Dark Univ. 1, 1 (2012) [arXiv:1201.1303[astro-ph.CO]].

[31] A. Hektor and L. Marzola, “Coy Dark Matter and theanomalous magnetic moment,” Phys. Rev. D 90, 053007(2014) [arXiv:1403.3401 [hep-ph]].

[32] P. Agrawal, B. Batell, D. Hooper and T. Lin, “FlavoredDark Matter and the Galactic Center Gamma-Ray Ex-cess,” Phys. Rev. D 90, 063512 (2014) [arXiv:1404.1373[hep-ph]].

[33] D. G. Cerdeno, M. PeirA´o and S. Robles, “Low-massright-handed sneutrino dark matter: SuperCDMS andLUX constraints and the Galactic Centre gamma-rayexcess,” JCAP 1408, 005 (2014) [arXiv:1404.2572 [hep-ph]].

[34] S. Ipek, D. McKeen and A. E. Nelson, “A Renormal-izable Model for the Galactic Center Gamma Ray Ex-cess from Dark Matter Annihilation,” Phys. Rev. D 90,055021 (2014) [arXiv:1404.3716 [hep-ph]].

[35] P. Ko, W. I. Park and Y. Tang, “Higgs portal vectordark matter for GeV scale γ-ray excess from galacticcenter,” JCAP 1409, 013 (2014) [arXiv:1404.5257 [hep-ph]].

[36] C. Boehm, M. J. Dolan and C. McCabe, “A weighty in-terpretation of the Galactic Centre excess,” Phys. Rev.D 90, 023531 (2014) [arXiv:1404.4977 [hep-ph]].

[37] M. Abdullah, A. DiFranzo, A. Rajaraman,T. M. P. Tait, P. Tanedo and A. M. Wijangco,“Hidden On-Shell Mediators for the Galactic CenterGamma-Ray Excess,” Phys. Rev. D 90, 035004 (2014)[arXiv:1404.6528 [hep-ph]].

[38] D. K. Ghosh, S. Mondal and I. Saha, “Confrontingthe Galactic Center Gamma Ray Excess With a LightScalar Dark Matter,” arXiv:1405.0206 [hep-ph].

[39] A. Martin, J. Shelton and J. Unwin, “Fitting the Galac-tic Center Gamma-Ray Excess with Cascade Annihila-tions,” arXiv:1405.0272 [hep-ph].

[40] A. Berlin, P. Gratia, D. Hooper and S. D. McDermott,“Hidden Sector Dark Matter Models for the GalacticCenter Gamma-Ray Excess,” Phys. Rev. D 90, 015032(2014) [arXiv:1405.5204 [hep-ph]].

[41] T. Basak and T. Mondal, “Class of Higgs-portal DarkMatter models in the light of gamma-ray excess fromGalactic center,” arXiv:1405.4877 [hep-ph].

[42] J. M. Cline, G. Dupuis, Z. Liu and W. Xue, “The win-dows for kinetically mixed Z′-mediated dark matter andthe galactic center gamma ray excess,” JHEP 1408, 131(2014) [arXiv:1405.7691 [hep-ph]].

[43] A. Alves, S. Profumo, F. S. Queiroz and W. Shepherd,“The Effective Hooperon,” arXiv:1403.5027 [hep-ph].

[44] A. Berlin, D. Hooper and S. D. McDermott, “Sim-plified Dark Matter Models for the Galactic CenterGamma-Ray Excess,” Phys. Rev. D 89, 115022 (2014)[arXiv:1404.0022 [hep-ph]].

[45] E. Izaguirre, G. Krnjaic and B. Shuve, “The GalacticCenter Excess from the Bottom Up,” Phys. Rev. D 90,055002 (2014) [arXiv:1404.2018 [hep-ph]].

[46] K. Kong and J. C. Park, “Bounds on dark matter in-terpretation of Fermi-LAT GeV excess,” Nucl. Phys. B888, 154 (2014) [arXiv:1404.3741 [hep-ph]].

[47] T. Han, Z. Liu and S. Su, “Light Neutralino Dark Mat-ter: Direct/Indirect Detection and Collider Searches,”JHEP 1408, 093 (2014) [arXiv:1406.1181 [hep-ph]].

[48] F. Calore, I. Cholis and C. Weniger, “Background modelsystematics for the Fermi GeV excess,” arXiv:1409.0042[astro-ph.CO].

[49] K. N. Abazajian, “The Consistency of Fermi-LAT Ob-servations of the Galactic Center with a Millisecond Pul-sar Population in the Central Stellar Cluster,” JCAP1103, 010 (2011) [arXiv:1011.4275 [astro-ph.HE]].

[50] W. Wang, Z. J. Jiang and K. S. Cheng, “Contribution todiffuse gamma-rays in the Galactic Center region fromunresolved millisecond pulsars,” Mon. Not. Roy. Astron.Soc. 358, 263 (2005) [astro-ph/0501245].

[51] A. Boyarsky, D. Malyshev and O. Ruchayskiy, “A com-ment on the emission from the Galactic Center as seenby the Fermi telescope,” Phys. Lett. B 705 (2011) 165[arXiv:1012.5839 [hep-ph]].

[52] F. Yusef-Zadeh, J. W. Hewitt, M. Wardle, V. Tatis-cheff, D. A. Roberts, W. Cotton, H. Uchiyama andM. Nobukawa et al., “Interacting Cosmic Rays withMolecular Clouds: A Bremsstrahlung Origin of DiffuseHigh Energy Emission from the Inner 2deg by 1degof the Galactic Center,” Astrophys. J. 762, 33 (2013)[arXiv:1206.6882 [astro-ph.HE]].

[53] T. Linden, E. Lovegrove and S. Profumo, “The Mor-phology of Hadronic Emission Models for the Gamma-Ray Source at the Galactic Center,” Astrophys. J. 753,41 (2012) [arXiv:1203.3539 [astro-ph.HE]].

[54] C. Gordon and O. Macias, “Dark Matter and PulsarModel Constraints from Galactic Center Fermi-LATGamma Ray Observations,” Phys. Rev. D 88 (2013)083521 [arXiv:1306.5725 [astro-ph.HE]].

[55] S. K. N. Portillo and D. P. Finkbeiner, “Sharper FermiLAT Images: instrument response functions for an im-proved event selection,” arXiv:1406.0507 [astro-ph.IM].

[56] O. Y. Gnedin, A. V. Kravtsov, A. A. Klypin and D. Na-gai, “Response of dark matter halos to condensation ofbaryons: Cosmological simulations and improved adia-batic contraction model,” Astrophys. J. 616, 16 (2004)[astro-ph/0406247].

[57] J. F. Navarro, C. S. Frenk and S. D. M. White, Astro-phys. J. 462, 563 (1996) [astro-ph/9508025].

[58] F. Iocco, M. Pato, G. Bertone and P. Jetzer, “DarkMatter distribution in the Milky Way: microlensing

20

and dynamical constraints,” JCAP 1111, 029 (2011)[arXiv:1107.5810 [astro-ph.GA]].

[59] L. Pieri, J. Lavalle, G. Bertone and E. Branchini, “Im-plications of High-Resolution Simulations on IndirectDark Matter Searches,” Phys. Rev. D 83, 023518 (2011)[arXiv:0908.0195 [astro-ph.HE]].

[60] M. Cirelli, G. Corcella, A. Hektor, G. Hutsi,M. Kadastik, P. Panci, M. Raidal and F. Sala etal., “PPPC 4 DM ID: A Poor Particle PhysicistCookbook for Dark Matter Indirect Detection,” JCAP1103, 051 (2011) [Erratum-ibid. 1210, E01 (2012)][arXiv:1012.4515 [hep-ph]].

[61] X. X. Xue et al. [SDSS Collaboration], “The MilkyWay’s Circular Velocity Curve to 60 kpc and an Esti-mate of the Dark Matter Halo Mass from Kinematics of2400 SDSS Blue Horizontal Branch Stars,” Astrophys.J. 684, 1143 (2008) [arXiv:0801.1232 [astro-ph]].

[62] T. Lacroix, C. Boehm and J. Silk, “Fitting the Fermi-LAT GeV excess: On the importance of including thepropagation of electrons from dark matter,” Phys. Rev.D 90, 043508 (2014) [arXiv:1403.1987 [astro-ph.HE]].

[63] A. A. Abdo et al. [The Fermi-LAT Collaboration], “TheSecond Fermi Large Area Telescope Catalog of Gamma-ray Pulsars,” Astrophys. J. Suppl. 208, 17 (2013)[arXiv:1305.4385 [astro-ph.HE]].

[64] D. Hooper, I. Cholis, T. Linden, J. Siegal-Gaskins andT. Slatyer, “Millisecond pulsars Cannot Account for theInner Galaxy’s GeV Excess,” Phys. Rev. D 88, 083009(2013) [arXiv:1305.0830 [astro-ph.HE]].

[65] F. Calore, M. Di Mauro and F. Donato, “Diffusegamma-ray emission from galactic pulsars,” Astrophys.J. 796, 1 (2014) [arXiv:1406.2706 [astro-ph.HE]].

[66] Q. Yuan and B. Zhang, “Millisecond pulsar interpreta-tion of the Galactic center gamma-ray excess,” JHEAp3-4, 1 (2014) [arXiv:1404.2318 [astro-ph.HE]].

[67] F. Aharonian et al. [H.E.S.S. Collaboration], “Discoveryof very-high-energy gamma-rays from the galactic centreridge,” Nature 439, 695 (2006) [astro-ph/0603021].

[68] J. Petrovic, P. D. Serpico and G. Zaharijas, “Galac-tic Center gamma-ray ”excess” from an active past ofthe Galactic Centre?,” JCAP 1410, no. 10, 052 (2014)[arXiv:1405.7928 [astro-ph.HE]].

[69] E. Carlson and S. Profumo, Phys. Rev. D 90, 023015(2014) [arXiv:1405.7685 [astro-ph.HE]].

[70] P. Gondolo, J. Edsjo, P. Ullio, L. Bergstrom,M. Schelke, E. A. Baltz, T. Bringmann and G. Duda,http://www.darksusy.org; P. Gondolo, J. Edsjo, P. Ul-lio, L. Bergstrom, M. Schelke and E. A. Baltz, “Dark-SUSY: Computing supersymmetric dark matter prop-erties numerically,” JCAP 0407, 008 (2004) [astro-ph/0406204].

[71] T. Sjostrand, S. Mrenna and P. Z. Skands, “PYTHIA6.4 Physics and Manual,” JHEP 0605, 026 (2006) [hep-ph/0603175].

[72] J. Silk and M. Srednicki, “Cosmic Ray anti-Protons asa Probe of a Photino Dominated Universe,” Phys. Rev.Lett. 53, 624 (1984).

[73] For a review see, e.g., P. Salati, F. Donato and N. For-nengo, “Indirect Dark Matter Detection with CosmicAntimatter,” In *Bertone, G. (ed.): Particle dark mat-ter* 521-546 [arXiv:1003.4124 [astro-ph.HE]].

[74] T. Bringmann and P. Salati, “The galactic antiprotonspectrum at high energies: Background expectation vs.exotic contributions,” Phys. Rev. D 75, 083006 (2007)

[astro-ph/0612514].[75] F. Donato, D. Maurin, P. Salati, A. Barrau, G. Boudoul

and R. Taillet, “Anti-protons from spallations of cos-mic rays on interstellar matter,” Astrophys. J. 563, 172(2001) [astro-ph/0103150].

[76] D. Maurin, F. Donato, R. Taillet and P. Salati, “Cos-mic rays below z=30 in a diffusion model: new con-straints on propagation parameters,” Astrophys. J. 555,585 (2001) [astro-ph/0101231].

[77] M. di Mauro, F. Donato, A. Goudelis and P. D. Serpico,“New evaluation of the antiproton production cross sec-tion for cosmic ray studies,” Phys. Rev. D 90, no. 8,085017 (2014) [arXiv:1408.0288 [hep-ph]].

[78] R. Kappl and M. W. Winkler, “The Cosmic Ray An-tiproton Background for AMS-02,” JCAP 1409, no. 09,051 (2014) [arXiv:1408.0299 [hep-ph]].

[79] N. Fornengo, L. Maccione and A. Vittino, “Constraintson particle dark matter from cosmic-ray antiprotons,”JCAP 1404, 003 (2014) [arXiv:1312.3579 [hep-ph]].

[80] L. J. Gleeson and W. I. Axford, “Solar Modulation ofGalactic Cosmic Rays,” Astrophys. J. 154, 1011 (1968).

[81] J. S. Perko, Astron. Astrophys. 184, 119 (1987).[82] O. Adriani, G. A. Bazilevskaya, G. C. Barbarino, R. Bel-

lotti, M. Boezio, E. A. Bogomolov, V. Bonvicini andM. Bongi et al., “Measurement of the flux of primarycosmic ray antiprotons with energies of 60-MeV to 350-GeV in the PAMELA experiment,” JETP Lett. 96, 621(2013) [Pisma Zh. Eksp. Teor. Fiz. 96, 693 (2012)].

[83] O. Adriani et al. [PAMELA Collaboration], “PAMELAresults on the cosmic-ray antiproton flux from 60 MeVto 180 GeV in kinetic energy,” Phys. Rev. Lett. 105,121101 (2010) [arXiv:1007.0821 [astro-ph.HE]].

[84] M. Boezio, private communication.[85] F. Donato, N. Fornengo, D. Maurin and P. Salati, “An-

tiprotons in cosmic rays from neutralino annihilation,”Phys. Rev. D 69, 063501 (2004) [astro-ph/0306207].

[86] G. Di Bernardo, C. Evoli, D. Gaggero, D. Grasso andL. Maccione, “Unified interpretation of cosmic-ray nu-clei and antiproton recent measurements,” Astropart.Phys. 34, 274 (2010) [arXiv:0909.4548 [astro-ph.HE]].

[87] A. Putze, L. Derome and D. Maurin, “A Markov ChainMonte Carlo technique to sample transport and sourceparameters of Galactic cosmic rays: II. Results for thediffusion model combining B/C and radioactive nuclei,”Astron. Astrophys. 516, A66 (2010) [arXiv:1001.0551[astro-ph.HE]].

[88] T. Delahaye, A. Fiasson, M. Pohl and P. Salati, “TheGeV-TeV Galactic gamma-ray diffuse emission I. Uncer-tainties in the predictions of the hadronic component,”Astron. Astrophys. 531, A37 (2011) [arXiv:1102.0744[astro-ph.HE]].

[89] [Fermi-LAT Collaboration], “Fermi-LAT Observationsof the Diffuse Gamma-Ray Emission: Implications forCosmic Rays and the Interstellar Medium,” Astrophys.J. 750, 3 (2012) [arXiv:1202.4039 [astro-ph.HE]].

[90] T. Delahaye, F. Donato, N. Fornengo, J. Lavalle,R. Lineros, P. Salati and R. Taillet, “Galactic secondarypositron flux at the Earth,” Astron. Astrophys. 501, 821(2009) [arXiv:0809.5268 [astro-ph]].

[91] J. Lavalle, “Impact of the spectral hardening of TeVcosmic rays on the prediction of the secondary positronflux,” Mon. Not. Roy. Astron. Soc. 414, 985L (2011)[arXiv:1011.3063 [astro-ph.HE]].

21

[92] T. Bringmann, F. Donato and R. A. Lineros, “Ra-dio data and synchrotron emission in consistent cosmicray models,” JCAP 1201, 049 (2012) [arXiv:1106.4821[astro-ph.GA]].

[93] G. Di Bernardo, C. Evoli, D. Gaggero, D. Grasso andL. Maccione, “Cosmic Ray Electrons, Positrons andthe Synchrotron emission of the Galaxy: consistentanalysis and implications,” JCAP 1303, 036 (2013)[arXiv:1210.4546 [astro-ph.HE]].

[94] J. Lavalle, D. Maurin and A. Putze, “Direct constraintson diffusion models from cosmic-ray positron data: Ex-cluding the MIN model for dark matter searches,”Phys. Rev. D 90, 081301 (2014) [arXiv:1407.2540 [astro-ph.HE]].

[95] C. Evoli, I. Cholis, D. Grasso, L. Maccione and P. Ul-lio, “Antiprotons from dark matter annihilation in theGalaxy: astrophysical uncertainties,” Phys. Rev. D 85,123511 (2012) [arXiv:1108.0664 [astro-ph.HE]].

[96] L. Bergstrom, J. Edsjo and P. Ullio, “Cosmic anti-protons as a probe for supersymmetric dark matter?,”Astrophys. J. 526, 215 (1999) [astro-ph/9902012].

[97] W. A. Rolke, A. M. Lopez and J. Conrad, “Limitsand confidence intervals in the presence of nuisance pa-rameters,” Nucl. Instrum. Meth. A 551, 493 (2005)[physics/0403059].

[98] R. Kappl and M. W. Winkler, “Dark Matter af-ter BESS-Polar II,” Phys. Rev. D 85, 123522 (2012)[arXiv:1110.4376 [hep-ph]].

[99] M. Cirelli and G. Giesen, JCAP 1304 (2013) 015[arXiv:1301.7079 [hep-ph]].

[100] M. Tavakoli, I. Cholis, C. Evoli and P. Ullio, “Con-straints on dark matter annihilations from diffusegamma-ray emission in the Galaxy,” JCAP 1401, 017(2014) [arXiv:1308.4135 [astro-ph.HE]].

[101] M. Aguilar et al. [AMS Collaboration], “First Resultfrom the Alpha Magnetic Spectrometer on the Inter-national Space Station: Precision Measurement of thePositron Fraction in Primary Cosmic Rays of 0.5–350GeV,” Phys. Rev. Lett. 110, 141102 (2013).

[102] O. Adriani et al. [PAMELA Collaboration], “An anoma-lous positron abundance in cosmic rays with energies1.5-100 GeV,” Nature 458, 607 (2009) [arXiv:0810.4995[astro-ph]].

[103] M. Ackermann et al. [Fermi LAT Collaboration], “Mea-surement of separate cosmic-ray electron and positronspectra with the Fermi Large Area Telescope,” Phys.Rev. Lett. 108, 011103 (2012) [arXiv:1109.0521 [astro-ph.HE]].

[104] L. Bergstrom, T. Bringmann, I. Cholis, D. Hooper andC. Weniger, “New limits on dark matter annihilationfrom AMS cosmic ray positron data,” Phys. Rev. Lett.111, 171101 (2013) [arXiv:1306.3983 [astro-ph.HE]].

[105] A. Ibarra, A. S. Lamperstorfer and J. Silk, “Darkmatter annihilations and decays after the AMS-02positron measurements,” Phys. Rev. D 89, 063539(2014) [arXiv:1309.2570 [hep-ph]].

[106] R. D. Davies, D. Walsh, and R. S. Booth, “The radiosource at the galactic nucleus,” Mon. Not. Roy. Astron.Soc. 177 (319-333), (1976)

[107] P. Gondolo, “Either neutralino dark matter or cuspydark halos,” Phys. Lett. B 494, 181 (2000) [hep-ph/0002226].

[108] G. Bertone, G. Sigl and J. Silk, “Astrophysical limitson massive dark matter” Mon. Not. Roy. Astron. Soc.

326 (799-804), (2001) arXiv:0101134 [astro-ph][109] R. Aloisio, P. Blasi and A. V. Olinto, “Neutralino anni-

hilation at the Galactic Center revisited,” JCAP 0405,007 (2004) [astro-ph/0402588].

[110] M. Regis and P. Ullio, “Multi-wavelength signals of darkmatter annihilations at the Galactic center,” Phys. Rev.D 78, 043505 (2008) [arXiv:0802.0234 [hep-ph]].

[111] G. Bertone, M. Cirelli, A. Strumia, and M. Taoso,“Gamma-ray and radio tests of the e+e- excessfrom DM annihilations,” JCAP 0903, (2009) 009[arXiv:0811.3744[astro-ph],

[112] T. Bringmann, “Antiproton and Radio Constraints onthe Dark Matter Interpretation of the Fermi GammaRay Observations of the Galactic Center,” [arXiv:0911.1124 [hep-ph],

[113] Y. Mambrini, M. H. G. Tytgat, G. Zaharijas and B. Zal-divar, “Complementarity of Galactic radio and colliderdata in constraining WIMP dark matter models,” JCAP1211, 038 (2012) [arXiv:1206.2352 [hep-ph]].

[114] R. Laha, K. C. Y. Ng, B. Dasgupta and S. Hori-uchi, “Galactic Center Radio Constraints on Gamma-Ray Lines from Dark Matter Annihilation,” Phys. Rev.D 87, no. 4, 043516 (2013) [arXiv:1208.5488 [astro-ph.CO]].

[115] M. Asano, T. Bringmann, G. Sigl and M. Vollmann,“130 GeV gamma-ray line and generic dark mattermodel building constraints from continuum gammarays, radio, and antiproton data,” Phys. Rev. D 87,no. 10, 103509 (2013) [arXiv:1211.6739 [hep-ph]].

[116] F. Melia, “An accreting black hole model for SagittariusA,” Astrophys. J. 387, L25-L28 (1992)

[117] R. Beck and R. Wielebinski, “Magnetic fields in galax-ies,” in Planets, Stars, and Stellar Systems, edited by T.D. Oswalt and G. Gilmore (Springer, Dordrecht 2013)5, 978 [arXiv:1302.5663 [astro-ph.GA]].

[118] C. Boehm, J. Silk and T. Ensslin, “Radio observa-tions of the Galactic Centre and the Coma cluster asa probe of light dark matter self-annihilations and de-cay,” arXiv:1008.5175 [astro-ph.GA].

[119] R. P. Eatough, H. Falcke, R. Karuppusamy, K. J. Lee,D. J. Champion, E. F. Keane, G. Desvignes andD. H. F. M. Schnitzeler et al., “A strong magnetic fieldaround the supermassive black hole at the centre ofthe Galaxy,” Nature 501, 391 (2013) [arXiv:1308.3147[astro-ph.GA]].

[120] D. P. Marrone, J. M. Moran, J. -H. Zhao and R. Rao,“An Unambiguous Detection of Faraday Rotation inSagittarius A*,” Astrophys. J. 654, L57 (2006) [astro-ph/0611791].

[121] V. F. Shvartsman, “Halos around Black Holes,” Sov.Asron. 15, 377 (1971)

[122] S. L.Shapiro, “Accretion onto Black Holes: the Emer-gent Radiation Spectrum. II. Magnetic Effects,” Astro-phys. J. 185, 69-82 (1973)

[123] V. S. Berezinsky, A. V. Gurevich and K. P. Zybin, “Dis-tribution of dark matter in the galaxy and the lower lim-its for the masses of supersymmetric particles,” Phys.Lett. B 294, 221 (1992).

[124] P. Ullio, H. Zhao and M. Kamionkowski, “A Dark mat-ter spike at the galactic center?,” Phys. Rev. D 64,043504 (2001) [astro-ph/0101481].

[125] D. Merritt, M. Milosavljevic, L. Verde and R. Jimenez,“Dark matter spikes and annihilation radiation from thegalactic center,” Phys. Rev. Lett. 88, 191301 (2002)

22

[astro-ph/0201376].[126] S. Galli, F. Iocco, G. Bertone and A. Melchiorri, “CMB

constraints on Dark Matter models with large annihi-lation cross-section,” Phys. Rev. D 80, 023505 (2009)[arXiv:0905.0003 [astro-ph.CO]].

[127] T. R. Slatyer, N. Padmanabhan and D. P. Finkbeiner,“CMB Constraints on WIMP Annihilation: Energy Ab-sorption During the Recombination Epoch,” Phys. Rev.D 80, 043526 (2009) [arXiv:0906.1197 [astro-ph.CO]].

[128] S. Galli, F. Iocco, G. Bertone and A. Melchiorri,“Updated CMB constraints on Dark Matter annihila-tion cross-sections,” Phys. Rev. D 84, 027302 (2011)[arXiv:1106.1528 [astro-ph.CO]].

[129] T. R. Slatyer, “Energy Injection And Absorption In TheCosmic Dark Ages,” Phys. Rev. D 87, no. 12, 123513(2013) [arXiv:1211.0283 [astro-ph.CO]].

[130] J. M. Cline and P. Scott, “Dark Matter CMB Con-straints and Likelihoods for Poor Particle Physicists,”JCAP 1303, 044 (2013) [Erratum-ibid. 1305, E01(2013)] [arXiv:1301.5908 [astro-ph.CO]].

[131] L. Lopez-Honorez, O. Mena, S. Palomares-Ruiz andA. C. Vincent, “Constraints on dark matter annihilationfrom CMB observationsbefore Planck,” JCAP 1307,046 (2013) [arXiv:1303.5094 [astro-ph.CO]].

[132] J. Aleksic, S. Ansoldi, L. A. Antonelli, P. Antoranz,A. Babic, P. Bangale, U. B. de Almeida and J. A. Bar-rio et al., “Optimized dark matter searches in deep ob-servations of Segue 1 with MAGIC,” JCAP 1402, 008(2014) [arXiv:1312.1535 [hep-ph]].

[133] M. Ackermann et al. [Fermi-LAT Collaboration],“Dark Matter Constraints from Observations of 25Milky Way Satellite Galaxies with the Fermi LargeArea Telescope,” Phys. Rev. D 89, 042001 (2014)[arXiv:1310.0828 [astro-ph.HE]].

[134] I. Cholis and P. Salucci, “Extracting limits on DarkMatter annihilation from gamma-ray observations to-wards dwarf spheroidal galaxies,” Phys. Rev. D 86,023528 (2012) [arXiv:1203.2954 [astro-ph.HE]].

[135] E. Aliu et al. [VERITAS Collaboration], “VERI-TAS Deep Observations of the Dwarf SpheroidalGalaxy Segue 1,” Phys. Rev. D 85, 062001 (2012)[arXiv:1202.2144 [astro-ph.HE]].

[136] A. Geringer-Sameth and S. M. Koushiappas, “Exclu-sion of canonical WIMPs by the joint analysis of MilkyWay dwarfs with Fermi,” Phys. Rev. Lett. 107, 241303(2011) [arXiv:1108.2914 [astro-ph.CO]].

[137] A. Abramowski et al. [HESS Collaboration], “H.E.S.S.constraints on Dark Matter annihilations towards theSculptor and Carina Dwarf Galaxies,” Astropart. Phys.34, 608 (2011) [arXiv:1012.5602 [astro-ph.HE]].

[138] A. A. Abdo et al. [Fermi-LAT Collaboration], “Ob-servations of Milky Way Dwarf Spheroidal galax-ies with the Fermi-LAT detector and constraints onDark Matter models,” Astrophys. J. 712, 147 (2010)[arXiv:1001.4531 [astro-ph.CO]].

[139] S. Ando and D. Nagai, “Fermi-LAT constraints ondark matter annihilation cross section from observa-tions of the Fornax cluster,” JCAP 1207, 017 (2012)[arXiv:1201.0753 [astro-ph.HE]].

[140] S. Zimmer et al. [Fermi-LAT Collaboration], “A Com-bined Analysis of Clusters of Galaxies - GammaRay Emission from Cosmic Rays and Dark Matter,”arXiv:1110.6863 [astro-ph.HE].

[141] X. Huang, G. Vertongen and C. Weniger, “Probing DarkMatter Decay and Annihilation with Fermi LAT Obser-vations of Nearby Galaxy Clusters,” JCAP 1201, 042(2012) [arXiv:1110.1529 [hep-ph]].

[142] M. Ackermann, M. Ajello, A. Allafort, L. Baldini,J. Ballet, G. Barbiellini, D. Bastieri and K. Bech-tol et al., “Constraints on Dark Matter Annihilationin Clusters of Galaxies with the Fermi Large AreaTelescope,” JCAP 1005, 025 (2010) [arXiv:1002.2239[astro-ph.CO]].

[143] T. Bringmann, F. Calore, M. Di Mauro and F. Do-nato, “Constraining dark matter annihilation withthe isotropic γ-ray background: updated limits andfuture potential,” Phys. Rev. D 89, 023012 (2014)[arXiv:1303.3284 [astro-ph.CO]].

[144] A. A. Abdo et al. [Fermi-LAT Collaboration], “Con-straints on Cosmological Dark Matter Annihilation fromthe Fermi-LAT Isotropic Diffuse Gamma-Ray Measure-ment,” JCAP 1004, 014 (2010) [arXiv:1002.4415 [astro-ph.CO]].

[145] M. Shirasaki, S. Horiuchi and N. Yoshida, “Cross-Correlation of Cosmic Shear and Extragalactic Gamma-ray Background: Constraints on the Dark Matter Anni-hilation Cross-Section,” Phys. Rev. D 90, 063502 (2014)[arXiv:1404.5503 [astro-ph.CO]].

[146] N. Fornengo and M. Regis, “Particle dark mattersearches in the anisotropic sky,” Front. Physics 2, 6(2014) [arXiv:1312.4835 [astro-ph.CO]].

[147] S. Ando, A. Benoit-L‘evy and E. Komatsu, “Mappingdark matter in the gamma-ray sky with galaxy cata-logs,” Phys. Rev. D 90, 023514 (2014) [arXiv:1312.4403[astro-ph.CO]].

[148] S. S. Campbell and J. F. Beacom, “Combined Fluxand Anisotropy Searches Improve Sensitivity to GammaRays from Dark Matter,” arXiv:1312.3945 [astro-ph.HE].

[149] S. Camera, M. Fornasa, N. Fornengo and M. Regis,“A Novel Approach in the Weakly Interacting Mas-sive Particle Quest: Cross-correlation of Gamma-RayAnisotropies and Cosmic Shear,” Astrophys. J. 771, L5(2013) [arXiv:1212.5018 [astro-ph.CO]].

[150] D. Hooper, C. Kelso and F. S. Queiroz, “Stringent andRobust Constraints on the Dark Matter AnnihilationCross Section From the Region of the Galactic Center,”Astropart. Phys. 46, 55 (2013) [arXiv:1209.3015 [astro-ph.HE]].

[151] R. M. Crocker, N. F. Bell, C. Balazs and D. I. Jones,“Radio and gamma-ray constraints on dark matter an-nihilation in the Galactic center,” Phys. Rev. D 81,063516 (2010) [arXiv:1002.0229 [hep-ph]].

[152] N. Fornengo, R. A. Lineros, M. Regis and M. Taoso,“Galactic synchrotron emission from WIMPs at radiofrequencies,” JCAP 1201, 005 (2012) [arXiv:1110.4337[astro-ph.GA]].

[153] M. Wechakama and Y. Ascasibar, “Multi-messengerconstraints on dark matter annihilation into electron-positron pairs,” Mon. Not. Roy. Astron. Soc. 439, 566(2014) [arXiv:1212.2583 [astro-ph.CO]].

[154] E. Storm, T. E. Jeltema, S. Profumo and L. Rudnick,“Constraints on Dark Matter Annihilation in Clustersof Galaxies from Diffuse Radio Emission,” Astrophys.J. 768, 106 (2013) [arXiv:1210.0872 [astro-ph.CO]].

[155] K. Spekkens, B. S. Mason, J. E. Aguirre and B. Nhan,“A Deep Search for Extended Radio Continuum Emis-

23

sion From Dwarf Spheroidal Galaxies: Implications forParticle Dark Matter,” Astrophys. J. 773, 61 (2013)[arXiv:1301.5306 [astro-ph.CO]].

[156] A. Natarajan, J. B. Peterson, T. C. Voytek,K. Spekkens, B. Mason, J. Aguirre and B. Will-man, “Bounds on Dark Matter Properties from Ra-dio Observations of Ursa Major II using the GreenBank Telescope,” Phys. Rev. D 88, 083535 (2013)[arXiv:1308.4979 [astro-ph.CO]].

[157] A. E. Egorov and E. Pierpaoli, “Constraints on darkmatter annihilation by radio observations of M31,”Phys. Rev. D 88, no. 2, 023504 (2013) [arXiv:1304.0517[astro-ph.CO]].

[158] K. Abe, H. Fuke, S. Haino, T. Hams, A. Itazaki,K. C. Kim, T. Kumazawa and M. H. Lee et al., “Mea-surement of cosmic-ray low-energy antiproton spectrumwith the first BESS-Polar Antarctic flight,” Phys. Lett.B 670, 103 (2008) [arXiv:0805.1754 [astro-ph]].

[159] I. G. Usoskin, G. A. Bazilevskaya, and G. A. Kovaltsov,“Solar modulation parameter for cosmic rays since 1936reconstructed from ground-based neutron monitors andionization chambers”, J. Geophys. Res. 116, A02104(2011).

[160] L. Maccione, “Low energy cosmic ray positron frac-tion explained by charge-sign dependent solar modu-lation,” Phys. Rev. Lett. 110, no. 8, 081101 (2013)[arXiv:1211.6905 [astro-ph.HE]].

[161] Caballero-Lopez, R. A., & Moraal, H., ”Limitations ofthe force field equation to describe cosmic ray modula-tion”, Journal of Geophysical Research (Space Physics)109, 1101 (2004).

[162] M. Potgieter, “Solar Modulation of Cosmic Rays,” Liv-ing Rev. Solar Phys. 10, 3 (2013) [arXiv:1306.4421[physics.space-ph]].

[163] I. Cholis, D. Hooper and T. Linden, “A Critical Reeval-uation of Radio Constraints on Annihilating Dark Mat-ter,” arXiv:1408.6224 [astro-ph.HE].

[164] A. Bottino, F. Donato, N. Fornengo and P. Salati,“Which fraction of the measured cosmic ray anti-protons might be due to neutralino annihilation in thegalactic halo?,” Phys. Rev. D 58, 123503 (1998) [astro-ph/9804137].

[165] A. Bottino, F. Donato, N. Fornengo and P. Salati, “An-tiproton fluxes from light neutralinos,” Phys. Rev. D72, 083518 (2005) [hep-ph/0507086].

[166] J. Lavalle, “10 GeV dark matter candidates and cosmic-ray antiprotons,” Phys. Rev. D 82, 081302 (2010)[arXiv:1007.5253 [astro-ph.HE]].

[167] W. Detmold, M. McCullough and A. Pochinsky,“Dark Nuclei I: Cosmology and Indirect Detection,”arXiv:1406.2276 [hep-ph].

[168] E. Jones, T. Oliphant, P. Peterson, et al., “SciPy:Open source scientific tools for Python”, 2001.http://www.scipy.org/about.html

[169] F. James and M. Roos, “Minuit: A System for FunctionMinimization and Analysis of the Parameter Errors andCorrelations,” Comput. Phys. Commun. 10, 343 (1975).

[170] J. D. Hunter, “Matplotlib: A 2D graphics environ-ment”, Comput. in Science & Engineering 9, 90 (2007).

[171] M. Cirelli, D. Gaggero, G. Giesen, M. Taoso and A. Ur-bano, “Antiproton constraints on the GeV gamma-ray excess: a comprehensive analysis,” arXiv:1407.2173[hep-ph].