Abstract: Using the Fenchel-Eggleston theorem for convex hulls (an extension of the Caratheodory theorem), we prove that any likelihood can be maximized by either a dark matter 1-speed distribution F(v) in Earth's frame or 2-Galactic velocity distribution f(gal) ((u) over right arrow), consisting of a sum of delta functions. The former case applies only to time-averaged rate measurements and the maximum number of delta functions is (N-1), where N is the total number of data entries. The second case applies to any harmonic expansion coefficient of the time-dependent rate and the maximum number of terms is N. Using time-averaged rates, the aforementioned form of F(v) results in a piecewise constant unmodulated halo function (eta) over tilde (BF)-B-0 (v(min)) (which is an integral of the speed distribution) with at most (N-1) downward steps. The authors had previously proven this result for likelihoods comprised of at least one extended likelihood, and found the best-fit halo function to be unique. This uniqueness, however, cannot be guaranteed in the more general analysis applied to arbitrary likelihoods. Thus we introduce a method for determining whether there exists a unique best-fit halo function, and provide a procedure for constructing either a pointwise con fi dence band, if the best-fit halo function is unique, or a degeneracy band, if it is not. Using measurements of modulation amplitudes, the aforementioned form of f(gal) ((u) over right arrow), which is a sum of Galactic streams, yields a periodic time-dependent halo function (eta) over right arrow BF (v(min); t) which at any fixed time is a piecewise constant function of v(min) with at most N downward steps. In this case, we explain how to construct pointwise confidence and degeneracy bands from the time-averaged halo function. Finally, we show that requiring an isotropic Galactic velocity distribution leads to a Galactic speed distribution F(u)that is once again a sum of delta functions, and produces a time-dependent (eta) over tilde BF (v(min); t) function (and a time-averaged (eta) over tilde (0) BF (v(min))) that is piecewise linear, di ff ering significantly from best-fit halo functions obtained without the assumption of isotropy.

Abstract: We present the application of convolutional neural networks to a particular problem in gamma ray astronomy. Explicitly, we use this method to investigate the origin of an excess emission of GeV gamma rays in the direction of the Galactic Center, reported by several groups by analyzing Fermi-LAT data. Interpretations of this excess include gamma rays created by the annihilation of dark matter particles and gamma rays originating from a collection of unresolved point sources, such as millisecond pulsars. We train and test convolutional neural networks with simulated Fermi-LAT images based on point and diffuse emission models of the Galactic Center tuned to measured gamma ray data. Our new method allows precise measurements of the contribution and properties of an unresolved population of gamma ray point sources in the interstellar diffuse emission model. The current model predicts the fraction of unresolved point sources with an error of up to 10% and this is expected to decrease with future work.

Abstract: In the present work, we show that the Galactic Center Excess (GCE) emission, as recently updated by the Fermi-LAT Collaboration, could be explained by a mixture of Fermi bubbles-like emission plus dark matter (DM) annihilation, in the context of a scalar-singlet Higgs portal scenario (SHP). In fact, the standard SHP, where the DM particle, S, only has renormalizable interactions with the Higgs, is non-operational due to strong constraints, especially from DM direct detection limits. Thus we consider the most economical extension, called ESHP (for extended SHP), which consists solely in the addition of a second (more massive) scalar singlet in the dark sector. The second scalar can be integrated-out, leaving a standard SHP plus a dimension-6 operator. Mainly, this model has only two relevant parameters (the DM mass and the coupling of the dim-6 operator). DM annihilation occurs mainly into two Higgs bosons, SS -> hh. We demonstrate that, despite its economy, the ESHP model provides an excellent fit to the GCE (with p-value similar to 0.6-0.7) for very reasonable values of the parameters, in particular, ms similar or equal to 130 GeV. This agreement of the DM candidate to the GCE properties does not clash with other observables and keep the S – particle relic density at the accepted value for the DM content in the universe.