Dark Matter implications of the Fermi-LAT measurement of anisotropies in the diffuse gamma-ray background: status report
Mattia Fornasa, Jesus Zavala, Miguel A. Sanchez-Conde, Francisco Prada, Mark Vogelsberger
aa r X i v : . [ a s t r o - ph . C O ] O c t Dark Matter implications of the Fermi-LAT measurement of anisotropies in thediffuse gamma-ray background: status report
Mattia Fornasa a,b , Jesus Zavala c , Miguel A. S´anchez-Conde d , Francisco Prada a , Mark Vogelsberger e a Instituto de Astrof´ısica de Andaluc´ıa - CSIC, Glorieta de la Astronom´ıa, E-18008, Granada, Spain b MultiDark fellow c Department of Physics and Astronomy, University of Waterloo, 200 University Avenue West, Waterloo, Canada d KIPAC - SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, CA 94025, USA e Harvard-Smithsonian Center for Astrophysics, 60 Garden St., Cambridge, MA 02138, USA
Abstract
For the first time, the Fermi-LAT measured the angular power spectrum (APS) of anisotropies in the diffuse gamma-raybackground. The data is found to be broadly compatible with a model with contributions from the point sources inthe 1-year catalog, the galactic diffuse background, and the extragalactic isotropic emission; however deviations arepresent at both large and small angular scales. In this study, we complement the model with a contribution from DarkMatter (DM) whose distribution is modeled exploiting the results of the most recent N -body simulations, consideringthe contribution of extragalactic halos and subhalos (from Millenium-II) and of galactic substructures (from Aquarius).With the use of the Fermi Science Tools, these simulations serve as templates to produce mock gamma-ray count mapsfor DM gamma-ray emission, both in the case of an annihilating and a decaying DM candidate. The APS will then becomputed and compared with the Fermi-LAT results to derive constraints on the DM particle physics properties. Thepossible systematic due to an imperfect model of the galactic foreground is also studied and taken into account properly.The present paper reports on the status of the project. Keywords:
Dark Matter, anisotropies
1. Introduction
The Isotropic Gamma-Ray Background (IGRB) can bedefined as the radiation that remains after the resolvedsources (both point-like and extended) and the galacticforeground (produced from the interaction of the cosmicrays with the interstellar medium) are subtracted from thetotal gamma-ray emission. The most recent measurementof the IGRB energy spectrum was done by the Fermi-LATtelescope and presented in Refs. [1, 20]. Contrary to whatwas found by the EGRET telescope [3, 4], the IGRB ap-pears to be perfectly compatible with a power-law with aslope of − .
41, at least up to 10 GeV.The contribution of unresolved sources, both extra-galactic (e.g., blazars [5, 6, 7, 8, 9, 10, 11], star-forminggalaxies [6, 12] and radio galaxies [14, 13]) and galacticsources (like milli-second pulsars [15]) have been consid-ered. The contribution of each class is estimated frompopulation studies of the detected objects (see Ref. [11]for an example in the case of blazars) and it turns out thatall the components considered up to now may not be ableto account for the whole IGRB [16]. Thus there may beroom for additional contributions like, e.g., that of DarkMatter (DM) [17, 18, 9, 19, 2]. Actually, the authors ofRef. [2] have already used the Fermi-LAT measurement ofthe IGRB intensity to constrain the properties of the DMparticle, finding that, in their most optimistic scenario, values larger than 10 − cm s − for the annihilation crosssection ( σ ann v ) can be excluded.Complementary to the energy spectrum of the IGRB,we can also the recent analysis of the angular power spec-trum (APS) of anisotropies in the diffuse gamma-ray back-ground [21, 22, 23] to study the nature of the IGRB. Theanalysis was conducted by the Fermi-LAT collaborationand resulted in the detection of some angular power abovemultipoles of ℓ > σ ,in the each of the energy bins between 1 GeV and 10 GeV.More detailed information on this measurement will beprovided in Sec. 2. We simply note here that, even if sucha detection seems to be compatible to the signal predictedfor a population of unclustered, unresolved blazars, it canstill be used to put some useful constraints on the nature ofthe DM particle. The goal of the present work is to derivethose constraints using state-of-art numerical simuations.The project is divided in two parts: in the first onewe will make use of the most recents results from N -bodysimulations to derive all-sky maps of gamma-ray emissionfrom DM annihilations and decay. We will consider thecontributions of i ) extragalactic halos and subhalos (basedon the Millennium II N -body simulation [24]), ii ) the emis-sion from the smooth halo of the Milky Way (modeled as inRef. [25] and iii ) its subhalos (from the results of Aquar-ius [26, 27]). Moreover, we will also consider the emission Preprint submitted to Elsevier July 2, 2018 rom halos and subhalos below the mass resolution of thetwo simulations mentioned above, down to the minimalhalo mass M min . The all-sky maps will then be used tocompute the APS of anisotropies in the gamma-ray emis-sion from DM annihilation and decay. We plan to presentthe results of this first part in Ref. [28], where we will alsostudy the dependence of the APS from the assumptionsmade while building the maps of DM-induced gamma-rayemission. Refer also to Secs. 3 and 4 for more informationon this first part.The second part of the project will deal with the com-parison with Fermi-LAT APS data. The simulation mapsproduced in Ref. [28] will be used as templates for theDM contribution to the IGRB. We will use the most recentFermi Instrument Response Functions (IRFs) to estimatehow experimental issues may affect the APS. It will beparticularly important to take correctly into account theexperimental Point Spread Function (PSF) and the Fermi-LAT exposure. We will finally use the APS measurementto derive constraints on the nature of DM taking into ac-count also the constraints from the new measurement ofthe IGRB energy spectrum (see also Sec. 5).We will conclude this small introduction reminding thatthis note should be considered just as a status report, sincenone of the two parts of the project is complete up to now.We will present some preliminary results in Secs. 3 and 4,but we will mainly focus here on the methodology, empha-sizing that the final results will be extensively presentedin the near future [28].
2. Fermi-LAT measurement of the anisotropies inthe diffuse gamma-ray background
For the analysis in Ref. [23] the first 22 months ofFermi-LAT data have been analyzed, dividing the energyrange between 1 GeV and 50 GeV in 4 energy bins. Thepoint sources in the first 1 year catalog [29] have beenmasked, as well as the emission within a band of 30 de-grees above and below the galactic plane. This was doneto cover the regions in the sky where the emission is dom-inated by resolved sources and by the galactic foregound,and to restrict the analysis only to where the IGRB isa significant component. We note here that the analy-sis performed in Ref. [20] to measure the IGRB intensityspectrum is different since templates of emission are imple-mented to subtract known components in the gamma-rayemission, instead than masking portions of the sky. Thus,strictly speaking, the data used in Ref. [23] and analyzedto derive the APS are not the same used for the IGRBenergy spectrum in Ref. [20]. Moreover, even at high lat-itudes ( | l | ≥ ◦ ) the galactic emission is still importantand non-negligeble. We therefore expect that some level ofcontamination in the APS may be present from this kindof background. These contaminations are supposed to belocated primarly at low angular multipoles ℓ (large an-gular scales) and so only multipoles larger than 155 have been considered in Ref. [23]. On the other hand, mul-tipoles larger than 504 are also discarded since, at thesesmall angular scales, the signal is strongly damped by theexperimental PSF.Two definitions of APS are used: i ) the intensity APSas in Eqs. 1 and 2 below, for which the intensity gamma-ray maps are decomposed directly in spherical harmonics a ℓ,m = Z I (Ψ) Y ⋆ℓ,m (Ψ) d Ω , (1) C ℓ = | ℓ | X −| ℓ | | a ℓ,m | , (2)and ii ) the fluctuaction APS, that can be derived bythe intensity one, dividing for the average intensity squared.As a consequence, the fluctuation APS will not dependon the energy of the emission, if the distribution of thesources is energy-indenpendent.The Fermi-LAT reported detection of angular powerin all the 4 energy bins considered, with a significance oflarger than 3 σ in the energy bins from 1 GeV to 10 GeV.The data have been compared with the power spectrumof a source model made of i ) the point-like sources in Ref.[29], ii ) a model for the galactic foreground and iii ) anisotropic component at the level of the IGRB in Ref. [20].In the same regions outside the mask defined above, thegeneral features in the APS of the model are similar tothose in the data, but the model APS does not accuratelyreproduce the data APS in all energy bins on small or largeangular scales. Furthermore, the model angular power at155 ≥ ℓ ≥
504 is consistently below that measured in thedata.This seems to point to the possibility of having a pop-ulation of unresolved sources contributing to the APS, inorder to explain the data. The fact that the intensityAPS is compatible with being independent of multipole,together with the way the intensity and fluctuation APSchanges in the 4 energy bins suggests that one or morepopulations of unresolved, unclustered classes of sourcesmay be responsible for the missing power.If this hypothesis is true, then the data will provide ussome useful constraints on the DM particle: the normaliza-tion and shape of the APS from DM annihilation has beenstudied extensively in the last years, focusing on the case ofextragalactic halos and subhalos [18, 9, 30, 31, 32], on thecase of a galactic component [34, 33, 10] or both [19, 35].Comparing model predictions with the Fermi-LAT APSdata allows us to put constraints on how important areDM-induced gamma-rays in the IGRB and, consequently,draw exclusion lines on the annihilation cross section, orother quantities more difficult to constrain like the mini-mal halo mass M min .
3. Extragalactic halos and subhalos
This section and the next one will be devoted to de-scribe the methodology that will be used to compute the2aps of DM-induced radiation. To model the extragalac-tic emission, we use the catalogs of halos and subhalos ofthe Millennium-II N -body simulation: the simulation boxis a cube with a size of 100 Mpc /h and it contains DMhalos and subhalos down to a mass resolution of M res =6 . × M ⊙ /h [24]. Halo catalogs are available at mul-tiple snapshots with different redshifts up to z = 127. Weanalyze them in a very similar way to what has been donein Ref. [32]: we will only consider objects with more than100 particles and derive the properties of each halo (DMprofile, luminosity and concentration) from the maximalcircular velocity V max and radius r max (corrected from spu-rious effects related to numerical resolution, as done inRef. [32]) and assuming a Navarro-Frenk-White (NFW)profile [36]. Since we want to probe a volume which ismuch larger than the Millennium-II simulation box, weimplement the same technique described in Ref. [32] toconstruct sky-maps of the extragalactic signal, dividingthe past light-cone in concentric shells (each of them at aparticular redshift) and then filling them up with identi-cal copies of the Millennium-II simulation boxes at thatparticular redshift (see Fig.9 in Ref. [32]). Each cubeis randomly rotated and translated in order to avoid anyboundary effect. In this way one can compute the lumi-nosity from a particular direction in the sky Ψ simply byaccounting for all the halos encountered in the direction ofΨ. This was done for all halos above Millennium-II massresolution and you may see the results in Fig. 1 up to a z = 2 . M res . Actually,the authors of Ref. [32] already considered this contri-bution: fitting the Millennium-II halos, they derived thecumulative luminosity function F ( M ) = P L/ ¯ M ∆ log M ,providing the total luminosity of main halos with a massbetween M and M + dM . Then, they assumed that F ( M )can be extrapolated below M res in order to compute thegamma-ray flux predicted from main halo between M min and M res . This quantity was then used to boost up the lu-minosity of halos with a mass between 1 . × M ⊙ /h and6 . × M ⊙ /h . This was done under the assumption thatthe distribution of main halos below M res follows exactlythat of those between 1 . × M ⊙ /h and 6 . × M ⊙ /h ,such an approach is by the fact that the two-point correla-tion function (which is an indicator of clustering) is foundto reach a constant value when approaching M res (see Fig.10 of Ref. [24]).We want to test this assumption by implementing adifferent way of including the contribution of halos below M res . We will then look for differences in the APS to checkif the approach used to cover the range between M min and M res affects in any sense the shape of the APS. We there-fore proceeded as follows: • divide the range between M min and M res in massdecades ( M i , M i +1 ). For each mass decade, we con-sidered all the halos in the Millennium-II simula-tion box with a mass between 1 . × M ⊙ /h and6 . × M ⊙ /h and assign to each of them a newmass between M i and M i +1 , assuming masses fol-low a probability distribution equal to the halo massfunction dn/dM . • we also assign a luminosity to each of these halos.From these two quantities, we can completely derivethe halo profile. In this way, we end up by havinga box of simulated objects with masses between M i and M i +1 distributed as those between in the range1 . × − . × M ⊙ /h . • however, in the mass decades we are considering, thehalo mass function will predict more halos than wehave actually have in the simulated box. So, we stacktogether different copies of the box obtained in theprevious point until we reach the correct number ofhalos. The different copies are randomly rotated onewith respect to the other. • the box that comes out from the stacking is usedto fill up the region up to a maximal distance of R max , defined as the distance above which all halosin a given mass decade become point-like. Maps areproduced from this distribution of objects till R max . • for the regime beyond R max , we do not consider anystacking, we simply take the boxes coming from point2 of this list and create the sky-map from those. Mul-tiple copies of the map are then stacked together tillthe desidered flux is reached. Since we are now in theregime where halos are point-like, the procedure issimilar to what has been done below R max but with-out having to consider the 3D distribution of halos.This procedure, in a sense, moves in the opposite di-rection to what has been done in Ref. [32] since we startby assuming that halos below M res have the same distri-bution of those above, but then we pass through a lot ofindependent rotations so that, at the end, the final mapsare expected to be more isotropic than those in Ref. [32].Once we compute the APS from the two approaches wewill be able to see if differences show up in the shape ofthe APS.In Fig. 2 (left panel) the black crosses indicate theIGRB energy spectrum taken from Ref. [20]. The redpoints show the amount of flux produced in halos and sub-halos above M res until z = 2 . M res (implemented as described in the list above) theemission increases to be that one of the green points. Forannihilating DM the increase is approximately of an orderof magnitude, while for decaying DM it is completely neg-ligible (red and green empty points practically overlap).3 igure 1: All-sky maps of gamma-ray emission from DM annihilation (left panel) or decay (right panel) in halos and subhalos above themass resolution of Millennium-II, up to z = 2 .
6. Emission comes from hadronization of b quarks and is computed at 10 GeV. For the case ofannihilating DM, the mass is 200 GeV and the annihilation cross section 3 × − cm s − , while, for the decaying case, the mass is 2 TeVand the decay lifetime is τ = 2 × s. The total flux is still a factor of 100 (50) for annihilation(decay) below the IGRB, at least at 10 GeV.In order to complete the description of the extragalac-tic component, the only remaining ingredient is the emis-sion from subhalos below M res . Those will be describedfollowing the prescription derived in Ref. [37] and gener-alized in Ref. [38]. In the first reference the subhalos of theVia Lactea II N -body simulation are analyzed to computethe probability distribution P ( ρ, r ) of having a DM den-sity between ρ and ρ + dρ at a distance r from the centerof the MW halo. P ( ρ, r ) has two distinct components: i ) aparabolic regime due to the smooth halo and ii ) a power-law that extends to larger densities due to substructures(see Fig. 1 of Ref. [37]). The authors, then used P ( ρ, r )to compute the boost factor due to substructures, whileRef. [38] extended the prescription to halos larger andsmaller than the MW halos, having in mind the case ofgalaxy clusters and dwarf Spheroidal galaxies respectively.We will use it to boost up the emission of the halos below M res , accounting in this way for the emission of unresolvedsubhalos.
4. The Milky Way halo and its subhalos
We continue now with the implementation of the gamma-ray emission related to our own galaxy: we use the distanceof 700 kpc (approximately 3 times the virial radius of theMilky Way (MW) halo) as the limit between the extra-galactic and the galactic regime.The smooth halo of the MW is modeled with a NFWprofile with parameters taken from Ref. [25], a model thatis consistent with the available observation data on theMW. The total flux of the MW smooth halo is plotted inthe left panel of Fig. 2. It represents the largest amongthe different DM components plotted there. However weshould note that at the moment of computing the APS,we will mask the galactic plane, as it has been done bythe Fermi-LAT collaboration in Ref. [23]. This will have the effect of drastically decreasing the emission associatedwith the smooth halo.To include the galactic subhalos we will use the Aquar-ius N -body simulation [27]. The same procedure describedin the previous section will be used here for the Aquariussubhalos, without the need to considering replicas of thesimulation box since we are interested only in the regionwithin 700 kpc. The emission associated with galactic sub-halos is indicated as yellow points in Fig. 2. We have notyet implemented the contribution of subhalos below themass resolution of Aquarius M ′ res = 1 . × M ⊙ . Thiswill substantially increase the emission associated withgalactic subhalos, which is only subdominant if we onlyconsider objects above M ′ res .
5. Deriving constraints
The maps that will be obtained from the proceduresketched in the previous sections will then be used to com-pute the APS and to compare the results with the Fermi-LAT data. Some results can be seen in the central andright panels of Fig. 2 where the total fluctuation APS isplotted (black line). Also the contribution of the differ-ent components is present, multiplied by the square of theaverage flux of each component with respect to the to-tal average emission, so that the sum of the colored linesgives the total (black line) also visually. Let us stress thatthese are very preliminary results: not all the componentshave been included (the contribution of unresolved extra-galactic and galactic subhalos is missing) and we are notconsidering any mask.We can, however, already see some interesting trends: • the galactic component dominates the case of annihi-lating DM. This may change after we will include thecontribution of galactic subhalos less massive than M ′ res . • the extragalactic component below M res (both forannihilating and decaying DM) does not indicate any4 [MeV] ] - s r - s - / d E [ M e V c m Φ d E -7 -6 -5 -4 -3 -2 -1 Fermi-LAT IGRB res
Halos and subhalos larger than M res to MM -6 Halos with mass from 10MW smooth halo ’res
MW subhalos larger than M
Graph multipole l0 100 200 300 400 500 / < I > ^ [ s r ] l C -8 -7 -6 -5 -4 -3 -2 -1 Fermi APSTotal res
Halos and subhalos larger than M res to M M -6 Halos from 10 ’res
MW subhalos larger than M
Graph multipole l0 100 200 300 400 500 / < I > ^ [ s r ] l C -8 -7 -6 -5 -4 -3 -2 -1 Fermi APSTotal res
Halos and subhalos larger than M res to M M -6 Halos from 10 ’
MW subhalos larger than M
Graph
Figure 2: Left panel: Black crosses indicate the energy spectrum of the IGRB taken from Ref. [20]. Filled (empty) points refer to the case ofannihilating (decaying) DM. Red points indicate the flux coming from DM halos and subhalos above M res , while green points only considerthe extrapolation down to M min for main halos. Blue points show the emission from the smooth DM halo of the Milky Way, while the yellowones accounts for the emission from all the subhalos in the Aquarius simulation. The grey lines refer to the annihilation and decay energyspectrum (from the hadronization of b quarks) normalized to blue points. Central and right panel: APS of anisotropies in the gamma-rayemission from DM annihilation (central panel) and decay (right panel). The total fluctuation APS is plotted in black, while the colored linescorrespond to the different components, multiplied by the square of their average flux with respect to the total average flux. The red lineindicates the contribution of extragalactic halos and subhalos above the mass resolution of Millennium II. The green line refers to main halosbelow M res and down to M min , while the blue one accounts for the subhalos in the Aquarius simulation. intrinsic clustering, as expected. • the contributions of Aquarius subhalos (blue lines)and of Millennium-II halos and subhalos (red lines)decrease with multipole, a consequence of the factthat the APS is sensitive to the inner structures ofthe halos.In Fig. 2 we have also plotted the Fermi-LAT measure-ment of the fluctuation APS in the energy bin between 1GeV and 2 GeV. Some other ingredients are still neededin order to be able to perform a proper comparison be-tween the DM APS and the data. This will be done inthe future, taking into account experimental features likethe effect of the PSF, or a possible residual contaminationfrom the Galactic foreground. We plan to include the IRFof the telescope using the Fermi Science Tools and treatingthe DM component in the same way as one of the threedifferent components of the source model described in Sec.2.
6. Conclusions
Here we briefly summarized a project which is still inprogress. The goal is to compute realistic and completeall-sky maps of gamma-ray emission from DM annihilationand decay, taking into account the contribution of both ex-tragalactic and galactic halos and subhalos. For the mostmassive objects we will refer directly to the results of twoof the most recent N -body simulations (Millennium-II andAquarius), but we will also account for smaller halos, downto their minimal mass M min . Once obtained, these mapswill be used to compute the APS of anisotropies. Ourgoal is to compare it with the recent measurement of the APS by the Fermi-LAT collaboration in order to be ableto put constraints on the nature of the DM particle. Asthe project is still on-going, we only presented here themethodology and some preliminary results. We refer in-terested readers to keep an eye on the arXiv webpage forthe publication of the final results [28]. Acknowledgements
The simulations used in this paper were carried out inthe Cosmology Machine supercomputer at the Institute forComputational Cosmology, Durham. The Cosmology Ma-chine is part of the DiRAC facility jointly funded by STFC,the Large Facilities Capital Fund of BIS and Durham Uni-versity. We would also like to thank the Virgo Consortiumfor giving us access to the data of the Millnnium-II andAquarius simulations. Finally we thank the support of theConsolider-Ingenio 2010 Programme under grant Multi-Dark CSD2009-00064.
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