Search for Gamma-ray Emission from Dark Matter Annihilation in the Large Magellanic Cloud with the Fermi Large Area Telescope Matthew R. Buckley,1 Eric Charles,2 Jennifer M. Gaskins,3,4 Alyson M. Brooks,1 Alex Drlica-Wagner,5 Pierrick Martin,6 and Geng Zhao2 1Department of Physics and Astronomy, Rutgers University, Piscataway, NJ 08854, USA 2W. W. Hansen Experimental Physics Laboratory, Kavli Institute for Particle Astrophysics and Cosmology, Department of Physics and SLAC National Accelerator Laboratory, Stanford University, Stanford, CA 94305, USA 3California Institute of Technology, Pasadena, CA 91125, USA 4GRAPPA, University of Amsterdam, 1098 XH Amsterdam, Netherlands 5Center for Particle Astrophysics, Fermi National Accelerator Laboratory, Batavia, IL 60510 5 6Institut de Recherche en Astrophysique et Plan´etologie, 1 UPS/CNRS, UMR5277, 31028 Toulouse cedex 4, France 0 (Dated: April 16, 2015) 2 At a distance of 50 kpc and with a dark matter mass of ∼1010 M(cid:12), the Large Magellanic Cloud r (LMC) is a natural target for indirect dark matter searches. We use five years of data from the p A Fermi Large Area Telescope (LAT) and updated models of the gamma-ray emission from standard astrophysicalcomponentstosearchforadarkmatterannihilationsignalfromtheLMC. Weperform 5 arotationcurveanalysistodeterminethedarkmatterdistribution,settingarobustminimumonthe 1 amountofdarkmatterintheLMC,whichweusetosetconservativeboundsontheannihilationcross section. The LMC emission is generally very well described by the standard astrophysical sources, ] with at most a 1−2σ excess identified near the kinematic center of the LMC once systematic E uncertaintiesaretakenintoaccount. Weplacecompetitiveboundsonthedarkmatterannihilation H cross section as a function of dark matter particle mass and annihilation channel. . h p I. INTRODUCTION - o r The structure of the visible Universe cannot be explained only by the known physics of the Standard Model. t s Measurements of galactic rotation curves [1] and galaxy cluster dynamics [2], precision measurements of the Cosmic a Microwave Background [3], observations of the primordial abundances of heavy isotopes produced by Big Bang Nu- [ cleosynethesis[4],andotherlinesofevidenceprovideorthogonalsetsofdatathatallpointtoasignificantcomponent 2 of the Universe’s energy density being made up of a new form of matter without significant interaction with the v Standard Model. Further evidence comes from the excellent concordance between observation and computer simu- 0 lations of large-scale structure when cold dark matter is included. Observationally, we know dark matter interacts 2 0 gravitationally, is non-relativistic during the formation of large-scale structure, and does not have large scattering 1 cross sections with either itself [5] or the Standard Model [6]. No particle in the Standard Model meets the necessary 0 requirements to make up the dark matter energy density. Other than these pieces of information, we have no solid . experimental or theoretical understanding of the fundamental nature of dark matter. 2 0 While it is not a necessary condition for a successful model of dark matter, it is theoretically well motivated to 5 expect the dark matter to be composed of heavy (mχ >∼ 1 GeV) particles that have a significant annihilation cross 1 section into Standard Model particles. The canonical example of such dark matter is a non-relativistic thermal relic v: that froze out of equilibrium with the Standard Model particle bath in the early Universe. A dark matter particle i with the thermally averaged annihilation cross section (cid:104)σv(cid:105) ∼ 3×10−26 cm3/s can yield the measured dark matter X energy density today, Ωh2 = 0.1199±0.0027 [3]. This can be realized in models with SU(2) weak interactions, L r though other models can also work [7]. a Whilesignificantannihilationwouldceaseduringfreeze-out,ifthedarkmatterpairannihilationisduetoans-wave process and therefore velocity independent, low levels of annihilation would continue to the present day. The end products of this annihilation can be searched for as excesses relative to products from Standard Model astrophysical processes. (We will refer such background processes as “baryonic,” to distinguish them from the sought-after dark matter signals.) As we do not know the nature of the dark matter itself, we cannot know with any certainty which Standard Model channels are the most likely to contain evidence of this annihilation. Furthermore, relatively simple modifications of the canonical thermal relic theory can result in present-day annihilation cross sections that differ by many orders of magnitude from the standard assumption of (cid:104)σv(cid:105)∼3×10−26 cm3/s [8]. Thus, such indirect searches must be performed in as many channels as possible, including photons, neutrinos, positrons, antiprotons, and heavier antinuclei. We must also remain open to annihilation rates far from that expected of a simple thermal relic. Of particular interest is the indirect search for dark matter annihilating into gamma rays. Such signatures are the result of many possible annihilation channels, and so are a generic expectation of dark matter annihilation. In 2 addition to annihilation into pairs of gamma rays, which have a characteristic line spectrum with E = m , dark γ χ matter may convert into pairs (or a larger multiplicity) of quarks, leptons, gluons, or SU(2) gauge bosons, all of L whichwillresultinacontinuumspectrumofgammarays,asunstableparticlesdecay,lightquarkshadronize,andthe showered mesons themselves decay into states that include gamma rays. It is this continuum emission that we search for in this paper. As gamma rays travel relatively unimpeded through the Universe compared to charged cosmic rays (CRs), the dependence on propagation models is reduced compared to charged-particle final states, though not completely eliminated. The Large Area Telescope (LAT) on board the Fermi Gamma-ray Space Telescope (Fermi LAT) is currently the most sensitive instrument for indirect searches via gamma rays in the energy range from ∼100 MeV to over 300 GeV [9]. At present, the Fermi LAT is the only instrument sensitive to gamma-ray signals of dark matter annihilation in the O(10−100 GeV) mass range with cross sections that are on the order of a thermal relic. Gamma rays from dark matter annihilation would be preferentiallydetectedfrom nearbyoverdense regions of dark matter. Prior to this work, searches for indirect signals using Fermi LAT data have been performed targeting dwarf spheroidal galaxies orbiting the Milky Way [10–13], unresolved halo substructure [14–17], galaxy clusters [18, 19], the isotropic gamma-ray background [20–23], and the Milky Way Galactic Center [24–34]. In a number of these analyses of the Galactic Center, a spatially extended anomalous excess has been reported in the Fermi LAT data. This excess hasnotbeenpositivelyidentifiedwithanypreviouslyknownastrophysicalsource,thoughsomepossibilitieshavebeen considered as the source of these gamma rays. For example, a previously unknown population of several hundred millisecondpulsarsintheGalacticCenter[35–39],alarger-than-expectedCRprotonflux[40],orCRelectronsinjected in a past burst event [41] could be non-exotic astrophysical explanations for the observed signal. Alternatively, this excess can be well fit by dark matter with a standard halo density profile, annihilating into Standard Model quarks or leptons with an approximately thermal cross section. The origin of these gamma rays remains a topic of much debate and the source of a great deal of model-building interest [36, 42–61]. Given the uncertainties and observational limitations in the Galactic Center, resolving the origin of this signal will likely require input from observations of other targets. The most sensitive indirect constraints have come from combinedobservationsofdwarfspheroidalgalaxies. Unfortunately,thesensitivityofthatsearchiscurrentlytooweak to resolve the controversy [10, 13]. New sky surveys [62, 63] are likely to identify additional dwarf galaxies in the near future, which would improve the sensitivity of a combined satellite search. However, the current bound is driven by a small number of dwarfs with high expected fluxes and low backgrounds; and it is by no means assured that the upcoming surveys will identify another such “good” dwarf, which would be needed for large improvements [64]. With that motivation in mind, it is desirable to identify a new target for indirect detection with the potential for sensitivitycompetitivewiththedwarfspheroidalgalaxysearch. Inthispaper,wepresentforthefirsttimetheindirect detectionconstraintsderivedfromFermiLATobservationsoftheLargeMagellanicCloud(LMC),thelargestsatellite galaxy of the Milky Way. Galaxies in the mass range of the LMC are expected to be dark matter-rich, and evidence suggests that the LMC is on its first infall to the Milky Way and has not been tidally stripped [65, 66]. Due to its large dark matter mass and relative (∼50 kpc) proximity to Earth [67, 68], the LMC would be the second brightest source of gamma rays from dark matter annihilations in the sky, after the Galactic Center, and a promising target [69, 70]. Unlike the dwarf spheroidal galaxies, the LMC has significant baryonic backgrounds. Despite this, we can place robust and conservative upper bounds on the dark matter annihilation signal that are competitive with those extracted from the dwarf spheroidal observations. The paper is organized as follows. Section II covers the theory of indirect detection of dark matter annihilation, our derivation of the dark matter profile of the LMC, and implications for the expected indirect detection signal. In Section III, we discuss the baryonic backgrounds present in the LMC, and our methods of separating them from dark matter indirect detection signals. The Fermi LAT instrument, data selection, and data preparation are described in SectionIV.OurstatisticaltechniquesanddataanalysisarepresentedinSectionV,andweshowtheresultingbounds in Section VI. We place our results into the larger context and propose directions for future work in the concluding Section VII. II. DARK MATTER ANNIHILATION IN THE LMC The gamma-ray flux from dark matter annihilation depends on the the product of factors related to the particle physics and the spatial distribution of dark matter. Gamma-ray observatories viewing a solid angle ∆Ω will see a differential flux of photons from dark matter annihilation given by dφ (cid:18)x(cid:104)σv(cid:105)dN 1 (cid:19)(cid:18)(cid:90) (cid:90) (cid:19) = γ dΩ d(cid:96) ρ2((cid:126)(cid:96)) , (1) dE 8π dE m2 χ γ γ χ ∆Ω l.o.s. 3 where x = 1 if dark matter is its own antiparticle, x = 1/2 if it is not, and dN /dE is the differential spectrum of γ γ gamma rays from annihilation of a pair of dark matter particles [71]. In this paper we make the standard assumption that x=1. The elements inside the first set of parentheses of Eq. (1) depend on the particle physics of dark matter, and are the same for all targets of indirect detection. These are completely unknown experimentally, though we may have theoretical reasons to assume certain ranges of masses and final states. For our search we scan over these assumed ranges, testing for a signal at each combination of mass m and annihilation channel. These choices, along with the χ astrophysical factors discussed next, are sufficient to determine the differential flux of gamma rays up to an overall normalization, allowing us to place bounds on the total thermally averaged annihilation cross section (cid:104)σv(cid:105). We will return to the choices of differential spectrum dN /dE in Section IIC. γ γ The factors in the second set of parentheses in Eq. (1) are the astrophysical quantities that are target-dependent. Finding an astronomical object that maximizes this quantity then is a key step in designing a sensitive search for indirect signals of dark matter. This integral depends on the dark matter density profile ρ as a function of position (cid:126)(cid:96) in the direction of the line-of-sight (l.o.s.). The integral of the density squared over a solid angle ∆Ω is known as the J-factor: (cid:90) (cid:90) J(∆Ω)≡ dΩ d(cid:96) ρ2((cid:126)(cid:96)). (2) χ ∆Ω l.o.s. Note that the definition of the J-factor depends implicitly on the distance to the dark matter target. The density profiles of dark matter halos as a function of position must be determined from a combination of observation and simulation. In this work, we adopt the six-parameter generalized dark matter density profile as a function of the distance r from the profile center [72–74]: ρ ρ(r)= 0 Θ(r −r), (3) (cid:16) (cid:17)γ(cid:104) (cid:16) (cid:17)α(cid:105)β−γ max r 1+ r α rS rS whereΘ(x)istheHeavisidestepfunction. Here,thecharacteristicdensityρ ,thescaleradiusr ,andthecoefficients 0 S α, β, and γ are all free and must be fit to a particular dark matter halo. We terminate the profile at some distance r ∼ 100 kpc. Setting (α,β,γ) = (1,3,1) yields the classic NFW profile [75], transitioning from an inner slope of max −1 to −3 at large radii. An isothermal profile has a core rather than an NFW-like cusp, and can be obtained from Eq. (3) with (α,β,γ)=(2,2,0). As can be seen from the definition of J, huge gains in the sensitivity to the annihilation cross section can be made bytargetingthoseobjectsthatarebothdark-matter-denseandnearby. Priortothiswork, themostlikelytargetsfor indirectsearcheshavebeenthecenteroftheMilkyWayandthedwarfgalaxiesorbitingtheMilkyWay, asthesehave the largest J-factors relative to their baryonic backgrounds. However, the LMC is both very massive and relatively nearby. ThoughthereisuncertaintyinthedarkmatterprofileoftheLMC,wewillshowthat,evenunderconservative assumptions, our largest Galactic satellite is the second-brightest target for dark matter annihilation searches, after the Galactic Center itself. A. The LMC Dark Matter Profile Proper motion data for the LMC indicate that it may be on its first infall into the Milky Way’s virial halo [65]. If true, then little dark matter may have been lost from the LMC through tidal stripping with the Milky Way [76, 77], which gives our search for dark matter annihilation an added advantage. The LMC has a prominent stellar bar, suggesting that it may have been a barred spiral before capture by the Milky Way, but now generally has a more irregular morphology. Unlike the Galactic Center, which is viewed edge on, we view the LMC closer to face on, at lowinclination. Thisorientationmakesitdifficulttomeasuretheinclinationangleprecisely, henceuncertaintyinthe inclinationisthelargestsourceoferrorindeterminingtheLMCdarkmatterdensityprofilefromrotationcurvedata. Inaddition,thegravitationalcenteroftheLMCisuncertaintowithin∼1◦.5. Theobservedstellarkinematicsfavor rotation about a center located near the eastern end of the stellar bar [78] (denoted in this paper as the stellar center), while the kinematics of the Hi gas favor rotation about a center located at the western end [79] (the HI center). Thesetwolocations are1◦.41±0◦.43apart. Arecentdeterminationofthecenterof the LMCbasedonproper motion data favors a position in agreement with the Hi center to within errors [80]. For our study, we adopt three centers as benchmarks: the previously mentioned stellar and HI centers derived from the stellar and Hi rotation curves, and an outer center defined as the center of the outer lines of equal surface brightness (corrected for viewing angle). The HI and stellar centers are roughly at the edges of the LMC bar, and therefore define the extremes of 4 our profile center uncertainties. The coordinates of these centers are listed in Table I. In addition to these center locations motivated by astronomical observations, we will perform scans of center locations over the entire LMC, as the dark matter center is not necessarily exactly co-located with any of the rotation centers of the visible LMC (see e.g., Ref. [81]) Center (cid:96) (◦) b (◦) stellar 280.54 −32.51 HI 279.78 −33.77 outer 280.07 −32.46 TABLE I: Coordinates of our three benchmark LMC centers, in both right ascension/declination and Galactic coordinates. Given these uncertainties, as well as others (e.g., how to convert the light of the stars into stellar mass), we choose not to determine the “best” fit to the dark matter distribution of the LMC, but rather to find the range of allowed distributions. Below, we use the observed rotation curve data to place upper and lower limits on the dark matter density profile in the LMC, from which we derive a range of potential J-factors for this target. As we will show, the observational data place a robust floor of ∼ 1020 GeV2/cm5 on the integrated J-factor of the LMC, though the stellar rotation curves are also consistent with much larger J-factors. Future observational work might reduce this uncertainty, but we again emphasize that even under the most conservative assumption, the LMC is a viable source of dark matter annihilation products. Undertheassumptionofcircularorbits,ameasurementoftherotationalvelocityofagalaxyisadirectmeasurement of the mass enclosed as a function of radius, v2 =GM(<r)/r. For the inner 3 kpc of the LMC, we adopted the Hi rot rotation curve of Ref. [79].1 The distribution of Hi velocities was binned in 100 pc radial bins, and the 1σ variation within those bins were adopted as the errors in the Hi velocities. Beyond 3 kpc, we adopted the flat rotation curve observed in stellar kinematics [83]. For these large radii, we adopted the value v = 97.7±18.8 km/s determined flat by Ref. [80], but we corrected it to the same inclination as the data from Ref. [79] (we discuss the inclination angle in greater detail below). To determine the dark matter contribution to the rotation curve, the contributions from the Hi gas and stars were subtracted in quadrature (as the enclosed mass is proportional to velocity squared). We adopted the Hi+He mass as a function of radius from Ref. [84]. For stars, we assumed an exponential stellar disk (neglecting the obvious bar) with total stellar mass of 2.7×109 M within 8.9 kpc [78] and scale length of 1.5 kpc (cid:12) [85]. We allowed the stellar mass contribution to vary (see below), equivalent to allowing a range of mass-to-light ratios. This procedure adopted the same position for the kinematic center of the LMC as the Ref. [79] data (which is our HI center, see Table I). The inclination angle i is the largest source of uncertainty in interpreting the LMC’s rotation curve. Hence, we fit for dark matter contributions at the extremes of what is allowed by the inclination and velocity errors. The Hi data favor an inclination of 33◦ [79], but the kinematics of young stars favors a lower inclination of 26◦.2±5◦.9. The proper motion data alone favor 39◦.6±4◦.5 [80]. Taking the central values of these two extremes and neglecting the errors on the individual measurements, the uncertainty of the inclination angle spans 14◦. Adopting a lower inclination raises the normalization of the rotation curve, while higher inclination values lower it. Hence, we find a minimum contribution from the dark matter by adopting i = 39.6◦ and rescaling the rotation velocities accordingly, and a maximum by adopting i=26◦.2. At each inclination extremum, we perform a Levenberg-Marquardt least-squares fit to both a purely isothermal density profile (α,β,γ) = (2,2,0), and an Navarro-Frenk-White (NFW) density profile (α,β,γ) = (1,3,1). As mentioned above, the stellar contribution was allowed to vary so as to contribute the largest possible mass to the inner rotation curve in each case. By maximizing the stellar contribution consistent with the rotation curve, we ensure that our dark matter contributions are always lower limits. In practice, the stellar mass varied between 1.2×109 M at maximum inclination and 2.4×109 M at minimum inclination. In Figure 1, we (cid:12) (cid:12) plot the rotation curve data for the LMC, at the maximum and minimum inclination angles, along with the best-fit profiles. The data points beyond 3 kpc represent a flat rotation curve, as found in Ref. [80] based on data from 1 Ref.[79]usedGaussianfitstotheHidatatodeterminethevelocitiesasafunctionofradius. Tobetterfitnon-circularmotionsinthe Hi data, Hermite polynomials are a better choice [82]. The fact that we have neglected non-circular motions means that the rotation curve could rise more quickly in the center than Ref. [79] determined. Hence, all of our fits will be lower limits on the contribution from dark matter to the rotation curve. Likewise, Ref. [79] adopted a high transverse motion of the LMC on the sky that has since beenupdatedwithnewpropermotionmeasurements. Wemakenocorrectionhere,butagainnotethatthismakesourdarkmatterfits conservativeunderestimations. 5 Ref. [83]. We will use nfw-max and iso-max to denote the NFW and isothermal profiles fit to the data at i = 26◦.2, and nfw-min and iso-min the results of the fit with an inclination angle of i=39◦.6. 120 120 100 100 80 80 sin(i)=26.2◦ sin(i)=39.6◦ m/s) Stellar Mass m/s) Stellar Mass k 60 HI mass k 60 HI Mass (vrot. DSiMm uSliamtiuolna tSiounm (vrot. DSiMm uSliamtiuolna tSiounm 40 DM NFW 40 DM NFW NFW sum NFW Sum DM isothermal DM Isothermal 20 Isothermal sum 20 Isothermal Sum HI data HI data Stellar data Stellar data 0 0 0 2 4 6 8 10 0 2 4 6 8 10 r (kpc) r (kpc) FIG. 1: LMC rotation curve data, assuming an inclination i that maximizes (left) and minimizes (right) the dark matter density. Stellarv dataareshownwithorangepoints[80],andHiv data[79]ingreen. Theorangedottedlinedenotesthe rot rot contribution to v from the stellar mass, and the contribution from the Hi+He gas is shown in dotted green [84]. The v rot rot values predicted by NFW and isothermal profiles fit to data are shown by red and blue dashed lines, respectively. Solid lines show v of the dark matter profiles plus contribution from the stars and gas, with the maximum values in the left plot and rot the minimum on the right. Grey lines show the mean profile of dark matter fit from simulations of LMC-like galaxies (dashed is dark matter-only, solid is dark matter plus stars and gas), and are not fit to the stellar and Hi data points. The simulated darkmatterrotationcurveisindependentofinclinationangle,andtheflatrotationcurvebeyond3kpcisbasedontheresults of Ref. [80]. The assumptions of pure NFW or isothermal profiles are simplifications that we do not expect to be realized in the actual LMC. Thus, we have taken a separate approach to determine what the “typical” dark matter density profile of an LMC–mass galaxy might be. Recent cosmological simulation results have demonstrated that energetic feedback from stars and supernovae can transform an initially steep inner density profile into a shallower profile [86–88]. The degree of transformation is sensitive to the mass of stars formed [88, 89], and the stellar mass is dependent on halo mass [90, 91]. Ref. [92] has provided a general relation for the generalized NFW parameters (α,β,γ) as a function of stellar-to-halo mass ratio. Therefore, we can extract a range of generalized NFW profiles appropriate for the LMC from simulations, provided we know the stellar and halo masses of the galaxy. We adopt a stellar mass of 2.7×109 M from Ref. [78]. The allowed dark matter halo mass range of the LMC is (cid:12) uncertain by an order of magnitude, e.g., (3 – 25)×1010 M [93], and allows for the whole range of density profiles (cid:12) between isothermal and NFW. To better constrain the stellar-to-halo mass ratio, we use a sample of cosmologically simulated galaxies from Ref. [94] that has been shown to match the observed stellar-to-halo mass relation. This sample was chosen to have halo masses in the range (3 – 25)×1010 M , stellar masses ≥ 109 M , and logarithmic (cid:12) (cid:12) stellar-to-halo mass ratios ranging from −1.2 to −1.7. We have adopted the (α,β,γ) values for the extrema of these halos from Ref. [92], which provide an “envelope” of typical dark matter density profiles in an LMC–mass galaxy predicted by state-of-the-art cosmological simulations. We take the average values of (α,β,γ), defining the mean simulated profile. Figure 2 shows the density profiles of the simulated galaxies, and the overlaid best-fit profiles. The resulting generalized NFW parameters of these three simulated profiles are shown in Table II. In Figure 3, we plot the density profiles ρ(r) of our benchmark models: the two NFW and isothermal models, and our three generalized NFW profiles forming the range of results from simulation. In Figure 1, showing the rotation curve data to which the NFW and isothermal profile parameters were fit, we overlay the simulated profiles. Note that dark matter distributions drawn from simulations are not directly fit to the LMC data and are not corrected for inclination angle. 6 1010 109 108 ) 3 c p /k 107 fl M ( ρ 106 105 104 10-1 100 101 102 r (kpc) FIG. 2: Density profiles of the four LMC-mass cosmological simulations (red, blue, green, purple lines), and maximum, minimum,andaverageofthefittedgeneralizedNFWprofileswith(α,β,γ)valuesderivedfromRef.[92],whichextendtodown to r=0 (solid black lines). B. J-factors of the LMC We now have three different classes of dark matter profiles that span the measured rotation curves for the LMC. From our fits to the rotation curve data, we have profiles that maximize and minimize the LMC dark matter density, assuming both an NFW profile (nfw-max and nfw-min) and an isothermal profile (iso-max and iso-min). Fitting the measured stellar-to-halo mass ratio to simulation, we also have a range of profiles fit to a generalized NFW. In addition to the profile parameters consistent with the mass ratio that maximize and minimize the dark matter density consistent with simulation (sim-max and sim-min), we also include a profile that has the average values of the (α,β,γ) parameters from the simulated galaxies (sim-mean). As the J-factor depends on the integrated density profile squared, the maximum and minimum profiles within a specific class of profiles (i.e., NFW, isothermal, or simulated) will also have the maximum or minimum J-factor within their class of halo profiles. Recall that, in order to be maximally conservative in our NFW and isothermal dark matter profiles, we at every opportunity maximized the baryonic contributions to the observed rotation curves, minimizing the assumed dark matter density. We summarize these benchmark models in Table II, including the integrated J-factor out to 15◦ (though we note that the majority of the contribution to the J-factor comes from the inner few degrees of the LMC), and the dark matter mass within 8.7 kpc. The range of dark matter masses inferred from these fits is consistent with the observed total (dark matter plus baryon) mass of the LMC inside this radius M(8.7 kpc) = (1.7±0.7)×1010 M [95]. In (cid:12) Figure 4, we plot the differential J-factor dJ/dΩ as a function of observation angle from the profile center, as well as theintegratedJ-factor. Ascanbeseen, despitetherangeofprofilechoicesavailable, thetotalJ-factoroftheLMCis remarkably consistent for six of our seven benchmarks, with log J/(GeV2/cm5)∼19.5−20.5. For comparison, the 10 most promising dwarf spheroidal galaxies have log J/(GeV2/cm5) ∼ 19−19.5 [96, 97], while the Galactic Center 10 within1◦ haslog10J/(GeV2/cm5)>∼21−24(dependingonassumptionsfortheinnerslopeofthedarkmatterprofile, see e.g. [27]). When setting bounds on dark matter annihilation, we will take the average for each of these classes of dark matter profiles. For the NFW and isothermal profiles, we take the geometric mean of the maximum and minimum profiles, and use the logarithmic difference of the maximum and minimum J-factors as an estimate of the 1σ uncertainty on the J-factor. We will refer to these two profiles as nfw-mean and iso-mean. For our generalized profiles taken from simulation, we will use the sim-mean profile. RecallthatthemeanprofileisobtainedfromtheaveragegeneralizedNFWparameters(α,β,γ)fitfromsimulation, 7 1010 109 Simulation 108 ) 3 pc 107 Isothermal k / fl NFW M ( 106 ) r ( ρ 105 104 103 10-1 100 101 102 r (kpc) FIG.3: DensityprofilesasafunctionofradiusrfromtheLMCcenterforthebenchmarkmodels(listedinTableII).Maximum and minimum NFW (blue), isothermal (red), and range of simulated (black) profiles constitute the upper, lower edges of the shaded regions. The average simulated profile is shown as a line in the shaded black region. ratherthanaveragingtheJ-factorsofthesimulatedprofiles. Thisdistinctionisimportantastheextremegeneralized NFW profile sim-max has a much higher J-factor than any other profile we consider, despite having a total dark matter mass that is consistent with the other benchmarks. This is because this profile has a very steep inner slope, and the annihilation is proportional to density squared. It is possible that future observations of the LMC can be used to reduce the uncertainties in our derivation of the LMC dark matter distribution. If the resulting profile is in the upper range of the generalized NFW envelope obtained from simulation, the LMC would set the best bounds on dark matter annihilation by far, compared to other targets. However, this extreme profile is an outlier that, while consistent with the total mass within 8.7 kpc, seems inconsistent with the rotation curve data. Instead, we focus here on the conservative profiles profiles using the averaged nfw-mean, iso-mean, and sim-mean, which still have J-factors that are larger than those of the “best” individual dwarf spheroidal galaxies. This gain is tempered by the higher baryonic backgrounds (discussed in detail in Section III). Profile α β γ r (kpc) ρ (M /kpc3) J (GeV2/cm5) M(8.7 kpc) (M ) S 0 (cid:12) (cid:12) nfw-max 1 3 1 17.0 2.5×106 2.0×1020 1.1×1010 nfw-mean 1 3 1 12.6 2.6×106 9.4×1019 7.7×109 nfw-min 1 3 1 12.6 1.8×106 4.4×1019 5.3×109 iso-max 2 2 0 2.0 6.2×107 4.6×1020 2.0×1010 iso-mean 2 2 0 2.4 3.7×107 2.8×1020 1.5×1010 iso-min 2 2 0 2.4 2.9×107 1.7×1020 1.2×1010 sim-max 0.35 3 1.3 5.4 1.1×108 5.6×1021 1.6×1010 sim-mean 0.96 2.85 1.05 7.2 8.4×106 2.3×1020 1.4×1010 sim-min 1.56 2.69 0.79 4.9 1.2×107 1.7×1020 1.3×1010 TABLE II: Parameters of LMC benchmark profiles, along with derived quantities J and the mass M enclosed up to 8.7 kpc. J is calculated out to 15◦ (12.8 kpc). Average values for the isothermal and NFW J-factors are obtained from the geometric mean of the maximum and minimum profiles. 8 1028 1022 Simulation 1027 Simulation 1021 1026 5m/sr)1025 5cm)1020 NFW 2V/c1024 2eV/1019 (GedJ/dΩ11002223 Isothermal NFW (GJ(∆Ω)11001178 1021 1016 Isothermal 1020 1019 1015 10-2 10-1 100 101 10-2 10-1 100 101 Degrees Degrees FIG.4: Differential(left)andintegrated(right)J-factorsasafunctionofanglefromtheLMCcenterforthebenchmarkmodels (listed in Table II). Labeling and color coding is as in Fig. 3. C. Gamma-Ray Spectrum As the particle physics of dark matter is as yet unknown, we do not know the mass or the final state products of the annihilation of dark matter. However, if dark matter annihilates into a pair of Standard Model particles other than neutrinos, be it W/Z gauge bosons, gluons, quarks, or charged leptons, then (with the exception of the stable e±), those particles must decay or hadronize. This leads to a cascade of Standard Model particles, decaying down to electrons, protons, their antipartners, and a large multiplicity of photons with gamma-ray energies. Photons are also emitted as final state radiation from the charged particles, including e+e− pairs. As a result of this cascade, the gamma rays from dark matter annihilation do not feature a sharp line at E =m , γ χ but rather a continuous spectrum with characteristic energies significantly lower than the dark matter mass. Indeed, in this analysis we do not perform a line-search for dark matter annihilating directly into photons. The annihilation channels we consider in this work are χχ→ss¯, b¯b, tt¯, gg, W−W+, e+e−, µ+µ−, and τ−τ+. (4) Annihilation into pairs of u or d quarks produces a similar spectrum as annihilation into gluon pairs, cc¯ is similar to ss¯, as are ZZ and W−W+, so bounds on such channels can be roughly extrapolated from the subset of channels we analyze in detail. We scan over all dark matter masses between 5 GeV and 10 TeV. Channels of dark matter annihilating to massive particles are only open above the mass threshold, when the dark matter mass is equal to that of the heavy Standard Model particle in the final state. For each final state, we calculate the resulting spectrum of gamma rays as a function of dark matter mass using code available as part of the Fermi LAT ScienceTools.2 In Figure 5, we show representative spectra dN/dE per pair γ annihilation for a range of channels and dark matter masses. 2 The DMFitFuction spectral model described at: http://fermi.gsfc.nasa.gov/ssc/data/analysis/documentation/Cicerone/ Cicerone_Likelihood/Model_Selection.html, see also Ref. [98]. We note that this formulation does not include electroweak cor- rections[99–103]. Theelectroweakcorrectionsareexpectedtobeimportant(assumings-waveannihilation)whenthedarkmattermass ismuchheavierthan1TeV,andwouldalterthespectrasubstantiallyfortheW+W−,e+e−,µ+µ− andτ+τ− channels,increasingthe numberofexpectedγraysperdarkmatterannihilationbelow∼10GeV[103,104]. However,theboundsinthehighmassregimecome primarily from the highest energy bins. Even for 10 TeV dark matter masses in the most affected channels, including the electroweak correctionsimprovesthelimitson(cid:104)σv(cid:105)by<∼20%. 9 200 GeV Dark Matter b¯b Annihilation 10-1 10-1 10-2 10-2 10-3 10-3 ) ) 1− 1− V V Me 10-4 Me 10-4 (dEγ10-5 (dEγ10-5 / / Nγ Nγ d 10-6 d 10-6 e+e− gg µ+µ− b¯b 10 GeV 100 GeV 10-7 τ+τ− t¯t 10-7 25 GeV 1000 GeV W+W− s¯s 50 GeV 10000 GeV 10-8 10-8 102 103 104 105 102 103 104 105 106 E (MeV) E (MeV) γ γ τ+τ− Annihilation W+W− Annihilation 10-1 10-1 10-2 10-2 10-3 10-3 ) ) 1− 1− V V Me 10-4 Me 10-4 ( ( dEγ10-5 dEγ10-5 / / Nγ Nγ d 10-6 d 10-6 2 GeV 100 GeV 5 GeV 1000 GeV 100 GeV 1000 GeV 10-7 10-7 10 GeV 10000 GeV 250 GeV 10000 GeV 25 GeV 500 GeV 10-8 10-8 102 103 104 105 106 102 103 104 105 106 E (MeV) E (MeV) γ γ FIG. 5: Gamma-ray spectra dN /dE of dark matter pair annihilation. Upper left: Annihilation spectra of 200 GeV dark γ γ matter into each of the channels we consider in this work. Upper right: Annihilation spectrum into b¯b for a range of dark matter masses. Lower left: Annihilation spectrum into τ+τ− for a range of dark matter masses. Lower right: Annihilation spectrum into W+W− for a range of dark matter masses. III. BARYONIC BACKGROUNDS Thegamma-rayemissionfromtheLMCwasfirstdetectedbytheEGRETinstrumentaboardtheCompton Gamma Ray Observatory [105, 106], operating from 1991 to 2000. [107]. The LMC was established as an extended source, but the limited angular resolution of EGRET prevented a deep investigation of the origin and composition of the high-energy emission. With more than an order of magnitude improvement in sensitivity, better angular resolution, and extended energy coverage compared to its predecessor, the Fermi LAT instrument enabled a strong detection of theLMCearlyinthemission. From11monthsofcontinuousallsky-surveyobservations,[108]reportedadetectionof theLMCwithformalsignificance∼33σ in∼100MeV–10GeVgammaraysandconfirmedtheextendednatureofthe source. The emission is relatively strong in the direction of the 30 Doradus star-forming region, but more generally the emission seems spatially correlated to classical tracers of star formation activity (such as the Hα emission). The extension and spectrum of the source suggest that the observed gamma rays originate from CRs interacting with the interstellar medium through inverse-Compton scattering, bremsstrahlung, and hadronic interactions. Yet, contributions from discrete objects such as pulsars could not be (and were not) ruled out at that time. Compared to this early work, we now utilize five years of LAT data. These data are of better quality than the initialdataset,thankstoimprovementsintheinstrumentcalibration,eventreconstruction,andbackgroundrejection 10 (i.e., Pass 7 reprocessed data instead of Pass 6 data).3 Recently, a new analysis of the high-energy gamma-ray emission of the LMC was performed using 5.5 years of Pass 7 reprocessed LAT data, which resulted in a more accurate description of the source. This new effort will be presented in detail elsewhere.4 The present work is based on an intermediate version of the diffuse emission model from that work, with only very minor differences compared to the final model described in the upcoming paper. We briefly summarize here the main features of the emission model and the approach followed to derive it. This is of prime importance to understand the possible limitations and systematic effects that may affect the search for dark matter signals on top of this astrophysical background. A region of interest (ROI) specific to the LMC was defined as a 10◦ × 10◦ square centered on (RA,DEC) = (80◦.894,−69◦.756)andalignedonequatorialcoordinates(J2000.0epoch). Theenergyrangeconsideredinthatanalysis was200MeV–50GeVandcountswerebinnedinsixlogarithmicbinsperdecade. Thelowerenergyboundwasdictated by the poor angular resolution at the lowest energies, while the upper bound was imposed by the limited statistics at the highest energies. The data-set used to build the background model largely overlaps with (but is not identical to) the data-set we use in the remainder of the paper to perform our search for dark matter. The emission model is built from a fitting procedure using a maximum likelihood approach for binned data and Poisson statistics. A given model is composed of several components, accounting for different sources in the field. Each component has a spatial description, a spectral description, and a certain number of free parameters. The expected distribution of counts in energy and across the ROI is obtained by convolution of the model with the point- spread function (PSF), taking into account the exposure achieved for the data set. The free parameters of the model are then adjusted until the distribution of expected counts provides the highest likelihood given the actual binned spatial-energy cube of observed counts. AsafirststepintheprocessofmodelingtheemissionovertheROI,andbeforedevelopingamodelfortheLMC,we have to account for known background and foreground emission, in the form of diffuse and/or isolated sources. The basemodeliscomposedoftheisotropiccontribution(extragalacticemissionandresidualcharged-particlebackground misclassified as gamma rays) the Galactic diffuse model (from CRs interacting with the interstellar medium in our Galaxy)5, and all objects listed in the second Fermi LAT source catalog [109] within the ROI but outside the LMC boundaries (including sources as far as 2◦ away from the edges of the ROI to account for spill-over effects due to the poor angular resolution at low energies). Starting from this base model, we aim to describe the remaining emission with a combination of point-like sources and extended spatial intensity distributions, adding new components successively. Point-like sources can easily be found if they have hard spectra, because the angular resolution is relatively good at high energies, or if they exhibit a variability pattern reminiscent of an already-known object. In the case of the LMC, three new point sources were recognized in this way.6 For the rest of the emission, an iterative procedure is required to develop the model. At each step, a scan over position in the LMC and size of the source is performed to identify the new component that provides the best fit to the data. For each trial position and size, a fit is performed assuming a power-law spectral shape for the new component (which is a good approximation for most components). If the improvement in the likelihood is significant – that is, has a log-likelihood test statistic (TS, see Section V) greater than 25 – then the component is added to the model and a new iteration starts. The process stops when adding a new component yields a TS lower than 25. At the end of this process, a nearly complete model is obtained. Next, we again optimize the positions and sizes of the extended components within this nearly complete model, from the brightest to the faintest in turn. The final stage consists of deriving bin-by-bin spectra for all components to check that the initially adopted power-lawspectralshapeisappropriate. Ifnot,itisreplacedbyapowerlawwithexponentialcutofforalog-parabola shape, depending on which provides the best fit and a significant improvement relative to the power law. InthecaseoftheLMC,thebestmodelwasobtainedundertheassumptionthatextendedemissionarisesfromlarge- scalepopulationsofCRsinteractingwiththeinterstellarmedium. Inthe∼100MeVto100GeVrange,theinterstellar radiation is dominated by gas-related processes, especially hadronic interactions in which CR nuclei interact with interstellar gas to produce mesons that decay into gamma rays. The corresponding gamma-ray emission follows the gasdistribution(see,forinstance,Ref.[111]). FortheLMC,wethereforemodeledeachextendedemissioncomponent as the product of the gas column density distribution with a two-dimensional Gaussian emissivity distribution whose positionandsizewereiterativelyoptimized. Oneadvantageofthisassumptionisthatthemodelretainsthesmall-scale 3 http://fermi.gsfc.nasa.gov/ssc/data/analysis/documentation/Pass7REP_usage.html 4 Fermi LAT Collaboration, in preparation, see also http://fermi.gsfc.nasa.gov/science/mtgs/symposia/2014/program/05_Martin. pdf 5 The diffuse background models are available at http://fermi.gsfc.nasa.gov/ssc/data/access/lat/BackgroundModels.html as iso clean v05.txtandgll iem v05.fits. 6 IntherecentlyreleasedthirdFermisourcecatalog(3FGL)producedwithfouryearsofdatathesesourceswerenotindividuallydetected butratherabsorbedintotheextendedLMCsource,3FGLJ0526.6−6825e[110].