Die another day (about some dark particle issues)
The unexpected increase of the positron fraction in cosmic rays with energies above 10 GeV (also known as the “positron anomaly”) was observed for the first time in the PAMELA experiment  and was later confirmed by AMS-02 . A lot of attention was paid to this discovery since the standard mechanisms of positron production and acceleration predicted a much steeper energy spectrum of cosmic positrons. The list of possible explanations includes, inter alia, decays or annihilations of dark matter (DM) particles, implying the existence of interconnection between our world and “dark world”. This intriguing possibility is though highly constrained by a set of direct, indirect and accelerator-based observations, which force DM models to become more and more sophisticated. But no matter how complicated a DM model explaining the positron anomaly is, it should obviously fulfill the principal requirement that it produces a sufficient amount of high-energy positrons. The undesirable consequence of this fact is that, regardless of the prior (internal) processes, production of charged particles is accompanied by gamma-ray emission (see Fig. 1).
In addition, gamma rays are produced during the propagation of charged particles through the Galactic gas and the electromagnetic media, mainly in such processes as Bremsstrahlung and inverse Compton scattering (ICS). As we are going to show, even this at first sight small contribution to Galactic gamma rays may come in conflict with the latest Fermi-LAT data on the isotropic diffuse gamma-ray background [4, 5] and, furthermore, rule out DM explanations of the high-energy cosmic positron excess. Basically, the reason of this problem is the following: the total amount of positrons and photons depends on the size of the volume in which their sources are concentrated, and though physically both positrons and photons have the same source, the volume of space from which they mostly arrive is substantially different. While only those positrons that were produced in the ∼ 3 kpc proximity can approach the Earth (due to their stochastic motion in the Galactic magnetic fields and the corresponding energy losses), gamma rays can come to us directly from any point of the DM halo, where they were born. Now, since the DM halo is indeed large, the amount of gamma rays can simply overwhelm the observed limits...
Figure 1: A diagram illustrating an example of the dark matter (DM) annihilation process providing a positron via W+ decay and some variety of states X. The positron emits final state radiation (FSR).
The no-go theorem we are considering can be expressed as follows: any model of DM providing a satisfactory explanation of the high-energy cosmic positron data and assuming an isotropic distribution of annihilating or decaying DM particles in the Galactic halo produces an overabundance of gamma rays that contradicts the latest experimental data on the diffuse gamma-ray background...
One of the key assumptions of our theorem is the conventional isotropic distribution of annihilating/decaying DM. As it was shown in one of our works  one can circumvent this no-go theorem by assuming a non-isotropic positron source distribution, e.g. a dark matter disk.
(Submitted on 7 Jul 2016 (v1), last revised 8 Jul 2016 (this version, v2))
... the existence of a dark disk, mostly populated by active DM, could cure the DM interpretation of the positron anomaly in cosmic rays from the overproduction of gamma rays, which, as we have proved, inevitably appears in any DM model that explains this phenomenon and assumes an isotropic distribution of DM.
The only properties of the dark disk which can be derived in a model-independent way from our analysis are its thickness and the local emissivity of DM in it. Properties such as local DM density or Galactic luminosity require additional assumptions about the nature of active DM and about its distribution over galactic scales.
The same actually holds for the gamma-ray luminosity of other galaxies, including dwarf satellites, and even the luminosity of the whole Universe. However, we think that the extragalactic gamma-ray flux (as well as the luminosity of dwarf spheroidal galaxies) is likely to be suppressed sufficiently in the case of a dark disk, as can be expected in the following speculative mechanisms of dark disk formation.
One mechanism is based on purely gravitational effects of galactic collisions and mergers, which result in the formation of a co-rotating dark matter disk . This mechanism does not require multicomponent DM. However, as we mentioned above, the resulting disk cannot be sufficiently dense, which means that decaying DM is strongly disfavoured in this case. To make this mechanism an effective framework for a positron anomaly explanation one should probably consider long-range self-interacting DM models. Since DM particles in the disk are expected to have a very different velocity distribution from that of DM particles in the halo, such interactions can naturally provide a boost of annihilation rate in the disk due to the Sommerfeld-Sakharov enhancement. Dwarf satellite galaxies are not expected to emit many gamma rays because they are not likely to store a dark disk within them.
The second mechanism implies multi-component DM models with the dominant “faint” component distributed isotropically in the halo and the subdominant “active” component which forms a disk mainly due to its non-trivial dynamics. This “active” component can be introduced by simply adding an ad hoc new form of DM to the “ordinary” one. As an example, one may consider self-interacting DM particles able to form dark atoms , and dissipate energy during collisions, which can lead to disk emergence.
One can also think of another scenario, in which “active” DM is ab initio presented on par with a “faint” component. Suppose some new particles a+ and b− with opposite dark charges bound together play the role of “ordinary” DM. If the Universe is asymmetric towards the abundance of their corresponding antiparticles then the free leftovers of a+ and b− will annihilate with free a and b. Since the motion of these particles is dissipative as well, it might be possible for them to form a disk-like structure. The mechanism under consideration also provides a very diluted concentration of active DM in dwarf galaxies that makes them dimmer in gamma rays.
The list of mechanisms and models given here does not pretend to be comprehensive and fully developed, but rather gives the examples of theoretical endeavors to build an appropriate model.
(Submitted on 3 Jun 2016)