Molecular Clouds as the Origin of the Fermi Gamma-Ray GeV-Excess
Wim de Boer, Leo Bosse, Iris Gebauer, Alexander Neumann, Peter Biermann
MMolecular Clouds as the Origin of the Fermi Gamma-Ray GeV-Excess
Wim de Boer, ∗ L´eo Bosse, † Iris Gebauer, ‡ and Alexander Neumann § Dept. of Phys., Karlsruhe Inst. for Technology KIT, Karlsruhe, Germany
Peter L. Biermann ¶ MPI for Radioastronomy, Bonn, GermanyDept. of Phys., Karlsruhe Inst. for Technology KIT, Karlsruhe, GermanyDept. of Phys. & Astr., Univ. of Alabama, Tuscaloosa, AL, USA andDept. of Phys. & Astron., Univ. Bonn, Bonn, Germany (Dated: June 25, 2019)The so-called “GeV-excess” of the diffuse Galactic gamma-ray emission, as observed by the Fermi-LAT satellite, is studied with a spectral template fit based on energy spectra for each relevant processof gamma-ray emission. This has the advantage over “conventional” analysis that one includes thespectral knowledge of physical processes into the fit, which allows to determine simultaneouslythe standard background processes and contributions from non-standard processes, like the Fermi-Bubbles or the “GeV-excess”, in each sky direction. The spectral templates can be obtained in adata-driven way from the gamma-ray data, which avoids the use of emissivity models to subtractthe standard background processes from the data. Instead, one can determine these backgroundssimultaneously with any “signals” in any sky direction, including the Galactic disk and the Galacticcenter.Using the spectral template fit two hypothesis of the “GeV-excess” were tested: the dark matter(DM) hypothesis assuming the excess is caused by DM annihilation and the molecular cloud (MC)hypothesis assuming the “GeV-excess” is related to a depletion of gamma-rays below 2 GeV, as isdirectly observed in the Central Molecular Zone (CMZ). The origin of the depletion below 2 GeVis not important, but is most likely caused by a magnetic cutoff of cosmic rays approaching MCs,as will be discussed later.Both hypotheses provide acceptable fits, if one considers a limited field-of-view centered within20 ◦ around the Galactic center and applies cuts on the energy range and/or excludes low latitudes,cuts typically applied by the proponents of the DM hypothesis. However, if one considers the wholegamma-ray sky and includes gamma-ray energies up to 100 GeV we find that the MC hypothesis ispreferred over the DM hypothesis for several reasons: i) The MC hypothesis provides significantlybetter fits; ii) The morphology of the “GeV-excess” follows the morphology of the CO-maps, a tracerof MCs, i.e. there exists a strong “GeV-excess” in the Galactic disk also at large longitudes; iii) Themassive CMZ with a rectangular field-of-view of l × b (cid:39) . ◦ × . ◦ shows the maximum of theenergy flux per log bin in the diffuse gamma-ray spectrum at 2 GeV, i.e. the “GeV-excess”, alreadyin the raw data without any analysis. The rectangular profile contradicts the spherical morphologyexpected for DM annihilation. I. INTRODUCTION
An apparent “GeV-excess” of diffuse gamma-rays in the data from the Fermi-LAT satellite around energies of 2GeV towards the Galactic center has been studied by many groups. [1–38] The “GeV-excess” is usually assumed tooriginate from the Galactic center with the most exciting interpretations being the contributions from dark matter(DM) annihilation [16] and/or unresolved sources, like millisecond pulsars, see e.g. Refs. [18, 24, 27, 29, 39] andreferences therein.The “conventional” approach to search for excesses is the use of spatial templates for the gas and interstellarradiation field, which are the targets for the “standard” background processes: π production by propagated cosmicrays (PCR), Bremsstrahlung (BR) and inverse Compton (IC) scattering. The diffuse gamma-ray emission is assumedto follow these spatial templates; the emissivity can either be calculated with propagation models, as studied e.g. inRef. [21] or one uses a diffuse model from Fermi, as done e.g. in Ref. [16]. The problem is that neither approachprovides a good description of the gamma-ray emissivity in the inner Galaxy and the Galactic disk, since the fitting ∗ [email protected] † [email protected] ‡ [email protected] § [email protected] ¶ [email protected] a r X i v : . [ a s t r o - ph . H E ] J u l of spatial templates implies fitting over extended regions, thus averaging over rapidly varying emissivities, like theemissivity from molecular clouds (MCs) or unresolved sources. In these regions (MCs or unresolved sources) thegamma-ray emissivity varies in intensity and as function of energy. Inside MCs the maximum of the energy flux perlog bin in the diffuse gamma-ray spectrum is shifted from 0.7 GeV to up to 2 GeV, as is apparent from the spectrumof the Central Molecular Zone, a dense assembly of MCs in the Galactic center with a total mass of 5 · M (cid:12) in thesolid angle limited by − . ◦ < l < ◦ and | b | < . ◦ [40, 41]. The density of molecules inside the CMZ is as highas 10 / cm . Further details on the CMZ can be found in a recent review [42] and references therein. The mass ofthe CMZ represents about 5% of the total molecular mass of the Milky Way, so it is not surprising that in the tinysolid angle of the CMZ the gamma-ray flux is dominated by the MCs. The origin of the shift in the maximum ofthe emissivity of MCs is not important, but it is most likely caused by a magnetic cutoff of cosmic rays inside MCs(MCRs) enhanced eventually with energy losses, as will be discussed later.Cosmic rays inside unresolved sources (SCRs) lead to a hard spectrum by the π production in the shocked gas, aswas first discussed in detail in Ref. [43], which leads to a high energy tail in the gamma-ray emissivity. This high tailwas investigated in Refs. [30, 44] and its correlation with unresolved sources was apparent from the spatial correlationwith the 1.8 MeV line from Al, which traces sources. [45]In the latest diffuse model from the Fermi collaboration [46] the deficiency of low energy gamma-rays as well asthe excess of high energy gamma-rays were taken into account ad hoc by an HI correction template with negativeemission and an increase of emissivity above 50 GeV, but they did not realize the correlation with MCRs and SCRs.In order to have a high spatial resolution, which can capture changes in emissivity from molecular clouds andunresolved sources we follow an approach orthogonal to the “conventional” approaches: instead of spatial templateswe use spectral templates, one for each physical process describing the gamma-ray spectrum for that specific process.The reason for high and uncorrelated spatial resolutions is simple: including the spectral knowledge of all processesleads to an over-constrained fit for each field-of-view in a certain sky direction (called cones in the following), sincethe observed gamma-ray spectrum for a certain cone has 21 data points (= 21 energy bins) and 5 free normalizationparameters for 5 physical processes, namely gamma-ray production by PCRs, IC, BR, MCRs and SCRs. Withthe fitting of spectral templates one can observe in each direction if there is an excess independent of neighboringdirections. As a result one obtains an uncorrelated and spatially highly resolved distribution of the “GeV-excess”. Wewill show that the shift in the maximum of the energy flux per log bin in the gamma-ray spectrum, or equivalentlythe “GeV-excess”, is observed in all directions, where MCs are present; these directions are available from the highresolution all-sky CO maps from the Planck satellite [47], which agree with previous CO sky maps. [48]The spectral templates for each physical process can be obtained in a data-driven way from the gamma-ray data[30, 32, 44], see Sect. II C. In particular, the initial spectra for SCRs can be obtained from the high energy tail inregions towards unresolved sources, as traced by the Al line, while the inital spectral template for MCRs can beobtained from the CMZ. Initial spectral templates for other background processes can be calculated from the locallyobserved cosmic ray spectra. The initial spectra for all templates are then optimized by the fit to the data in aniterative procedure, so one obtains the spectral templates without having to rely on poorly fitting diffuse models orpropagation models.How can one distinguish the two hypothesis for the “GeV-excess”: is it an excess provided by DM annihilation ora depletion of low energy photons in MCs, as observed in the CMZ? Both rely on the same observation, namely ashift in the maximum of the energy flux per log bin in the gamma-ray spectrum towards higher energies. Note thatthe “GeV-excess” is only observed along lines-of-sight, so the spatial origin is not clear: it can originate either in theGalactic center, as expected for DM, or in the Galactic disk, as expected for MCs. This lines-of-sight argument alsosolves the problem that one observes the excess up to large latitudes, although the MCs are located in the disk: theCO sky map shows a column density of MCs up to large latitudes as well with a steeply falling latitude distribution, asexpected from the lines-of-sight crossing smaller parts of the disk with increasing latitude. The latitude distributionfrom MCs resembles the latitude distribution from a DM annihilation signal with an NFW-like DM profile [49], aswill be shown later.A comparison of both hypotheses is the main goal of this paper. Is there a preference for one or the other? Theresult is: if one only considers a limited field-of-view around the Galactic center and if one considers only a limitedenergy range of the gamma-ray spectrum (up to 10 GeV), both interpretations lead to acceptable fits of the data.However, if one considers as field-of-view the whole sky - and especially the whole disk, where the MCs reside - andthe whole gamma-ray spectrum extending from 0.1 to 100 GeV it is clear that the interpretation of MCs provides notonly better fits, but the “GeV-excess” has a morphology following the MCs.The observation that a DM template does not describe the spectrum of the “GeV-excess” for any WIMP mass wasobserved recently by the Fermi Collaboration [36] as well, who studied the spectrum up to 1 TeV. They also observedthe excess in the Galactic disk, but did not realize the correlation with MCs. The fact that the “GeV-excess” isso clearly observed in the non-spherical CMZ - even in the raw data on diffuse gamma-rays without any analysis -provides already evidence against the DM hypothesis, which predicts a centered and almost spherical morphology ofthe “GeV-excess” in the Galactic center.The paper is organized as follows: In Sect. II the analysis procedure is described including the determination of theenergy templates from the data; In Sect. III a comparison of the two hypothesis (DM or MC) for the “GeV-excess” arecompared. The comparison excludes that DM annihilation is the dominant source of the “GeV-excess”, as has beensummarized in Sect. IV. Spectral fits to all 797 uncorrelated cones are given in the Appendices for both hypotheses(MC or DM).
II. ANALYSISA. Fermi data
The data selection is as in our previous papers. [30, 44] We use gamma-rays in the energy range between 0.1 and100 GeV using the diffuse class of the public P7REP SOURCE V15 data collected from August, 2008 till July 2014(72 months) by the Fermi Space Telescope. [50] The data were analyzed with the recommended selections for thediffuse class using the Fermi Science Tools (FST) software. [51] This included the zenith angle cut of 100 ◦ to reduceEarth limb events and energy bins wider than the LAT energy resolution (10 bins per decade), so no energy dispersioncorrections are needed in this energy range. Gamma-rays converted in the front and back end of the detector wereincluded. The residual hadronic background was included in the isotropic template. The point sources from thesecond Fermi point source catalog [52] were subtracted using the gtsrc routine in the FST.The sky maps were binned in longitude and latitude in 0.5 ◦ × . ◦ bins, which were combined to form a total of 797cones covering the whole sky. In and around the Galactic disk the cones were one degree in latitude with a longitudesize adapted to the structures, like the CMZ and the Fermi Bubbles. In the halo the cone size was increased in regionswithout structure, i.e. outside the Fermi Bubbles, typically to 18.5 ◦ (10 ◦ ) for latitudes above 55 ◦ (5 ◦ ), while the conesize in longitude was increased similarly. The precise cone sizes and fit results for each of the 797 cones are given inthe fits in the Online Supplemental Material or can be estimated from the sky maps discussed later. From Fig. 7(b)it can be seen that the binning is adequate to resolve the structure of MCs as function of longitude.The morphology of the “GeV-excess” is hardly smeared by the limited angular resolution of the Fermi-LAT instru-ment, given by the point-spread-function (PSF), since with our energy template fit the whole spectrum is fitted atonce, so the energy dependence of the PSF is marginalized over implying that we are not sensitive to the larger PSFsat the lower energies. The insensitivity to the PSF was checked by fitting the inner few degrees of the Galaxy, wherethe statistical error is small, with 0.5 ◦ × . ◦ bins. This did not change significantly the morphology. Hence, themorphology of the “GeV-excess” was not corrected for the smearing by the PSF.The gamma-ray flux is proportional to the product of the cosmic ray densities, the ‘target densities” (gas or gamma-rays in the interstellar radiation field) and the cross sections. A template fit combines the product of these threefactors into a single normalization factor for each gamma-ray component k , thus eliminating the need to know themindividually.The total flux in a given direction can be described by a linear combination of the gamma-ray fluxes from variousprocesses: | Φ tot > = n | Φ P CR > + n | Φ BR > + n | Φ IC > + n | Φ SCR > + n | Φ MCR > + n | Φ ISO >, (1)where the normalization factors n i determine the fraction of the total flux for a given process: PCR from the π production by propagated cosmic rays, BR from Bremsstrahlung, IC from inverse Compton, SCR from the π production by SCRs, MCR from the π production inside MCs and ISO for the isotropic background. In case onetests the DM hypothesis the MCR template is replaced by the DM template.The factors n i can be found from a χ fit, which adjusts the intensity n i of the gamma-ray fluxes from the spectraltemplates, one for each physical process, to best describe the data. The spectrum of a each cone has 21 energy binswith only n i ≤ B. Test Statistic
As test statistic we use the χ function defined as χ = N (cid:88) i =1 21 (cid:88) j =1 (cid:34) (cid:104) data ( i, j ) − (cid:80) k =1 n ( i, k ) × tem ( i, j, k ) (cid:105) σ ( i, j ) (cid:35) , (2) (a) (b) (c)FIG. 1. (a) Diffuse gamma-ray spectral templates fror Bremsstrahlung (BR), inverse Compton scattering (IC) and π pro-ductions by propagated cosmic rays (PCRs), cosmic rays inside unresolved point sources (SCRs) and cosmic rays inside MCs(MCRs). The templates are normalized around 2 GeV. The blue band shows the allowed region for the gamma-ray spectrafrom the Fermi Bubbles [53], which are consistent with the SCR template. Also shown is the gamma-ray template expected fora DM candidate with a mass of 45 GeV annihilating into b ¯ b quark pairs. (b) Power law proton cosmic ray spectra describingthe PCR, MCR, and SCR gamma-ray templates in (a). (c) A power law electron cosmic ray spectrum with a break at 1 GeVdescribing the IC and BR gamma-ray templates in (a). At high energies the power law cosmic ray spectra have spectral indicescompatible with the ones from the locally observed electron and proton data from AMS-02 [54, 55], which are shown as well.The spectra are normalized at 70 GV. where the sum is taken over the N=797 cones in different sky directions i , data ( i, j ) represents the total Fermi-LATgamma-ray flux in direction i for energy bin j , tem ( i, j, k ) the template contribution with normalization n ( i, k ) fortemplate k and σ ( i, j ) is the total error on data ( i, j ), obtained by adding the statistical and systematic errors inquadrature.The recommended systematic errors in the Fermi Software on the total gamma-ray flux are 10% for gamma-ray energies below 100 MeV, 5% at 562 MeV, and 20% above 10 GeV. We used a linear interpolation for energies inbetween. With these large systematic errors the fit usually leads to too high probabilities resulting in a reduced χ /dof well below 1. Therefore, we followed the usual procedure of rescaling these errors in order to obtain χ /dof ≈ χ /dof to ≈
1. The systematic errors between the bins are correlated, which implies that all data points are allowed to movesimultaneously up or down by an amount given by the correlated part of the systematic error. However, a template fitwith free normalizations for each template allows to move the fit up and down as well, which compensates a commonshift in the data. So adding a correlated error in the data can slightly change the overall gamma-ray flux, but hardlyaffects the relative contributions of the various templates, as was verified by explicitly adding a covariance matrixto Eq. 2 with a common positive correlation between all bins, which was varied between 10% and 70% of the totalsystematic error. We did not vary the size of the correlation as function of energy, which would change the shape ofthe template. But the shapes are optimized from the data in an iterative way, as will be discussed in the next section.
C. Determination of Spectral Templates
The spectral templates for the various processes in Eq. 1 can be obtained from the gamma-ray spectra in thefollowing way: we assume that the leptons and nuclei follow a power law spectrum in the interstellar space with atmost one break at a certain rigidity. For the spectral index above the break we take as a first estimate the spectralindex of the locally observed cosmic rays above 20 GV, a region which is not influenced strongly by solar modulation.[56] For given cosmic ray spectra the gamma-ray templates can be calculated by using e.g. the gamma-ray codes fromstandard propagation models, like Galprop [57, 58] or Dragon [59]. These codes need as input the energy spectra ofcosmic rays, which can either be obtained from a propagation model or one can simply provide cosmic ray power lawspectra as input. In the latter case the gamma-ray codes are independent of the propagation model parameters. Inour template fit we obtain the power laws of the interstellar cosmic ray spectra from a fit to the gamma-ray data inan iterative way: we start with an initial cosmic ray spectrum parametrized with a broken power law, calculate thegamma-ray spectra, perform a fit, modify the cosmic ray spectra and fit again. This procedure is iterated until the
FIG. 2. (a) MCR templates with different breaks in the proton spectra between 14 GV (maximum at the highest energy) and6 GV in steps of 1 GV; for comparison the PCR template from Fig. 1a is shown as well; (b) and (c): IC and BR templatessuperimposed for all cones. best fit to the gamma-ray data is obtained. How to obtain the initial cosmic ray spectra for each template will bediscussed in the following sections. The resulting templates and corresponding cosmic ray power law spectra havebeen summarized in Fig. 1.
1. Details on the PCR Template
The initial proton spectrum for the PCR template is obtained from the locally observed proton data from AMS-02[55], which can be approximated by an unbroken power law ( R − α ) with a spectral index ( α ) of 2.85 at rigidities above45 GV. At lower rigidities the data are below the power law because of solar modulation [56], as can be seen from Fig.1(b), where the AMS-02 data are plotted as well. To find the best parametrization a set of broken power laws with agrid of breaks and spectral indices above and below the break was constructed and the optimal parametrization wasfound by interpolation between the fits with the best test statistic. The gamma-ray data are well described by anunbroken power law for the protons with a spectral index ( α ) of 2.85 at all rigidities.
2. Details on the SCR Template
The proton spectra for the SCR template can be described by an unbroken power law with a spectral index of 2.1,as obtained from the best fit. The index 2.1 for the SCR template agrees with the data from the Fermi Bubbles,shown by the data points inside the shaded band in Fig. 1(a); the index 2.1 is expected from diffuse shock waveacceleration. [60, 61] The fact that the Fermi Bubbles and the cosmic rays inside sources have the same spectrumstrongly suggests that they are connected by point sources providing advective outflows of gas in the Galactic center.[44]
3. Details on the MCR Template
The decreasing gamma-ray emissivity from MCs below 2 GeV could be parametrized by a break in the power lawof the corresponding proton spectrum. Above the break the optimal spectral index of 2.85 was found to be the sameas for the PCR spectrum, as expected if the high energy propagated protons are above a certain magnetic cutoff. Butbelow the break, which varies according to the fit from 13 to 6 GV for the different clouds, the optimal spectral indexis 0.7, thus providing a significant suppression of protons below the break, as can be seen from Fig. 1(b). Energylosses alone cannot reproduce such a suppression of the proton spectrum below the break, but magnetic cutoffs areable to do so. Such a cutoff is well known from cosmic rays entering the Earth’s magnetic field: particles belowtypically 20 GV entering near the magnetic equator do not reach the Earth, but are repelled into outer space by thegeomagnetic cutoff. [62] The rigidity cutoff of 20 GV is proportional to the magnetic moment. Although the magneticfield near the Earth (0.5 G) is orders of magnitude higher than the typical magnetic fields in dense MCs [63], the muchlarger sizes of MCs - or its substructure of filaments and cloudlets [64] - yield magnetic moments of the same orderof magnitude as the Earth’s magnetic moment, so similar magnetic cutoffs are plausible. Variations in the magnetic (a) (b)FIG. 3. (a): The observed data versus the fitted data in various sky regions (i.e. for various gamma-ray fluxes) for a givenenergy, here for the energy bin between 3.7-5.2 GeV. The offset of a linear fit at the vertical axis represents the isotropiccomponent in the data, which moves the data in all bins upwards by this amount. A similar fit is repeated for all energy bins,so one determines the offset for each energy, which yields the isotropic template. (b) A comparison of the isotropic templateused in our analysis and the isotropic template given in the Fermi software with the insert showing the relative difference. cutoff in MCs are expected from the variations in size and in magnetic field; the latter increases with MC density.[63] The variations of the break in the proton spectrum between 13 and 6 GV varies the maximum of the gamma-rayspectrum from 2 to 1 GeV, as shown in Fig. 2(a). The fit prefers a constant spectral index below the break for allsky directions. Such a constant spectral index is plausible with regular magnetic fields oriented in the disk [65, 66]and the “cloudlets” inside MCs [64] form magnetic dipole fields. Then the maximum cutoff occurs for cosmic raysentering from the halo perpendicular into the cloud for any orientation of the magnetic dipole. For a given entranceangle the cutoff would provide a sharp break, but for an isotropic distribution of entrance angles the break points aresmeared. A distribution of break points will provide a slope below the maximum break determined largely by theisotropic distribution of the entrance angles into the disk. Since this distribution is the same for all MCs the slopesbelow the break will be similar for all MCs, even if the maximum break (= maximum magnetic cutoff) varies.
4. Details on the BR and IC Templates
The interstellar electron spectra needed a break around 1 GeV with a spectral index of 3.21 above the break, whichis compatible with the locally observed electron spectrum (see Fig. 1(c)); below the break the optimal spectral indexis 0.81, which implies a suppression of electrons. The break point might be related to the fact that around 1 GeVelectrons have the smallest energy losses, since above this energy synchrotron, BR and IC dominate the energy losses,while below this energy ionization losses become strong, thus depleting the electron spectrum below 1 GeV. A similarbreak in the electron spectrum was needed in the Fermi diffuse model. [46]The targets for the production of gamma-rays are the interstellar gas and the interstellar radiation field. Thelatter consists of photons from the cosmic microwave background, the infrared radiation from hot matter, like dustand the star light, so the photon composition varies with sky direction. Hence, for the IC templates we have tocalculate the templates for each sky direction. The variation over the sky is about ±
5. Details on the Isotropic Template
The isotropic template represents the contribution from the isotropic extragalactic background and hadron misiden-tification. Its spectral shape and absolute normalization are provided within the Fermi software. [51] The isotropictemplate was redetermined for our analysis in the following way. We fit the data in regions outside the Bubbles andGalactic disk using the isotropic template from the Fermi software as an initial estimate in the fit. If one plots thetotal observed gamma-ray flux versus the fitted flux in the various cones in a certain energy bin, one expects a linearrelation crossing the origin, if the isotropic flux is estimated correctly. However, if there is a missing or too highisotropic contribution, this leads to an offset at the origin of the linear curve, since the isotropic component is bydefinition the same for all cones, so it shifts the whole curve up and down for each energy bin. An example of such a fitis shown in Fig. 3(a) for an energy bin between 3.7-5.2 GeV. The offset can be determined for each energy bin, whichyields the spectral template of the isotropic component. The final spectral template is obtained by iteration untillzero offset at the origin is reached. The resulting template in our analysis has deviations from the Fermi template upto 35% above 2 GeV, as shown in the insert of Fig. 3(b).
6. Details on the DM Template
DM particles are expected to annihilate and just like in electron-positron annihilation the annihilation energy ofroughly twice the WIMP mass will lead to the production of hadrons, thus producing copiously gamma-rays from π decays. A smaller fraction of WIMP annihilation is expected to lead to tau lepton pairs, which can lead to π production in the hadronic tau decays. This contribution is expected to be small and is neglected. The DM templatecan be calculated with DarkSusy. [67, 68] The annihilation signal peaking at 2-3 GeV requires a WIMP mass around45 GeV, as shown in Fig. 1(a) as well. The difference to the MCR template is the cutoff at twice the WIMP mass,which is absent in the MCR template. III. A COMPARISON OF THE FIT RESULTS WITH THE MCR AND DM TEMPLATES
As mentioned before, the “GeV-excess” can be explained by an excess at energies around a few GeV from DMannihilation or by a depletion of gamma-rays below 2 GeV from the gamma-ray emissivity from MCs. The firstprocess would correspond to a process in the Galactic center, the second one to a process in the Galactic disk. Butsince we observe the excess along the lines-of-sight, these explanations are at first sight indistinguishable. However,there are two important differences: i) the DM and MCR templates differ significantly in shape above 50 GeV,so the test statistic might distiguish between them; ii) the MCs are distributed in the disk, the DM is distributedapproximately spherically around the Galactic center. So to distinguish between the two hypothesis one can eitherperform the fit with an MCR template or alternatively with a DM template including of course the other “background”templates (PCR,SCR,IC,BR, ISO) and perform a fit over the whole sky and all gamma-ray energies. If the “GeV-excess” is dominated by DM annihilation one expects to see the cutoff at twice the WIMP mass in the data and aspherical distribution of the intensity of “GeV-excess”, characterized by the normalization of the DM template in thefit. If the “GeV-excess” originates from the emissivity inside MCs, one expects a strong “GeV-excess” inside the diskand no hint for a cutoff in the high energy gamma-ray data.The templates of all physical processes are allowed in the fit for all cones. The fit is supposed to find out if theexpected backgrounds from the PCR, BR, IC and ISO templates fit the data or if the maximum of the spectrum isshifted (a feature recognized by the DM or MCR template) or if the data has a high energy tail above the expectationsfrom the known backgrounds (a feature recognized by the SCR template).Fits in three cones are shown as examples in Fig. 4: one for the Galactic center, where the size of the CMZ hasbeen selected ( − . ◦ < l < ◦ and | b | < . ◦ ), one in the halo with − ◦ < l < ◦ and 2 ◦ < | b | < ◦ and onealong the nearby tangent point of the Scutum-Centaurus spiral arm with − ◦ < l < − ◦ and − . ◦ < | b | < . ◦ .The longitude and latitude ranges are indicated in the panels. The left (right) panels show the fits with the MCR(DM) template. For the MCR fits all MCR templates in Fig. 2(a) with varying breaks between 6 and 14 GV weretried in the fit. The best fitted break in the proton spectrum for the MCR template is indicated in the fits on theleft, while the maximum of the DM flux is indicated for the DM fits on the right. The DM fits all use a WIMP massof 44.9 GeV, which is the optimal mass for the Galactic center. Both, the WIMP mass and the DM flux from ouranalysis, are compatible with “conventional” analysis. [16, 22]The field-of-view of the CMZ ( l × b (cid:39) . ◦ × . ◦ ) is known from the CS or CO maps. [40, 47] The rotation linesof both molecules are good tracers of MCs. In the top row of Fig. 4 one observes that the spectrum towards the CMZis dominated by the “GeV-excess”, which is either proportional to the contribution of the MCR template (left panel)or DM template (right panel). We checked that the “GeV-excess” is maximal inside the rectangular field-of-view ofthe CMZ by repeating the fit with a sliding window of constant size. If the window moved out of the field-of-viewof the CMZ the flux of the “GeV-excess” decreased. The fact that the “GeV-excess” has a longitudinally elongatedmorphology in the inner few degrees of the Galactic center shows that the “GeV-excess” cannot be dominated by DMannihilation, which would correspond to a spherical instead of a rectangular spatial morphology. (a) (b)(c) (d)(e) (f)FIG. 4. Spectral template fits to the Fermi diffuse gamma-ray data for the following regions of interest: towards the CMZ(top row), halo (middle row) and the nearby tangent point of the Scutum-Centaurus arm (bottom row) using either the MCRtemplate (left) or DM template (right). (a) (b)FIG. 5. χ /dof values of fits in all 797 cones with either the MCR template (a) or a DM template for a DM candidate with amass of 44.9 GeV annihillating into b ¯ b quark pairs (b).(a) (b)FIG. 6. Sky maps of the fluxes of the MCR (a) and DM for a DM candidate with a mass of 44.9 GeV annihiilating into b ¯ b quark pairs (b). The fluxes are in units of GeVcm − s − sr − at an energy of 2.41 GeV. The SCR template in the middle row has contributions from both, the π production inside point sources and inthe Fermi Bubbles, since they both contribute in this field-of-view up to latitudes of 20 ◦ , but they have the same hardSCR template, see Fig. 1. Note that our analysis does not need the spatial template for the Fermi Bubbles, sinceits contribution is determined by the energy template for each cone. From the contribution in each cone we find thewell-known shape of the Fermi-Bubbles.The last row in Fig. 4 shows the fits towards the tangent point of the Scutum-Centaurus arm. Here the data areagain dominated by the “GeV-excess”, but this region cannot be described by the DM template nor by the background0 (a) (b)FIG. 7. A summary of the fourfold correlation between the “GeV-excess” (= MCR), the CO maps, the π production inunresolved point sources (= SCR) and the point source distribution traced by the Al line: (a) Longitude and latitude ofMCR (green histogram, this analysis) and CO (red line). [69] The latitude distibution of the MCR flux at an energy of 2.41GeV was integrated over a longitude range of | l | < . ◦ . The black line in the bottom panel corresponds to the NFW templatefrom the “conventional” analysis, adapted from Fig. 1 from Ref. [22]. One observes that the CO latitude distribution from thePlanck satellite resembles an average NFW profile with some clumpiness. (b): the longitude distribution of the fluxes from theSCR and MCR templates, which have a similar morphology, as expected since both are connected to MCs. The lower panelshows the Al sky map [70, 71], which is correlated with the top panel, as indicated by the vertical arrows. This correlationis expected, since both, the Al flux and the SCR flux, are tracers of cosmic ray sources. templates alone (PCR, IC, BR, ISO), which is again a strong case for the MC hypothesis of the “GeV-excess”, sincethe DM template is not expected to dominate so far from the Galactic center. The MCR breaks can shift the maximumof the MCR template between 1 and 2 GeV (see Fig. 2(a)), which is not allowed for DM templates because of therequirement of the same WIMP mass in all sky directions. The fits for all 797 cones are shown in the Appendices,both, for the MCR and DM template fits.From the 797 fits to all cones it is clear that the χ of the MCR fit is better than the DM fit in regions where astrong “GeV-excess” is observed, as shown in Fig. 5 and the χ values in the panels of Fig. 4. The DM fit leads to χ /dof of typically 3 or higher inside the disk, while the fits including the MCR templates provide a good χ /dof over the whole gamma-ray sky.The sky maps of the various contributions can be directly obtained by plotting the fitted normalization constants inEq. 1. The sky map of the “GeV-excess” corresponds to the sky maps of either the MCR or DM template, which areshown in Fig. 6. One observes in both cases a strong component along the whole disk with rapidly decreasing latitudecontributions up to 15-20 ◦ . This does not look like a DM profile, but resembles the morphology of MCs. This can bechecked by comparing the MCR sky map with the CO sky map, which is a tracer of MCs and was precisely measuredby the Planck satellite. [47] These data are publicly available. [69] Since the agreement is difficult to visualize withcolor coded sky maps the longitude and latitude profile of the MCR sky map are histogrammed (green) in Fig. 7(a)together with the MC column density, as obtained from the Planck sky maps for the CO rotation lines (red line). The1 FIG. 8. Sky map of the CO rotation line as measured with the Planck satellite[69]. The yellow (light) contour is the DMcontour from Fig. 6(b). fluxes from the MCR templates and CO sky maps are normalized. Both show a strong contribution in the Galacticcenter from the CMZ. The longitude distribution decreases rapidly outside the Galactic bar region ( − ◦ < l < ◦ )[44], both for the CO flux and the MCR flux which implies a high density of MCs in the Galactic bar. This similarityin morphology between the MCR and CO fluxes points to a strong correlation, which is not expected to be exact,since the gamma-ray flux from the MCR template is determined by the molecular gas density convolved with thecosmic ray density along the lines-of-sight, while the CO maps are proportional to the MC column density only. Thelatitude distribution in Fig. 7(a) shows also the expectation from a generalized NFW profile, which was taken fromthe “conventional” analysis, as presented in Fig. 1 from Ref. [22]. From the bottom panel in Fig. 7(a) one observesthat the latitude distribution from the CO map of Planck resembles a DM profile (compare black and red lines). Inaddition, this panel proves that our template fit (green histogram) is in reasonable agreement with the flux from the“conventional” analysis, represented by the black line. In longitude the “GeV-excess” does not follow an NFW profile,as shown in the top panel of Fig. 7(a), but follows closely the structure from the Galactic bar with the CMZ at thecenter. Within the first two degrees in longitude, i.e. within the CMZ, the flux of the “GeV-excess” does not fallrapidly in contrast to the expectation for the DM hypothesis.Since sources are expected to reside inside MCs one expects a strong correlation in the spatial distributions of theSCR fluxes and the MCR fluxes, i.e. if there is a long tail in the gamma-ray spectra above 30 GeV, one expects asimultaneous shift in the maximum of the spectrum from 0.7 up to 2 GeV. The strong correlation between the SCRand MCR fluxes is indeed observed, as shown in the top panel of Fig. 7(b). Here the gamma-ray fluxes from the SCR(MCR) templates are integrated over a latitude range of | b | < ◦ (0 . ◦ ), respectively. The larger latitude range for theSCR component is just to increase the statistics of the SCR fluxes, since the sources can have outflows towards higherlatitudes, as suggested by the broad latitude distribution of Al in the bottom panel of Fig. 7(b). The radioactive Al isotope is synthesized by proton capture of Mg in heavy, magnesium rich sources [45] and can be traced by the1.8 MeV gamma-line emitted in its decay. This line has been studied by the Integral/Spi satellite [70] and is publiclyavailable as sky map. [71] The strong correlation between the SCR fluxes, MCR fluxes and Al fluxes is emphasizedby the vertical arrows in Fig. 7(b) between the sky map of the Al line (bottom panel) and the longitude distributionof the SCR and MCR fluxes (top panel). The sky map of the DM template in Fig. 6(b) has the morphology of a COsky map instead of a spherical halo profile expected for DM. This is demonstrated in Fig. 8.2It was noticed recently [72] that the gamma-rays have a much harder spectrum towards the Galactic center thanin the opposite direction. However, the reason was not understood, but is provided by the strong SCR contributionin the bar region (see top panel in Fig. 7(b)), which is largely absent in the opposite direction (longitude ≈ ◦ ).The sky map of the “GeV-excess” in Fig. 6 shows some clumpiness, as expected from the discrete nature ofMCs or its filamentary substructure. In Ref. [27] some deviation from smooth sky maps for the “GeV-excess” wasinterpreted as evidence for unresolved point sources, a feature used to support the millisecond pulsar interpretationof the “GeV-excess”. But the nature of the clumpiness is unknown and could be related to MCs as well. [18] IV. CONCLUSION
We have compared two hypothesis for the “GeV-excess”: an excess of gamma-rays peaking around 2 GeV from DMannihilation (DM hypothesis) or a depletion of gamma-rays below 2 GeV as observed in the gamma-ray emissivity ofMCs (MC hypothesis). The DM hypothesis leads to an excess falling rapidly with distance from the Galactic center,as expected for a typical DM profile. The MC hypothesis leads to a “GeV-excess” falling rapidly with distance fromthe Galactic center as well, because of the decreasing column densities of MCs along the lines-of-sight away from theGalactic center. This decrease happens to resemble a DM profile, as is known from the sky maps of the CO rotationlines, a tracer of MCs.We find that the MC hypothesis is preferred over the DM hypothesis for the following reasons:i) the MC hypothesis provides a significantly better fit, especially if one considers the gamma-ray energies up to100 GeV; the groups proposing the DM hypothesis [16] excluded data above 10 GeV for the fits towards the Galacticcenter, but the DM template does not describe the “GeV-excess”, if higher energies are included, as shown in thispaper and observed recently by the Fermi Collaboration as well. [36] ii) the “GeV-excess” has in latitude for bothhypotheses the morphology from a generalized NFW profile (see bottom panel of Fig. 7(a) for the MCR template),but the excess is strong in all directions towards MC regions in the Galactic disk, as could be proven by the spatialcorrelation with the CO maps from the Planck satellite. [47] Especially, the DM sky map does not resemble theexpected spherical DM halo profile if the whole gamma-ray sky is considered, but has a morphology similar to theCO sky map, as demonstrated in Fig. 8. iii) The single, most convincing evidence, which leads us to believe thatDM cannot be the dominant source of the “GeV-excess” is provided by the strong “GeV-excess” in the longitudinallyextended field-of-view with the rectangular shape of the CMZ, the dense MC conglomerate encircling the Galacticcenter. Here the “GeV-excess”, observable as a shift in the maximum of the energy flux per log bin in the gamma-rayspectrum to 2 GeV, is obvious already from the raw diffuse gamma-ray data without any analysis. Such a rectangularshape is not compatible with the expected spherical morphology of a DM annihilation signal.
ACKNOWLEDGMENTS
Financial support from the Deutsche Forschungsgemeinschaft (DFG, Grant BO 1604/3-1) is warmly acknowledged.We are grateful to the Fermi scientists, engineers and technicians for collecting the Fermi data and the Fermi ScienceSupport Center for providing the software and strong support for guest investigators.3
Appendix A: Figs. 9-29 show the template fits in each of the 797 cones using the MCR template to describethe “GeV-excess”. The figures start with the highest latitudes and in each figure the longitude varies for agiven stripe in latitude, as indicated in the legends.
FIG. 9. Template fits for latitudes with 72 . ◦ < b < . ◦ and longitudes decreasing from 180 ◦ to -180 ◦ .FIG. 10. Template fits for latitudes with 55 . ◦ < b < . ◦ and longitudes decreasing from 180 ◦ to -180 ◦ . FIG. 11. Template fits for latitudes with 45 . ◦ < b < . ◦ and longitudes decreasing from 180 ◦ to -180 ◦ . FIG. 12. Template fits for latitudes with 35 . ◦ < b < . ◦ and longitudes decreasing from 180 ◦ to -180 ◦ . FIG. 13. Template fits for latitudes with 25 . ◦ < b < . ◦ and longitudes decreasing from 180 ◦ to -180 ◦ . FIG. 14. Template fits for latitudes with 15 . ◦ < b < . ◦ and longitudes decreasing from 180 ◦ to -180 ◦ . FIG. 15. Template fits for latitudes with 5 . ◦ < b < . ◦ and longitudes decreasing from 180 ◦ to -180 ◦ . FIG. 16. Template fits for latitudes with 1 . ◦ < b < . ◦ and longitudes decreasing from 180 ◦ to 0 ◦ . FIG. 17. Template fits for latitudes with 1 . ◦ < b < . ◦ and longitudes decreasing from 0 ◦ to -180 ◦ . FIG. 18. Template fits for latitudes with 0 . ◦ < b < . ◦ and longitudes decreasing from 180 ◦ to -180 ◦ . FIG. 19. Template fits for latitudes with − . ◦ < b < . ◦ and longitudes decreasing from 180 ◦ to -180 ◦ .
38 39FIG. 20. Template fits for latitudes with − . ◦ < b < − . ◦ and longitudes decreasing from 180 ◦ to -180 ◦ . FIG. 21. Template fits for latitudes with − . ◦ < b < − . ◦ and longitudes decreasing from 180 ◦ to 0 ◦ . FIG. 22. Template fits for latitudes with − . ◦ < b < − . ◦ and longitudes decreasing from 0 ◦ to -180 ◦ . FIG. 23. Template fits for latitudes with − . ◦ < b < − . ◦ and longitudes decreasing from 180 ◦ to -180 ◦ . FIG. 24. Template fits for latitudes with − . ◦ < b < − . ◦ and longitudes decreasing from 180 ◦ to -180 ◦ . FIG. 25. Template fits for latitudes with − . ◦ < b < − . ◦ and longitudes decreasing from 180 ◦ to -180 ◦ . FIG. 26. Template fits for latitudes with − . ◦ < b < − . ◦ and longitudes decreasing from 180 ◦ to -180 ◦ . FIG. 27. Template fits for latitudes with − . ◦ < b < − . ◦ and longitudes decreasing from 180 ◦ to -180 ◦ . FIG. 28. Template fits for latitudes with − . ◦ < b < − . ◦ and longitudes decreasing from 180 ◦ to -180 ◦ .FIG. 29. Template fits for latitudes with − . ◦ < b < − . ◦ and longitudes decreasing from 180 ◦ to -180 ◦ . Appendix B: Figs. 30-50 show the template fits in each of the 797 cones using the DM template to describethe “GeV-excess”. The figures start with the highest latitudes and in each figure the longitude varies for agiven stripe in latitude, as indicated in the legends.
FIG. 30. Template fits for latitudes with 72 . ◦ < b < . ◦ and longitudes decreasing from 180 ◦ to -180 ◦ .FIG. 31. Template fits for latitudes with 55 . ◦ < b < . ◦ and longitudes decreasing from 180 ◦ to -180 ◦ . FIG. 32. Template fits for latitudes with 45 . ◦ < b < . ◦ and longitudes decreasing from 180 ◦ to -180 ◦ . FIG. 33. Template fits for latitudes with 35 . ◦ < b < . ◦ and longitudes decreasing from 180 ◦ to -180 ◦ . FIG. 34. Template fits for latitudes with 25 . ◦ < b < . ◦ and longitudes decreasing from 180 ◦ to -180 ◦ . FIG. 35. Template fits for latitudes with 15 . ◦ < b < . ◦ and longitudes decreasing from 180 ◦ to -180 ◦ . FIG. 36. Template fits for latitudes with 5 . ◦ < b < . ◦ and longitudes decreasing from 180 ◦ to -180 ◦ . FIG. 37. Template fits for latitudes with 1 . ◦ < b < . ◦ and longitudes decreasing from 180 ◦ to 0 ◦ . FIG. 38. Template fits for latitudes with 1 . ◦ < b < . ◦ and longitudes decreasing from 0 ◦ to -180 ◦ . FIG. 39. Template fits for latitudes with 0 . ◦ < b < . ◦ and longitudes decreasing from 180 ◦ to -180 ◦ . FIG. 40. Template fits for latitudes with − . ◦ < b < . ◦ and longitudes decreasing from 180 ◦ to -180 ◦ .
38 39FIG. 41. Template fits for latitudes with − . ◦ < b < − . ◦ and longitudes decreasing from 180 ◦ to -180 ◦ . FIG. 42. Template fits for latitudes with − . ◦ < b < − . ◦ and longitudes decreasing from 180 ◦ to 0 ◦ . FIG. 43. Template fits for latitudes with − . ◦ < b < − . ◦ and longitudes decreasing from 0 ◦ to -180 ◦ . FIG. 44. Template fits for latitudes with − . ◦ < b < − . ◦ and longitudes decreasing from 180 ◦ to -180 ◦ . FIG. 45. Template fits for latitudes with − . ◦ < b < − . ◦ and longitudes decreasing from 180 ◦ to -180 ◦ . FIG. 46. Template fits for latitudes with − . ◦ < b < − . ◦ and longitudes decreasing from 180 ◦ to -180 ◦ . FIG. 47. Template fits for latitudes with − . ◦ < b < − . ◦ and longitudes decreasing from 180 ◦ to -180 ◦ . FIG. 48. Template fits for latitudes with − . ◦ < b < − . ◦ and longitudes decreasing from 180 ◦ to -180 ◦ . FIG. 49. Template fits for latitudes with − . ◦ < b < − . ◦ and longitudes decreasing from 180 ◦ to -180 ◦ .FIG. 50. Template fits for latitudes with − . ◦ < b < − . ◦ and longitudes decreasing from 180 ◦ to -180 ◦ . [1] L. Goodenough and D. Hooper, “Possible Evidence For Dark Matter Annihilation In The Inner Milky Way From TheFermi Gamma Ray Space Telescope”, arXiv:0910.2998 .[2] D. Hooper and L. Goodenough, “Dark Matter Annihilation in The Galactic Center As Seen by the Fermi Gamma RaySpace Telescope”, Phys.Lett.
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