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APS/123-QED Astrophysical inputs on the SUSY dark matter annihilation detectability F. Prada1, A. Klypin2, J. Flix3, M. Mart´ınez3 and E. Simonneau4 1 Ramón y Cajal Fellow, Instituto de Astrof´ısica de Andaluc´ıa (CSIC), E-18008 Granada, Spain 2 Department of Astronomy, New Mexico State University, Las Cruces NM 88003-8001, USA 3 Institut de F´ısica D’Altes Energies, Universitat Autonoma, E-08193 Barcelona, Spain 4 Institut d’Astrophysique de Paris, CNRS, 75014 Paris, France (Dated: January 8, 2004) If dark matter (DM), which is considered to constitute most of the mass of galaxies, is made of supersymmetric(SUSY)particles,thecentersofgalaxies shouldemitγ-raysproducedbytheirself- 4 annihilation. Wepresentaccurateestimatesofcontinuumγ-rayfluxesduetoneutralinoannihilation 0 inthecentralregionsoftheMilkyWay. WeusedetailedmodelsofourGalaxy,whichsatisfyavailable 0 observationaldata,andincludesomeimportantphysicalprocesses,whichwerepreviouslyneglected. 2 Ourmodelspredictthatspatiallyextendedannihilationsignalshouldbedetectedathighconfidence levelsbyincomingexperimentsassumingthatneutralinosmakeupmostoftheDMintheUniverse n and that they annihilate according to current SUSYmodels. a J PACSnumbers: 98.80.-k,98.35.Ce,98.35Gi,95.35.+d,14.80.Ly 3 2 1 ofTImheargeinisgaAntminocsrpeahseirnicg ChˇoepreentkhoavtTtheleesnceowpesge(nIeArCatTiosn) YSUS= N2γmhσ2vi, U(Ψ0)=Z J(Ψ)B(Ω)dΩ, v χ would detect in the very near future the γ-ray signal 2 1 coming from the annihilation products of the SUSY DM where the factor YSUS (back-spelled SUSY) depends 5 in galaxy halos (e.g., [1, 2, 3, 4]). The success of such only on the physics of annihilating particles and all 1 a detection in competition with other indirect or direct the astrophysical properties (such as the DM distri- 0 experiments including accelerators will solve one of the bution and geometry considerations) appear only in 4 most fundamental questions in Astrophysics and Parti- the factor U(Ψ ). This factor also accounts for the 0 0 cle Physics: the nature of the dark matter. The light- beam smearing, where J(Ψ) = ρ2 (r)dl, dl = / l.o.s dm h est supersymmetric particle (LSP) has been proposed to rdr/ r2 d2 sin2Ψ,isthe integRraloftheline-of-sight p be a suitable candidate for the non-baryonic cold DM ± q − ⊙ - of the square of the DM density along the direction Ψ, ([5, 6], see also [7, 8] for a review). The LSP is stable o and B(Ω)dΩ is the Gaussian beam of the telescope: r in SUSY models where R-parity is conserved [9, 10, 11] t s and its annihilation cross section and mass has the ap- a propriate relic densities [8, 12] in the range allowed by B(Ω)dΩ=exp θ2 sinθdθdϕ. (2) v: WMAP, i.e. 0.095 < ΩCDMh2 < 0.129 [13]. We focus (cid:20)−2σt2(cid:21) i in the Minimal Supersymmetric extension of the Stan- X The angles θ and ϕ are related with the direction of ob- dard Model of particle physics (MSSM) where the LSP r istheneutralino(χ). Newupperlimitsontheneutralino servation Ψ0 and the line-of-sight angle Ψ by cosΨ = a cosΨ cosθ+sinΨ sinθcosϕ. We have assumed spher- mass (m ) havebeen estimateddue to the constrainson 0 0 χ the neutralino relic densities Ω h2 provided by WMAP; ical symmetry for the DM particles around the Galactic χ Center and that the observer is located in the Calactic m < 1500GeV based on the MSSM including mini- χ mal supergravity (mSUGRA) [12, 14]. A lower limit of equatorial plane at a distance d⊙ (here 8.0 kpc). m 100GeV has been set by the accelerators[15]. The factor YSUS/4π represents the isotropic proba- χ ∼ bility of γ-ray production per unit of DM density. It The number of neutralino annihilations in galaxy ha- can be determined for any SUSY model given the neu- los and therefore the expected gamma signal arriving at tralino mass m , the number of continuum γ-ray pho- χ the Earthdepends notonlyonthe adoptedSUSYmodel tons N emitted per annihilation, with energyabove the γ but also strongly depends on the DM density ρ (r). dm IACT energy threshold (E ), and the thermally aver- th This is why the central region r < 200pc of the Milky age cross section σv of the DM particles. We can Way, where the density is the largest, is the favorite site h i then estimate a YSUS parameter range, given a neu- to search for this signal. The expected total number of tralino mass interval of 100 1500GeV, and a cross continuum γ-ray photons receivedper unit time and per section σv interval of 5 1−0−27 3 10−26 cm3s−1 unit area, from a circular aperture on the sky of width h i × − × obtained for a sample of MSSM models computed in σ (the resolution of the telescope) observing at a given t [4, 21]with relic densities inagreementwiththe WMAP direction Ψ relative to the center of the Milky Way can 0 constrains. The number of continuum gamma photons be written as: produced per annihilation N is obtained by integrat- γ ing the continuum spectrum given by the decay of π0 1 mesons produced in the fragmentation of quarks. It F(E >Eth)= YSUS U(Ψ0), (1) can be well approximated by the eq.(18) in [3], i.e. 4π · 2 N =5/6x3/2 10/3x+5√x+5/(6√x) 10/3,where γ − − TABLEI:Models and constraintsfor theMilky WayGalaxy x E /m . This gives values of the YSUS parameter th χ in≡therangeof10−34to10−30photonsGeV−2cm3s−1 for Model A Model B Constr. E from 1 to 400GeV. NFW Moore et al. th A cuspy DM halo ρ (r) r−α predicted by the sim- Virial mass, 1012M⊙ 1.07 1.14 – dm ∝ Virial radius, kpc 264 270 – ulations of the Cold Dark Matter with the cosmological Halo concentration C 11 12 10.3-21.5 constant (ΛCDM ) is often assumed for the calculations (1.5σ) of U(Ψ0) (e.g., [1, 2, 3, 4, 16, 17, 18, 19, 20, 21, 22]). Disk mass, 1010M⊙ 3.7 4.0 – CosmologicalN body simulationsindicate thatthe dis- Disk scale length, kpc 3.2 3.5 2.5-3.5 − tribution of DM in relaxed halos varies between two Bulge mass, 109M⊙ 8.0 8.0 – shapes: theNFW[23]densityprofileρ(r)=ρ0/x(1+x)2, Black Hole mass, 106M⊙ 2.6 2.6 2.6 x r/rs with asymptotic slope α = 1 and the steeper M(<100kpc), 1011M⊙ 6.25 5.8 7.5±2.5 Mo≡oreetal. [24]profileρ(r)=ρ /x1.5(1+x)1.5,α=1.5. Σ , |z|<1.1 kpc 65 70 71±6 0 total ThedensityofDMalsodependsontwoparametersofthe at R⊙, M⊙pc−2 approximations: the virialmass Mvir and the concentra- Σbaryon at R⊙,M⊙pc−2 47 53 48±8 tion C rvir/rs, where rs is the characteristic radius Vcirc at 3 kpc,km/s 203 205 200±5 ≡ of assumed approximation. For Milky Way-size halos the average concentration C = 15 and the 1σ-variance is ∆log(C) = 0.11. For Moore et al profile we define radii x 1.72x0.82/(1+5x)0.085, x r/r . This ap- s concentration as Cmoore =CNFW 1.72. proximhaiti≈on predicts smaller contracti≡on in the central ∗ Milky Way mass models with adiabatic compression.— regions,whereindividualtrajectoriesareveryelongated. Thepredictionsforthe DMhalosarevalidonlyforhalos Itgivesbetterfitsthanthestandardapproximationwhen without baryons. Whennormalgas(“baryons”)losesits compared with realistic cosmologicalsimulations [30]. energy throughradiativeprocesses,it falls to the central In order to make realistic predictions for annihilation region of forming galaxy. As the result of this redistri- rates,weconstructtwodetailedmodelsoftheMilkyWay bution of mass, the gravitational potential in the center Galaxybyredoingthe fullanalysisofnumerousobserva- changes substantially. The dark matter must react to tional data collected in [31]. The models are compatible this deeper potential by moving closer to the center and with the available observational data for the Milky Way increasingits density. This increaseinthe DMdensity is and their main parameters are given in Table I. More often treated using adiabatic invariants. This is justified details on the model ingredients and the existing obser- becausethereisalimittothetime-scaleofchangesinthe vational constrains can be found in [31]. Fig. 1 presents massdistribution: changesofthepotentialatagivenra- thedistributionofmassanddensityinthemodels. While diuscannothappenfasterthanthedynamicaltime-scale allobservationswereincluded,someofthemaremoreim- definedbythemassinsidetheradius. Adiabaticcontrac- portantthanothers. Thesolarneighborhoodisrelatively tion of dark matter in a collapsingprotogalaxywas used well studied and, thus, provides important observational already in 1962 [25]. In 1980, Zeldovich et al. [26] used constraints. In Table I we present two local parameters: it to set constraints of properties of elementary particles thetotaldensityofmatterinside1.1kpcΣ (obtained total (annihilatingmassiveneutrinos). Theywerealsothefirst from kinematics of stars) and the surface density of gas topresentanalyticalexpressionforadiabaticcompression andstellarcomponentsΣ . CircularvelocityV at baryon circ (for pure radial orbits) and to make numerical tests to 3 kpc distance from the center provides another crucial confirm that the mechanism works. The present form of constraintonmodelsasemphasizedin[32]. Itisdifficult analyticalapproximation(circularorbits)wasintroduced toestimate errorsofthis parameterbecauseofuncertain in [27]. If M (r ) is the initialdistribution ofmass (the contribution of the galactic bar. We use 5km/s error, in in ± one predicted by cosmological simulations), then the fi- whichisrealistic,butitcanbe eventwicelarger. Proba- nal (after compression and formation of galaxy) mass blythemostdebatedconstraintiscomingfromcountsof distribution is given by M (r)r = M (r )r , where microlensingeventsinthedirectionofthegalacticbulge. fin in in in M = M + M . This approximation was tested Our models are expected to have the optical depth of fin DM bar innumericalsimulations[28,29]. Theapproximationas- microlensing events τ =1.2 1.6 10−6 and, thus, they − × sumesthatorbitsarecircularand,thusM(r)isthemass are compatible with the values of τ determined recently inside the orbit. This is not true for elongated orbits: from the observations τ = 1 1.5 10−6 [33], but are massM(r)issmallerthantherealmass,whichaparticle excludedifτ >2 10−6(see[3−1]for×adetaileddiscussion × “feels” when it travels along elongated trajectory. This on the bulge optical depth in our models). differenceinmassesrequiresarelativelysmallcorrection: Gamma-ray annihilation observability in the Milky mass M should be replaced by the mass inside time- Way.— The expected neutralino annihilation gamma averagedradius of trajectories passing through given ra- flux,inunits ofYSUS/10−32,canbe computedfromEq. dius r: M ( r )r = M ( r )r . We find the cor- 1 forthe compressedDM density profile providedby our fin in in in h i h i rection using Monte Carlo realizations of trajectories in Milky Way models as a function of the angular distance theNFWequilibriumhaloandfindingthetime-averaged Ψ from the Galactic Center. In Fig. 2 we show the pre- 0 3 -32YSUS/10110023 10 1 10-1 10-2 50 100 150 200 250 300 350 400 Eth (GeV) FIG.1: DensityandmassprofilesfortheMilkyWayGalaxy. FIG. 2: Predicted continuum gamma flux as a function of Symbols on right panel show observational constraints as distance Ψ0 from the Galactic Center for Models A and B. taken from Klypin et al. [31]. The full and dashed curves The thick line shows the flux for the compressed NFW DM labeled”Total”aretotalmassinNFWandMooreetal. mod- density profile of the Model A and the thin line for the com- elswithadiabaticcompression. DMmassintheNFWmodel pressed Moore et al. profile of the Model B. The flux profile is shown by the thick curve. In the central region most of for the uncompressed NFW profile is also shown for com- the mass is in baryons. Left panel shows the density. The parison (dotted line). The dashed line give the minimum top full curve is the density of baryons. The dashed and full detectable gamma flux Fmin at 5σ level for exposure of 250 curveslabeled”DM”arefortheMooreetal. andNFWmod- hoursandE =100GeVforatypicalIACT.Theinsertedpan- th elswith adiabatic compression. Thelong-dashed curveisthe nel shows the YSUS/10−32 dependence with the IACT E . th uncompressed NFW profile for comparison. ForagivenEth,theshadowregionscansallthemχ,hσviand Nγ intervals (see text). dictedfluxes. Wealsoshowasacomparisontheexpected fluxfortheuncompressedNFWdensityprofile. Theflux rejected at lower E . The diffuse galactic and extra- th profilesweredeterminedforatypicalIACTofresolution galactic gamma radiation are negligible compare to this σt =0.1◦ and solid angle ∆Ω=10−5sr. We have multi- background. Gamma point-like sources within the f.o.v pliedthe flux profilesbyafactorof1.7quotedby Stoehr canberesolvedandtakenoutaposteriori. TheE ofan th et al. [4] to account for the presence of substructure in- IACT depends on the zenith angle of observation. The side the Milky Way halo [34, 35]. GalacticCenteris visibleatdifferentzenith anglesbyall The success of a detection requires that the mini- presentIACTs(e.g. CANGAROO-III,H.E.S.S.,MAGIC, mum detectable gamma flux Fmin for an exposure of t VERITAS),butinthebestcaseanEth ofabout100GeV seconds, given an IACT of effective area A , angular canbeachieved. Nevertheless,futureplanedinstallations eff resolution σt and threshold energy Eth exceeds a sig- may reduce the Eth below 10GeV. The Aeff is also sen- nificant number M of standard deviations (M σ) the sible to the zenithangle ofobservation,here we choosea s s background noise √N , i.e. F A t/√N M (see, value of 1 109 cm2. This detectability condition will b min eff b ≥ s × e.g., [1, 3]). The background counts (N ) due to elec- allow us to compute the 5σ minimum detectable flux b tronic and hadronic (cosmic protons and helium nucle- Fmin in 250 hours of integration with a typical IACT ids) cosmic ray showers have been estimated using the of Aeff = 1 109 cm2 and Eth = 100GeV (dashed line following expressions [1]: N = 3 10−2E−2.3tA ∆Ω, in Fig. 2). A×t a given distance from the Galactic Center N = 6.1 10−3E−1.7tA e∆Ω. ×As an adtdhitionaleffback- only the flux values, for a particular model of the Milky grhound, o×ne has tothconsideeffr also the contamination due Way, greater than Fmin will be detected. The detection to isolated muons which depending on the f.o.v. and al- willbemuchharderandmayresultonlyinacentralspot titude location of the telescope may be even the dom- inthecaseofanIACTwithhigherEth,astheYSUSpa- inant background at some energy range (the “muon rameter declines with Eth (see Fig. 2). wall”). Preliminary studies [36] show that the muon The Milky Way models presented here include adia- background could be as relevant as the hadronic back- batic compression and likely will result in a detection of ground at E & 100GeV while it can be effectively the annihilation signal no matter what was the initial th 4 (uncompressed) DM density profile. For current experi- Transferoftheangularmomentumtothedarkmatteras ments this detection will be successful only for the very suggested in [31] is an option. Yet, recent simulations of centralregions,lessthan 0.4◦ inthe caseof the Model formationof barsindicate that itis difficult to arrangea A and close to 1◦ in ∼the case of the Model B. The significanttransferoftheangularmomentumtothedark ∼ compressed Moore et al. DM profile will provide a more matter. TheDMdensityinthecentralfewparseccanbe extended gamma flux profile. The uncompressed NFW reducedif the centralblackhole formedby spiralingand DM profile of the Model A will not be detected even in merging of two black holes [37]. It can also be changed the directionof the Galactic Center. Onthe other hand, (probablyreduced)byscatteringofDMparticlesbystars eventhe uncompressedMooreet al. profileof the Model inthecentral2pc[38]. Ifthishappens,thefluxfromthe B will give a positive detection in the very inner regions central2pccanbesignificantlyreduced. Yet,itwillonly of the Milky Way. decrease the amplitude of the central spike. The signal Theeffectoftheadiabaticcompressionincludedinour from0.4◦ stillcouldbe detectedbecauseitmostlycomes Milky Way mass models, which was previously ignored, from distances 30-50pc, which are much less affected by is a crucial factor. It should be emphasized that for the the uncertain physics around the black hole. central 3kpc of the Milky Way, where the baryons ∼ dominate, it does not make sense to use the dark mat- terprofilesprovidedbycosmologicalN-bodysimulations: Acknowledgments the DM must fall into the deep potential well createdby the collapsed baryons. Thus, the models presented here We acknowledge support of NASA and NSF grants to are not extreme: they are the starting point for realistic NMSU. We thank J. Primack, O. Gnedin, J. Betancort, predictions of the annihilation fluxes. One can envision A. Tasitsiomi and W. Wittek for discussions. few mechanisms to reduce the effect of the compression. [1] L. Bergström, P. Ullio, and J.H. Buckley, Astropart. [21] A. Tasitsiomi, J. Gaskins, and A.V. Olinto, Phys,9, 137 (1998). astro-ph/0307375 (2003). [2] E.A. Baltz, C. Briot, P. Salati, R. Taillet, and J. Silk, [22] N.W. Evans, F. Ferrer, and S. Sarkar, astro-ph/0311145 Phys.Rev.D 61, 23514 (2000). (2003). 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