Resolving Cosmic Gamma Ray Anomalies with Dark Matter Decaying Now
UCI-TR-2007-17
Resolving Cosmic Gamma Ray Anomalies with Dark Matter Decaying Now
Jose A. R. Cembranos, Jonathan L. Feng, and Louis E. Strigari
Department of Physics and Astronomy, University of California, Irvine, CA 92697, USA
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 γ-ray excess may be simultaneously 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.
PACS numbers: 95.35.+d, 11.10.Kk, 12.60.-i, 98.80.Cq
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 laborato-
ries, products fromWIMP 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 sce-
narios, 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 for-
mation [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 de-
generacies, the WIMP lifetime may be of the order of or
greater than the age of the Universe t0 ≃ 4.3 × 1017 s,
leading to the tantalizing possibility that dark matter is
decaying now.
For very long WIMP lifetimes, the diffuse photon back-
ground is a promising probe [3, 5]. Particularly interest-
ing is the (extragalactic) cosmic gamma ray background
(CGB) shown in Fig. 1. Although smooth, the CGB
must be explained by multiple sources. For Eγ <∼ 1 MeV
and Eγ >∼ 10 MeV, the CGB is reasonably well-modeled
by thermal emission from obscured active galactic nu-
clei (AGN) [9] and beamed AGN, or blazars [10], respec-
tively. However, in the range 1 MeV <∼ Eγ <∼ 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 (dot-
ted), 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 Eγ <∼ 10 MeV is shown in Fig. 1. Dif-
fuse 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 spec-
trum [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 ≫ t0. In-
triguingly, 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 univer-
sal extra dimensions (mUED) [17], one of the simplest
imaginable models with extra dimensions. In mUED all
http://arxiv.org/abs/0704.1658v3
particles propagate in one extra dimension compactified
on a circle, and the theory is completely specified by mh,
the Higgs boson mass, and R, the compactification ra-
dius. (In detail, there is also a weak, logarithmic depen-
dence on the cutoff scale Λ [18]. We present results for
ΛR = 20.) Every particle has a Kaluza-Klein (KK) part-
ner 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,mh) parameter
space where the two lightest KK particles are the KK
hypercharge gauge boson B1, and the KK graviton G1,
with mass splitting ∆m <∼ O(GeV) [19]. This extreme
degeneracy, along with the fact that KK gravitons inter-
act only gravitationally, leads to long NLKP lifetimes
b cos2 θW
(∆m)3
4.7× 1022 s
, (1)
where MP ≃ 2.4× 1018 GeV is the reduced Planck scale,
θW is the weak mixing angle, b = 10/3 for B
1 → G1γ,
and b = 2 for G1 → B1γ [20]. Note that τ depends only
on the single parameter ∆m. For 795 GeV <∼ R
−1 <∼
809 GeV and 180 GeV <∼ mh <∼ 215 GeV, the model is
not only viable, but the B1 thermal relic abundance is
consistent with that required for dark matter [21] and
∆m <∼ 30 MeV, leading to lifetimes τ(B
1 → G1γ) >∼ t0.
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 light-
est supersymmetric particles are a Bino-like neutralino B̃
and the gravitino G̃, the heavier particle’s decay width
is again given by Eq. (1), but with b = 2 for B̃ → G̃γ,
and b = 1 for G̃ → B̃γ. As in mUED, τ depends only on
∆m, and ∆m <∼ 30 MeV yields lifetimes greater than t0.
The present photon flux from two-body decays is
δ (Eγ − aεγ) , (2)
whereN(t) = N ine−t/τ andN in is the number of WIMPs
at freeze-out, V0 is the present volume of the Universe,
a is the cosmological scale factor with a(t0) ≡ 1, and
εγ = ∆m is the energy of the produced photons. Pho-
tons 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
N in e−P (Eγ/εγ )/τ
V0τEγH(Eγ/εγ)
Θ(εγ − Eγ) , (3)
where P (a) = t is the solution to (da/dt)/a = H(a) =
ΩMa−3 +ΩDE a−3(1+w) with P (0) = 0, and ΩM
and ΩDE are the matter and dark energy densities. If
dark energy is a cosmological constant Λ with w = −1,
P (a) ≡
ΩΛa3 +
ΩM +ΩΛa3
. (4)
The flux has a maximum at Eγ = εγ [
U(H20 τ
2ΩΛ)]
where U(x) ≡ (x+ 1−
3x+ 1)/(x− 1).
The energy spectrum is easy to understand for very
long and very short decay times. For τ ≪ t0,
H20 τ
2ΩDE ≪ 1, and the flux grows due to the deceler-
ated expansion of the Universe as dΦ/dEγ ∝ E1/2 until
it reaches its maximum at Emaxγ ≃ εγ(ΩMH20 τ2/4)1/3.
Above this energy, the flux is suppressed exponentially
by the decreasing number of decaying particles [3].
On the other hand, if τ ≫ t0, H20 τ2ΩDE ≫ 1, and
the flux grows as dΦ/dEγ ∝ E1/2 only for photons that
originated in the matter-dominated epoch. For decays
in the vacuum-dominated Universe, the flux decreases
asymptotically as dΦ/dEγ ∝ E(1+3w)/2 due to the accel-
erated expansion. The flux reaches its maximal value at
Emaxγ ≃ εγ [−ΩM/((1 + 3w)ΩDE)]−1/(3w) 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 ΩM = 0.25, ΩDE = 0.75,
w = −1, and h = 0.7, and that these particles make up
all of non-baryonic dark matter, so that
= 1.0× 10−9 cm−3
ΩNBDM
, (5)
we find that the maximal flux is
(Emaxγ ) = 1.33× 10
−3 cm−2 s−1 sr−1 MeV−1
1021 s
ΩNBDM
. (6)
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 Eγ ∼ MeV. These frameworks are, however, highly
constrained: once ∆m is chosen, τ and the flux are es-
sentially 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 model-
dependent constraints and consider τ and ∆m to be in-
dependent 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 max-
imal 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 ob-
served diffuse photon background and so are excluded.
The shaded band in Fig. 3 is the region where the max-
imal flux falls in the unaccounted for range of 1-5 MeV.
FIG. 2: Data for the CGB in the range of the MeV excess,
along with predicted contributions from extragalactic dark
matter decay. The curves are for B1 → G1γ in mUED with
lifetime τ = 103 t0 and mB1 = 800 GeV (solid) and B̃ → G̃γ
in SUSY with lifetime τ = 5 × 103 t0 and mB̃ = 80 GeV
(dashed). We have assumed ΩNBDM = 0.2 and smeared all
spectra with energy resolution ∆E/E = 10%, characteristic
of experiments such as COMPTEL. The dot-dashed curve is
the upper limit to the blazar spectrum, as in Fig. (1).
For τ >∼ t0, E
γ ≃ 0.55∆m. However, for τ <∼ t0, E
does not track ∆m, as the peak energy is significantly
redshifted. For example, for a WIMP with mass 80 GeV,
τ ∼ 1012 s and ∆m ∼ MeV, Emaxγ ∼ keV. The over-
lap of this band with the labeled contours is where the
observed excess may be explained through WIMP de-
cays. We see that it requires 1020 s <∼ τ <∼ 10
22 s and
1 MeV <∼ ∆m <∼ 10 MeV. These two properties may
be simultaneously realized by two-body gravitational de-
cays: the diagonal line shows the relation between τ and
∆m given in Eq. (1) for B1 → G1γ, and we see that this
line passes through the overlap region! Similar conclu-
sions 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× 1020 s can
explain the MeV excess in the CGB. This preferred region
is realized for the decay B1 → G1γ 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 G1 → B1γ for R−1 ≈ 810.5 GeV, though in
this case the G1 must be produced non-thermally to have
the required dark matter abundance [20, 22].
So far we have concentrated on the cosmic, or extra-
galactic, photon flux, which is dependent only on cosmo-
logical 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 pho-
tons are not redshifted and so will appear as lines with
Eγ = ∆m. INTEGRAL has searched for photon lines
within 13◦ from the Galactic center [23]. For lines with
energyE ∼ MeV and width ∆E ∼ 10 keV, INTEGRAL’s
FIG. 3: Model-independent analysis of decaying dark mat-
ter in the (τ,∆m) plane. In the shaded region, the result-
ing extragalactic photon flux peaks in the MeV excess range
1 MeV ≤ Emaxγ ≤ 5 MeV. On the contours labeled with
WIMP masses, the maximal extragalactic flux matches the
extragalactic flux observed by COMPTEL; points above these
contours are excluded. The diagonal line is the predicted re-
lation between τ and ∆m in mUED. On the dashed line, the
predicted Galactic flux matches INTEGRAL’s sensitivity of
10−4 cm−2 s−1 for monoenergetic photons with Eγ ∼ MeV.
energy resolution at these energies, INTEGRAL’s sensi-
tivity is Φ ∼ 10−4 cm−2 s−1. The Galactic flux from
decaying dark matter saturates this limit along the ver-
tical line in Fig. 3, assuming mχ = 800 GeV. This flux is
subject to halo uncertainties; we have assumed the halo
density profiles of Ref. [24], which give a conservative up-
per 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 sensi-
tive probe of this possibility, even for lifetimes τ ≫ t0.
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 comple-
mentary probes in the future. We have also shown that
dark matter with mass splittings ∆m ∼ MeV and life-
times τ ∼ 103−104 Gyr can explain the current excess of
observations above astrophysical sources at Eγ ∼ MeV.
Such lifetimes are unusually long, but it is remarkable
that these lifetimes and mass splittings are simultane-
ously 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
Excluded Charged DM
Excluded Overproduction
R (GeV)
807 808 809 810 811
FIG. 4: Phase diagram of mUED. The top and bottom shaded
regions are excluded for the reasons indicated [19]. In the
yellow (light) shaded region, the B1 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 B1 → G1γ
(G1 → B1γ) 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 ΩM/ΩDE and w. The CGB may therefore, in
principle, provide novel constraints on dark energy prop-
erties and other cosmological parameters.
We thank John Beacom, Matt Kistler, and Hasan Yuk-
sel 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.
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