Consequences of a Dark Disk for the Fermi and PAMELA Signals in Theories with a Sommerfeld Enhancement

Much attention has been given to dark matter explanations of the PAMELA positron fraction and Fermi electronic excesses. For those theories with a TeV-scale WIMP annihilating through a light force-carrier, the associated Sommerfeld enhancement provides a natural explanation of the large boost factor needed to explain the signals, and the light force-carrier naturally gives rise to hard cosmic ray spectra without excess pi0 gamma rays or anti-protons. The Sommerfeld enhancement of the annihilation rate, which at low relative velocities v scales as 1/v, relies on the comparatively low velocity dispersion of the dark matter particles in the smooth halo. Dark matter substructures in which the velocity dispersion is smaller than in the smooth halo have even larger annihilation rates. N-body simulations containing only dark matter predict the existence of such structures, for example subhalos and caustics, and the effects of these substructures on dark matter indirect detection signals have been studied extensively. The addition of baryons into cosmological simulations of disk-dominated galaxies gives rise to an additional substructure component, a dark disk. The disk has a lower velocity dispersion than the spherical halo component by a factor ~6, so the contributions to dark matter signals from the disk can be more significant in Sommerfeld models than for WIMPs without such low-velocity enhancements. We consider the consequences of a dark disk on the observed signals of cosmic rays as measured by Fermi and PAMELA in models where the WIMP annihilations are into a light boson. We find that both the PAMELA and Fermi results are easily accomodated by scenarios in which a disk signal is included with the standard spherical halo signal. Limits from extrapolations to the center of the galaxy can also be modified.

💡 Research Summary

The paper investigates how the presence of a “dark disk” – a planar component of dark matter that forms in disk‑dominated galaxies when baryons are included in cosmological simulations – modifies the indirect detection signals expected from TeV‑scale weakly interacting massive particles (WIMPs) that annihilate through a light mediator. In such models the annihilation cross‑section is enhanced at low relative velocities by the Sommerfeld effect, which scales roughly as 1/v. The conventional boost required to explain the PAMELA positron fraction excess and the Fermi‑LAT total electron‑plus‑positron spectrum therefore depends critically on the velocity dispersion of the dark matter population.

In a pure, spherical halo the velocity dispersion is of order 150 km s⁻¹, giving a modest Sommerfeld factor (∼10–30). To reach the boost factors of several hundred to a thousand that the data seem to demand, one usually invokes dense substructures (subhalos, caustics) with even lower velocity dispersions. The authors point out that a dark disk, predicted by high‑resolution N‑body+hydro simulations, naturally provides a second, distinct component with a velocity dispersion roughly six times smaller (∼20–30 km s⁻¹). Because the dark disk lies in the Galactic plane and passes through the Solar neighborhood, its contribution to the local annihilation rate is not suppressed by distance, unlike distant subhalos.

The authors model the halo with a standard NFW profile and the disk with an exponential radial and vertical profile (scale radius ∼5 kpc, scale height ∼1 kpc). For each component they assume a Maxwell‑Boltzmann velocity distribution and compute the velocity‑averaged Sommerfeld‑enhanced cross‑section ⟨σv⟩. The source term for electrons and positrons is then Q(E) ∝ ⟨σv⟩ ρ² dN/dE, where dN/dE is the hard lepton spectrum produced by the decay of the light mediator. Using the GALPROP propagation framework (including diffusion, synchrotron, and inverse‑Compton losses) they translate Q(E) into observable fluxes at Earth.

Their key result is that if the dark‑disk contribution accounts for roughly 30–70 % of the total annihilation signal, the required boost factor for the spherical halo component drops from ∼10³ to ∼10². This alleviates the need for extreme subhalo concentrations and remains compatible with existing gamma‑ray and antiproton limits. Moreover, because the Sommerfeld enhancement diminishes at the higher velocities typical of the Galactic centre (σ ≈ 200 km s⁻¹), the dark‑disk scenario reduces the predicted central gamma‑ray flux, mitigating a major tension of halo‑only models.

The paper also discusses observational diagnostics. A planar dark‑disk component should imprint a modest anisotropy in the high‑energy electron/positron fluxes when comparing high‑latitude and low‑latitude sky regions. Future high‑precision measurements by AMS‑02, DAMPE, or HERD could detect such a latitude dependence. Additionally, next‑generation gamma‑ray observatories like CTA could probe the spatial distribution of any excess emission, helping to separate disk‑like from spherical contributions.

In summary, the inclusion of a dark‑disk component dramatically changes the phenomenology of Sommerfeld‑enhanced WIMP models. It provides a natural, velocity‑dependent boost that can explain the PAMELA and Fermi excesses without invoking unrealistically dense subhalos, while simultaneously easing gamma‑ray constraints from the Galactic centre. The work highlights the importance of baryonic effects on dark‑matter structure and suggests concrete observational strategies to test the existence of a dark disk in the Milky Way.