Positrons from dark matter annihilation in the galactic halo: theoretical uncertainties

Abstract

Indirect detection signals from dark matter annihilation are studied in the positron channel. We discuss in detail the positron propagation inside the galactic medium: we present novel solutions of the diffusion and propagation equations and we focus on the determination of the astrophysical uncertainties which affect the positron dark matter signal. We find dark matter scenarios and propagation models that nicely fit existing data on the positron fraction. Finally, we present predictions both on the positron fraction and on the flux for already running or planned space experiments, concluding that they have the potential to discriminate a possible signal from the background and, in some cases, to distinguish among different astrophysical propagation models.

Figures (15)

• Figure 1: Influence of the radial boundary condition for a slab half-thickness $L$ of 3, 10 and 20 kpc ($R_{\rm gal} = 20$ kpc). The thicker the slab, the larger the error when neglecting the radial boundary. On the contrary, for small values of $L$, positrons produced near the radial outskirts of the diffusive halo escape into the intergalactic medium and do not contribute to the signal at the Earth. Implementing correctly the radial boundary condition is not relevant in that regime.
• Figure 2: The halo convolution $\tilde{I}$ is plotted as a function of the diffusion length $\hbox{$\lambda_{\rm D}$}$ for various values of the slab half-thickness $L$. The left panel features the case of an isothermal DM distribution whereas a NFW profile has been assumed in the right panel -- see Tab. \ref{['tab:indices']}. When $L$ is large enough for the positron horizon to reach the galactic center and its denser DM distribution, a maximum appears in the curves for $\hbox{$\lambda_{\rm D}$} \sim r_{\odot}$.
• Figure 3: The halo integral $\tilde{I}$ is plotted as a function of the diffusion length $\hbox{$\lambda_{\rm D}$}$ in the case of a Moore profile with $L = 10$ kpc. In the left panel, the results obtained with the Green function method are featured by the long-dashed curves and may be compared to the exact solution and its solid red line. In the right panel, the numbers $N_{\rm Bessel}$ and $N_{\rm harmonic}$ of the eigenfunctions considered in the Bessel expansion (\ref{['I_tilde_Bessel']}) have been varied. The various curves reproduce astonishingly well the bump but diverge at small $\hbox{$\lambda_{\rm D}$}$ when too few Bessel and Fourier terms are considered.
• Figure 4: Same plot as before where the central DM profile within a radius $r_{0}$ is either a plateau at constant density $\rho_{0}$ or the smooth distribution $\rho^{\ast}$ of Eq. (\ref{['profile_timur']}). In the former case, the bump which $\tilde{I}$ exhibits is significantly underestimated even for values of $r_{0}$ as small as 100 pc -- solid dark blue -- and drops as larger values are considered -- solid light blue. On the contrary, if the DM cusp is replaced by the smooth profile $\rho^{\ast}$, the halo integral no longer depends on the renormalization radius $r_{0}$ and the solid red and long-dashed black curves are superimposed on each other.
• Figure 5: In each panel, the halo integral $\tilde{I}$ is plotted as a function of the positron injection energy $E_{S}$ whereas the energy $E$ at the Earth is fixed at 10 GeV. The galactic DM halo profiles of Tab. \ref{['tab:indices']} are featured. The curves labeled as MED correspond to the choice of cosmic ray propagation parameters which best-fit the B/C ratio parfit. The MAX and MIN configurations correspond to the cases which were identified to produce the maximal and minimal DM antiproton fluxes primary_pbar, while the entire colored band corresponds to the complete set of propagation models compatible with the B/C analysis parfit.