Constraining dark matter annihilation with the isotropic

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Constraining dark matter annihilation with the isotropic γ-ray background:
updated limits and future potential
Bringmann, T.; Calore, F.; Di Mauro, M.; Donato, F.
DOI
10.1103/PhysRevD.89.023012
Publication date
2014
Document Version
Final published version
Published in
Physical Review D. Particles, Fields, Gravitation, and Cosmology
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Citation for published version (APA):
Bringmann, T., Calore, F., Di Mauro, M., & Donato, F. (2014). Constraining dark matter
annihilation with the isotropic γ-ray background: updated limits and future potential. Physical
Review D. Particles, Fields, Gravitation, and Cosmology, 89(2), 023012.
https://doi.org/10.1103/PhysRevD.89.023012
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PHYSICAL REVIEW D 89, 023012 (2014)
Constrainingdarkmatterannihilation withtheisotropic γ-raybackground:
Updated limits and future potential
Torsten Bringmann*
II.InstituteforTheoreticalPhysics,UniversityofHamburg,LuruperChaussee149,22761Hamburg,Germany
andDepartmentofPhysics,UniversityofOslo,Box1048NO-0316Oslo,Norway
†
Francesca Calore
II.InstituteforTheoreticalPhysics,UniversityofHamburg,LuruperChaussee149,22761Hamburg,Germany
andGRAPPAInstitute,UniversityofAmsterdam,SciencePark904,
1090GLAmsterdam,TheNetherlands
Mattia Di Mauro,‡ and Fiorenza Donato§
Dipartimento di Fisica, Università di Torino and INFN, Sezione di Torino, Via P. Giuria 1,
10125 Torino, Italy
(Received 11 June 2013; published 27 January 2014)
Thenatureoftheisotropicγ-raybackground(IGRB)measuredbytheLargeAreaTelescope(LAT)on
theFermiγ-rayspacetelescope(Fermi)remainspartiallyunexplained.Non-negligiblecontributionsmay
originate from extragalactic populations of unresolved sources such as blazars, star-forming galaxies or
galacticmillisecondpulsars.Arecentpredictionofthediffuseγ-rayemissionfromactivegalacticnuclei
(AGN) with a large viewing angle with respect to the line of sight has demonstrated that this faint but
numerouspopulationisalsoexpectedtocontributesignificantlytothetotalIGRBintensity.Amoreexotic
contribution to the IGRB invokes the pair annihilation of dark matter (DM) weakly interacting massive
particles (WIMPs) into γ rays. In this work, we evaluate the room left for galactic DM at high latitudes
(>10∘)byincludingphotonsfrombothpromptemissionandinverseComptonscattering,emphasizingthe
impact of the newly discovered contribution from misaligned AGN (MAGN) for such an analysis.
SummingupallsignificantgalacticandextragalacticcomponentsoftheIGRB,wefindthatanimproved
understanding of the associated astrophysical uncertainties is still mandatory to put stringent bounds on
thermallyproducedDM.Ontheotherhand,wealsodemonstratethattheIGRBhasthepotentialtobeone
ofthemostcompetitive futurewaystotesttheDMWIMPhypothesis,oncethepresentuncertaintiesare
evenslightlyreduced.Infact,ifMAGNcontributeevenat90%ofthemaximallevelconsistentwithour
current understanding, thermally produced WIMPs would be severelyconstrained as DM candidates for
masses up to several TeV.
DOI: 10.1103/PhysRevD.89.023012 PACSnumbers:95.30.Cq,95.35.+d,95.85.Pw,96.50.sb
I. INTRODUCTION nearbyobjects,aswellasincosmologicalstructures[3–7].
The incontrovertible DM signature would be a γ-ray
Thenatureofdarkmatter(DM)remainsoneofthemost
monochromatic line at energies around the WIMP mass.
intriguing mysteries in fundamental physics and cosmol-
ArecentanalysisofFermi-LATdataofthegalacticcenter
ogy.Aviableinvestigationtechniqueconsistsinthesearch
region has unveiled the feature of a narrow line close to
for its stable annihilation products in the halo of galaxies,
130 GeV [8–11], with an angular distribution consistent
and in particular in the Milky Way. Making the common
with the expectation for WIMP DM [1] and a statistical
hypothesisforDMtoconsistofweaklyinteractingmassive
significance of at least 3σ after trials factor correction (in
particles (WIMPs), one of the most promising indirect
detection channels is through annihilation into γ rays (see fact, more than 5σ when taking into account both spectral
Ref. [1] for a recent review). Unprecedented γ-ray obser- andspatialinformationoftheincomingevents[11]).While
confirmingthisexcess,theFermi-LATCollaborationfinds
vationsofdiffuseemissionandpointsourcesbytheFermi-
thatitssignificanceissubstantiallyreducedtoamere1.6σ
LAT [2] have stimulated the search for exotic components
(albeit in somewhat different target regions) when consid-
from DM annihilation in the Milky Way, in extragalactic
eringalargersetofreprocesseddataandatwo-dimensional
modeling of the energy dispersion [12,13]. The interpre-
*[email protected]
† tation in terms of annihilating DM would in any case
[email protected]
‡ requiretheloop-suppresseddirectannihilationintophotons
[email protected]
§[email protected] tobelargerthantypicallyexpectedforthermallyproduced
1550-7998=2014=89(2)=023012(11) 023012-1 © 2014 American Physical Society
BRINGMANN et al. PHYSICAL REVIEW D 89, 023012 (2014)
DM, a fact that has already inspired considerable model- thuswellturnouttobethenewdrivingforceinsettingever
buildingefforts(see,e.g.thecompilationinRefs.[1,14]for more stringent limits on the DM annihilation rate.
anoverview).Onlyalargerexposurewillallowustofinally The paper is organized as follows. In Sec. II we present
settle possible issues concerning the statistical robustness the possible contributions to the IGRB and we discuss the
and potential instrumental effects of the line feature; with relevance of unresolved extragalactic sources, notably
the proposed new observation strategy for Fermi, recently MAGN. The expected galactic DM signal is described in
positively reviewed by the collaboration, this could be Sec.III.TheDMspectrumismadeupbythepromptγ-ray
achievable until the end of 2014 [14]. component and photons from inverse Compton scattering
A faint γ-ray emission at high latitudes (jbj>10∘) has (ICS) of electrons and positrons produced by DM annihi-
beenmeasuredbyFermi-LAT[15],showingahighdegree lation. By subtracting the astrophysical components from
ofisotropy[16]andanenergyspectrumcompatiblewitha the high latitudes γ-ray emission, in Sec. IV we derive
powerlaw.Thoughitsverynatureisstillunexplained,itis upper limits on the DM annihilation cross section for
reasonable tobelieveittobethesuperpositionof(mainly) several annihilation channels and under various assump-
extragalactic unresolved point sources and, to a lesser tions for the MAGN contribution. We discuss the impli-
extent, of astrophysical diffuse processes (see Ref. [17] cations for DM indirect detection, as well as the
and Sec. II for a detailed discussion). A possible contri- dependence on the other possible astrophysical contribu-
bution from DM annihilation, both from galactic and tions. In Sec. V we present our conclusions.
cosmological distances, can be hidden in this isotropic
γ-raybackground(IGRB)dataaswell[17–25].1Previous II. DIFFUSE γ-RAY EMISSION FROM
upperlimitsontheDMannihilationcrosssectionfromthe
UNRESOLVED ASTROPHYSICAL SOURCES
high latitudes γ-ray emission were derived e.g. in [17], by
subtracting from the IGRB [15] the minimum estimated The IGRB found at high latitudes (jbj>10∘) has been
fluxes for the most significant unresolved source popula- obtained by the Fermi-LAT Collaboration [15] after sub-
tions.ThefaintbutnumerouspopulationofActiveGalactic tractingfrom the LAT data thecontributions frompointlike
Nuclei (AGN) whose jet axes have a large viewing angle sources, the galactic diffuse emission (which represents the
with respect to the line of sight (l.o.s.) has recently been majorsystematicuncertaintyofthatanalysis),thebackground
shown[26–28]tocontributebetween10%and100%tothe from CRs in the detector and solar photons. The energy
IGRB intensity, depending on the astrophysical uncertain- spectrumoftheIGRBisconsistentwithapower-lawhaving
ties involved. In the present paper, we extend and update spectral index α¼2.41(cid:1)0.05 and integrated intensity
the analysis in Ref. [17] by taking into account those new Ið>100MeVÞ¼ð1.03(cid:1)0.17Þ×10−5 cm−5s−1 sr−1.This
resultsontheisotropicdiffusefluxpredictedformisaligned diffuseemissionlikelyarisesfromthesuperpositionofseveral
AGN (MAGN) [26,27]. We find that the annihilation contributions from unresolved point-source populations, as
intensity of DM in the galactic halo may be severely wellasfromphotonsoriginatingfromtrulydiffuseprocesses
constrainedbytheinclusionofthisnewdiffuseastrophysi- (i.e.extendedsourcecontributionslikefromultrahighenergy
cal background, dependingon the WIMPmassand onthe cosmicrays,nearbygalaxyclustersorgravitationallyinduced
annihilation channel considered. shock waves during structure formation, see Ref. [17] and
In this context, it is worth noting that classical DM references therein). Most of the photons in the IGRB are
indirect detection targets like the galactic center or dwarf believed to be of extragalactic origin. The truly diffuse
spheroidal galaxies, which currently result in the best processes are subdominant and may be non-negligible (%
available limits on DM annihilation [3,7,30–33], will at level)onlyatthehigh-energyendoftherangeexploredbythe
some point inevitably face fundamental limitations in the Fermi-LAT.WehavecheckedthatthetotalUHECRdiffuse
sensethatevengreatlyincreasedstatisticswillnotallowus emissionpredictedby[35]contributestoatmost0.3%ofthe
to further improve those limits [1]. For ground-based measured IGRB. On the other side, the high energy
telescopes, this is likely the case already for anything (>100 GeV) emission from galaxy clusters predicted by
beyondtheplannedCherenkovTelescopeArray[34],while [36] is Oð10−2Þ of the IGRB at 100 GeV. Given their very
for future space-based missions there might be room for marginal role in the analysis undertaken here, they will be
further improvement of the limits by up to one order of neglectedfromnowon.
magnitudewithrespecttowhatcanbeexpectedbytheend
oftheFermimission.OncetheMAGN-relatedastrophysi-
A. Misaligned AGN
cal uncertainties are under better control, the IGRB may
Recently, a thorough analysis of the γ-ray flux from
unresolved MAGN has demonstrated that this numerous
1The130GeVfeaturedescribedabovedoesnotshowupinthe butfaintpopulationmaycontributebetween10%and100%
IGRB—as expected for the annihilation rate of ðσvÞ ∼
10−27 cm3s−1 inferred from the galactic center observationγγ[6] tothemeasuredIGRB[26,27].Ajetdisplacementofabout
(unless one adopts very optimistic models for the evolutionand 14° marks the separation between blazars and nonblazar
distribution of DM subhalos [29]). (namely misaligned) AGN. In the unification model [37],
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CONSTRAINING DARK MATTER ANNIHILATION WITH … PHYSICAL REVIEW D 89, 023012 (2014)
radiogalaxiesarethosemisalignedactivegalaxieswhosejet C. Millisecond pulsars
points on average at an angle >44∘, while lower angles
Thesecond-mostabundantpopulationoftheFermi-LAT
indicatetypicallysteepspectrumradioquasars.Theresultin
sky is represented by galactic pulsars and Milli-
Refs. [26,27] is based on the γ-ray data of 12 MAGN by
Second Pulsars (MSPs). It has been argued that the latter
Fermi-LAT,andisbasedonacorrelationbetweentheirγ-ray populationmay be brighter in γ rays thanordinary pulsars
andcoreradioluminosities.Thiscorrelationhasbeentested
as a consequence of their rapid spin frequency [44].
againsttheMAGNnumbercountdistribution,andvalidated
Moreover, MSPs are expected to be more numerous at
by95%fluxupperlimitsontheFermi-LATγ-raydatafora
highlatitudes,sincetheyhavetypicalagesthatcanlargely
large sample of bright core radio MAGN. These results
exceed the oscillation time across the galactic disk [45].
support the hypothesis that γ-ray photons are produced by Thepredictionofthediffuseγ-rayfluxduetohighlatitudes
synchrotron-selfComptonscatteringsbythesameelectrons (jbj>10∘)unresolvedMSPsisestimatedtobeabout10%
responsibleforthesynchrotronemissionatGHzfrequencies. at≃3 GeV,whereitreachesitsmaximumvalueduetothe
Ref. [26] quantifies several sources of uncertainty and
adopted broken power-law spectrum [17]. The considered
estimatesthemtoaffectthediffuseemissionfromunresolved modelresultstobecompatiblewiththeanalysisoftheγ-ray
MAGNbyaboutafactorof10.Theexpectedfluxistherefore
anisotropies performed in [16]. Indeed we derived the
providedasaband(roughlydecreasingwithE−2.35)affected integrated flux from MSPs for jbj>30∘, which results to
by the extragalactic background light (EBL) absorption be 1.44% and 1.11% of the IGRB in the 1–2 GeV and
above 50 GeV. At 1 GeV, the MAGN flux (multiplied by 2–5GeV,respectively.Thesenumbersarecompatiblewith
E2) ranges from 6×10−7 GeV cm−2s−1sr−1 to
the upper limits of about 1.5% found by [16] in the
5×10−6 GeVcm−2s−1sr−1, while at 100 GeV the EBL anisotropy analysis. In the Second Fermi catalog [39]
absorptionstartstobeeffectiveandthefluxspansfrom9× onlyabout20MSPsatjbj>10∘ arelisted,butthenumber
10−9 GeV cm−2s−1 sr−1 to 9×10−8 GeV cm−2 s−1sr−1.
ofgalactic(nonglobularcluster)MSPshasrecentlyrisento
TheresultinRef.[26]statesthatMAGNaccountforatleast 40 [46]. The statistical properties of such a population
10%oftheIGRBmeasuredbyFermi-LAT[15]andcanin could improve the prediction for the unresolved compo-
principleexplainmostofit.Addedtootherpossiblediffuse nent. Such an analysis is beyond the scope of the present
emissioncomponents,thismightalmostclosetheroomtoan paper, but is anyway not expected to modify any of the
exoticdiffusecontributionsuchasfromDMannihilationin resultsandconclusionspresentedhere.Inthefollowing,we
space.Thispointisthefocusofourpaper:evaluatinghow refer to the unresolved MSPs diffuse γ-ray flux and its
much the MAGN γ-ray diffuse emission constrains the estimated uncertainty as reported in Ref. [17].
presenceofWIMPDMannihilatinginthegalactichalo.In
the remainder of this section, we briefly discuss the astro- D. Star-forming galaxies
physical sources leading to a non-negligible diffuse γ-ray
emissionatjbj>10∘ (seeRef.[17]forfurtherdetails). Though their number density is larger than that of the
blazars, star-forming (SF) galaxies are more difficult to
detect in γ rays because of their less intense luminosities.
B. Blazars
BasedonthreeyearsofFermi-LATdata,Ref.[47]analyzes
The census of the sources detected by the Fermi-LAT a sample of 64 SF galaxies beyond the Local Group,
[38,39]indicatesthatthelargestpopulationismadebyblazars, detecting only four objects in γ rays: two are typical star-
a class of AGN with their jet oriented along the l.o.s., thus burst galaxies (M82 and NGC 253), while the other two
leadingtoasignificantobservedγ-rayflux.Theanalysisofthe hostSeyfert2nuclei(NGC1068,NGC4945).Noneofthe
spectral andstatisticalpropertiesoftheresolved Fermi-LAT remaining60sourcecandidateshasshownanexcessabove
blazars[40]showsthattheunresolvedcounterpartisasizable the background. The contribution of SF galaxies to the
component,abletoexplainupto20%–30%oftheIGRB.The IGRBisevaluatedinRef.[47]byexploitingthecorrelation
contributionfromthetwodistinctpopulationsofFlatSpectrum between infrared and γ-ray luminosities [48]. In order to
RadioQuasars(FSRQs)andBLLacertae(BLLacs)objects compute the diffuse emission, the differential photon flux
hasbeenfoundtofollowapower-lawspectrumwithrespec- of an individual galaxy has to be modeled. Given the lack
tivelya somewhatsofter (α ¼2.45(cid:1)0.03)andharder of statistics, the γ-ray average spectral properties of SF
FSRQs
(α ¼2.23(cid:1)0.03)spectralindex.Recently,Ref.[41]has galaxies are difficult to firmly establish, although
BLLacs
evaluatedtheFSRQcontributiontothediffuseγ-rayfluxusing differences in the spectra of quiescent and star-burst
a new determination of the spectral energy distribution and galaxies are expected to be present. To take into account
luminosity function. The resulting flux is predicted with an this effect, Ref. [47] adopts two possible γ-ray spectra
uncertaintyoflessthanafactoroftwo.Itrepresentsnomore supposedtobracketthepossiblecontributionfrommultiple
than 10% of the IGRB in the 0.1–100 GeV, and becomes typesofSFgalaxies.ThefirstonereferstoMilkyWay-like
negligible for E ≳ 20 GeV. Also, [42,43] find that the SF galaxies (model MW), the second one assumes a
maximalcontributionfromblazarsareabout10%and20%, power-law spectrum in agreement with the properties of
respectively. the Fermi-LAT detected star-burst galaxies (model PL).
023012-3
BRINGMANN et al. PHYSICAL REVIEW D 89, 023012 (2014)
MAGN Di Mauro et al. 2013 Minimal bkg
SF Ackermann et al. 2012 Best fit bkg
FSRQ Ajello et al. 2012 High bkg 1
10-3 MBLS PLsa cC Aablodreo eett aall.. 22001120 10-3 FHeigrmh ib EkGg B2
2m/s/sr] Fermi EGB 2m/s/sr]
V/c V/c
N/dE [Me 10-4 N/dE [Me10-4
2E d 2 dE
10-5
10-5
102 103 104 105 102 103 104 105
Eγ [MeV] Eγ [MeV]
FIG. 1 (color online). The diffuse γ-ray fluxes predicted for FIG. 2 (color online). Different representative choices for the
various unresolved point-source populations, along with the astrophysical backgrounds shown in Fig. 1. The solid blue (red
IGRB data from the Fermi-LAT Collaboration based on high dashed) line corresponds to the minimal (best fit)prediction for
galactic latitude (jbj>10∘) observations [15]. The displayed all the contributions. The green short-dashed (brown dotted)
contributions to the IGRB and corresponding uncertainty bands curvehasbeenobtained fromthesumofthebestfitmodelsfor
arise from: MAGN [26] (solid dark-green curve and light-green Σ and the 60% (85%) of the maximally expected flux from
BMS
band),MWmodelforSFgalaxies[47](dot-dashedredlineand MAGN. Data points are again for the IGRB [15].
orangeband),MSPs[17](dot-dashedredlineandorangeband),
BL Lacs [40] (dotted dark-grey line and light-grey band), and
FSRQs [41] (purple dotted line and pink band). 3–4 GeV. A similar low-energy bumped flux comes from
the SF galaxies contribution. The MAGN is clearly the
dominant component over the whole energy range (notice
Thepredictionsdifferinparticularabove5GeV,wherethe thatforEγ ≳30 GeVtheBLLacsfluxisactuallyexpected
MW model gets significantly softer. At 100 GeV the PL to drop in the same way as the MAGN flux, due to EBL
modeloverpredictstheMWonebyoneorderofmagnitude. absorption, but this has not been taken into account in the
The estimates span 4%–23% of the IGRB intensity above fluxestimate referred to here). In the following, we define
100 MeV. Higher predictions, in particular in the low Σ asthesumofthecontributionsfromBlazars(bothBL
BMS
energy tail (not relevant in deriving the constraints on the Lacs and FSRQs), MSPs and SF galaxies.
DM annihilation cross section), have been obtained in InFig.2wedisplayafewrepresentativechoicesforthe
[49,50].Asasummaryofthissection,weshowinFig.1the astrophysical backgrounds, as a function of the photon
contributions to the IGRB discussed above, with uncer- energy.Thesolidblue(reddashed)linecorrespondstothe
taintybandsasreportedintherelevantreferences(roughly minimal (best fit) prediction for all the contributions. The
corresponding to 1σ deviations). The Fermi-LAT IGRB greenshort-dashed(browndotted)curvehasbeenobtained
data [15] are shown along with the power-law fit (solid from the sum of the best fit models for Σ and 60%
BMS
black line). The solid dark-green curve refers to the (85%) of the maximally expected flux from MAGN. We
expected diffuse γ-ray flux from unresolved MAGN alsodisplaythedatafortheIGRB[15]with1σerrorbands.
[26], the light-green band bracketing the corresponding These figures illustrate that by varying the contribution
uncertainty. The other displayed components are: SF of each component within its uncertainty band, the IGRB
galaxies (the MW model is depicted by the dashed dark- datacanbesaturatedbymultiplecombinationsoftheabove
(light-) blue line (area)), MSPs (dot-dashed red line and fluxes. Alternatively, only little room is left to other
orange band), FSRQs (purple dotted line and pink band), unknown γ-ray sources as, e.g. DM.
and BL Lacs (dotted dark-grey line and light-grey band).
The BL Lacs flux follows a power-law, while the specific
III. DIFFUSE γ-RAY EMISSION FROM DARK
shape of the FSRQ contribution is the result of a more
MATTER IN THE GALACTIC HALO
recent, sophisticated analysis of their spectral energy
distribution and luminosity function [41]. The crossing The self-annihilation of DM particle pairs in the haloes
point for the two curves is around 1–2 GeV: above this ofgalaxiesmaygive birth,amongotherspecies,toγ rays.
energy the BL Lacs flux dominates over the one from The intensity of these energetic photons depends on
FSRQs.Theγ raysfromunresolvedMSPsshowapeculiar the elementary process at stake and on the spatial distri-
spectrum peaked at about 1 GeV (resulting from the bution of DM. The flux ΦγðEγ;ψÞ of γ rays produced by
primary electron cooling due to curvature radiation) and WIMPpairannihilationintheangulardirectionψ isgiven
dominate over the blazar spectra from 300 MeV up to by [51–53]:
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CONSTRAINING DARK MATTER ANNIHILATION WITH … PHYSICAL REVIEW D 89, 023012 (2014)
ΦγðEγ;ψÞ¼41πhmσv2iddNEγ12IðψÞ; (1) raatdhiaigtihonlawtiotuudldesin[5cr7e–a6s0e].thSewICitcShiγn-grayofffluthxefrsoymncDhrMotrboyn
χ γ
lessthan30%,resultinginadecreaseoftheupperlimitson
where mχ is the WIMP mass. The factor hσvi defines the hσvi (shown in the following Sect. IV) by 10%.
annihilation cross section times the relative velocity, Numerical cold DM simulations predict cuspy density
averaged over the galactic velocity distribution function, distributionintheinnerpartsofgalaxies,liketheNavarro-
whiledNγ=dEγ istheγ-rayproductionsourcespectrumper Frenk-White(NFW)[61]orEinasto[62]profile.Following
DM annihilation event. The last term IðψÞ is the integral a conservative approach, however, we evaluate the geo-
performed along the l.o.s. of the squared DM density metrical factor IðψÞ in Eq. (2) by adopting the cored
distribution: Burkert model [63] for the radial DM density distribution,
Z which is used as an alternative parameterization to fit
IðψÞ¼ ρ2ðrðλ;ψÞÞdλ: (2) observed rotation curves [64]:
l:o:s:
ρ
Here ψ is the angle between the l.o.s. and the direction ρðrÞ¼ s : (4)
ð1þðrÞ2Þð1þ rÞ
towards the galactic center, defined as a function of the r r
s s
galactic latitude b and longitude l (cos ψ ¼cos b cos l).
When comparing with experimental data, Eq. (2) must be
Wenotethatnumericalsimulationstypicallysupportmore
averaged over the telescope viewing solid angle, ΔΩ:
cuspyprofilesandourchoiceisthusexclusivelymotivated
Z
1 bythatfactthat it resultsin ratherconservativelimits ona
IΔΩ ¼ΔΩ Iðψðb;lÞÞdΩ: (3) DMcontributiontotheIGRB.Thevaluesofrsandρshave
ΔΩ been derived fixing the local DM density ρðr¼r⊙Þ¼
ThephotonspectrumdNγ=dEγ dependsontheelementary 0.4 GeVcm−3 [65,66](r⊙ ¼8.33 kpc)andfittingthehalo
processes ruling the annihilation. For the continuum γ-ray DM mass Mðr<r0Þ contained within a certain radius r0.
flux, we consider here i) prompt emission, where the Using available Mðr<r0Þ data for different values of r0
photonsarefoundinfinal-stateshowersorhadronicdecays [67–75], roughly in the range 20 kpc≲r0≲300 kpc, we
of the annihilation products, and ii) ICS by energetic findabestfitvalueofrs ¼15 kpc.Numerically,wederive
electrons and positrons—produced in the same way—off for IΔΩ in Eq. (3)): 2.4, 1.9, 1.7, 2.0 (in units of
the interstellar radiation field (ISRF). We have calculated GeV2 cm−6 kpc) for the sky regions 10∘ <jbj<20∘,
the spectrum for the prompt emissionof both photons and 20∘ <jbj<90∘, jbj>60∘, and jbj>10∘, respectively.
e(cid:1) with the PYTHIA MONTE CARLO code (version 8.162) While in principle limits might somewhat improve when
[54].TheICShasbeencomputedfromthosee(cid:1)interacting takingintoaccountthedifferentvaluesofIΔΩ fordifferent
with ambient photons, following the prescription in [55]. regions of the sky, we will in the following only consider
Once produced, energetic electrons may diffuse due to the whole region jbj>10∘ considered by the Fermi-LAT
stochastic scatterings on galactic magnetic field inhomo- analysis [15] because not all of the astrophysical contri-
geneities, and loose energy through interactions with the butions quoted above can be easily rescaled to smaller
ISRF. The ISRF is composed by the Cosmic Microwave subregions. We also note that when integrating Eq. (2)
Background (CMB) photons, the infrared radiation (IR) around the galactic center, different DM distributions ρðrÞ
producedbytheabsorptionandthesubsequentreemission mayleadtoverydifferentresults.However,sincewestudy
of starlight by the galactic dust, and by the starlight (SL) hereonlyhighlatituderegions,thevariousmodelsforρðrÞ
originating from stars of the Galactic disk. Given the givecomparablevaluesforIðψÞ,andtheuncertaintydueto
energiesatstake,galacticdiffusionmaybesafelyneglected DMdensitymodelingisrathersmall.Forexample,wefind
and only energy losses have been included, as usually IΔΩðjbj>10∘Þ×GeV−2 cm6kpc−1 ¼ 2.4 (2.5, 2.8) for
assumed in the literature [56]. Electromagnetic energy the case of an isothermal sphere (a NFW [61], an
losses are treated here in the fully relativistic Klein- Einasto [62]) profile. While the existence of a dark disk
Nishina regime. The photon density distribution has been [76]mayfurtherenhancethosevaluesslightly,wewillnot
assumed as an average field with different normalizations consider this possibility in the following. We also do not
for different sky regions (the SL and IR are concentrated include any contribution from subhaloes, which are pre-
along the galactic disk), following Ref. [55]. Specifically, dicted in numerical simulations of cosmological structure
between10°and20°allthethreefields(CMB,IR,SL)are formation[77,78],andassumeasmoothdistributionofDM
present, while for latitudes jbj>20∘ only CMB remains. in the galactic halo for the sake of deriving conservative
Energylossesduetosynchrotronradiationhavebeentaken limits. Including the effect of substructures leads to an
intoaccountintheregionoflatitude10∘ <jbj<20∘,with increase of the geometrical factor in Eq. (3), see e.g.
a value of B¼2μG for the galactic magnetic field, and Ref.[79],whichwouldaccordinglylowertheupperlimits
neglectedabovejbj>20∘giventheverylowintensityofB we are going to present on hσvi.
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BRINGMANN et al. PHYSICAL REVIEW D 89, 023012 (2014)
IV. CONSTRAINTS ON DARK MATTER b-b (min ΣBSM)
ANNIHILATION INTO γ RAYS 10-21 Min MAGN
Best fit MAGN
The constraints on DM are set, as usual, in terms of the 10-22 5700%% mmaaxx MMAAGGNN
velocityaveragedannihilationcrosssectionintoγrayshσviasa
10-23
function of the WIMP mass mχ. All the other quantities in 3m/s]
Eq. (1) are kept fixed. The galactic DM contribution is > [c 10-24
calculated following the prescriptions outlined in Sec. III. σ v
We do not include the diffuse γ-ray flux from DM in extra- < 10-25
galacticstructures[80,81],giventhelargemodeldependence
10-26
ontheassumedDM(sub-)haloprofilesandtheirevolution.If
theγraysfromDMinextragalacticstructuresorsubhaloesin 10-27
theMilkyWayhalowereaddedtoourfluxes,theensuingupper 101 102 103 104
limitsonhσviwouldbefurtherdecreased.Intheseregards,the Mχ [GeV]
resultswearegoingtopresentaremeanttobeconservative,i.e. FIG. 3 (color online). Conservative 2σ upper limits on the
leadingtothehighestpossiblevaluefortheexcludedhσvi. velocity averaged DM annihilation cross section hσvi into e(cid:1)
As discussed in Sec. III, the geometrical factor at high finalstates,asafunctionoftheWIMPmassmχ.Thebluedashed
latitudesisveryslightlyaffectedbymodelinguncertainties. curve corresponds to the γ-ray spectrum from the prompt
component only, the solid red line refers to the inclusion of
The choice we made on the Burkert profile and a smooth
ICS. The grey area indicates the typically adopted value
haloismeanttobeconservativeanddifferentassumptions
for the cross section of thermally produced WIMPs,
on the DM profile would lower the upper bounds we find hσvi∼3×10−26 cm3s−1.
by up to about 30% (in fact, considerably more for
optimistic assumptions about DM substructure [80–82]).
A further uncertainty factor is the value of the local As can be anticipated from Fig. 1, those limits are always
DM density, which can span the (generous) range setbythethreedatabinsat6.4–12.8,12.8–25.6and25.6–
0.2–0.7 GeVcm−3 [66]. Since ρ⊙ enters squared in the 51.2 GeV.
flux, it has a non-negligible impact on the hσvi bounds. Fig.3representstheexclusionplotfor DMannihilation
If not explicitly stated differently, we will take ρ⊙ ¼ into e(cid:1) and it is emblematic of the effect of the ICS
0.4 GeVcm−3 in the following. To keep the analysis as inclusion in the DM spectrum. The blue dashed curve
model independent as possible, we will show our results correspondstoupperlimitsonhσviwhentheDMinduced
assuming that DM annihilation proceeds via a single spectrumoriginatesonlyfromthepromptγ-raycomponent,
channel(branchingratioequaltoone),studyingseparately while the solid red line refers to the inclusion of ICS. The
the effect of each final state leading to γ-ray production. astrophysical background is set to the minimal choice
Finally,wederiveconservativelimitsonhσvibyrequiring illustrated in Fig. 2. The effect of ICS inclusion starts to
thatthetotalgamma-rayfluxdoesnotexceedanyoftheFermi- beimportantforhighenergies,i.e.athighDMmasses,and
LATdatapoints[15]bymorethannσ,whichisacommonly thedeviationfromthepromptonlylimitsreachesabouttwo
adoptedpracticeforthiskindofconstraints(seee.g.Ref.[6]). orders of magnitude at ∼10 TeV. We notice that the
Ourlimitsarethussetbythemaximalhσvivalueforwhich uncertainties from ICS are small at the energies at which
Φtot ≤Φexpþn×ΔðΦexpÞinallenergybinsi,whereΦtotis it is effective. For comparison, we also indicate in the
i i i i
same plot the “thermal” cross section of hσvi∼3×
thesumoftheDMandastrophysicalbackgroundfluxesina
given bin i, and Φexp is the experimental data with error 10−26 cm3s−1 that results in the correct DM relic density
i
ΔðΦexpÞ. Given the one-sided nature of the limit, a 2σ (3σ) in the simplest WIMP scenarios (i.e. velocity-independent
i
annihilation and no coannihilations with other particles
upper limit from the intensity data points thus nominally
close in mass to the WIMP).
corresponds to a confidence level of 97.7% (99.9%). We
typicallyquote2σlimits—exceptforthecaseofalargeMAGN InFig.4westudytheeffectofthevariousastrophysical
backgrounds described in Sect. II on the room left for a
contribution,c.f.thebrowndottedlineinFig.2,wherewewill
possibleDMcontributiontothediffuseγ-rayflux,studying
insteadconsiderthemoreconservativelimitsresultingfromthe
requirementthatnodatapointisexceededbymorethan3σ.2 in particular the effect of MAGN and SF galaxies. The
annihilation channel is fixed to bb¯. In the left panel, we
study the impact of the previously neglected MAGN
2Notethatinsuchasituation,wherethesignalmustobviously componentbyfixingΣ totheminimallyallowedvalue:
BMS
be very small, the upper limit on hσvi that is inferred from an by increasing the MAGN contribution from its minimal to
analysis like ours may be anomalously low (e.g. if the data
70% of its maximally expected value [26], limits on a
“fluctuateverylowrelativetotheexpectationofthebackground-
only hypothesis” [83]). For a general introduction to this possibleDMcontributioncouldbeimprovedbyatleastone
problem, see Sec. 36.3.2.2 of the Particle Data Group review order of magnitude compared to the most conservative
[83], or Ref. [84,85] for more details. assumptions concerning the astrophysical contributions
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CONSTRAINING DARK MATTER ANNIHILATION WITH … PHYSICAL REVIEW D 89, 023012 (2014)
b-b (min ΣBSM) b-b (best fit MAGN)
10-21 10-21
10-22 5700B%%e mmsMt aaifnixxt MMMMAAAAGGGGNNNN 10-22 MBBeinMesMtsΣ atfBa ixtfM xitΣΣ SΣΣBB MMMBBMMSSW SSMM /PPPWWLLL SSSSSFFFFF
10-23 10-23
s] s]
3m/ 3m/
> [c 10-24 > [c 10-24
v v
σ σ
< 10-25 < 10-25
10-26 10-26
10-27 10-27
101 102 103 104 101 102 103 104
Mχ [GeV] Mχ [GeV]
FIG.4(coloronline). 2σupperlimitsonthevelocityaveragedDMannihilationcrosssectionhσviasafunctionoftheWIMPmass,for
differentlevelsofΣ andMAGN.Theparametersinthecoloredareasareallowedbyγ-raydataandastrophysicalbackgroundsbythe
BMS
Fermi-LAT IGRB data [15]. In the left panel, we fix Σ at the minimal level compatible with the expectations and vary the
BMS
contribution from MAGN from the minimal to 70% of the maximally expected level. The right panel shows the impact of various
choices for Σ on the limits, fixing the MAGN contribution to the best-fit value derived in Ref. [26]. The constant line at
BMS
3×10−26cm3 s−1 represents the “thermal” cross section of DM in the simplest WIMP models.
(note that setting the γ-ray flux from MAGN to the theIGRBtoconstraingalacticDMannihilation.Assuming
maximally allowed value would actually overshoot the MAGN to contribute at 60% of the maximal flux (high
Fermi data by more than 2σ). background 1, corresponding to the short-dashed green
TherightpanelofFig.4,ontheotherhand,demonstrates curve in Fig. 2), for example, would result in limits that
that the uncertainty in the flux from other astrophysical clearly start to approach the “thermal” cross section of
backgrounds generally has a less significant impact on hσvi∼3×10−26 cm3s−1. Moving to the possibility of
the final limits. Here, we fix the MAGN contribution to even higher levels for the MAGN contribution, we note
its best-fit value [26] and vary Σ from its minimally that one quickly reaches a situation where already a small
BMS
to maximally predicted contribution as described in increaseintheMAGNfluxhasanenormousimpactonthe
Section II. We also show that the choice of the underlying allowedDMcontribution—simplybecausetheastrophysi-
SF galaxy model introduces a certain systematic uncer- cal backgrounds are already extremely close to the IGRB
tainty: depending on the WIMP mass, the resulting limits datapoints(with2σerrors).Inthislimit,thevalidityofour
areuptoafactorof∼3strongerforthePLthanfortheMW method to obtain upper bounds clearly breaks down and a
model (unless Σ only contributes at the minimal level, moresophisticatedstatisticaltreatmentwouldbeneeded.In
BMS
in which case there is no difference because the MAGN order to illustrate that one may still potentially be able to
contribution always dominates). constrainthe“thermal” annihilation rateuptoDMmasses
InFig.5,weshowtheeffectoftheMAGNcontribution ofseveralTeV,weshowinthebottomrightpanelofFig.5
forvariousDMannihilationchannels.Inthetopleftpanel, thelimitsthatresultforanassumedMAGNcontributionat
we present our most conservative limits, derived by fixing 85% of the maximally predicted flux (high background 2,
thebackgroundtotheminimalscenario(seeFig.2).Forbb¯, corresponding to the dotted brown curve in Fig. 2). Note
μþμ− and τþτ− final states, and DM masses below that those limits were derived by requiring that no data
∼100 GeV,theyarecomparablewiththelimitspreviously pointisexceededbymorethan3σ,ratherthan2σ,inorder
derived in Ref. [17], where a similar modeling of the to (partially) meet the above concerns.
astrophysical background was considered; for mχ ≳ LetusstressinpassingthattheinclusionofICSγraysis
100 GeV the inclusion of ICS becomes important and particularly relevant for large DM masses (mχ ≳1 TeV).
consequently significantly improves our new limits with This is the mass range which—for leptonic final states
respect to those for leptonic channels. The right panel [86–89]—couldinprinciplecontributetotheobservedrise
shows a more realistic scenario, where we take all astro- in the cosmic ray positron fraction [90–92]. Our results
physicalbackgroundstocontributeattheirexpectedbest-fit strongly disfavor a DM candidate annihilating mainly into
values (dashed red curve in Fig. 2). Compared to the eþe− with hσvi ≳ 0.3ð1Þ×10−23 cm3 s−1 for masses of
conservative case, this shifts down the upper bounds by a about 1–3 (10) TeV. A bit looser constraints are obtained
factor of roughly 2. forannihilationintomuonsortauleptons,thelatterroughly
In the lower panels of Fig. 5, we take a more optimistic at the level which is required to fit the AMS-02 data
approach in order to illustrate the full potential of using [87,89]. Assuming a relatively large MAGN contribution,
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BRINGMANN et al. PHYSICAL REVIEW D 89, 023012 (2014)
Minimal bkg Best fit bkg
10-21 10-21
e+ e- e+ e-
µ+µ- µ+µ-
10-22 τ+τ-- 10-22 τ+τ--
bb bb
- -
tt tt
10-23 W+W- 10-23 W+W-
s] s]
3m/ 3m/
> [c 10-24 > [c 10-24
v v
σ σ
< 10-25 < 10-25
10-26 10-26
10-27 10-27
101 102 103 104 101 102 103 104
Mχ [GeV] Mχ [GeV]
High bkg 1 High bkg 2
10-21 10-21
e+ e- e+ e-
µ+µ- µ+µ-
10-22 τ+τ-- 10-22 τ+τ--
bb bb
- -
tt tt
10-23 W+ W- 10-23 W+ W-
s] s]
3m/ 3m/
> [c 10-24 > [c 10-24
v v
σ σ
< 10-25 < 10-25
10-26 10-26
10-27 10-27
101 102 103 104 101 102 103 104
Mχ [GeV] Mχ [GeV]
FIG.5(coloronline). UpperlimitsonthevelocityaveragedDMannihilationcrosssectionhσviintoγraysfromtheFermi-LATIGRB
data [15], for various possible annihilation channels. The top left (right) panel shows our most conservative (more realistic) limits,
obtainedbysettingallastrophysicalcontributionstotheminimallyallowed(best-fit)level.Thebottompanels,wherewealsofixΣ at
BMS
thebest-fitvalue,representamoreoptimisticchoicefortheMAGNcontributionconcerningpotentialDMlimits:intheleft(right)panel
MAGNareassumedtoactuallycontribute60%(85%)ofthemaximallyexpectedflux.Notethatforthelimitsinthebottomrightpanel
werequirethetotalγ-rayfluxnottoovershootanydatapointby3σ(ratherthan2σlikeinallothercasespresentedinthiswork).The
grey area indicates the typical benchmark value for the cross section of thermally produced WIMPs, hσvi∼3×10−26 cm3s−1.
likee.g.inthescenariodisplayedinthebottom-leftpanelof the ICS contribution alone in an analysis of preliminary
Fig. 5, the IGRB would thus allow us to firmly rule out a Fermi data [55], and stronger by an overall factor of
DM explanation of the rising positron fraction. The non- roughly 4 (for bb¯) compared to those obtained for the
inclusionoftheEBLabsorptionfortheBLLacpopulation analysis of 1y IGRB data in a smaller sky region than
might have some effect only in the minimal background considered here [96]. Compared to the Fermi analysis of
scenario.From[93],onecanestimatethattheγ-rayfluxat possible galactic DM contributions to the IGRB [3],
80GeV(thehighestFermi-LATenergy,seeFigs.1and2) with no background modeling, our conservative limits
forapopulationatz¼0.5ð1Þisreducedby20(50)%from are comparable for bb¯ and τþτ− final states (for
the source to the Earth. The upper limits on hσvi would mχ ≳20 GeV). Very similar (projected) limits are also
therefore be modified by a negligible factor, and only for found in an independent analysis [24], which however
the highest masses shown in our plots (constrained indeed tendstofindslightlymorestringentconstraintsonTeVDM
by the highest experimental data). models than Ref. [3]. The adopted background modeling
As already mentioned, our results improve the limits in the Fermi analysis [3], on the other hand, leads to
derivedinRef.[17]atDMmassesabove∼100 GeVdueto bounds comparable with our MAGN best fit choice for
the inclusion of ICS; the best-fit scenario displayed in mχ ∼100 GeV;forhighermassesmχ ≳1 TeV,thebounds
Fig.5strengthensthoselimitsfurtherbyafactorof∼2due intheMAGNbestfitcaseareafactorofroughly3stronger.
to the contribution from MAGN. Our constraints for high Let us finally remark that the bounds on hσvi we have
masses are significantly stronger than those obtained from derived here are consistent with constraints from different
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CONSTRAINING DARK MATTER ANNIHILATION WITH … PHYSICAL REVIEW D 89, 023012 (2014)
targetsintheskyobtainedwithverydifferentastrophysical sizable ICS emission in γ rays that is induced by the high
backgrounds and measurement systematics. In particular, annihilation rate into leptonic channels required to fit the
our“optimistic”limitsontheDMannihilationcrosssection positron data.
—assuming an MAGN flux which is 60% of its maximal Evenmoreimportantly,wehavedemonstratedthatthere
theoretical prediction—are generally competitive with the issignificantroomforfutureimprovementoflimitsonthe
bounds from the joint likelihood analysis of 10 dwarf DMannihilationratederivedfromtheIGRB.Infact,under
spheroidalgalaxies[7].Infact,forTeVmassesandleptonic theoptimistic(thoughbynomeansunrealistic)assumption
final states, our constraints are at least comparable even thattheastrophysical processesconsideredherecontribute
under the conservative assumption of a minimal MAGN more or less at the maximal level consistent with our
contribution (though one should note that for such large present understanding, a “thermal” value of 3×
DM masses, galactic center constraints are typically even 10−26 cm3s−1 for the annihilation cross section could be
stronger [94]). We also obtain comparable results at low excludeduptoDMmassesofseveralTeV.Notably,sucha
masses with bounds on leptonic channels from radio limitwillbeimpossibletoreachevenforfar-futureground-
emission [95], which in turn depend significantly on basedobservationsofpointorextendedsourceslikedwarf
astrophysical and cosmological assumptions. At masses galaxies or the galactic center. Even for space-based
mχ ≳100 GeV our bounds from γ rays are stronger, observations of dwarf galaxies, which presently set the
independently of the amount of MAGN included in the most robust and stringent bounds of this kind, it will be
background. Finally, our conservative constraints are extremely challenging for extended future missions to
stronger than those obtained from galaxy cluster [5,96] probe thermally produced DM for such large masses.
and CMB observations [97]. ThemostimportantcontributiontotheIGRBoriginates
from unresolved MAGN, which we have included here
V. CONCLUSIONS for the first time in the context of putting limits on DM
annihilation.Inordertoactuallyexploitthegreatpotential
In this work, we have considered the contribution of
annihilating galactic DM to the IGRB and presented an of the IGRB discussed above, a reduction of the relatively
updated calculation of the resulting upper bounds on the large theoretical uncertainty on the diffuse γ-ray flux from
DM annihilation cross section hσvi. In deriving these unresolved MAGN is thus mandatory. In particular, one
bounds, we took into account both prompt and ICS wouldneedseveraltensofdetectedMAGNinγ raystobe
emission for DM-induced γ rays. For the astrophysical able to directly determine their γ-ray luminosity function
γ-raybackground,weincludedallrelevantcontributionsat (which is presently derived from radio observations); this
their minimally expected level, in particular the contribu- goal is well in reach for Fermi-LAT and next generation
tionfromunresolvedMAGNthathasbeenpointedoutonly γ-ray telescopes. At some point, also an improved under-
very recently. Given that we only consider high galactic standing of the other astrophysical contributions will help
latitudes, our results arevery robust and barely depend on topushlimitsfurtherdown—especiallyifonecandevelop
the choice of DM density profile (apart from an overall theunderlyingmodelingtoalevelthatallowsustopredict
normalization corresponding to the local DM density, those contributions not only as an all-sky average but as a
which may either strengthen or weaken those bounds by function of the viewing angle. Given the expected signifi-
afactorofatmost3).Letusstressthatourboundsarevery cantly increased statistics for future IGRB observations,
conservativeinthattheydonotincludetheexpected—and finally,chancesaregoodthattheIGRBwill turnouttobe
potentially very sizable—effect from DM substructures at oneofthemostefficientfuturemeansofprobingthermally
galactic or extragalactic distances. produced DM.
TheresultingIGRBboundsonhσviarestillcompetitive
with, or more stringent than, limits from radio data,
ACKNOWLEDGMENTS
CMB or galaxy cluster observations. In particular, our
results—along with stringent limits from antiproton data We warmly thank A. Bottino, N. Fornengo and L.
[98–100]—strongly disfavor a DM-based explanation of Latronico for useful discussions and a careful reading of
the unexpected rise in the cosmic ray positron fraction at the manuscript. We also thank J. Siegal-Gaskins for
highenergiesthatwasrecentlyconfirmedbyAMS-02[92], clarifying discussions. T.B. and F.C. gratefully acknowl-
at least if MAGN do not contribute at the most minimal edgesupportfromtheGermanResearchFoundation(DFG)
level currently allowed. The main reason for this is the through Emmy Noether Grant No. BR 3954/1-1.
023012-9