Searching for Kaluza-Klein Dark Matter Signatures in the LAT Electron Flux
aa r X i v : . [ a s t r o - ph ] N ov Presented at 5-th International Workshop on Science with the new generation highenergy gamma-ray experiments, Frascati, Italy, June 2007
Searching for Kaluza-Klein Dark Matter Signaturesin the LAT Electron Flux
A.A. Moiseev § , E.A. Baltz ∗ , J.F. Ormes ¶ , and L.G. Titarchuk + § CRESST and AstroParticle Physics Laboratory, NASA/GSFC, Greenbelt, USA ∗ KIPAC, Menlo Park, USA ¶ University of Denver, Denver, USA + NRL, Washington DC, USACorresponding author: [email protected]
Abstract.
We present here the prospects for the GLAST Large Area Telescope(LAT) detection of the signature of the lightest Kaluza-Klein particle (LKP). It decaysby direct annihilation into electron-positron pairs that may be detectable in the highenergy electron flux. We discuss the LAT capability for detecting the high energy (20GeV - 1 TeV) cosmic ray electron flux and we analyze the LAT sensitivity to detectLKP-produced electrons for various particle masses. We include an analysis of thediffusive propagation of the electrons in the galaxy.
1. Introduction.
The nature of dark matter and dark energy is one of the most exciting and criticalproblems in modern astrophysics. A number of theoretical models predict the existenceof dark matter in different forms; so the experimental detection will be crucial. Alarge number of experiments are ongoing and planned to detect dark matter, directlyand indirectly, both at accelerators and in space, where they search for dark mattersignatures in cosmic radiation (see [1] and references therein). In this paper we explorethe capability of GLAST Large Area Telescope (LAT), scheduled for launch in thebeginning of 2008, to detect the signature of dark matter in the high energy cosmic rayelectron flux. We have previously demonstrated that LAT will be a powerful detectorof cosmic ray electrons, and will provide measurement of their flux with high statisticalconfidence [2]. We should mention that LAT is not designed to distinguish electronsfrom positrons, so we refer to their sum as electrons for simplicity. LAT will detect ≈ electrons per year above 20 GeV with the energy resolution 5-20%. Such goodstatistics permits detection of spectral features, among which could be ones caused byexotic sources such as Kaluza-Klein particles which manifest higher spatial dimensions.The possibility of the annihilation of the Lightest Kaluza-Klein Particles (LKP), whichcan be a stable and viable dark matter candidate, directly into electron-positron pairs,was investigated in, e.g. [1] and [3]. They estimated that electron-positron pairs areproduced in approximately 20% of the annihilation cases, which makes the observationsviable within the model assumptions.There are some indications of spectral features in the electron spectrum observed byATIC [4] and PPB-BETS [5] around 300-500 GeV, as well as in the positron spectrummeasured by HEAT [6], encouraging us for measurements with the LAT.
2. LAT Capability to detect cosmic ray electrons
It was demosnstrated earlier that the LAT can efficiently detect cosmic ray electrons[2]. Being a gamma-ray telescope, it intrinsically is an electron spectrometer. The mainproblem is to separate the electrons from all other species, mainly protons. In order tokeep the hadron contamination in the detected electron flux under 10%, the hadron-electron separation power must be 10 − . At very high energy (above a few TeV)the diffuse gamma-radiation could be a potential background, but it will be effectivelyeliminated by the LAT AntiCoincidence Detector. LAT’s onboard trigger accepts allevents with the detected energy above ≈
20 GeV, which is very important in order tohave unbiased data sample. We took advantage of this LAT feature and explored theinstrument sensitivity in the energy range above 20 GeV. It is also good to mentionthat there should be no problem with albedo and geomagnetic variation in this energyrange.We have developed a set of analysis cuts that select electrons and applied them tosimulated LAT data. The approach was based on using the difference in the showerdevelopment between hadron-initiated and electron-initiated events. In order to obtainthe instrument response function for electrons we simulated the electron spectrumincident on LAT and applied our selections. In the energy range from 20 GeV to 1TeV the effective geometric factor (for electrons) after applying our cuts is 0 . − srand energy resolution is 5-20% depending on the energy. We also applied the selectionsto the simulated cosmic ray flux (LAT background flux is used, see [7]) and determinedthe residual hadron contamination to be ≈
3% of the remaining electron flux.In order to test the approach, we run an independent simulation of the incidentflux and used the response function obtained to reconstruct the spectrum. For thesimulation of the electron flux we used the diffusion equation solution given in [8]. Fig.1shows our spectrum reconstruction for the simulated electron flux collected during 1year of LAT observations. The flux originated from an ”hypothetical” single burst-likesource, 2 × years old, at a distance of 100 pc. The diffusion coefficient D was assumedto be energy dependent as D = D (1 + E/E ) . with D = 10 cm s − . The expectedspectral cutoff for this model is ≈ . Energy, GeV
30 40 50 100 200 300 F l u x , a r b i t r a r y un i t s × E Simulated FluxDetected Flux
Reconstructed Flux
Figure 1.
Simulated electron flux reconstruction for LAT
3. Diffusive propagation of the LKP signal
Now we want to include the contribution from the LKP annihilation into the electronflux, and see how it can be detected by the LAT. We consider this contribution as acontinuous injection from a single point source of monoenergetic electrons, assumingdark matter clumpiness, and determine the effect of their propagation through space tothe Earth. After that we will test LAT response to such a spectrum, varying the sourceparameters LKP mass and distance. We treat the propagation of electrons using thestationary diffusion equation which in the spherical symmetric case is presented as Dr ∂∂r r ∂f∂r + ∂∂γ ( P f ) = Q (1)where f ( r, γ ) is a distribution of electron number over γ = E/m e c and radius r at time t . We assume that the continuous energy loss is dictated by synchrotron and inverseCompton losess − dγ/dt = P ( γ ) = p γ (2)where p = 5 . × − w / cm s − (3)and ω ≃ (see [8] for the propagation details)We choose the energy-dependent diffusion coefficient in the form D ( γ ) = D (1 + γ/γ g ) η cm s − (4)where γ g and D are model parameters.We derive the general solution of Eq. (1) for arbitrary source function in thefactorized form Q = ϕ ( r ) ψ ( γ ) (5)as well as a solution for a δ − function injection, i.e. for Q ( r, γ ) = δ ( γ − γ ∗ ) δ ( r − r ) / πr . (6)Using Eq. (1) it can be shown that the Green’s function G ,γ ∗ ( r, γ ), as a solutionfor the delta-function source (see Eq. 6) is presented as G ,γ ∗ ( r, γ ) = 1 D R [ r, u ( γ, γ ∗ )] γ (7)where R [ r, u ( γ, γ ∗ )] and u ( γ, γ ∗ ) are determined by Eq. (8) and Eq. (9) respectively: R ( r, u ) = 18 u ( πu ) / exp( − r / u ) . (8) u ( γ, γ ) = D p Z γ γ (1 + γ/γ g ) η dγγ . (9)Integral (9) can be presented in the analytical form in two cases: for γ g → ∞ or η = 0it is (see [9]) u ( γ, γ ) = D p (cid:18) γ − γ (cid:19) . (10)and for η = 0 . u ( γ, γ ) = D p × " γ (cid:18) γγ g (cid:19) / − γ (cid:18) γ γ g (cid:19) / + 1 γ g ln ( γ g /γ ) / + (1 + γ g /γ ) / ( γ g /γ ) / + (1 + γ g /γ ) / (11) -Factor γ , a r b i t r a r y un i t s F l u x , J E -7 -6 -5 -4 -3 -2 -1
150 pc
300 pc
Figure 2.
Propagation of the signal from LKP with the mass of 500 GeV, fromdifferent distances
Fig.2 illustrates the solution obtained and shows the propagation of the signalfrom annihilation of LKP, with mass of 500 GeV, for different distances. Due to lossesduring propagation, both the peak energy and the signal magnitude decrease with theincreasing distance. There will be a superposition of contributions from dark matterclumps at different distances, which could reveal themselves as bumps in the spectrum,but the closest clump should determine the edge in the spectrum which should be clearlyseen.
4. Prospects for LAT to observe LKP
Our analysis of the LAT capability for detection of electrons demonstrated the lowresidual hadron contamination in the resulting electron flux ( < m − LKP dN e dE e = Q line ( m LKP ) b ( E e ) θ ( m LKP − E e ) (12) ∼ h σv i (cid:18) ρ m LKP (cid:19) (cid:18) E e (cid:19) θ ( m LKP − E e ) ∼ m − LKP (13)where h σv i is the total annihilation cross section of LKP, and Q line is the rate of electronand positron injection from direct LKP annihilation.Using the numbers from [1]: boost factor B = 5 and ρ local = 0 . , themagnitude of the signal after propagation is estimated as (cid:18) dN e dE e (cid:19) ≈ . × m LKP [GeV] m − s − sr − GeV − . (14) Electron Energy (LKP mass), GeV
300 400 500 600 700 800 G e V - s r - s - , m F l u x J E Observed electron flux
LKP annihilation
Figure 3.
Expected electron flux from LKP annihilation, along with the observedelectron flux
Fig.3 shows the expected signal from LKP vs. the m LKP plotted along with the”conventional” electron flux for the comparison. Of course, even in this optimistic model,
LKP mass, GeV
300 400 500 600 N u m b e r o f S i g m a LKP mass, GeV
400 500 600 T i m e , y r LAT mission duration
Figure 4.
LKP detection in LAT electron spectrum. Left panel - detection significancefor 1 year. Right panel - time needed to detect LKP feature with 5 σ confidence the background dominates over the signal, but we now determine what will be the LATsensitivity. Fig.4 shows the significance of LKP detection in the LAT-detected electronflux in one year of ovservation, and the observation time needed to detect LKP featurewith 5 σ confidence for a source at 100 pc. We can conclude that 600 GeV is probablythe heaviest LKP which could be observed within the constrains assumed. Taking intoaccount that for thermal freeze-out, LKP mass in the range 600-700 GeV is preferred,the feasible window for LKP mass in the LAT search is rather narrow.Now we illustrate our analysis by adding the signal from LKP (mass 300 GeV),from a single clump at a distantce of 100 pc, to the ”conventional” electron flux shownin Fig.1, using the solution obtained in Section 3. The result is shown in Fig.6, witha clear signature of presence of a monoenergetic component. This is a very favorablesituation, but to some extent consistent with references [4] and [5]. Electron energy, GeV
60 70 100 200 300 400 1000 G e V - s r - s - J , m × E l ec t r on F l u x E Spectral break corresponding toLKP with mass 300 GeV
Spectral break corresponding toLKP with mass 600 GeV
Figure 5.
Illustration of the simulated reconstructed LAT electron spectrum with thepresence of signal from LKP with the mass of 300 GeV and 600 GeV, for five yearsof observations. Black filled circles - ”conventional” electron flux, blue open circles -with added signal from 300 GeV LKP, red oped squares - with added signal from 600GeV LKP
5. Conclusion
We analyzed the capability of the LAT to detect high energy cosmic ray electrons andapplied it to the model of LKP direct annihilation into electron-positron pairs. Usingthe estimates for this model as given in [1] as an example to demonstrate the detectionfeasibility, we estimated that within this model, the LAT will be able to recognize theLKP-caused spectral edge in the electron spectrum up to a LKP mass of 600-700 GeV.The results obtained can be applied to any dark matter model where electrons areproduced in order to estimate the LAT sensitivity. The important feature is that thedominating background in these measurements will be only the ”conventional” electronflux. We want to thank all LAT team members, and especially the members of LATDark Matter Science Working Group for their support and valuable suggestions. Weare grateful to Robert Hartman and Jan Conrad for their comments on this paper.
6. References6. References