Two Emission Mechanisms in the Fermi Bubbles: A Possible Signal of Annihilating Dark Matter
FFERMILAB-PUB-13-052-A
Two Emission Mechanisms in the
Fermi
Bubbles: A Possible Signal of AnnihilatingDark Matter
Dan Hooper
1, 2 and Tracy R. Slatyer Fermi National Accelerator Laboratory, Theoretical Astrophysics Group, Batavia, IL 60510 University of Chicago, Department of Astronomy and Astrophysics, Chicago, IL 60637 School of Natural Sciences, Institute for Advanced Study, Princeton, NJ 08540.
We study the variation of the spectrum of the
Fermi
Bubbles with Galactic latitude. Far from theGalactic plane ( | b | > ∼ ◦ ), the observed gamma-ray emission is nearly invariant with latitude, and isconsistent with arising from inverse Compton scattering of the interstellar radiation field by cosmic-ray electrons with an approximately power-law spectrum. The same electrons in the presence ofmicrogauss-scale magnetic fields can also generate the the observed microwave “haze”. At lower lat-itudes ( | b | < ∼ ◦ ), in contrast, the spectrum of the emission correlated with the Bubbles possesses apronounced spectral feature peaking at ∼ E dN/dE ) which cannot be generated by anyrealistic spectrum of electrons. Instead, we conclude that a second (non-inverse-Compton) emissionmechanism must be responsible for the bulk of the low-energy, low-latitude emission. This secondcomponent is spectrally similar to the excess GeV emission previously reported from the GalacticCenter (GC), and also appears spatially consistent with a luminosity per volume falling approxi-mately as r − . , where r is the distance from the GC. Consequently, we argue that the spectralfeature visible in the low-latitude Bubbles is most likely the extended counterpart of the GC excess,now detected out to at least ∼ ∼
10 GeV dark matter particles annihilatingto leptons, or from ∼
50 GeV dark matter particles annihilating to quarks, following a distributionsimilar to, but slightly steeper than, the canonical Navarro-Frenk-White (NFW) profile. We alsoconsider millisecond pulsars as a possible astrophysical explanation for the signal, as observed mil-lisecond pulsars possess a spectral cutoff at approximately the required energy. Any such scenariowould require a large population of unresolved millisecond pulsars extending at least 2-3 kpc fromthe GC.
PACS numbers: 95.85.Pw, 98.70.Rz, 95.35.+d
I. INTRODUCTION
Data from the
Fermi
Gamma-Ray Space Telescopehave revealed a pair of large gamma-ray lobes extend-ing approximately 50 ◦ north and south of the GalacticCenter [1]. These lobes, known as the Fermi
Bubbles,are visible in gamma-rays between ∼ dN/dE ∝ E − ) than thegamma-ray emission associated with the Galactic Disk.The Bubbles were originally studied as a possiblegamma-ray counterpart to the WMAP haze [2], a spec-trally hard microwave excess in the inner Galaxy mostclearly visible in
WMAP ’s 23 and 33 GHz frequencybands. The haze was first discovered in 2003 [3], and hasbeen studied over the past decade as a possible signatureof a new hard electron population in the inner Galaxy[4–6], producing microwave synchrotron radiation in theGalactic magnetic field. Recently, the existence of themicrowave haze has been confirmed by the
Planck exper-iment [7], whose data indicate a strong degree of spatialcoincidence between the microwave haze and the gamma-ray Bubbles, further supporting the hypothesis that thesesignals have a common origin. Perhaps the simplest pos-sibility is that the gamma rays arise from inverse Comp-ton scattering (ICS) by the same hard electron popula-tion that produces the haze via synchrotron. The question of the origin and nature of the
Fermi
Bubbles has been the subject of much debate. Onekey question is whether these gamma-rays are producedby a hadronic [8–10] or leptonic [11–15] mechanism, i.e.whether they arise from the scattering of energetic pro-tons on the gas of the interstellar medium, or from theICS of photons from the interstellar radiation field by en-ergetic electrons. An example of a hadronic scenario wasproposed by Aharonian and Crocker [8], in which theBubbles are billion-year-old reservoirs of energetic pro-tons, which were injected as a result of star formationin the Galactic Center and are confined within the Bub-bles by magnetic fields. Leptonic scenarios have garneredsomewhat more attention in the literature, and providea straightforward link with the spatially correlated emis-sion observed in the microwave and radio [16] (hadronicscenarios will also generate synchrotron emission throughthe electrons produced in charged pion decays, but sincethese electrons will diffuse after being produced, the con-nection between their spectrum and spatial distributionand that of the gamma-rays is not as straightforward as inthe leptonic scenario). In such leptonic models, electronsare accelerated by a shock or a series of shocks and/orby Fermi acceleration in turbulent magnetic fields behindthe shock front [17]; the shock(s) may be fueled by ac-cretion onto the supermassive black hole at the Galactic a r X i v : . [ a s t r o - ph . H E ] F e b Center, by starburst activity, or by some other mecha-nism.In this article, we reexamine the
Fermi
Bubbles andthe variation of their spectrum with Galactic latitude.Far from the Galactic plane ( | b | > ∼ ◦ ), the observedgamma-ray spectrum is nearly invariant with latitudeand fairly flat over the energy range observed by Fermi .This spectrum can be well explained by inverse Comp-ton scattering of cosmic microwave background (CMB),infrared, and starlight photons by a population of GeV-TeV electrons with an approximately power-law spec-trum ( dN e /dE e ∼ E − e ). Furthermore, we find that thissame population of cosmic ray electrons leads to syn-chrotron emission of the same amplitude as the observedmicrowave haze, if microgauss-scale magnetic fields arepresent in the high-latitude regions of the Bubbles. Thesuccess of this simple and self-consistent picture providesstrong support for a leptonic origin of the high-latitudeemission from the Fermi
Bubbles.At latitudes closer to the disk, however, a leptonic ori-gin of all the emission associated with the Bubbles doesnot appear possible. The gamma-ray spectrum of the
Fermi
Bubbles at latitudes within approximately 20 ◦ ofthe Galactic plane possesses a peak at energies of a fewGeV, and cannot be generated by inverse Compton scat-tering of starlight, infrared, or cosmic microwave back-ground radiation by any realistic steady-state electronpopulation. Furthermore, no realistic spectrum of cosmicray protons is capable of accounting for the gamma-rayspectrum observed at these low latitudes.Gamma-ray emission with a similar spectrum has beenpreviously identified from the region surrounding theGalactic Center (GC) [18–22]. Proposed origins for thisexcess include annihilating dark matter [18–20, 22], apopulation of millisecond pulsars [18, 19, 22–24], or cos-mic ray interactions with gas [18, 19, 22, 25, 26]. In thispaper, we show that the non-inverse Compton compo-nent of the emission from the Fermi
Bubbles identifiedin this study is spectrally and morphologically consistentwith being the extended counterpart of this GC excess,revealing that this emission is not confined to the GC,but extends out to at least ∼ ρ ∝ r − . , where r is the distance to the GC (the GC excess, in isola-tion, favors a power-law slope in the range of 1 . . ∼
10 GeVannihilating to leptons, or by ∼
50 GeV particles annihi-lating to quarks. In either case, the normalization of theobserved signal requires an annihilation cross section onthe order of σv ∼ (6 − × − cm /s, similar to thatexpected of a thermal relic of the Big Bang.The remainder of this paper is structured as follows.In Sec. II we describe the analysis used to extract thespectra from various regions of the Fermi
Bubbles. In Sec. III we demonstrate that the high-latitude regions ofthe Bubbles can be accounted for with an approximatelypower-law spectrum of GeV-TeV electrons, which can si-multaneously produce the observed microwave haze assynchrotron. In Sec. IV we turn our attention to thelow-latitude regions of the
Fermi
Bubbles, and show thattheir spectra cannot be accounted for by inverse Comp-ton scattering. Instead, an additional mechanism is re-quired, capable of producing a spectrum which peaksstrongly at energies of a few GeV. In Sec. V we com-pare this signal with that previously observed from theGalactic Center. In Sec. VI, we study the residuals re-maining when the (best-fit) known backgrounds are sub-tracted, and demonstrate how the few-GeV peak appearsin these residuals. In Sec. VII, we show that the emis-sion observed at low-latitudes is better described by aspherically symmetric, NFW-like morphology than by aflat-brightness distribution confined to the regions of the
Fermi
Bubbles. In Sec. VIII we discuss possible interpre-tations of this signal, including annihilating dark matterand a population of gamma-ray pulsars. We summarizeour results and draw conclusions in Sec. IX. This paperalso includes five appendices, which describe various crosschecks of our results and other supplementary material.
II. EXTRACTING THELATITUDE-DEPENDENT SPECTRUM OF THEGAMMA-RAY BUBBLES
In our analysis, we employ the publicly available
Pass7 Version 6 data release from
Fermi , with 4.5 years ofphoton data. We apply a standard zenith angle cutto exclude the Earth limb, rejecting events with zenithangles greater than 100 ◦ . We also employ the recom-mended diffuse analysis cuts on the data quality, nominalscience configuration and rocking angle: DATA QUAL==1 , LAT CONFIG==1 , ABS(ROCK ANGLE) < . Throughout, weuse the class of events designated ULTRACLEAN , but haveconfirmed that employing the
SOURCE or CLEAN classesdoes not alter our conclusions.We generate skymaps for 30 log-spaced energy binsspanning the range from 0.3 GeV to 300 GeV, binning thephotons on an
NSIDE=256
HEALPix grid, and smooth allmaps to 2 ◦ FWHM (full width at half maximum). As inRef. [1], we use front-converting events only (which havebetter inherent angular resolution) at energies below 1GeV. We follow the prescription from Ref. [1] for pointsource subtraction, using the
Fermi The dataset we employ may be downloaded from http://heasarc.gsfc.nasa.gov/FTP/fermi/data/lat/weekly . FIG. 1: The regions of the sky considered in our analysis.The
Fermi
Bubbles themselves are broken into five pairs ofregions according to Galactic latitude ( | b | < ◦ , 10 ◦ − ◦ ,20 ◦ − ◦ , 30 ◦ − ◦ , and 40 ◦ − ◦ ). Also shown as dashed linesis the inner complement region to the Bubbles, as describedin Appendix D. from the likelihood by ∆ ln L = 1 /
2, and do not takeinto account the systematic error in the event that thelinear combination of templates is a poor description ofthe data. Further details of the fitting procedure may befound in Ref. [1] and in Appendix B of Ref. [2]. We em-ploy several different template combinations to test therobustness of our results to the foreground model.In the Galactic disk, there is a substantial popula-tion of unsubtracted point sources, as well as brightdiffuse emission; consequently, we mask the inner disk.Throughout our study, we will show results for maskswith | b | < ◦ , | b | < ◦ and | b | < ◦ , to test the depen-dence of our results on this parameter.To determine the spectrum of the Fermi
Bubbles as afunction of latitude, we divide the standard spatial tem-plate for the Bubbles (as defined in Ref. [1]) into sub-regions by (absolute) latitude: | b | < ◦ , 10 ◦ < | b | < ◦ ,20 ◦ < | b | < ◦ , 30 ◦ < | b | < ◦ , and 40 ◦ < | b | < ◦ (see Fig. 1). We smooth all templates to the scale ofthe maps. We fit separately for the spectrum in each ofthese latitude bands, varying the degree of masking ofthe Galactic Disk, and with a range of template-basedmodels for the known backgrounds. All fits include anisotropic offset, to absorb residual cosmic-ray contami-nation and isotropic diffuse emission. The two primarypossibilities we consider for the additional templates are: • Diffuse model : We take the
Fermi diffuse modelfrom version
P6V11 of the
Fermi
Science Tools,smooth it to match the maps we are using, in-terpolate to the appropriate energies, and performthe fit using only this template (in addition to the latitude-sliced Bubbles templates and the isotropictemplate, which are universal to all subtractionmethods). This version of the diffuse model hasbeen adjusted to fit the data assuming no contri-bution from the Bubbles; consequently it may ab-sorb some of the Bubbles-correlated emission at thecost of oversubtraction in neighboring regions. Itwas also designed primarily to model the emissionat energies (cid:46)
50 GeV, and is not recommended foruse at very low latitudes, | b | < ◦ . However, sinceour signal extends to quite high latitudes and theenergies of greatest interest are at (cid:46)
50 GeV, theselatter caveats do not pose severe problems for ourstudy. • Low-energy template : We employ the Schlegel-Finkbeiner-Davis (SFD) dust map [27] as a tem-plate for emission from cosmic-ray protons scat-tering on the gas (see Refs. [1, 2] for a discus-sion). We take the
Fermi data at 0.5-1.0 GeV(where the Bubbles are less pronounced [1]) andsubtract the SFD dust map to obtain an approxi-mate template for emission from inverse Comptonscattering by cosmic-ray electrons; this is the dom-inant contribution to the diffuse background afterthe dust/gas-correlated emission has been removed.We then fit the higher-energy data using this tem-plate, the SFD dust map, and a flat template forthe large soft-spectrum structure known as
Loop I .This method avoids the use of complicated mod-els and minimizes the use of external maps, but byconstruction cannot probe the Bubbles spectrumat energies around or below 1 GeV, and does nottake into account spectral variation in the variousemission components with position in the Galaxy.Each of these templates has been discussed in greaterdepth in Ref. [1]; we refer the reader to that work forfurther details. We also employ the same normalizationconvention as Ref. [1]; the coefficients of the SFD dustmap, 0.5-1.0 GeV map, and
Fermi diffuse model are mul-tiplied by the average value of these templates within theentire region defined by the Bubbles (and outside of themask). The other templates are flat (in projected inten-sity) within the regions that they are non-zero (over agiven latitude range within the Bubbles, for example).We employ the “diffuse model” fit for our primary re-sults, and use the “low-energy template” fit as a checkfor possible systematic errors introduced by our use ofthe
Fermi diffuse model. We have also tested the “sim-ple disk” model as employed in Ref. [1], where the ICSemission is described by a simple geometric diffused disktemplate. As this template proved inadequate for mod-elling the data close to the Galactic plane, and the resultsobtained using it were found to depend strongly on thedegree of masking of the disk, we have relegated discus-sion of this model to Appendix A.In Fig. 2 we show the extracted spectrum for each ofthe fitted templates, masking only the region within one -8 -7 -6 -5 E d N / d E [ G e V / c m / s / s r ] Uniform0-10 degrees10-20 degrees20-30 degrees30-40 degrees40-50 degreesDiffuse modelGALPROP π decayGALPROP bremGALPROP IC -8 -7 -6 -5 E d N / d E [ G e V / c m / s / s r ] Uniform0-10 degrees10-20 degrees20-30 degrees30-40 degrees40-50 degreesDiffuse modelGALPROP π decayGALPROP bremGALPROP IC -8 -7 -6 -5 E d N / d E [ G e V / c m / s / s r ] UniformSFD dustLoop I0.5 - 1.0 GeV Fermi - SFD dust0-10 degrees10-20 degrees20-30 degrees30-40 degrees40-50 degreesGALPROP π decayGALPROP bremGALPROP IC FIG. 2: The spectra of the various fit components, including five separate latitude-sliced templates for the Bubbles (see Fig. 1),for the two foreground models we employ (see text). The Galactic Disk is masked for | b | < ◦ in each case. The left and center panels employ the “diffuse model” fit, for the entire sky in the left panel and the southern hemisphere in the center panel. The right panel employs the “low-energy template” fit over the entire sky (see text for the details of the fitting procedures). degree of the Galactic plane, | b | < ◦ . We show resultsfound using the “diffuse model” and the “low-energy tem-plate”. In the center frame, we show the fit restrictingto the southern sky ( b < E dN/dE ,which is nearly absent in the diffuse model fit; these is-sues are discussed in further detail in Appendix B.We note that the spectrum is almost invariant from | b | = 20 ◦ − ◦ . This suggests that the electrons respon-sible for the observed emission in any leptonic scenariomust either be accelerated in situ or instead travel fromthe inner Galaxy very rapidly, avoiding significant energylosses (the distance over which TeV electrons propagatevia standard diffusion without significant energy losses isconsiderably less than the 5 or more kpc to which thisangular range corresponds). In contrast, a pronouncedchange in the Bubbles’ spectrum is observed at lower lat-itudes. In an attempt to quantify the significance of thistransition, we have compared the quality of the fit foundusing five separate latitude-sliced Bubbles templates tothat found using only a single Bubbles template. Evenconservatively limiting our analysis to the cleaner south- ern bubble, and masking within 5 ◦ of the disk, we findthat the five-Bubbles-templates model is favored over thesingle Bubbles template at the level of approximately16 σ . However, it is important to note that this is a formal significance, accounting only for statistical error; there isa degree of unavoidable and unaccounted-for systematicerror in that neither model is a “good fit”, in the senseof describing the sky to the level of Poisson noise. III. COSMIC RAY ELECTRONS AS THESOURCE OF THE HIGH-LATITUDEGAMMA-RAY BUBBLES AND SYNCHROTRONHAZE
Following Blumenthal and Gould [28], we employ thefull Klein-Nishina formula to compute the spectrum of in-verse Compton emission from an arbitrary electron pop-ulation. For the problem at hand, we need to considerscattering with the CMB as well as with starlight andinfrared radiation. In our calculations, we adopt the in-terstellar radiation model of Ref. [29]. At energies below ∼ × − eV, the CMB dominates the energy density,while starlight is important at higher energies.The gamma-ray spectra observed from various regionsof the Fermi
Bubbles are shown again in Fig. 4 (asfound using the diffuse model template fit, and mask-ing within 1 degree of the disk). To determine whetherthese gamma-rays could be the product of inverse Comp-ton scattering, we take an arbitrary (binned) spectrumof electrons and compare the resulting inverse Comptonemission to that shown in Fig. 4. In Fig. 5, we plot theelectron spectrum which provides the best possible fit tothe gamma-ray spectrum for each latitude range (anderror bars around the best fit). The solid line in eachframe of Fig. 4 denotes the best-fit spectrum of inverseCompton photons. At high latitudes, an approximately E d N / d E ( k e V / c m / s / s r) Diffuse model40-50 degrees 1 10 1000.010.101.0010.00 Diffuse model, southern sky40-50 degrees 1 10 1000.010.101.0010.00 Low-energy template40-50 degrees1 10 1000.010.101.0010.00 E d N / d E ( k e V / c m / s / s r) Diffuse model30-40 degrees 1 10 1000.010.101.0010.00 Diffuse model, southern sky30-40 degrees 1 10 1000.010.101.0010.00 Low-energy template30-40 degrees1 10 1000.010.101.0010.00 E d N / d E ( k e V / c m / s / s r) Diffuse model20-30 degrees 1 10 1000.010.101.0010.00 Diffuse model, southern sky20-30 degrees 1 10 1000.010.101.0010.00 Low-energy template20-30 degrees1 10 1000.010.101.0010.00 E d N / d E ( k e V / c m / s / s r) Diffuse model10-20 degrees 1 10 1000.010.101.0010.00 Diffuse model, southern sky10-20 degrees 1 10 1000.010.101.0010.00 Low-energy template10-20 degrees1 10 100Energy(GeV)0.010.101.0010.00 E d N / d E ( k e V / c m / s / s r) Diffuse model0-10 degrees 1 10 100Energy(GeV)0.010.101.0010.00 Diffuse model, southern sky0-10 degrees 1 10 100Energy(GeV)0.010.101.0010.00 Low-energy template0-10 degrees
FIG. 3: The spectrum extracted for the gamma-ray Bubbles in ten-degree latitude bands: in order from the top row,40 ◦ < | b | < ◦ , 30 ◦ < | b | < ◦ , 20 ◦ < | b | < ◦ , 10 ◦ < | b | < ◦ , | b | < ◦ . The left and center panels use the “diffusemodel” template fit (see text); in the center panels, the fit is restricted to b < right panelsuse the “low-energy template” approach (see text). The different colors show different choices for the latitude cut to removethe Galactic Disk: | b | < ◦ (black), | b | < ◦ (blue), | b | < ◦ (red). Where the 1 σ error bars overlap with zero, we instead plotdownward-pointing arrows corresponding to the 3 σ upper limits on the emission. FIG. 4: The gamma-ray spectrum of the
Fermi
Bubbles, broken into different regions by Galactic latitude (see Fig. 1). Thesolid lines denote the best-fit spectrum of inverse Compton emission, as calculated from the central values of the electron spectrashown in Fig. 5. At high latitudes, the spectrum of the
Fermi
Bubbles is consistent with originating entirely from the inverseCompton scattering of GeV-TeV electrons, while at lower latitudes inverse Compton scattering alone cannot account for theobserved emission. The dashed line in each frame denotes the spectrum of inverse Compton scattering that would be predictedfrom a spectrum of electrons the same as that required to generate the inverse Compton scattering spectrum observed in thehighest latitude region ( | b | = 40 ◦ − ◦ ), as discussed in Sec. IV. FIG. 5: The spectrum of electrons within the volume of the
Fermi
Bubbles that is best able to fit the observed gamma-rayspectrum (see Fig. 4) through inverse Compton scattering alone. At high latitudes, the electron spectrum yields a good fit tothe observed gamma-ray spectrum, while at low latitudes no spectrum of electrons is able to produce a gamma-ray spectrumconsistent with observations. power-law spectrum of electrons ( dN e /dE e ∝ E − e ) be-tween GeV and TeV energies can produce a spectrumof gamma-rays consistent with that observed from the Fermi
Bubbles. At | b | = 40 ◦ − ◦ , for example, thebest-fit electron spectrum shown in Fig. 5 provides anexcellent fit ( χ = 21 . Fermi
Bubbles is supported by theobservation of spatially correlated emission at both mi-crowave [7] and radio [16] wavelengths. For a givenmagnetic field strength (or distribution of magnetic field Frequency (GHz)10 ν I ν ( G H z Jy / s r) |b|=40-50 ° B=100.000 muGB=30.0000 muGB=10.0000 muGB=6.50000 muGB=3.00000 muGB=1.00000 muGB=0.100000 muG 10 Frequency (GHz)10 ν I ν ( G H z Jy / s r) |b|=30-40 ° B=100.000 muGB=30.0000 muGB=10.0000 muGB=6.50000 muGB=3.00000 muGB=1.00000 muGB=0.100000 muG10 Frequency (GHz)10 ν I ν ( G H z Jy / s r) |b|=20-30 ° B=100.000 muGB=30.0000 muGB=10.0000 muGB=6.50000 muGB=3.00000 muGB=1.00000 muGB=0.100000 muG 10 Frequency (GHz)10 ν I ν ( G H z Jy / s r) |b|=10-20 ° B=100.000 muGB=30.0000 muGB=10.0000 muGB=6.50000 muGB=3.00000 muGB=1.00000 muGB=0.100000 muG
FIG. 6: The spectrum of synchrotron emission predicted from the best-fit electron spectra as shown in Fig. 5, for variousvalues of the magnetic field (see legend). Each frame represents a range of latitudes of the
Fermi
Bubbles: 40 ◦ − ◦ away fromthe Galactic plane ( top left ), 30 ◦ − ◦ away from the Galactic plane ( top right ), 20 ◦ − ◦ away ( bottom left ), and 10 ◦ − ◦ away ( bottom right ). Red data points indicate the spectrum of the haze in the southern sky within each given latitude range, asderived from Ref. [6]; the average over l is performed for − ◦ < l < ◦ , as in Fig. 5 of Ref. [6]. At somewhat lower frequencies,the green triangles and dashed lines connecting them denote the spectral index ( not amplitude) for polarized emission between2.3 GHz and 23 GHz, as extracted from S-PASS [30] data by Ref. [16]; the averaging is performed over − ◦ < l < ◦ andrestricted to | b | > ◦ to avoid depolarization associated with the Galactic plane. This comparison demonstrates that in thepresence of microgauss-scale magnetic fields, the electron population responsible for the observed ICS emission can also accountfor the observed synchrotron haze. Also shown for comparison as blue data points is the spectrum of the microwave haze as awhole, as given by Ref. [7]. As these results are not binned by latitude, however, they should not be directly compared to thepredicted synchrotron spectra. strengths), we can calculate the spectrum of synchrotronemission that is predicted to result from the spectrumof electrons shown in Fig. 5. For simplicity, we take thecentral values for the extracted spectrum and assume anisotropic electron population; we do not extrapolate toenergies above the highest bin. In Fig. 6, we show the re-sulting synchrotron spectra for a range of magnetic fieldsfrom 0.1-100 µ G, assumed to be uniform throughout theregion of the Bubbles template in question. For compar-ison, the magnetic field strength in the local region ofthe Milky Way is thought to be of order a few µ G [31].One should keep in mind, however, that magnetic fieldsin localized regions and filaments may be much higherthan the spatially averaged value.To compare the predicted synchrotron spectrum to ob-servations, we employ the
WMAP We also show the recent re-sults combining data from
WMAP and
Planck [7], butthese results were not binned by latitude so should not bedirectly compared to the predicted synchrotron curves.The amplitudes of the gamma-ray Bubbles and mi-crowave haze appear consistent with arising from a com-mon population of cosmic ray electrons for magneticfields on the order of a few µ G. The spectrum deducedfrom
WMAP is somewhat harder than expected fromthe corresponding gamma-ray data, but this may be theresult of contamination by the CMB (which would be ex-pected to produce the appearance of spectral hardening).In contrast, the spectral index for the polarized emissionfound by the authors of Ref. [16] appears consistent withexpectations from the gamma-rays. If the spectral hard-ness observed in
WMAP data is confirmed by
Planck ,however, it could suggest a scenario in which most of thesynchrotron emission is produced in regions with higherthan average magnetic fields. For example, if magneticfields as high as ∼ µ G are present in even ∼
1% of thevolume of the Bubbles, then this discrepancy could beameliorated.We caution that the success of this picture does not rule out hadronic scenarios; we focus on leptonic scenar-ios in this work because their consistency can be checkedin a straightforward and model-independent way, sincethe microwaves and gamma-rays originate from the samesteady-state electron population. In hadronic scenarios,in contrast, the gamma-rays provide a probe of the pro-ton CR spectrum, but the microwaves probe the electronspectrum after diffusion and cooling, and so the consis-tency may depend on diffusion parameters in additionto the magnetic field. Consequently, we leave a carefulstudy of consistency in the hadronic case for future work. We thank Greg Dobler for providing us with the numerical valuescorresponding to Fig. 5 of Ref. [6] and the authors of Ref. [16] forproviding the spectral index map corresponding to their Fig. S4.
Later in this article, we treat the inverse-Compton-likeemission present in the Bubbles as a background to besubtracted; this “background” is an approximately flatspectrum in E dN/dE with a downturn around 50 GeV,and while it is modeled as inverse Compton emission,instead treating it as emission from a hadronic cascadeshould not impact our results in any significant way. IV. EVIDENCE OF NON-INVERSE COMPTONEMISSION AT LOW LATITUDES
In the previous section, we demonstrated that the spec-trum observed from the high latitude ( | b | > ∼ ◦ ) regionsof the Fermi
Bubbles can be accounted for by inverseCompton scattering of an approximately power-law spec-trum of cosmic ray electrons. The same electrons, inthe presence of µ G-scale magnetic fields, can also ac-count for the observed amplitude of the
WMAP haze.At lower Galactic latitudes, however, we find that in-verse Compton scattering alone cannot account for theobserved gamma-ray emission. In particular, we find thatthe gamma-ray spectrum climbs rapidly between 0.3 and1 GeV at low-latitudes (see Fig. 4), and this rise cannotbe accounted for by the inverse Compton scattering ofany physically realistic spectrum of electrons. Quantita-tively, for the choice of binning used in Fig. 5, we findthat an entirely inverse-Compton origin for the gamma-rays observed from the | b | = 1 ◦ − ◦ or | b | = 10 ◦ − ◦ re-gions of the Fermi
Bubbles yields best-fits of χ = 100 . Fermi
Bubbles is not the re-sult of inverse Compton scattering. If we assume that the spectral shape of electronspresent throughout the volume of the
Fermi
Bubblesdoes not change significantly with latitude, and thatthe gamma-ray emission from the highest latitude region( | b | = 40 ◦ − ◦ ) is dominated by the products of in-verse Compton scattering, we can calculate the inverseCompton contribution from each of the lower latituderegions. In each frame of Fig. 4, the dashed line denotesthis predicted contribution from inverse Compton scat-tering. Not surprisingly, this component makes up mostor all of the total observed emission at high latitudes,but only a small fraction at low latitudes. Note that the The conclusion that no spectrum of electrons can produce thelow-latitude gamma-ray emission could, in principle, be evadedif we had adopted a much more finely binned electron spectrumin our analysis. In particular, a cosmic ray electron spectrumthat is described by a delta function at 16 GeV provides a goodfit to the low-latitude feature. As such a feature is not expectedfrom the perspective of cosmic ray acceleration, nor realistic inlight of non-negligible energy loss processes, we do not considerthis possibility further. FIG. 7: The gamma-ray spectrum of the
Fermi
Bubbles after subtracting a contribution from inverse Compton emission,derived using the electron spectrum (up to normalization) found in our best-fit to the | b | = 40 ◦ − ◦ region. This illustratesthe characteristics of the additional (non-inverse Compton) component of the gamma-ray emission from the Fermi
Bubbles,which is quite bright at low Galactic latitudes. We caution that these extracted spectra are subject to a number of systematicuncertainties, such as those associated with the interstellar radiation field model, and due to uncertainties and variations in theelectron spectra throughout the volume of the Bubbles. These extracted spectra can, however, be taken as indicative of thebroad spectral features of the non-inverse Compton component of the Bubbles emission. Shown as dashed lines is the predictedcontribution of gamma-rays from the annihilations of 10 GeV dark matter particles (to τ + τ − ) distributed according to ageneralized NFW profile with an inner slope of γ = 1 .
2, as described in Sec. V. We remind the reader that the backgrounds arelargest near the disk and thus there are significant systematic uncertainties in the spectrum from the low latitude ( | b | = 1 ◦ − ◦ )region, especially at low energies. Fermi
Bubbles in each latitude range. This residualspectrum is plotted in Fig. 7. While one should keep inmind that the error bars shown in this figure do not takeinto account any variations in the spectral shape of cos-mic ray electrons throughout the volume of the Bubbles,this provides us with what is likely to be a reasonable es-timate of the spectrum and intensity of the non-inverseCompton emission exhibited in the low-latitude regionsof the
Fermi
Bubbles.The spectra shown in Fig. 7 exhibit some rather dis-tinctive features. In particular, this spectral componentpeaks strongly at energies of ∼ ∼
10 GeV. Furthermore,the intensity of this component is a very strong functionof Galactic latitude, being more than an order of magni-tude brighter at low latitudes than at intermediate lati-tudes. These spectral and morphological characteristicsare quite similar to those exhibited by the gamma-rayemission previously observed from the inner few degreessurrounding the Galactic Center [18–22]. In the followingsection, we will discuss this comparison in more detail.
V. COMPARISON WITH GAMMA-RAYEMISSION FROM THE GALACTIC CENTER
In previous studies of
Fermi data, multiple sets of au-thors have identified the presence of a bright and spa-tially extended gamma-ray source around the GalacticCenter, peaking at energies of a few GeV [18–22]. Inparticular, Ref. [19] reports that the morphology of thissource implies a luminosity per volume that scales as r − . to r − . , where r is the distance to the GalacticCenter. Similar profiles were found to provide good fitsin Refs. [18, 21, 22]. Each of these studies also found thatthe spectrum of this spatially extended emission peaksstrongly at energies of a few GeV, very similar to the peakfound in this study in the low-latitude emission from the Fermi
Bubbles.This comparison strongly suggests that the non-inverseCompton emission we have identified in the low-latituderegions of the
Fermi
Bubbles is in fact the more spa-tially extended counterpart of the gamma-ray signal pre-viously reported from the innermost few degrees aroundthe Galactic Center. To further explore this comparison,we plot as a dashed line in each frame of Fig. 7 the contri-bution predicted by an annihilating dark matter modelfound in Ref. [32] to provide a good fit to the GalacticCenter signal. In this model, 10 GeV dark matter parti-cles annihilate to tau lepton pairs (with σv = 2 × − cm /s to τ + τ − , or σv = 6 × − cm /s if annihila-tions proceed equally to τ + τ − , µ + µ − and e + e − ), and aredistributed following a generalized Navarro-Frenk-White profile, with an inner slope of γ =1.2 (the classic NFWprofile corresponds to an inner slope of γ = 1), a scaleradius of 20 kiloparsecs, and normalized such that thelocal dark matter density is 0.4 GeV/cm . Specifically,the functional form is: ρ ( r ) ∝ r − γ (cid:16) rR s (cid:17) − γ , γ = 1 . , R s = 20 kpc . (1)From this comparison of both the spectrum and mor-phology of these signals, we conclude that the gamma-ray component we have identified within the low-latituderegions of the Fermi
Bubbles is the more spatially ex-tended continuation of the gamma-ray signal previouslyobserved in the Galactic Center. Furthermore, we con-firm that the dark matter models previously shown to becapable of accounting for the gamma-ray emission in theinner Galaxy are also capable of providing an explana-tion for the non-inverse Compton emission observed inthe low-latitude spectrum of the
Fermi
Bubbles.
VI. MORPHOLOGY OF THE LOW-LATITUDESIGNAL
One approach to extracting the morphology of the few-GeV spectral feature discussed in the previous sectionsis to examine the residual sky maps produced when thebackground templates (for example, the diffuse modeltemplate and isotropic background), multiplied by theirbest-fit coefficients, are subtracted from the data. Equiv-alently, these maps are produced by taking the residu-als of the template fit, and re-adding the latitude-slicedBubbles templates, weighted by their best-fit coefficients.This largely cancels out structure due to mismatches be-tween the shape of the Bubbles templates and the actualexcess, although such mismatches may still bias the fit.(This procedure has been recommended for extractingthe spectrum of an excess in Ref. [7].)Fig. 8 shows these “residual” maps (in average E dN/dE ) for the “diffuse model” fit, masked within 5degrees of the Galactic plane, in four energy bands span-ning the range from 1 −
20 GeV. The high-latitude
Fermi
Bubbles are visible in all bins with comparable bright-ness, as expected since the high-latitude spectrum is ap-proximately flat in E dN/dE . At low latitudes, thereis a pronounced excess around the Galactic Center, notdisk-like in shape, which is clearly visible in the 1 − − b , within a narrow longitude range( | l | < −
50 GeV (residual) map from the 1 −
10 GeV (resid-ual) map, where the excess is most pronounced (we ignoreenergies higher than 50 GeV because the
P6V11
Fermi diffuse model was not designed for studies at those en-ergies and, due to low photon statistics, little informa-tion would be gained from higher-energy photons in any2 -30-20-100102030 00 -60-40-20020406000 -2-1012345-2-1012345 -30-20-100102030 00 -60-40-20020406000 -2-1012345-2-1012345 -30-20-100102030 00 -60-40-20020406000 -2-1012345-2-1012345 -30-20-100102030 00 -60-40-20020406000 -2-1012345-2-1012345 k e V / c m / s / s r FIG. 8: The residual emission after re-adding the latitude-sliced Bubbles templates with their best-fit coefficients, in E dN/dE .Equivalently, these maps are obtained by subtracting the best-fit model for the background (in which we include all templatesbut the latitude-sliced Bubbles) from the data. The “diffuse model” fit is used, performed over regions greater than 5 ◦ fromthe plane (although the mask shown in the figure is at | b | = 3 ◦ ). -60 -50 -40 -30 -20 -10b (degrees)-10123 ∆ ( E d N / d E ) ( k e V / c m / s / s r) FIG. 9: The difference of the residual emission maps (after re-adding the latitude-sliced Bubbles templates with their best-fitcoefficients), between the 1-10 GeV bin and the 10-50 GeV bin, in E dN/dE averaged over − ◦ < l < ◦ . The error barsdescribe the pixel-to-pixel scatter within each bin (standard deviation of pixel values). This analysis employs the “diffusemodel” fit (see text), masked at 5 ◦ from the plane. The red line shows the anticipated intensity resulting from a (squared,projected) NFW profile with inner slope of γ = 1 . case). For more details, see Appendix E. Since the mapsare given in E dN/dE , a zero result indicates an averagespectrum of dN/dE ∝ E − between these two bins. Theresults for the southern hemisphere, where there are fewerbright sources and local features, are shown in Fig. 9.While we find that at high latitudes the spectrum is con-sistent with dN/dE ∝ E − , the lower latitude emission ( | b | < ◦ − ◦ ) reveals significant additional emissionat low energies. The error bars shown in this figure, com-puted from the standard deviation of the pixel values ineach ∆ b = 2 ◦ bin, are quite large and non-negligibly cor-related, but provide a sense of the uncertainty in the rateat which the signal falls off away from the Galactic plane.3 E d N / d E ( k e V / c m / s / s r) Diffuse modelNFW profile, γ =1.2 1 10 100Energy(GeV)0.010.101.0010.00 Diffuse model + Loop INFW profile, γ =1.2 1 10 100Energy(GeV)0.010.101.0010.00 Diffuse model, southern skyNFW profile, γ =1.2 1 10 100Energy(GeV)0.010.101.0010.00 Low-energy templateNFW profile, γ =1.2 FIG. 10: The spectrum of the emission fit by the NFW template ( γ = 1 . far left , center left and center right panelsemploy the “diffuse model” fit, while the far right panel uses the “low-energy template” fit (see text for details). In all casesan additional (squared, projected) NFW template is added to the fit, and its extracted spectrum is plotted. The center left panel also includes a template for Loop 1, and in the center right panel the fit is performed using the southern hemisphereonly, where there is less bright residual structure. The different colors show different choices for the latitude cut to remove theGalactic Disk: | b | < ◦ (black), | b | < ◦ (blue), | b | < ◦ (red). Where the 1 σ error bars overlap with zero, we instead plotdownward-pointing arrows corresponding to the 3 σ upper limits on the emission. VII. FITTING THE SPECTRAL BUMP WITHAN NFW PROFILE
So far, we have focused our attention on the region ofthe sky occupied by the Bubbles. If annihilating darkmatter is responsible for the signal observed at low lati-tudes, however, this signal should be distributed aroundthe Galactic Center with approximate spherically sym-metry, and will not be restricted to the Bubbles. In thissection, we include an additional template in our anal-ysis, corresponding to the signal expected from annihi-lating dark matter distributed according to a somewhatsteepened NFW profile (with an inner slope of γ = 1 . ◦ from the Galactic Center.With the inclusion of this additional NFW template,we find that the low-latitude (non-inverse Compton)emission prefers the morphology of the NFW templateover being absorbed into the low-latitude portion of theBubbles. The significant improvement in the fit is drivenboth by the spherical symmetry of the NFW profile, andthe fact that the imposed Bubbles templates are flat inbrightness rather than falling off with increasing Galacto-centric radius (see also Appendix D). With the inclusionof this NFW template in the fit, the spectrum of theemission associated with the Bubbles is not only largelyconstant at high latitudes (as expected), but also hasa similar (near-flat) spectral shape at low latitudes, atleast where it can be detected (in several cases there isno significant detection of Bubbles-correlated emissionin the lowest-latitude band, after the addition of theNFW template). The significant GeV-scale feature iden-tified in Sec. IV is no longer absorbed by these Bubblestemplates, but instead is present in the spectrum of thespherically symmetric NFW template. The spectrum as- sociated with the NFW template peaks at ∼ ∼
10 GeV (there is little or no evi-dence for emission above 10 GeV in the spectrum of theNFW template, at least in the diffuse model fit). Thetotal flux (integrated over solid angle) associated withthis template is ∼ /s, corresponding to a totalluminosity within the solar circle of ∼ erg/s.The regions of the sky that are most important for dis-criminating between the NFW template and the Bubblestemplates are those near the inner Galaxy but outside theBubbles themselves. Unfortunately, such regions are alsonear the Galactic plane. As a result, the extracted spec-trum associated with the NFW template depends some-what on the details of the fit, including the mask of theGalactic plane, especially below ∼ Fermi is somewhat poor. In the sim-plest case, in which we employ the “diffuse model” fit andadd the NFW template, the spectrum we extract below1 GeV is considerably softer than that extracted fromthe Bubbles templates (see the left frame of Fig. 10).Masking | b | < ◦ hardens the low-energy spectrum, asdoes adding a separate template to absorb soft-spectrumemission from Loop I, or restricting the fit to the southernhemisphere where the structures associated with Loop Ido not contaminate the signal (see left center and rightcenter frames of the figure). Given these results, we findit plausible that the low-energy emission (below 1 GeV)associated with the NFW template can be attributed inlarge part to contamination from the disk and Loop I.In Fig. 12, we show how the spectral feature at a fewGeV is reallocated from the lowest-latitude slices of theBubbles to the NFW template, once the NFW templateis added. In order to minimize background contamina-tion, we examine the spectra masking | b | < ◦ and re-stricted to the southern hemisphere. As discussed above,we find that the “bump” is much better fitted by theNFW template and there is no remaining significant evi-dence for emission correlated with the low-latitude Bub-4 E d N / d E ( k e V / c m / s / s r) Diffuse model40-50 degrees 1 10 1000.010.101.0010.00 Diffuse model, southern sky40-50 degrees 1 10 1000.010.101.0010.00 Low-energy template40-50 degrees1 10 1000.010.101.0010.00 E d N / d E ( k e V / c m / s / s r) Diffuse model30-40 degrees 1 10 1000.010.101.0010.00 Diffuse model, southern sky30-40 degrees 1 10 1000.010.101.0010.00 Low-energy template30-40 degrees1 10 1000.010.101.0010.00 E d N / d E ( k e V / c m / s / s r) Diffuse model20-30 degrees 1 10 1000.010.101.0010.00 Diffuse model, southern sky20-30 degrees 1 10 1000.010.101.0010.00 Low-energy template20-30 degrees1 10 1000.010.101.0010.00 E d N / d E ( k e V / c m / s / s r) Diffuse model10-20 degrees 1 10 1000.010.101.0010.00 Diffuse model, southern sky10-20 degrees 1 10 1000.010.101.0010.00 Low-energy template10-20 degrees1 10 100Energy(GeV)0.010.101.0010.00 E d N / d E ( k e V / c m / s / s r) Diffuse model0-10 degrees 1 10 100Energy(GeV)0.010.101.0010.00 Diffuse model, southern sky0-10 degrees 1 10 100Energy(GeV)0.010.101.0010.00 Low-energy template0-10 degrees
FIG. 11: The spectrum extracted for the gamma-ray Bubbles in ten-degree latitude bands, now including an NFW templatein the fit: in order from the top row, 40 ◦ < | b | < ◦ , 30 ◦ < | b | < ◦ , 20 ◦ < | b | < ◦ , 10 ◦ < | b | < ◦ , and | b | < ◦ . The left and center panels use the “diffuse model” template fit (see text); in the center panels, the fit is restricted to b < right panels use the “low-energy template” fit (see text). In all cases an additional (squared, projected)NFW template is added to the fit, as in Fig. 10. The different colors show different choices for the latitude cut to remove theGalactic Disk: | b | < ◦ (black), | b | < ◦ (blue), | b | < ◦ (red). Where the 1 σ error bars overlap with zero, we instead plotdownward-pointing arrows corresponding to the 3 σ upper limits on the emission. -8 -7 -6 -5 E d N / d E [ G e V / c m / s / s r ] Uniform0-10 degrees10-20 degrees20-30 degrees30-40 degrees40-50 degreesDiffuse modelGALPROP π decayGALPROP bremGALPROP IC -8 -7 -6 -5 E d N / d E [ G e V / c m / s / s r ] Uniform0-10 degrees10-20 degrees20-30 degrees30-40 degrees40-50 degreesNFW profile, gamma=1.2Diffuse modelGALPROP π decayGALPROP bremGALPROP IC FIG. 12: The spectra of the various fit components, including five separate latitude-sliced templates for the Bubbles (see text),for the diffuse model foreground template, when the fit is restricted to the southern sky only. The Galactic Disk is maskedfor | b | < ◦ in all cases. The left and right panels correspond to the case with ( right ) and without ( left ) an additional NFW( γ = 1 .
2) template in the fit. γ ∆ χ |b| > 5 ° , southern sky|b| > 1 ° , full sky FIG. 13: The formal statistical −
2∆ ln L values (referred to as ∆ χ ) extracted from the likelihood fit using the diffuse model,the sliced Bubbles templates and a projected squared NFW template, for varying values of the NFW inner slope γ . The ∆ χ values are with respect to the tested γ value with the highest likelihood (so the minimum is zero by definition). Red starscorrespond to the full-sky fit masked for | b | < ◦ , black diamonds to the southern-sky fit masked for | b | < ◦ . σ . Again, though,we reiterate that this is a formal significance derived in-cluding statistical errors only , whereas there are signifi-cant systematics originating from the fact that the mod-els we are using do not fully describe the data.We have performed fits using generalized NFW pro-files with a variety of inner slopes, γ . Fitting over bothhemispheres and masking within 1 degree of the Galacticplane, we find that γ (cid:39) . γ =1.2 as our default value). Ifwe restrict our fit to the southern hemisphere and maskwithin five degrees of the Galactic plane, however, wefind that a somewhat steeper distribution is preferred, γ ∼ . −
2. This may reflect a slope which varies withdistance from the GC, although systematic uncertaintiesprevent us from making any strong statement to that ef-fect. We show the ∆ ln L values for various choices of γ ,in both these cases, in Fig. 13.We note that it is not surprising that a sphericallysymmetric signal centered around the Galactic Centerwould first become apparent in an analysis of the regionof the Fermi
Bubbles. By their shape, the Bubbles ex-clude both most of the background from the disk, andthe arc structures associated with Loop I, making themreasonably well designed for extracting even a sphericallysymmetric excess (note the similarities between the Bub-bles regions and the dark matter regions-of-interest asdescribed in Refs. [33–35]).
VIII. INTERPRETATION
In the existing literature, a number of possibilities havebeen discussed for the origin of the extended gamma-rayemission observed from the region of the Galactic Center,including annihilating dark matter [18–20, 22], a popula-tion of millisecond pulsars [18, 19, 22–24], and cosmic rayinteractions with gas [18, 19, 22, 25, 26]. In this section,we discuss these possibilities in light of the new informa-tion provided in this study, including the evidence thatthis emission is not confined to the inner Galaxy, but in-stead extends out to at least 2-3 kpc from the Galacticplane.
A. Diffuse Emission Mechanisms
As we have previously argued in Sec. IV, no realisticspectrum of cosmic ray electrons can produce the ob-served spectral features of the GeV emission identifiedin this study. Cosmic ray protons scattering with gasalso fail to provide a reasonable explanation for the ob-served gamma-rays. Firstly, the morphology of the ob-served emission is not highly correlated with the distri-bution of gas in the Milky Way, as would be predictedin such a scenario. Secondly, the spectral shape of the observed gamma-ray emission requires a peculiar spec-trum of cosmic ray protons, sharply peaked at approx-imately 25 GeV. In the upper left frame of Fig. 14, wecompare the observed spectrum of this emission to thespectral shape predicted from proton collisions with gasfor a proton spectrum given by a delta function at 25 GeV( solid ), or by a broken power-law, following E − p below25 GeV and E − p at higher energies ( dashed ). While nei-ther provides a particularly good fit, it is clear that fromthis comparison that a very sharply peaked spectrum ofprotons would be required to potentially account for thisemission. And while we cannot absolutely rule out theexistence of such a strongly peaked cosmic ray protonspectrum, this rather extreme requirement further dis-favors cosmic ray origins for the observed low-latitudeemission.Note that in each frame of Fig. 14, we make compar-isons to the observed gamma-ray spectrum (after sub-tracting the contribution from inverse Compton), as ex-tracted using the diffuse model template and from the | b | = 10 ◦ − ◦ regions of the Bubbles. We have cho-sen to compare to this region over that extracted fromlower latitudes, or from the NFW-template, as this re-gion provides a spectrum that is more robust to contam-ination from the Galactic Disk. In particular, a com-parison of the low-energy spectrum extracted from the | b | < ◦ Bubbles template or (especially) the NFW tem-plates varies considerably depending on how the disk ismasked, and on whether we consider both hemispheres,or only the southern sky. On the other hand, the spec-tral shape extracted at higher latitudes depends morestrongly on the subtraction of the inverse Compton com-ponent, which is negligible compared to the bump for | b | < ◦ , but increasingly substantial as one moves far-ther from the Galactic plane. However, the consistency inthe spectrum of the bump between the 10 − ◦ band andeven higher latitudes supports the simple picture wherethe electron spectrum generating the ICS component (orthe proton spectrum, in a hadronic scenario) is essentiallyinvariant. B. Millisecond Pulsars
Instead of relying on diffuse emission mechanisms, alarge population of unresolved gamma-ray point sourcescould, in principle, be responsible for the observed emis-sion. In particular, the spectrum of gamma-ray pulsarshas been observed to peak at GeV energies, and it hasbeen suggested that a collection of ∼ such objects maybe able to account for the extended gamma-ray emissionobserved from the Galactic Center [22–24]. Of partic-ular interest are millisecond pulsars, which are thoughtto be formed as parts of low-mass X-ray binary systems.This could help to accommodate the very concentrateddistribution of the gamma-ray emission observed aroundthe Galactic Center (the stellar distribution in the innerGalaxy scales as n ∝ r − . , but objects formed through7 FIG. 14: Comparisons of the observed gamma-ray spectrum of the low-latitude emission, after subtracting the contributionfrom inverse Compton scattering (see Fig. 7) to that predicted from the scattering of cosmic ray protons with gas ( upper left ),millisecond pulsars ( upper right ), and dark matter annihilations ( lower ). For proton-gas collisions, the solid and dashed linesdenote cosmic ray proton spectra which take the form of a delta function at 25 GeV or a broken power-law following E − p below25 GeV and E − p at higher energies, respectively. To accommodate the spectral shape of the observed gamma-ray emission,the cosmic ray proton spectrum throughout the inner several kiloparces of the Fermi
Bubbles must peak very strongly atapproximately 25 GeV. The spectrum shown for pulsars is that corresponding to the average millisecond pulsar observed bythe
Fermi collaboration [36, 37]. For annihilating dark matter, we show results for two models: 10 GeV particles annihilatingto tau leptons (dashed) and 50 GeV particles annihilating to b ¯ b . In each case, we have adopted a generalized NFW profile withan inner slope of γ = 1 .
2, and normalized the signal to a local density of 0.4 GeV/cm and an annihilation cross section of σv = 2 × − cm /s ( τ + τ − ) or σv = 8 × − cm /s ( b ¯ b ). interactions between stars could plausibly be distributedas steeply as the square of this distribution) [22, 38]. Thebinary companions of such pulsars could also act as atether, explaining why they do not free-stream out of theGalactic Center as a result of velocity kicks. Further-more, millisecond pulsars are spun up through accretion,and can thus produce high luminosities of gamma-rayemission over much longer timescales than other types ofpulsars.Unfortunately, relatively little is known about thegamma-ray spectrum of millisecond pulsars. Fermi hasreported spectra from only eight millisecond pulsars,which together yield an average spectrum that is well fitby dN γ /dE γ ∝ E − . γ exp( − E γ / . Fermi may not be represen-tative, perhaps being biased toward the brightest or mostlocally common examples of such objects. To address thisissue, it has been suggested that the gamma-ray spectraof globular clusters (which are thought to contain largenumbers of millisecond pulsars) could provide a more re-liable determination of the average spectrum from mil-lisecond pulsars [23]. At present, however, the error barson the gamma-ray spectra of globular clusters are quitelarge, and (on average) do not appear to favor a much8harder spectral index than is observed from individualresolved pulsars [39] (see also Fig. 9 of Ref. [19]). Futuredata from
Fermi could potentially be useful in furthertesting the possibility that millisecond pulsars produce agamma-ray spectrum compatible with the low-latitude,GeV emission under consideration here.In addition to their gamma-ray spectra, the distribu-tion of millisecond pulsars within the Milky Way is notwell constrained empirically. That being said, one ex-pects the formation of millisecond pulsars to roughly fol-low that of stars, possibly with an additional preferencefor regions of very high stellar density, such as in globu-lar clusters. To account for the observed morphology ofthis signal, however, there would have to be a significantnumber of millisecond pulsars in the halo, at distancesof at least a few kpc outside the Galactic plane. If thisemission is generated by such objects, they would requirea distribution that is very different from that observedamong other stellar populations. And while such distri-butions have been proposed [40], such distributions areconstrained by the small number of millisecond pulsarsresolved by
Fermi and by the high degree of isotropyobserved in the gamma-ray background [41].
C. Annihilating Dark Matter
In the previous two sub-sections, we have describedsome of the possibilities and challenges involved in ex-plaining this gamma-ray signal with astrophysical sourcesor mechanisms. Annihilating dark matter can providea simple explanation for the sharply peaked spectrumand distinctive morphology of this emission. In the lowerframe of Fig. 14, we compare the gamma-ray spectrumpredicted in two dark matter scenarios to the observedspectrum. First, we consider a 10 GeV dark matter par-ticle species annihilating to tau leptons. We also showthe spectrum resulting from a 50 GeV particle annihilat-ing to b ¯ b which, given the systematic uncertainties in theextraction of the spectrum, we also consider to be a vi-able possibility. For a generalized NFW profile ( γ = 1 . , we requirean annihilation cross section of σv = 2 × − cm /sin the 10 GeV τ + τ − case, or σv = 8 × − cm /sin the case of a 50 GeV particle annihilating to b ¯ b . Asannihilations to electrons, muons, or neutrinos do notsignificantly contribute to the gamma-ray spectrum, thetotal annihilation cross section in the leptonic case maybe larger by a factor of a few or several.We note that the dark matter distribution required tofit the observed signal is well supported by the results ofnumerical simulations. As has been known for some time,N-body simulations which model the evolution of colddark matter without baryons typically find halos of theNFW form, with inner slopes of ρ ∝ r − ( γ = 1) [42, 43].Hydrodynamical simulations, which include the effects ofbaryonic processes involved in galaxy formation and evo-lution, in many cases predict the steepening of this inner slope, typically from γ = 1 to γ = 1 . γ = 1 . The annihilation cross section required to normalizethe signal in question is also an attractive value froma theoretical perspective. To be produced thermally inthe early universe in an abundance equal to the mea-sured dark matter density, a ( ∼ (cid:104) σv (cid:105) ≈ × − cm /s, when thermally averaged overthe process of freeze-out [48]. In many typical dark mat-ter models, however, the annihilation cross section in thelow velocity limit (as is relevant for annihilation in thehalo) is smaller than this value by a factor on the or-der of a few. Neutralinos, for example, when annihilat-ing to leptons through the t -channel exchange of slep-tons typically exhibit (cid:104) σv (cid:105) FO /σv v =0 ∼
5. While neu-tralino annihilations through p -wave amplitudes (whichare suppressed at low velocities) significantly contributeto the relic abundance calculation, they do not factorinto the current annihilation rate. We also note thatannihilation cross sections in the range required here( σv ∼ (2 − × − cm /s) are currently consistentwith all observational and experimental constraints, in-cluding those derived from dwarf galaxies [49, 50], thecosmic microwave background [51–53], the spectrum ofcosmic-ray antiprotons [54, 55], and from searches formonophoton-plus-missing energy events at LEP [56].From a dark matter model building perspective, thereare a number of possibilities one could consider. Inthe case of light dark matter particles which annihi-late primarily to leptons, the annihilations could proceedthrough the t -channel exchange of new charged parti-cles which carry lepton number (such as sleptons), orthorough the exchange of a leptophillic Z (cid:48) [57] or a lep-tophillic higgs [58]. Alternatively, one could imagine ascenario in which the dark matter itself carries leptonnumber. The dark matter could also annihilate to a pairof light force carriers which interact with the StandardModel only through kinetic mixing the with photon. Thedecays of the light force carrier then yield combinationsof mesons and charged leptons, leading to a gamma-rayspectrum that is very similar to that predicted from taudecays [59].One additional consideration is that if the ∼
10 GeVdark matter particles also annihilate to e + e − at a ratesimilar to τ + τ − , then they would also be capable of ex-plaining the anomalous synchrotron emission observedfrom the Milky Way’s radio filaments [60], and possi- Note, however, that the inclusion of baryonic feedback processesmay flatten cusps in dark matter halos (e.g. [46]), and there isobservational evidence for profiles shallower than NFW in somedwarf galaxies [47].
IX. DISCUSSION AND CONCLUSIONS
In this study, we have identified a new component ofgamma-ray emission from the low-latitude regions of the
Fermi
Bubbles. This emission does not appear to becompatible with originating from either inverse Comptonscattering or proton collisions with gas (for any physi-cally realistic spectrum of cosmic rays). The spectrumof this emission peaks at energies of a few GeV and isdistributed with an approximately spherically symmetricmorphology about the Galactic Center, with a luminosityper volume that is consistent with a squared (generalized)NFW profile with an inner slope of ρ ∝ r − . (althoughthe best-fit slope depends somewhat on the region chosenfor the fit). The broad features of this signal are robustto the various details of our analysis, such as the choiceof templates and the degree of masking around the disk.The diffuse gamma-ray signal we have identified here isconsistent both in spectrum and morphology with beingthe more spatially extended counterpart of the emissionpreviously observed from the Galactic Center [18–22].In addition to further confirming the existence of thisgamma-ray source, the results presented here are impor-tant in that they confirm that the morphology of thissignal extends to at least ∼ − is consistent with that predicted a priori from an-nihilating dark matter.If annihilating dark matter is responsible for the emis-sion reported here, we find that a halo profile of the gen-eralized NFW form, with an inner slope of ρ ∝ r − . , ispreferred. The spectral shape of the emission is well de-scribed by an approximately 10 GeV particle annihilatingto tau leptons, with a normalization corresponding to anannihilation cross section of σv ∼ × − cm /s (inaddition to annihilations proceeding to electrons, muonsand/or neutrinos, each of which provide comparativelyfew gamma-rays). We note that dark matter in this massrange may also be capable of accommodating a numberof other anomalous signals reported from direct and indi-rect detection experiments (for a summary, see Ref. [32]).Alternatively, the annihilations of a ∼ σv ∼ × − cm /s. Acknowledgments
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Appendix A: The Simple Disk model
The primary template subtraction technique initiallyused in Ref. [1] to reveal the Bubbles employed a sim-ple geometric template to model ICS emission from thedisk. The functional form of this template is csc | b | − σ l = 30 ◦ in longitude. Sucha model, while oversimplified relative to the actual emis-sion associated with the Galactic Disk, is smooth andcannot mimic sharp features, and is demonstrably effec-tive in subtracting ICS emission at high latitudes.In the current work, we attempted to fit the data us-ing this template to model ICS, along with the SFDdust map to trace emission from pion decay, the isotropicbackground model, a flat template for Loop 1, and the latitude-sliced Bubbles templates. This is identical tothe “low-energy template” fit described in the main textexcept that the dust-subtracted 0 . − | b | causes the fitto be largely driven by the lowest-latitude data, wherethe data are known to be contaminated by unsubtractedpoint sources.1 E d N / d E ( k e V / c m / s / s r) Simple disk40-50 degrees 1 10 100Energy(GeV)0.010.101.0010.00 Simple disk30-40 degrees 1 10 100Energy(GeV)0.010.101.0010.00 Simple disk20-30 degrees E d N / d E ( k e V / c m / s / s r) Simple disk10-20 degrees 1 10 100Energy(GeV)0.010.101.0010.00 Simple disk0-10 degrees -8 -7 -6 -5 E d N / d E [ G e V / c m / s / s r ] UniformSFD dustSimple diskLoop I0-10 degrees10-20 degrees20-30 degrees30-40 degrees40-50 degreesGALPROP π decayGALPROP bremGALPROP IC FIG. 15: The spectrum extracted for the gamma-ray Bubbles in ten-degree latitude bands: in order from the top left,40 ◦ < | b | < ◦ , 30 ◦ < | b | < ◦ , 20 ◦ < | b | < ◦ , 10 ◦ < | b | < ◦ , | b | < ◦ . The fit is performed using the simple diskmodel as a template for ICS, the SFD dust map, a uniform map, a template for Loop I, and the five latitudinal slices throughthe Bubbles templates. The different colors show different choices for the latitude cut to remove the Galactic Disk: | b | < ◦ (black), | b | < ◦ (blue), | b | < ◦ (red). Where the 1 σ error bars overlap with zero, we instead plot downward-pointing arrowscorresponding to the 3 σ upper limits on the emission. The bottom right panel shows the spectrum of the various templates inthe fit for the | b | < ◦ mask. Appendix B: Consistency of results using the diffusemodel and low energy template
At first appearance, the gamma-ray spectra as ex-tracted using the diffuse model and low-energy templatemethods are quite different (see the left and right framesof Fig. 3). This comparison can be misleading, however,as the spectra extracted using the low-energy templatedo not describe the emission present in the Bubbles re-gion after subtraction of some physical model – rather,they describe the degree to which the Bubbles-correlatedemission is harder than the ordinary ICS emission as-sociated with the disk (which dominates the 0.5-1 GeVskymap after removal of the dust-correlated emission),with a pivot point at 0.5-1 GeV. In contrast, the diffusemodel template fit extracts the excess over the diffusemodel spatially correlated with the
Fermi
Bubbles. Ofcourse, the diffuse model is fitted to the data, and somay also soak up emission physically associated with the Bubbles.In this Appendix, we provide a direct comparison ofthese techniques. Comparing the gamma-ray spectra ex-tracted using the two methods, we see that there are dis-crepancies at both low and high energy (with the latterbeing particularly pronounced at low latitudes). Thesediscrepancies have different origins; we will discuss themin turn.At high energies and low latitudes, the low-energy tem-plate fit returns a roughly flat (in E dN/dE ) Bubbles-correlated spectrum, similar to the spectrum obtainedat high latitudes. In contrast, the diffuse model fit de-tects virtually no emission. This indicates that the dif-fuse model is “soaking up” this hard-spectrum emissionin some way. The diffuse model has, of course, beenadjusted to fit the data, and has the potential to over-subtract Bubbles-correlated emission in trying to fit thedata without the freedom to include the Bubbles explic-itly. Given the information to hand, it is not possible2to distinguish between this scenario and one where the Fermi diffuse model is adequately capturing the physicsof this spectral component, which should be assigned tothe ordinary Galactic emission even though it is harderthan the norm. The amplitude of this hard spectral com-ponent, at low latitudes, is not of great interest for thepurposes of this study; to facilitate checking agreement ofthe few-GeV spectral feature between the two methods,we subtract a component with dN γ /dE γ ∝ E − γ fromthe results for the low-energy template fit, designed toremove this high-energy emission.The low-energy discrepancy is simpler to deal with,as it is an entirely natural and expected consequence ofthe different methodologies being employed. Since thelow-energy template already includes some contributionfrom the Bubbles, to obtain the true Bubbles spectrumwe should re-add a component with the same spectrum asthe low-energy template ( dN γ /dE γ ∝ E − . γ , to a goodapproximation). The normalization of this component isa priori unknown, but to check consistency between thetwo methods, we can normalize it to match the diffusemodel result at 0.5-1 GeV.Having chosen these two free parameters (the ampli-tude of the high-energy spectrum and the amplitude ofthe correction due to the low-energy template), we com-pare in Fig. 16 the spectra extracted using the diffusemodel template (black) to that extracted using the low-energy template, after performing the adjustments de-scribed in this Appendix (blue). After these corrections,the low-energy template results are almost identical tothose derived using the diffuse model template. Appendix C: The symmetry of the signal
One might ask if the signal possesses north-south sym-metry, as well as left-right symmetry (negative vs positive l ). In Fig. 17 we show the variation in the results whenthe fit is performed only in the north, only in the south,only for l <
0, or only for l >
0. In all cases, the spectralfeature is apparent in the lowest latitude bin. The largestdifference is in the relatively flat-spectrum (in E dN/dE )emission attributed to the high-latitude Bubbles; this islarger in the north and for l >
0. This is to be expected,as Loop I and the associated gamma-ray arcs occur inthe north quadrant with l > Appendix D: Searching outside the Bubbles
In Sec. VII, we showed that the low-latitude GeV-scalespectral feature is considerably better fit by a sphericallysymmetric NFW profile than by the Bubbles templates.In this Appendix, we perform a cross check of this conclu-sion by explicitly asking whether this spectral componentis observed from the regions of the sky not associatedwith the Bubbles. The absence of such emission from the “bubble complement” region would strongly disfavorany dark matter interpretation of the signal.To address this question, we re-fit the data with anadditional template, corresponding to the region lyingwithin 20 ◦ of the Galactic Center, but not within theBubbles. This region is indicated by dotted lines inFig. 1. Fig. 18 shows the results for the “diffuse model”and “low-energy template” fits with this componentadded.In each frame (corresponding to differing degrees ofmasking of the disk), the spectrum of the Bubblescomplement template exceeds or equals the predictedgamma-rays from dark matter (for the same dark mat-ter model and distribution as shown by dashed lines inFig. 7). In contrast, little or no such emission is associ-ated with this template at energies above 10 GeV.At low energies, the spectrum and amplitude of theBubbles complement template is quite dependent on thedegree to which we mask the Galactic Disk, and has re-semblances in shape to the spectra associated with theNFW template. This supports our earlier hypothesis thatthe low-energy emission associated with the NFW tem-plate in these cases is being largely driven by the struc-tures associated with Loop I and the Galactic disk. Appendix E: Residuals
As discussed in Sec. VI, residual maps with thelatitude-sliced Bubbles re-added provide a characteriza-tion of the excess emission which is less dependent onthe choice of signal templates. As in the main text, werestrict ourselves to | l | < ◦ , and bin in latitude in twodegree steps, ∆ b = 2 ◦ . In Fig. 19, we show the resulting“Bubbles residuals” for energy bands from 0.5-1 GeV, 1-10 GeV, and 10-50 GeV. The residuals are relatively flatin b for | b | > ◦ , and similar (in E dN/dE ) for the threeenergy bands. At smaller | b | , in contrast, the results forlow energies diverge from those for the high-energy band.In Fig. 20, we look more closely at the 1 −
10 GeVenergy band, where the signal is present. We displaythe total emission, the Bubbles residual (i.e. the residualof the fit + the best-fit Bubbles templates), and the fitresidual. We see that, with the exception of the regionclose to the Galactic plane where the Bubbles templatesvanish, the absolute value of the fit residual is generally afactor of a few lower than the best-fit Bubbles-correlatedemission, and fluctuates between positive and negativevalues; the Bubbles-correlated emission is another factorof several below the total emission in this energy band,depending on latitude. Thus, except for the region clos-est to the Galactic plane, this approach appears to pro-vide an adequate model of the features in the data, andunaccounted-for residuals are unlikely to skew the signal.Close to the Galactic plane, there are large residuals, asthe small extent of the Bubbles means they are unableto absorb an extended signal; given the uncertainty inthe shape of the Bubbles close to the plane, this is not3
FIG. 16: A comparison of the gamma-ray spectra extracted from various latitude regions of the
Fermi
Bubbles using the diffusemodel template (black) to that extracted using the low-energy template, after performing the corrections described in the text(blue). After accounting for these corrections, the low-energy template results are almost identical to those derived using thediffuse model template. unexpected, and motivates the addition of a template to absorb this additional emission.4 -8 -7 -6 -5 E d N / d E [ G e V / c m / s / s r ] Uniform0-10 degrees10-20 degrees20-30 degrees30-40 degrees40-50 degreesDiffuse modelGALPROP π decayGALPROP bremGALPROP IC -8 -7 -6 -5 E d N / d E [ G e V / c m / s / s r ] Uniform0-10 degrees10-20 degrees20-30 degrees30-40 degrees40-50 degreesDiffuse modelGALPROP π decayGALPROP bremGALPROP IC -8 -7 -6 -5 E d N / d E [ G e V / c m / s / s r ] Uniform0-10 degrees10-20 degrees20-30 degrees30-40 degrees40-50 degreesDiffuse modelGALPROP π decayGALPROP bremGALPROP IC -8 -7 -6 -5 E d N / d E [ G e V / c m / s / s r ] Uniform0-10 degrees10-20 degrees20-30 degrees30-40 degrees40-50 degreesDiffuse modelGALPROP π decayGALPROP bremGALPROP IC FIG. 17: The spectra of the various fit components, including five separate latitude-sliced templates for the Bubbles (see text),for the diffuse model foreground template, restricting the fit to b < top left ), b > top right ), l < bottom left ), l > bottom right ). The Galactic Disk is masked for | b | < ◦ in all cases.FIG. 18: The spectrum of the “bubble complement” region, defined as √ b + l < ◦ and that does not lie within theBubbles templates, as extracted from a fit including the complement template, the five latitudinally sliced component Bubblestemplates, and background templates as described in Fig. 3. Here, we have used the Fermi diffuse model. The different framescorrespond to different choices for the latitude cut to remove the Galactic disk: | b | < ◦ , | b | < ◦ , | b | < ◦ . (Note that thissubstantially changes the region over which the complement spectrum is averaged, and thus may truly modify the result.) Thedashed line in each frame denotes the average spectrum expected in this region from the dark matter model and distributionas shown in Fig. 7 -60 -50 -40 -30 -20 -10b (degrees)-101234 E d N / d E ( k e V / c m / s / s r) E d N / d E ( k e V / c m / s / s r) FIG. 19: The residual emission after re-adding the latitude-sliced Bubbles templates with their best-fit coefficients, as afunction of energy. Emission is E dN/dE averaged over | l | < ◦ and in bins of width ∆ b = 2 ◦ ; the error bars describe the pixel-to-pixel scatter within each bin. The upper panel shows the fit using the diffuse model, the lower the fit using the low-energytemplate, both masked at 5 ◦ from the plane. -50 0 50b (degrees)0.010.101.0010.00100.00 E d N / d E ( k e V / c m / s / s r) -50 0 50-1.0-0.50.00.51.01.52.0 -50 0 50b (degrees)0.010.101.0010.00100.00 E d N / d E ( k e V / c m / s / s r) -50 0 50-1.0-0.50.00.51.01.52.0 FIG. 20: The absolute value of the residual emission after subtraction of all templates (dotted line) and the emission afterre-adding the latitude-sliced Bubbles templates with their best-fit coefficients (red stars), for 1-10 GeV. The total emission isshown in black diamonds. Emission is E dN/dE averaged over | l | < ◦ and in bins of width ∆ b = 2 ◦ ; the error bars describethe pixel-to-pixel scatter within each bin. The second and fourth panels show the residual emission after subtraction of alltemplates (not its absolute value). The upper two panels show the fit using the diffuse model, the lower the fit using thelow-energy template; in both cases the fit was performed for | b | > ◦◦