The dark connection between the EGRET excess of diffuse Galactic gamma rays, the Canis Major dwarf, the Monoceros ring, the INTEGRAL 511 keV annihilation line, the gas flaring and the Galactic rotation curve
aa r X i v : . [ a s t r o - ph ] N ov November 27, 2018 2:15 WSPC - Proceedings Trim Size: 9in x 6in dark2007 THE DARK CONNECTION BETWEEN THE EGRET EXCESS OFDIFFUSE GALACTIC GAMMA RAYS, THE CANIS MAJOR DWARF,THE MONOCEROS RING, THE INTEGRAL 511 keV ANNIHILATIONLINE, THE GAS FLARING AND THE GALACTIC ROTATION CURVE.
W. DE BOER
University of KarlsruhePostfach 6980, D-76131 Karlsruhe, Germany ∗ E-mail: [email protected]
The EGRET excess of di ff use Galactic gamma rays shows all the key features of dark matterannihilation (DMA) for a WIMP mass in the range 50-100 GeV, especially the distributionof the excess is compatible with a standard halo profile with some additional ringlike sub-structures at 4 and 13 kpc from the Galactic centre. These substructures coincide with thegravitational potential well expected from the ring of dust at 4 kpc and the tidal stream ofdark matter from the Canis Major satellite galaxy at 13 kpc, as deduced from N-body simu-lations fitting to the Monoceros ring of stars. Strong independent support for this substruc-ture is given by the gas flaring in our Galaxy. The gamma rays from DMA are originatingpredominantly from the hadronization of mono-energetic quarks, which should producealso a small, but known fraction of protons and antiprotons. Bergstr¨om et al. an antiprotonflux far above the observed antiproton flux and they conclude that the DMA interpretationof the EGRET excess can therefore be excluded. However, they used an isotropic propa-gation model, i.e. the same di ff usive propagation in the disk and the halo. It is shown thatan anisotropic propagation model is consistent with the EGRET gamma ray excess, the an-tiproton flux and the ratios of secondary / primary and unstable / stable cosmic ray particles.Such an anisotropic propagation is supported by the large bulge / disk ratio of the positronannihilation line, as observed by the INTEGRAL satellite. In this case no need for newsources specific to the bulge are needed, so the claimed evidence for strong DMA in thebulge from these observations is strongly propagation model dependent. In the frameworkof Supersymmetry cross section predictions for direct dark matter searches are presentedtaking into account the EGRET data, the WMAP data and other electroweak constraints.
1. Introduction
Cold Dark Matter (CDM) is well established by the high rotation speeds in galax-ies and clusters of galaxies. Recent cosmological measurements yield a dark mat-ter (DM) density of 22 ±
2% of the energy of the Universe. If this DM is createdthermally during the Big Bang the present relic density is inversely proportionalto h σ v i , the annihilation cross section σ of DM particles, usually called WIMPS ovember 27, 2018 2:15 WSPC - Proceedings Trim Size: 9in x 6in dark2007 (Weakly Interacting Massive Particles), times their relative velocity. The averageis taken over these velocities. This inverse proportionality is obvious, if one con-siders that a higher annihilation rate, given by h σ v i n χ , would have reduced therelic density before freeze-out, i.e. the time, when the expansion rate of the Uni-verse, given by the Hubble constant, became equal to or larger than the annihila-tion rate. The relation can be written as: Ω χ h = m χ n χ ρ c h ≈ ( 3 · − cm s − h σ v i ) . (1)For the present value of Ω h = . ± . the ther-mally averaged total cross section at the freeze-out temperature of m χ /
22 musthave been around 3 · − cm s − . Note that h σ v i as calculated from Eq. 1 is inde-pendent of the WIMP mass (except for logarithmic corrections) as can be shownby detailed calculations. If the s-wave annihilation is dominant, as expected inmany supersymmetric models, then the annihilation cross section is energy inde-pendent, i.e. the cross section given above is also valid for the cold temperaturesof the present universe. Such a large cross section will lead to a production rateof mono-energetic quarks a in our Galaxy, which is 40 orders of magnitude abovethe rate produced at any accelerator. The fragmentation of these mono-energeticquarks will lead to a large flux of neutrinos, photons, protons, antiprotons, elec-trons and positrons in the Galaxy. From these, the protons and electrons disappearin the sea of many matter particles, but the photons and antimatter particles maybe detectable above the background, generated by cosmic ray interactions withthe gas in the Galaxy. Such searches for indirect Dark Matter detection have beenactively pursued. Recent reviews and references to earlier work can be found inRefs. Gamma rays have the advantage that they point back to the source and donot su ff er energy losses, so they are the ideal candidates to trace the dark matterdensity and have a spectral shape characteristic for mono-energetic quarks. Thecharged components interact with Galactic matter and are deflected by the Galac-tic magnetic field, so they do not point back to the source. Therefore the chargedparticle fluxes have large uncertainties from the propagation models, which deter-mine how many of the produced particles arrive at the detector. For gamma raysthe propagation is straightforward: only the ones pointing towards the detectorwill be observed.An excess of di ff use gamma rays compatible with dark matter annihilation a The quarks are mono-energetic, since the kinetic energy of the cold dark matter particles is expectedto be negligible with the mass of the particles, so the energy of the quarks equals the mass of theWIMP. ovember 27, 2018 2:15 WSPC - Proceedings Trim Size: 9in x 6in dark2007 (DMA) has indeed been observed by the EGRET telescope on board of NASA’sCGRO (Compton Gamma Ray Observatory). Below 1 GeV the CR interactionsdescribe the data perfectly well, but above 1 GeV the data are up to a factor twoabove the expected background. The excess shows all the features of DMA anni-hilation for a WIMP mass between 50 and 70 GeV. Masses up to 100 GeV arepossible if one assumes the cosmic ray energy spectrum to vary in the Galaxy. Theexcess was observed in all sky directions, which would imply that DM is not darkanymore, but shining in gamma rays. Of course, such an important observationneeds to be scrutinized heavily. Among the most important criticism was a paperby Bergstr¨om et al. claiming that the antiproton flux from DMA, using the DMdistribution from the EGRET excess, would be an order of magnitude higher thanthe observed antiproton flux. However, they use an isotropic propagation modelwith the same propagation in the disk and the halo. For the expected anisotropicpropagation models everything can be made consistent by having a faster prop-agation perpendicular to the disk than in the disk, in which case the antiprotonsfrom DMA in the halo do not return to the disk. This demonstrates the large un-certainties from propagation models for indirect dark matter searches.It is interesting to note that anisotropic propagation models can easily explaina large bulge / disk (B / D) ratio of the positron annihilation, as observed from the in-tensity of the 511 keV annihilation line of thermalized positrons. These positronsare e.g. produced in the β -decays of radioactive nuclei from supernova explosions.A large B / D ratio is simply due to the di ff erent geometries of the disk and thebulge: in the bulge the positrons and electrons can annihilate and radiate beforeescaping to the halo, in the disk they enter the halo much faster without havingtime to radiate and / or annihilate. In contrast, in isotropic propagation models onecan only explain the large bulge / disk ratio by a new source for positrons for thebulge alone. Anisotropic propagation models have enough freedom to explain theresults without new sources. So the claimed evidence for DMA from these obser-vations are strongly propagation model dependent.The paper is organized as follows: in section 2 we summarize the DMA in-terpretation of the EGRET excess. In section 3 we discuss the problems with theisotropic propagation models. An anisotropic propagation model, which simul-taneously describes the antiproton flux, the EGRET excess and the observationsconcerning primary and secondary cosmic rays and cosmic clocks is discussed insection 4, while in section 5 the consequences for the INTEGRAL excess of the511 keV line in this anisotropic propagation model are discussed. In section 6 theconstraints from direct dark matter searches are discussed. Section 7 summarizesthe results. ovember 27, 2018 2:15 WSPC - Proceedings Trim Size: 9in x 6in dark2007
2. The DMA Interpretation of the EGRET Excess of di ff use GalacticGamma Rays It is well known that the EGRET satellite data on di ff use gamma rays shows anexcess above 1 GeV in comparison with the expectations from CR interactions. Below 1 GeV the CR interactions describe the data perfectly well. The excessshows all the features of DMA annihilation for a WIMP mass between 50 and70 GeV. Especially, the two basic constraints expected from any indirect DMAsignal are fulfilled: • the excess should have the same spectral shape in all sky directions. • the excess should be observable in a large fraction of the sky with anintensity distribution corresponding to the gravitational potential of ourGalaxy. The latter means that one should be able to relate the distributionof the excess to the rotation curve.The analysis of the EGRET data is simplified by the fact that the spectral shapesof the DMA contribution and the background from CR interactions with the gas ofthe disk are well known from accelerator experiments: (i) the DMA signal shouldhave the gamma ray spectrum from the fragmentation of mono-energetic quarks,which has been studied in great detail at LEP. (ii) the background in the energyrange of interest is dominated by CR protons hitting the hydrogen of the disk.Therefore the dominant background spectral shape is known from fixed-target ex-periments. Given that these shapes are known from the two best studied reactionsin accelerator experiments allows to fit these known shapes to the observed gammaray spectrum in a given sky direction and obtain from the fitted normalization con-stants the contribution of both background and annihilation signal. So in this caseone does not need propagation models to estimate the background, since the dataitself calibrates the amount of background. A typical spectrum is shown in Fig.1, which clearly shows the rather distinct shapes of DMA and background, so thetwo normalization constants are not strongly correlated. The shape of the DMAcontribution shifts to the right for heavier WIMP masses. The preferred WIMPmass is between 50 and 70 GeV with a maximum allowed value of 100 GeV. Repeating these fits over 180 independent sky directions showed that indeed: (i)the shape of EGRET excess is consistent with a 60 GeV WIMP mass in each skydirection (ii) the intensities of the EGRET excess in various sky directions are asexpected from the gravitational potential, which could be proven by reconstruc-ting the rotation curve from the EGRET data after adding the known distributionof visible matter to the DM halo. A parametrization of the best fitted DM halo isshown in Fig. 1 on the right hand side, which clearly shows the ringlike structuresat 4 and 13 kpc, as determined from the enhanced intensity of the EGRET excess ovember 27, 2018 2:15 WSPC - Proceedings Trim Size: 9in x 6in dark2007 Fig. 1:
Left: Fit of the shapes of background and DMA signal to the EGRET datain the direction of the Galactic centre The dark shaded (red) area indicatesthe signal contribution from DMA for a 60 GeV WIMP mass using theshape from high energy electron-positron annihilation experiments, whilethe area below it represents the background with the various indicated con-tributions. The (blue) area between the dotted lines just below the shadedarea is the estimated uncertainty in the background, which is dominatedby solar modulation. The normalization of both the background and theDMA contribution have been left free in the fit of the known shapes. Right:Parametrization of the dark matter density profile as determined from thedistribution of the EGRET excess in the sky. Both pictures are taken fromRef. in these regions. The ring at 4 kpc (inner ring) coincides with the ring of dust inthis region. The dust is presumably kept there because of a gravitational poten-tial well, which is provided by the ring of DM. The ring at 13 kpc (outer ring)is thought to originate from the tidal disruption of the Canis Major dwarf galaxy,which circles the Galaxy in an almost circular orbit coplanar with the disk. Three independent observations confirm this picture of the ring originating fromthe tidal disruption of a dwarf galaxy:(i) a ring of DM is expected in this region from the observed ring of stars,called Monoceros ring, which was discovered first with SDSS data.
Follow-upobservations found that this structure surrounds the Galactic disk as a giant ring(observed over 100 degrees in latitude) at Galactocentric distances from 8 kpcto 20 kpc. Tracing this structure with 2MASS M giant stars, suggested that thisstructure might be the result from the tidal disruption of a merging dwarf galaxy.N-body simulations show indeed that the overdensity in Canis Major is indeed a ovember 27, 2018 2:15 WSPC - Proceedings Trim Size: 9in x 6in dark2007 -1000100200300400500 0 2.5 5 7.5 10 12.5 15 17.5 20 22.5 25 R [kpc] r o t. v e l o c i t y [ k m s - ] totalluminous diskbulge dmtriax haloinner ringouter ring Fig. 2:
Left: results of an N-body simulation of the tidal disruption of the CanisMajor dwarf Galaxy, whose orbit was fitted to the observed stars (sym-bols). The simulation predicts a ringlike structure of dark matter with aradius of 13 kpc. From Ref. Right:The rotation curve with the contri-butions of the bulge, the disk, the triaxial dark matter halo and the tworinglike structures. The outer ring causes the peculiar change of slope inthe rotation curve at about 11 kpc. From Ref. perfect progenitor for the Monoceros stream and they predict a DM ring at 13 kpcwith a low ellipticity and almost coplanar with the disk, as shown in the left panelof Fig. 2. The orientation of the major axis at an angle of 20 degrees with respect tothe axis sun-Galactic centre and the ratio of minor to major axis around 0.8 agreeswith the EGRET ring parameters given in Ref. This correlation with the EGRETexcess lends both support to the DMA interpretation of the EGRET excess and the interpretation that the Monoceros stream originates from the tidal disruptionof the Canis Major (CM) satellite galaxy, thus rejecting the interpretation that theoverdensity of stars forming the Canis Major dwarf is a warp of the Galactic disk(see discussions e.g. in Refs. ). A further rejection from the hypothesis that theCM overdensity is just due to the warp comes from the gas flaring discussed below,which shows that the Monoceros stream is connected to an enormous amount ofdark matter.(ii) Such a massive ring structure influences the rotation curve in a peculiarway: it decreases the rotation curve at radii inside the ring and increases it outside.This is apparent from the change in direction of the gravitational force from thering on a tracer, since this force decreases the force from the galactic centre for ovember 27, 2018 2:15 WSPC - Proceedings Trim Size: 9in x 6in dark2007 no ring with ring Fig. 3:
The half-width-half-maximum (HWHM) of the gas layer of the Galacticdisk as function of the distance from the Galactic center. Clearly, the fit in-cluding a ring of dark matter above 10 kpc describes the data much better.Adapted from data in Ref. a tracer inside the ring, but increases it outside the ring. This is indeed observedas shown in the right hand panel of Fig. 2, where the negative contribution of theouter ring is clearly visible.(iii) A direct proof of the large amount of DM mass in the outer ring comesfrom a recent analysis of the gas flaring in our Galaxy. Using the new data ofthe LAB survey of the 21 cm line in our Galaxy led to a precise measurement ofthe gas layer thickness up to radii of 40 kpc. The increase of the half width of thelayer after a decrease to half its maximum value (HWHM) as function of distanceis governed by the decrease in gravitational potential of the disk. The outer ringincreases the gravitational potential above 10 kpc, which is expected to reducethe gas flaring. Only after taking the ring like structure into account the reducedgas flaring in this region could be understood. The e ff ect is shown in Fig. 3. Afit averaged over all longitudes requires a DM ring with a mass of 2 . solarmasses, in rough agreement with the EGRET excess.Clearly, these three independent astronomical observations need a ringlike DMstructure above 10 kpc, thus providing independent evidence for the DMA inter-pretation of the EGRET excess.These independent observations cannot be explained by alternative explana-tions of the EGRET excess, of which the strongest one is provided by the ”op- ovember 27, 2018 2:15 WSPC - Proceedings Trim Size: 9in x 6in dark2007 timized” model. In this case the cosmic ray spectrum of protons and electronsis not taken to be the locally observed one, but modified to increase the gammaray spectrum at high energies. This requires a strong break in the injection spec-trum of electrons and protons in order not to change the gamma ray spectrumbelow 1 GeV, but only above 1 GeV. However, the gamma ray spectra at interme-diate and high latitudes are created by the local cosmic rays. Still they show theexcess. Furthermore, spectral shape di ff erences are not expected, since di ff usionis fast compared with the energy loss time, so di ff usion equalizes the spectrumeverywhere in agreement with the observation that the gamma ray spectra in alldirections can be described with the same CR spectrum in all directions, i.e. thesame spectral shape everywhere in the Galaxy.Another explanation is provided by tuning the e ffi ciency of the EGRET spec-trometer to simulate DMA. However, this requires the e ffi ciency already to bemodified around 1 GeV and reaching a change in e ffi ciency of 80% at 10 GeV inclear disagreement with the calibration error in a photon beam before launch andthe residual uncertainties below 20% during the flight after correcting for time de-pendent e ff ects. Although their is some uncertainty in the e ffi ciency of the vetocounter at higher energies because of the backsplash from the calorimeter, thise ff ect should not start at 1 GeV. Even the authors agree that the considered e ff ectsare too small individually and it is not clear that if one adds the errors all linearlythat one gets e ff ects up to 80%. And if these e ff ects add up, it would be a remark-able coincidence that the excess corresponds exactly to the very specific sharplyfalling spectrum from the fragmentation of mono-energetic quarks! An even moreremarkable coincidence is that the distribution of the excess in the sky follows thegravitational potential, as proven by the gas flaring and the rotation curve. There-fore the excess is not as isotropic as suggested by these authors, if one observes infiner sky bins, which reveals ringlike structures.
3. The Antiproton Flux from DMA in an Isotropic Propagation Model
As mentioned in the introduction, a serious objection about the DMA interpreta-tion concerns the antiproton flux. However, this depends strongly on the propaga-tion model. Here we summarize the concepts used for the “conventional” propa-gation model, discuss its priors and its alternatives.The main features of our Galaxy are a barred central bulge with a diameter ofa few kpc and a large spiral disk of about 15 kpc. Most of the gas is distributedin the disk, which extends to radii of 15-20 kpc, while the supernovae remnants(SNR) peak at a distance of a few kpc from the centre. They are thought to be thesource of the cosmic rays (CRs) with energies up to 10 eV. These CRs form aplasma of ionized particles, in which the electric fields can be neglected by virtue ovember 27, 2018 2:15 WSPC - Proceedings Trim Size: 9in x 6in dark2007 of the high conductivity and the magnetic fields form Alfv´en waves, i.e. a travel-ing oscillation of ions and the magnetic field. The ion mass density provides theinertia and the magnetic field line tension provides the restoring force. The wavepropagates in the direction of the magnetic field with the Alfv´en speed, althoughwaves exist at oblique incidence and smoothly change into magnetosonic waveswhen the propagation is perpendicular to the magnetic field. If the wavelengthof the Alfv´en waves equals a multiple of the gyration radius of a CR, resonantscattering occurs, which leads to a change in pitch angle of the CR (pitch anglescattering) without changing its energy. Such a process leads to a random walkof CRs, which can be described by a di ff usion equation (see review in Ref. ). Ifthe B-field has no preferred direction, i.e. if the turbulent small scale componentis much stronger than the regular large scale component, the waves propagate ran-domly in all directions and the di ff usion of CRs is isotropic. From the isotropy ofCRs one usually assumes the propagation to be isotropic.Most primary nuclei show a power law spectrum falling with energy like E − . .This can be easily tuned by selecting the injection spectrum of the primary parti-cles accordingly. However, since the inelastic cross sections for secondary parti-cle production are usually not strongly energy dependent at higher energies, thiswould lead to rather flat spectra for the secondary / primary ratios in contrast tothe observed B / C ratio, which shows a maximum at about 1 GeV / nucleon and de-creases as E − . towards higher energy. This can be accommodated by assumingenergetic particles di ff use faster out of the Galaxy, i.e. the di ff usion constant isproportional to E . . This reduces the high energy part of the B / C spectra. Thedecrease at low energies can be accommodated by di ff usive reacceleration, whichshifts the spectrum to higher energies. Alternatively, one can have a strong in-crease of the di ff usion coe ffi cient at low energies because of the damping of theAlfv´en waves, thus reducing the B / C ratio at low energies as well.Both stable and unstable nuclei are produced in supernovae (SNe) explosionswith a ratio given by their known production cross sections. From the decay timeand the remaining amount of the unstable nuclei one can reconstruct the time ofCRs needed for their journey from the source to our local cavity, so they act as“cosmic clocks”. Such measurements yield an average residence time of CRs inthe Galaxy of the order of 10 yrs. Since they travel with relativistic speeds thelong residence time requires that they cannot move rectilinear from the source tous or to outer space, but the CRs must be scattering many times without loosingtoo much energy, i.e. the di ff usion must be e ff ective. During their journey CRsmay interact with the gas in the Galaxy and produce secondary particles. Thischanges the ratio of secondary / primary particles, like the B / C ratio. From the res-idence time and the amount of secondaries one can estimate the grammage, i.e. ovember 27, 2018 2:15 WSPC - Proceedings Trim Size: 9in x 6in dark2007 the amount of matter traversed by a CR during its lifetime t CR , which is given by ρ ct CR , where ct CR is the path length for a particle traveling with the speed of light c . It was found to be of the order of 10g / cm , which corresponds to a density ofabout 0.2 atoms / cm . This is significant lower than the averaged density ofthe disk of 1 atom / cm , which suggests that CRs travel a significant time in lowdensity regions, like the halo.The most advanced program providing a numerical solution to the di ff usionequation is the publicly available GALPROP code. The basic parameters arethe injection spectrum parameters, the di ff usion coe ffi cient, the convection speed,the Alfv´en speed and the size of the halo. The latter determines the CR residencetime inside the Galaxy, since as soon as they pass the border, they are assumedto escape to outer space. By tuning these parameters to the secondary / primaryspectra and the unstable / stable spectra one obtains a self-consistent propagationmodel of our Galaxy. The amount of secondary CR particles and gamma rays aredescribed by this model by the cross sections of the interactions of the primaryand secondary CR with the gas of the disk using a network with more than 2000cross sections. This is one of the great triumphs of GALPROP.Remaining problems are connected with the large scale structure of the propa-gation in the Galaxy, as sampled by gamma rays. The problems are twofold. Firstof all the gamma rays in the GeV range, which are mainly produced by inelasticcollisions of CRs with the gas of the disk, show a too small radial gradient: largeamounts of gamma rays are produced at large longitudes, i.e. towards the Galac-tic anticentre. This is unexpected, since the main sources of CRs are assumed tobe the SNe explosions, which are preferentially located at radii of a few kpc. Inaddition the gas decreases at large radii and the gamma ray flux is proportionalto the cosmic ray density times the gas density. This problem can be remedied byassuming much more gas at large radii than determined from the molecular hydro-gen ( H ) tracer, which is the λ = . = = H molecules. Explaining additional gas at large radii requires astrong radial dependence of the ratio X CO = N ( H ) / N ( CO ), i.e. X CO increases byan order of magnitude from the inner Galaxy to the outer Galaxy. An alternativeexplanation is provided by the Galactic wind models, in which case the transportfrom the disk to the halo is provided by the mass outflow from the disk to the halofrom the SNe explosions, which has a strong radial dependence because of thestrong radial dependence of the observed SNR. This leads to strong anisotropicpropagation with the convection being strongest in the regions with the highestcosmic ray pressure from the SNR, i.e. at distances between 4 and 10 kpc. Atsmaller radii the gravitational potential of the bulge limits the outflow, while at ovember 27, 2018 2:15 WSPC - Proceedings Trim Size: 9in x 6in dark2007 larger radii the CR pressure decreases. This reduces the CR intensity in the diskand the corresponding gamma ray production at the position of the sources.The second GALPROP problem is its failure to describe the EGRET excess ofgamma rays, which can be remedied by dark matter annihilation, as discussed insection 2. If one attributes the EGRET excess to DMA one runs into the problemof a too large flux of antiprotons, as discussed in detail by Bergstr¨om et al. Wehave implemented the DMA as a source term into the publicly available GAL-PROP code b and find a similar result, as shown in the left panel of Fig. 4 Thisis not surprising, since GALPROP uses the same priors as the program used byBergstr¨om et al.: (i) the propagation is dominated by di ff use scattering, which isassumed to be isotropic, i.e. the same in the halo and the disk (ii) the gas in the diskis smoothly distributed (iii) the influence of observed regular magnetic fields canbe neglected. These priors fulfill the basic picture of the origin and propagationof cosmic rays discussed above. The main reason for the large flux of antiprotonsfrom DMA is not that DMA produces so many antiprotons, but the fact that theresidence time of charged particles is required to be of the order of 10 yrs, as de-termined from the cosmic clocks. The last requirement can be fulfilled in a modelwith isotropic di ff usion only with a large halo, so CRs do not escape, but they per-form random walks in a large volume. In this case there is no di ff erence betweenprimary particles produced by SNe or primary particles produced by DMA, so all CRs are stored inside the Galaxy. In this case DMA increases the averaged den-sity of antiprotons by orders of magnitude, so the flux of antiprotons becomes ofthe same order of magnitude as the EGRET excess. Note that the production ratioof antiprotons / gammas from DMA is only at the percent level, as is well knownfrom accelerator experiments for the fragmentation of mono-energetic quarks. Ifone assumes that the propagation is not isotropic, the picture completely changes:the DMA antiprotons may be transported quickly to the halo by a combination ofconvection or fast di ff usion along the regular magnetic fields depicted in Fig. 5.Such an anisotropic propagation model will be discussed in the next section.
4. The Antiproton Flux from DMA in an Anisotropic PropagationModel
The propagation picture with isotropic propagation, as discussed above, is basedon hydromagnetic wave theories, in which the turbulent small-scale componentsof the magnetic field dominate over or are at the same order of magnitude as theregular large scale components. However, the turbulence is expected to be di ff er-ent in the halo and the disk, since the disk is not fully ionized in contrast to the b The GALPROP code can be obtained from http: // galprop.stanford.edu / . ovember 27, 2018 2:15 WSPC - Proceedings Trim Size: 9in x 6in dark2007 Energy [GeV] -3 -2 -1
10 1 10 G e V ] - s - s r - F l u x [ m -4 -3 -2 -1 Cosmic Rays +DMCosmic Rays
Energy [GeV] -3 -2 -1
10 1 10 G e V ] - s - s r - F l u x [ m -4 -3 -2 Cosmic Rays+DMCosmic Rays
Fig. 4:
Comparison of the antiproton production including DMA in the conven-tional model with isotropic propagation (left) and a model with anisotropicpropagation (right).halo. This implies that the Alfv`en waves are e ffi ciently dissipated in the disk byion-neutral damping. Furthermore the most important contribution to the randomfield in the disk is by turbulent mass motions, induced by supernova explosionsand other stellar mass loss activity, which leads to a di ff erent wave spectrum inthe disk as compared to the halo, thus leading to di ff erent di ff usion coe ffi cients inthe halo and disk. In addition one expects the di ff usion along the regular mag-netic fields to be an order of magnitude faster than the di ff usion perpendicularto the magnetic fields, even if the turbulent component is of the same order ofmagnitude (see e.g. and references therein). These analytical estimates of fastdi ff usion along the regular magnetic field lines as compared to the transverse dif-fusion were confirmed by following the trajectories of CRs in realistic magneticfields with both a regular and turbulent component. Given the toroidal field inthe disk found that the di ff usion along the azimuthal magnetic field is one totwo orders of magnitude faster than the transverse di ff usion. This means that CRspreferentially di ff use along the toroidal fields just above or below the disk or intothe halo via the poloidal fields sketched in Fig. 5. In such a picture our localcavity is situated between two thick pancake-like structures of higher CR densityonly 300 pc apart in the z-coordinate. This leads to a reduced grammage comparedwith the CR density, which is maximal in the disk, a longer residence time, a re-duced radial gradient in the gamma ray flux and an isotropization of the CR flux,all features di ffi cult to explain simultaneously in an isotropic propagation modelswith a source distribution located towards the centre.Another possible e ff ect concerning charged particles di ff using fast along reg- ovember 27, 2018 2:15 WSPC - Proceedings Trim Size: 9in x 6in dark2007 Fig. 5:
Left: a schematic picture of the magnetic fields in the Milky Way, consist-ing of a dipole (poloidal) field component (strongest in the center) and acircular (toroidal ) field component, which is strongest just above and be-low the disk at a distance of 150 pc (from Ref. ). Right: a parametrizationof the toroidal component (from Ref. ).ular magnetic field components is related to the molecular clouds: the gas densityin the disk varies from 10 − cm − in the warm ionized medium to 10 -10 cm − inclumps of cold gas with a size of a few pc. In the centre of these clumps the densitymay be as high as 10 cm − in dense molecular clouds (MC), where star formationoccurs. On average the gas density is 1 cm − in the disk. Inside these MC mag-netic fields far above the random components have been observed (see Ref. foran excellent review). What is more important, these fields seem to be correlatedwith the observed static magnetic fields outside the MCs. This can only be un-derstood, if the MCs remember the large scale magnetic fields in the interstellarmedium, i.e. if during the contraction flux freezing occurs. In this case the mag-netic field lines from the ISM will become highly concentrated near the MCs andCRs in the ISM, which preferentially di ff use fast along these field lines, will be re-flected by the higher density of the field lines near the MCs. So, as worked out byChandran. the MC act like magnetic mirrors for CRs, just like the concentrationof magnetic field lines near the poles from the earth trap the CRs in the famousVan Allen radiation belts. The large distances (10-100 pc scale) between the MCallows to trap particles up to the TeV scale, thus increasing the grammage and theresidence time, which are now increased by the trapping time between the MC inthe disk, not by how often they pass from the halo to the disk, as is the case inthe isotropic propagation model. So the halo size is not a sensitive parameter any-more and particles, once in the halo, will be preferentially transported away fromthe disk by a combination of convection or fast di ff usion along the regular field ovember 27, 2018 2:15 WSPC - Proceedings Trim Size: 9in x 6in dark2007 lines in the halo. It should be noted that only a small fraction of the CRs enter theMCs, if these act as magnetic mirrors. This could explain why positrons mainlyannihilate in the gas between the MCs, not with electrons from molecular hydro-gen inside the MCs, as deduced from the annihilation line shape. Of course,one could argue that although the MCs make up the largest mass fraction, theyhave the lowest filling factor. But if they have strong magnetic fields, the CRs areexpected to be tunneled towards the MCs by the high concentration of magneticfield lines.How can one implement such a propagation model? Existing programs arenot suitable. E.g. the CR tracing programs calculating the trajectories in a mag-netic field do not calculate all secondary particles and the GALPROP programwith isotropic di ff usion does not have a regular magnetic field in the propagationof charged particles. However, the basic modifications needed are: the propaga-tion follows preferentially the regular magnetic field lines, which are toroidal inthe disk and poloidal in the halo. Such a propagation would require tuning the3D version of GALPROP. However, this takes an excessive amount of CPU time.Therefore transporting the CRs to the halo by a combination of fast di ff usion andconvection in the z-direction in the 2D version is much more e ff ective and leads tothe same e ff ect: CRs in the halo will hardly come back to the disk. But it should bekept in mind that the parameters are e ff ective parameters in a simplified axisym-metric 2D version of the 3D reality, which has also preferred di ff usion directionsin the disk.We have modified the publicly available source code of GALPROP by (i) al-lowing for a di ff usion tensor instead of a di ff usion constant, thus modifying thedi ff usion equation and the Crank-Nickelson coe ffi cients accordingly; (ii) allowingan inhomogeneous grid in order to have step sizes below 100 pc in the disk re-gion and large step sizes in the halo; (iii) implement the dark matter annihilationas a source term of stable primary particles, especially antiprotons, positrons andgamma rays. The dark matter distribution was taken to be the one obtained fromthe EGRET excess, as discussed above. The grammage and escape time were ad-justed for charged particles to account for the fact that secondary particles are nowproduced largely locally, since particles produced far away from the solar systemare likely not to reach our local cavity. If in addition the trapping between molec-ular clouds is e ff ective, only a small fraction of CRs will penetrate the MCs andmost of them will be reflected. But the grammage in between the MCs will beenhanced by the multiple passages from the mirroring, so one would expect it toincrease the grammage and residence time by the same factor. This turns out to beworking, so this was simply introduced in GALPROP as a constant g, called gram-mage parameter, multiplying the HI and HII gas densities. A grammage paramater ovember 27, 2018 2:15 WSPC - Proceedings Trim Size: 9in x 6in dark2007 Energy [GeV/nucleon] -3 -2 -1
10 1 10 B / C Anisotropic Diffusion (with trapping between MCCs)Isotropic Diffusion (Conventional Model) energy [GeV/nucleon] -3 -2 -1
10 1 10 B e10 / B e9 -1 Anisotropic Diffusion (with trapping between MCCs)Isotropic Diffusion (Conventional Model)
Fig. 6:
Comparison of the secondary / primary ( B / C ) ratio and unstable / stable( Be / Be ) ratio in the conventional model with isotropic propagation andmodel with anisotropic propagation.of about 12 is needed to describe the B / C ratio combined with the Be / Be ratio.Note that this grammage parameter determines the local production of chargedparticle, so this grammage parameter is not necessarily the same as the grammageneeded for the gamma ray production, since the latter is determined by the largescale gas densities. Given the large fluctuations in and strong radial dependenceof the gas densities the di ff erence can be large. Also the CR density is expected tohave a radial dependence because of the convection having a radial dependence, asdiscussed before. The CR density can also have strong variations from the fact thatAlfv´en waves can be damped in high density gas regions, thus leading to strongvariations in the di ff usion coe ffi cient and corresponding CR density variations.The transport from the disk to the halo is quite uncertain. It should be notedthat the average scale height of SNIa is expected to be about 300 pc (thick disk)and the ejecta connect to the halo in chimney like structures (see e.g. Ref. andreferences therein), which can drive magnetic field lines towards high altitudes ( ≈ ff usion.This was simulated as an enhanced convection term starting at v = km / s at100 pc above the disk and then increasing with the distance z above the disk as dv / dz = km / s . The remaining GALPROP parameters can be found in Ref. Asshown in Figs. 4 and 6 the antiproton flux, the B / C ratio and the Be / Be ratio areall well described by this set of parameters. Clearly, the excess of di ff use gammarays can be well described together with the B / C ratio and the antiprotons.In summary, we do not believe that the DMA interpretation of the EGRETis ”excluded by a large margin” because of the overproduction of antiprotons as ovember 27, 2018 2:15 WSPC - Proceedings Trim Size: 9in x 6in dark2007 claimed by Bergstr¨om et al. Such a statement is only valid within their propa-gation model based on isotropic propagation . Anisotropic models with di ff erentpropagation in the halo and the disk can perfectly describe all observations inclu-ding DMA.
5. Positron Annihilation in our Galaxy
Additional support for the propagation picture with anisotropic propagation, asdiscussed in section 4, comes from the positron annihilation signal observed bythe INTEGRAL satellite.
Since positron annihilation is only e ffi cient at non-relativistic energies, the positrons must have energies in the MeV range. Sourcesof such positrons are largely coming from the decay of radioactive nuclei ex-pelled by dying stars, especially SNIa, since in this case the core makes up a largefraction of the mass. This makes it easier for the positrons to escape from therelatively thin layer of the ejecta. Light curves, which are sustained first by thegamma rays in the shock waves and later by the electrons and positrons, suggestthat only a few percent of the positrons escape from the ejecta and can annihilateoutside after thermalization. Positrons annihilating inside the ejecta will producealso gamma rays, but these will not be visible as a single 511 keV line because offurther interactions in the shock wave.The main observation is that the 511 keV line from the annihilation betweenthermalized positrons and electrons (either free or bound in nuclei) is largely con-fined to the bulge with a bulge / disk (B / D) ratio of a few, although additionaldata suggests a lower ratio. Taking the dominant source to be SNIa, one wouldexpect a B / D ratio to be well below one, because of the higher mass in the diskand the higher rate of SNIa explosions expected in the thick disk as comparedto the bulge. An additional problem presents the observation of the 1.8 MeVline from the Al radioactive isotope, which has clearly been observed, both inthe bulge and the disk by the Comptel detector on NASA’s CGRO observatory. These nuclei are thought to be produced by nucleosynthesis in massive stars in thethin disk and yield in their decay on average 0.85 positrons. Because of their non-relativistic speed and high charge Al nuclei loose their kinetic energy rapidlyand decay with a half life time of about 10 years close to the position where theywere created. The observed flux of positron annihilation in the disk seems to besaturated already by the positrons from Al and T i decays. So what happenedto the positrons from SNIa explosions in the disk?In an anisotropic propagation model a large B / D ratio for the positrons is ex-pected, since the bulge is a much more extended object than the disk, so the parti-cles have much more time to thermalize and annihilate in the bulge than in the diskbefore reaching the halo. Once in the halo they move away from the disk, where ovember 27, 2018 2:15 WSPC - Proceedings Trim Size: 9in x 6in dark2007 there is hardly any gas for them to annihilate. As mentioned before the fountainlike structures of SNR (see e.g. Refs. and references therein) can drive mag-netic field lines towards high altitudes ( ≈ ff usion for the relativistic positrons.A fraction of the positrons escaping the disk may move by the poloidal field tothe bulge, thus enhancing the B / D ratio. So the problem of the large B / D ratio forpositron annihilation is intimately related to the propagation of the positrons. Ina conventional propagation model without magnetic fields and homogeneous gasdistributions the positrons annihilate near their source and one must resort tonew positron sources specific for the bulge, like DMA of very light WIMPS.
The WIMP masses have to be below of few MeV, since else they would be visi-ble by synchrotron radiation above the limits set by Comptel and EGRET.
Inanisotropic propagation models the low strength of the annihilation signal in thedisk is simply a consequence of the fact that the disk is so thin, so positrons can es-cape easily to the halo, where they find no partners to annihilate. So it is the samesolution required by the ratio of antiprotons and EGRET excess of gamma rays:fast di ff usion perpendicular to the disk either by the regular magnetic fields orconvection. In this case no unnatural light WIMPs are needed. Such light WIMPswould need additionally new gauge bosons to have a large enough annihilationcross section compatible with Eq. 1.
6. Constraints from direct dark matter search experiments
Direct detection experiments search for signals of dark matter particles elasticallyscattering o ff the nuclei in their detector. The event rate is given by Γ = < σ v > n ,where n is the local number density of WIMPS, v the velocity between detec-tor and WIMP and σ the scattering cross section. The brackets indicate that theaverage over the velocity distribution and corresponding cross sections has to betaken. No positive results have been reported and experimental limits on the crosssection have been derived under the assumption that the local density of WIMPScorresponds to 0 . GeV / cm , as estimated from the rotation curve (see e.g. a re-cent review by Spooner ). The best limit obtained by the XENON10 experimentis about 5 . − pb at 90% C.L. for a 50 GeV WIMP. This is below the crosssection limit expected from the EGRET data, if one assumes the minimal super-symmetric model to be valid. The region allowed by all constraints (WMAP, LEPlimits on charginos and Higgses, b → s γ branching ratio, EGRET mass limits)is shown in Fig. 7 together with the limits from some typical direct dark mat-ter search experiments. No signal was found sofar, so the regions above theselines are excluded. Naively one could conclude that the DMA interpretation ofthe EGRET excess combined with all electroweak and relic density constraints ovember 27, 2018 2:15 WSPC - Proceedings Trim Size: 9in x 6in dark2007 m c [GeV] s S I ( c , n / p ) [ pb ] DAMA
C D M S E D E L W E I S S
C R E S S T X E N O N a ll o w e d b y E G R ET , Wc h , m h a nd B r ( b → c s g ) allowed bym c – , W c h ,m h and Br(b →c s g ) a ll o w e d b y m c– , m h , B r ( b → c s g ) , E G R ET , Wc h -9 -8 -7 -6 -5 Fig. 7:
The spin-independent cross section for neutralino-nucleon scattering com-pared with experimental constraints: the region above the XENON10 limitis excluded. Details can be found in Ref. (green region in Fig. 7) is excluded by the XENON10 data. However, there aresevere caveats. First of all, the event rate in these experiments is proportionalto the cross section and the local WIMP density. Both have large uncertainties:the cross section is model dependent and has only been calculated in the min-imal supersymmetric models. Although the EGRET data is perfectly consistentwith supersymmetry, it does not prove supersymmetry and in e.g. extra dimensionmodels the cross sections could be very di ff erent. Secondly the local relic densityhas large uncertainties, because the densities obtained from the rotation curve donot say anything about the clustering of dark matter, but yield only an averageddensity. From N-body simulations one knows that dark matter is clumpy, as can beexpected already from the fact that galaxies are formed by dark matter starting topull together from the initial density fluctuations in the early universe. The numberof clumps is very large because of the steep decrease of the mass spectrum withincreasing mass ( ∝ M − ) and the lightest clumps are very light (about 10 − M ⊙ ,see Ref. ). But even with this large number of clumps the probability of finding aclump in the solar neighbourhood is small, so the direct searches are more likelyto observe first interactions from the di ff use component, which originates from the ovember 27, 2018 2:15 WSPC - Proceedings Trim Size: 9in x 6in dark2007 tidal stripping of the clumps. How many are disrupted is an ongoing debate (seee.g. Refs. ), but it certainly depends sensitively on the dark matter profile of theclumps. These profiles cannot be calculated yet reliably from N-body simulations.It is conceivable that the density of the di ff use component is an order of magni-tude less than the clumpy component, so any statements concerning exclusionsfrom direct dark matter detection experiments should take this into account.
7. Conclusion
With an anisotropic propagation model the amount of antiprotons expected fromDMA annihilation can be reduced by one to two orders of magnitude. Thereforethe claim by Bergstr¨om et al. that the DMA interpretation of the EGRET excessof di ff use Galactic gamma rays is excluded “by a large margin” is strongly pro-pagation model dependent. It only applies for their simplified propagation model,which assumes the same di ff usion in the halo and in the disk. An anisotropic prop-agation model with di ff erent propagation in the halo and the disk can reconcilethe EGRET excess with the antiproton flux and the ratios of secondary / primaryand unstable / stable nuclei. In addition the di ff erence in geometry between bulgeand disk leads to much more radiation and annihilation of positrons and electronsin the bulge as compared to the disk, thus alleviating the need to introduce newsources of positrons and electrons for the bulge to explain the INTEGRAL excessof the 511 keV line in the bulge. Direct dark matter search experiments reach thecross section range expected from the EGRET excess. However, the experimen-tal limits are inversely proportional to these cross sections times the local relicdensity. Both are uncertain: for the cross section one assumes the WIMPS arethe lightest supersymmetric partners of the minimal supersymmetric model withgravity inspired breaking of supersymmetry, while for the local relic density oneassumes the WIMPS are smoothly distributed instead of the expected distributionin clumps. The clumpy nature can drastically reduce the local density if we arenot located inside a clump.In summary we consider DMA is a viable explanation of the EGRET excess ofdi ff use Galactic gamma rays, especially since it is observed with the same shape ofthe fragmentation of mono-energetic quarks in all sky directions and the intensitydistribution of the excess traces the DM profile, as shown independently by therotation curve, the gas flaring and the N-body simulation of the disruption of theCanis-Major satellite galaxy. ovember 27, 2018 2:15 WSPC - Proceedings Trim Size: 9in x 6in dark2007
8. Acknowledgements
I wish to thank the organizers for the kind invitation to this splendid conference.Furthermore I thank P. Blasi, D. Breitschwerdt and N. Prantzos for helpful dis-cussions and my close collaborators I. Gebauer, D. Kazakov, M. Weber and V.Zhukov for their contributions.This work was supported by the BMBF (Bundesministerium f¨ur Bildung undForschung) via the DLR (Deutsches Zentrum f¨ur Luft- und Raumfahrt).
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