Resolving Cosmic Gamma Ray Anomalies with Dark Matter Decaying Now

Dark matter particles need not be completely stable, and in fact they may be decaying now. We consider this possibility in the frameworks of universal extra dimensions and supersymmetry with very late decays of WIMPs to Kaluza-Klein gravitons and gravitinos. The diffuse photon background is a sensitive probe, even for lifetimes far greater than the age of the Universe. Remarkably, both the energy spectrum and flux of the observed MeV gamma ray excess may be naturally explained by decaying dark matter with MeV mass splittings. Future observations of continuum and line photon fluxes will test this explanation and may provide novel constraints on cosmological parameters.

The abundance of dark matter is now well known from observations of supernovae, galaxies and galactic clusters, and the cosmic mocriwave background (CMB) [1], but its identity remains elusive. Weakly-interacting massive particles (WIMPs) with weak-scale masses ∼ 0.1 − 1 TeV are attractive dark matter candidates. The number of WIMPs in the Universe is fixed at freeze-out when they decouple from the known particles about 1 ns after the Big Bang. Assuming they are absolutely stable, these WIMPs survive to the present day, and their number density is naturally in the right range to be dark matter. The standard signatures of WIMPs include, for example, elastic scattering off nucleons in underground laboratories, products from WIMP annihilation in the galaxy, and missing energy signals at colliders [2].
The stability of WIMPs is, however, not required to preserve the key virtues of the WIMP scenario. In fact, in supersymmetry (SUSY) and other widely-studied scenarios, it is just as natural for WIMPs to decay after freeze-out to other stable particles with similar masses, which automatically inherit the right relic density to be dark matter [3]. If the resulting dark matter interacts only gravitationally, the WIMP decay is very late, in some cases leading to interesting effects in structure formation [4] and other cosmological observables. Of course, the WIMP lifetime depends on ∆m, the mass splitting between the WIMP and its decay product. For high degeneracies, the WIMP lifetime may be of the order of or greater than the age of the Universe t 0 ≃ 4.3 × 10 17 s, leading to the tantalizing possibility that dark matter is decaying now.
For very long WIMP lifetimes, the diffuse photon background is a promising probe [3,5]. Particularly interesting is the (extragalactic) cosmic gamma ray background (CGB) shown in Fig. 1. Although smooth, the CGB must be explained by multiple sources. For E γ < ∼ 1 MeV and E γ > ∼ 10 MeV, the CGB is reasonably well-modeled by thermal emission from obscured active galactic nuclei (AGN) [9] and beamed AGN, or blazars [10], respectively. However, in the range 1 MeV < ∼ E γ < ∼ 5 MeV, no astrophysical source can account for the observed CGB. Blazars are observed to have a spectral cut-off ∼ 10 MeV, FIG. 1: The CGB measured by HEAO-1 [6] (circles), COMP-TEL [7] (squares), and EGRET [8] (triangles), along with the known astrophysical sources: AGN (long-dash), SNIa (dotted), and blazars (short-dash, and dot-dashed extrapolation). and also only a few objects have been detected below this energy [11,12]; a maximal upper limit [13] on the blazar contribution for E γ < ∼ 10 MeV is shown in Fig. 1. Diffuse γ-rays from Type Ia supernovae (SNIa) contribute below ∼ 5 MeV, but the most recent astronomical data show that they also cannot account for the entire spectrum [14,15]; previous calculations suggested that SNIa are the dominant source of γ-rays at MeV energies [16].
In this paper, we study the contribution to the CGB from dark matter decaying now. We consider simple models with extra dimensions or SUSY in which WIMP decays are highly suppressed by both the weakness of gravity and small mass splittings and are dependent on a single parameter, ∆m. We find that the CGB is an extremely sensitive probe, even for lifetimes τ ≫ t 0 . Intriguingly, we also find that both the energy spectrum and the flux of the gamma ray excess described above are naturally explained in these scenarios with ∆m ∼ MeV.
As our primary example we consider minimal universal extra dimensions (mUED) [17], one of the simplest imaginable models with extra dimensions. In mUED all particles propagate in one extra dimension compactified on a circle, and the theory is completely specified by m h , the Higgs boson mass, and R, the compactification radius. (In detail, there is also a weak, logarithmic dependence on the cutoff scale Λ [18]. We present results for ΛR = 20.) Every particle has a Kaluza-Klein (KK) partner at every mass level ∼ m/R, m = 1, 2, . . ., and the lightest KK particle (LKP) is a dark matter candidate, with its stability guaranteed by a discrete parity.
Astrophysical and particle physics constraints limit mUED parameters to regions of (R −1 , m h ) parameter space where the two lightest KK particles are the KK hypercharge gauge boson B 1 , and the KK graviton G 1 , with mass splitting ∆m < ∼ O(GeV) [19]. This extreme degeneracy, along with the fact that KK gravitons interact only gravitationally, leads to long NLKP lifetimes where M P ≃ 2.4 × 10 18 GeV is the reduced Planck scale, θ W is the weak mixing angle, b = 10/3 for 20]. Note that τ depends only on the single parameter ∆m. For 795 GeV < ∼ R −1 < ∼ 809 GeV and 180 GeV < ∼ m h < ∼ 215 GeV, the model is not only viable, but the B 1 thermal relic abundance is consistent with that required for dark matter [21] and ∆m < ∼ 30 MeV, leading to lifetimes τ (B 1 → G 1 γ) > ∼ t 0 . We will also consider supersymmetric models, where small mass splittings are also possible, since the gravitino mass is a completely free parameter. If the two lightest supersymmetric particles are a Bino-like neutralinoB and the gravitinoG, the heavier particle's decay width is again given by Eq. (1), but with b = 2 forB →Gγ, and b = 1 forG →Bγ. As in mUED, τ depends only on ∆m, and ∆m < ∼ 30 MeV yields lifetimes greater than t 0 . The present photon flux from two-body decays is where N (t) = N in e −t/τ and N in is the number of WIMPs at freeze-out, V 0 is the present volume of the Universe, a is the cosmological scale factor with a(t 0 ) ≡ 1, and ε γ = ∆m is the energy of the produced photons. Photons from two-body decays are observable in the diffuse photon background only if the decay takes place in the late Universe, when matter or vacuum energy dominates. In this case, Eq. (2) may be written as where P (a) = t is the solution to (da/dt)/a = H(a) = H 0 Ω M a −3 + Ω DE a −3(1+w) with P (0) = 0, and Ω M and Ω DE are the matter and dark energy densities. If dark energy is a cosmological constant Λ with w = −1, The flux has a maximum at . The energy spectrum is easy to understand for very long and very short decay times.
On the other hand, if τ ≫ t 0 , H 2 0 τ 2 Ω DE ≫ 1, and the flux grows as dΦ/dE γ ∝ E 1/2 only for photons that originated in the matter-dominated epoch. For decays in the vacuum-dominated Universe, the flux decreases asymptotically as dΦ/dE γ ∝ E (1+3w)/2 due to the accelerated expansion. The flux reaches its maximal value at where photons were produced at matter-vacuum equality. Note that this value and the spectrum shape depend on the properties of the dark energy. Assuming Ω M = 0.25, Ω DE = 0.75, w = −1, and h = 0.7, and that these particles make up all of non-baryonic dark matter, so that we find that the maximal flux is  Fig. 2 shows example contributions to the CGB from decaying dark matter in mUED and SUSY. The mass splittings have been chosen to produce maximal fluxes at E γ ∼ MeV. These frameworks are, however, highly constrained: once ∆m is chosen, τ and the flux are essentially fixed. It is thus remarkable that the predicted flux is in the observable, but not excluded, range and may explain the current excess above known sources.
To explore this intriguing fact further, we relax modeldependent constraints and consider τ and ∆m to be independent parameters in Fig. 3. The labeled curves give the points in (τ, ∆m) parameter space where, for the WIMP masses indicated and assuming Eq. (5), the maximal flux from decaying dark matter matches the flux of the observed photon background in the keV to 100 GeV range [6]. For a given WIMP mass, all points above the corresponding curve predict peak fluxes above the observed diffuse photon background and so are excluded.
The shaded band in Fig. 3 is the region where the maximal flux falls in the unaccounted for range of 1-5 MeV.
does not track ∆m, as the peak energy is significantly redshifted. For example, for a WIMP with mass 80 GeV, τ ∼ 10 12 s and ∆m ∼ MeV, E max γ ∼ keV. The overlap of this band with the labeled contours is where the observed excess may be explained through WIMP decays. We see that it requires 10 20 s < ∼ τ < ∼ 10 22 s and 1 MeV < ∼ ∆m < ∼ 10 MeV. These two properties may be simultaneously realized by two-body gravitational decays: the diagonal line shows the relation between τ and ∆m given in Eq. (1) for B 1 → G 1 γ, and we see that this line passes through the overlap region! Similar conclusions apply for all other decay models discussed above.
These considerations of the diffuse photon background also have implications for the underlying models. For mUED, ∆m = 2.7 − 3.2 MeV and τ = 4 − 7 × 10 20 s can explain the MeV excess in the CGB. This preferred region is realized for the decay B 1 → G 1 γ for R −1 ≈ 808 GeV. (See Fig. 4.) Lower R −1 predicts larger ∆m and shorter lifetimes and is excluded. The MeV excess may also be realized for G 1 → B 1 γ for R −1 ≈ 810.5 GeV, though in this case the G 1 must be produced non-thermally to have the required dark matter abundance [20,22].
So far we have concentrated on the cosmic, or extragalactic, photon flux, which is dependent only on cosmological parameters. The Galactic photon flux depends on halo parameters and so is less robust, but it has the potential to be a striking signature, since these photons are not redshifted and so will appear as lines with E γ = ∆m. INTEGRAL has searched for photon lines within 13 • from the Galactic center [23]. For lines with energy E ∼ MeV and width ∆E ∼ 10 keV, INTEGRAL's energy resolution at these energies, INTEGRAL's sensitivity is Φ ∼ 10 −4 cm −2 s −1 . The Galactic flux from decaying dark matter saturates this limit along the vertical line in Fig. 3, assuming m χ = 800 GeV. This flux is subject to halo uncertainties; we have assumed the halo density profiles of Ref. [24], which give a conservative upper limit on the flux within the field of view. Remarkably, however, we see that the vertical line also passes through the overlap region discussed above. If the MeV CGB anomaly is explained by decaying dark matter, then, the Galactic flux is also observable, and future searches for photon lines will stringently test this scenario.
In conclusion, well-motivated frameworks support the possibility that dark matter may be decaying now. We have shown that the diffuse photon spectrum is a sensitive probe of this possibility, even for lifetimes τ ≫ t 0 . This is the leading probe of these scenarios. Current bounds from the CMB [25] and reionization [26] do not exclude this scenario, but they may also provide complementary probes in the future. We have also shown that dark matter with mass splittings ∆m ∼ MeV and lifetimes τ ∼ 10 3 − 10 4 Gyr can explain the current excess of observations above astrophysical sources at E γ ∼ MeV. Such lifetimes are unusually long, but it is remarkable that these lifetimes and mass splittings are simultaneously realized in simple models with extra dimensional or supersymmetric WIMPs decaying to KK gravitons and gravitinos. Future experiments, such as ACT [27], with large apertures and expected energy resolutions of ∆E/E = 1%, may exclude or confirm this explanation of  [19]. In the yellow (light) shaded region, the B 1 thermal relic density is in the 2σ preferred region for non-baryonic dark matter [21].
In the vertical band on the left (right) the decay B 1 → G 1 γ (G 1 → B 1 γ) can explain the MeV diffuse photon excess.
the MeV excess through both continuum and line signals.
Finally, we note that if dark matter is in fact decaying now, the diffuse photon signal is also sensitive to the recent expansion history of the Universe. For example, as we have seen, the location of the spectrum peak is a function of Ω M /Ω DE and w. The CGB may therefore, in principle, provide novel constraints on dark energy properties and other cosmological parameters. We thank John Beacom, Matt Kistler, and Hasan Yuksel for Galactic flux insights. The work of JARC and JLF is supported in part by NSF Grants PHY-0239817 and PHY-0653656, NASA Grant No. NNG05GG44G, and the Alfred P. Sloan Foundation. The work of JARC is also supported by the FPA 2005-02327 project (DG-ICYT, Spain). LES and JARC are supported by the McCue Postdoctoral Fund, UCI Center for Cosmology.