Positrons from particle dark-matter annihilation in the Galactic halo: propagation Green's functions

TL;DR

This paper computes the propagation of positrons from particle dark matter annihilation in the Galactic halo using a 3D GALPROP framework and derives Green's functions $G(E,\epsilon)$ for several DM density profiles and halo sizes. The authors show that $G$ is largely insensitive to the detailed DM distribution when the local density $\rho_0$ is fixed, due to strong energy losses, and they provide a robust parametric fit for practical flux calculations. By comparing DM-induced positron fluxes with two distinct CR background scenarios, they find that a detectable DM signal requires favorable conditions or DM clumping, and emphasize that accurate background modeling is essential for interpretation. The work provides a more realistic propagation basis for predicting positron signals and highlights the critical role of background constraints in DM searches with cosmic-ray positrons.

Abstract

We have made a calculation of the propagation of positrons from dark-matter particle annihilation in the Galactic halo in different models of the dark matter halo distribution using our 3D code, and present fits to our numerical propagation Green's functions. We show that the Green's functions are not very sensitive to the dark matter distribution for the same local dark matter energy density. We compare our predictions with computed cosmic ray positron spectra (``background'') for the ``conventional'' CR nucleon spectrum which matches the local measurements, and a modified spectrum which respects the limits imposed by measurements of diffuse Galactic gamma-rays, antiprotons, and positrons. We conclude that significant detection of a dark matter signal requires favourable conditions and precise measurements unless the dark matter is clumpy which would produce a stronger signal. Although our conclusion qualitatively agrees with that of previous authors, it is based on a more realistic model of particle propagation and thus reduces the scope for future speculations. Reliable background evaluation requires new accurate positron measurements and further developments in modelling production and propagation of cosmic ray species in the Galaxy.

Figures (4)

• Figure 1: The radial profiles of the spherical halo models: the canonical isothermal model (solid line), Evans model (long dashes), alternative model (dots), and uniform distribution ($\rho = 0.4$ GeV cm$^{-3}$, short dashes).
• Figure 2: Calculated $G$-functions for the uniform dark matter distribution, $z_h=4$ kpc and 10 kpc, for $\epsilon = 25.76$, $103.0$, $412.1$ GeV (solid lines). The leaky-box functions $G_1$ and $G_2$ are shown by dashed and dotted lines respectively. The units of the abscissa are $10^{25}$ GeV cm sr$^{-1}$.
• Figure 3: Calculated $G$-functions for different models of the dark matter distribution: (a) "isothermal", (b) Evans, (c) alternative. Upper curves $z_h = 10$ kpc, lower curves $z_h = 4$ kpc, $\epsilon = 1.03$, $2.06$, $5.15$, $10.3$, $25.8$, $51.5$, $103.0$, $206.1$, $412.1$, $824.3$ GeV. The units of the abscissa are $10^{25}$ GeV cm sr$^{-1}$.
• Figure 4: Our predictions for two CR positron "background" models (C and HEMN: heavy solid lines), and positron signals from neutralino annihilation for $m_\chi=5.15$, $10.3$, $25.8$, $103.0$, $206.1$, $412.1$ (thin solid lines): (a) $z_h=4$ kpc, (b) $z_h=10$ kpc. In the case of $m_\chi=103.0$ GeV, the signal plus background (model C) is shown by the dotted line. Data and the best fit to the data (dashes) are from Ref. Barwick98 (HEAT collaboration).