Clumpiness enhancement of charged cosmic rays from dark matter annihilation with Sommerfeld effect

TL;DR

The paper analyzes how dark matter substructures and Sommerfeld enhancement (SE) jointly affect the local flux of charged cosmic rays from DM annihilation. By modeling DM density profiles (NFW and Moore) with a central cap and a detailed subhalo population, and by propagating positrons and antiprotons through the Galactic environment, it derives energy-dependent boost factors. The main finding is that, for non-resonant and moderately resonant SE, the SE-induced boosts are small due to saturation, and even strongly resonant SE yields only modest boosts for standard subhalo configurations (typically $B\lesssim 10$); only extreme, finely tuned scenarios with very cuspy subhalos can reach $B$ up to $\sim 10^3$. Consequently, DM clumpiness plus SE is unlikely to explain large local cosmic-ray enhancements, and GC observations plus multiwavelength constraints remain crucial for testing DM annihilation models.

Abstract

Boost factors of dark matter annihilation into antiprotons and electrons/positrons due to the clumpiness of dark matter distribution are studied in detail in this work, taking the Sommerfeld effect into account. It has been thought that the Sommerfeld effect, if exists, will be more remarkable in substructures because they are colder than the host halo, and may result in a larger boost factor. We give a full calculation of the boost factors based on the recent N-body simulations. Three typical cases of Sommerfeld effects, the non-resonant, moderately resonant and strongly resonant cases are considered. We find that for the non-resonant and moderately resonant cases the enhancement effects of substructures due to the Sommerfeld effect are very small ($\sim \mathcal{O}(1)$) because of the saturation behavior of the Sommerfeld effect. For the strongly resonant case the boost factor is typically smaller than $\sim \mathcal{O}(10)$. However, it is possible in some very extreme cases that DM distribution is adopted to give the maximal annihilation the boost factor can reach up to $\sim 1000$. The variances of the boost factors due to different realizations of substructures distribution are also discussed in the work.

Figures (8)

• Figure 1: Top-left: the SE enhancement factor $S$ as a function of coupling constant $\alpha$ and $m_{\phi}/m_{\chi}$, for a single velocity $\beta=220$ km s$^{-1}$; top-right: $S$ as a function of $m_{\phi}/m_{\chi}$ for several velocity $\beta$, in which $\alpha$ is fixed to be $1/30$; bottom-left: the average SE enhancement factor vs. velocity dispersion (in unit of light speed) of DM particles, for $\alpha=1/30$ and $m_{\chi}=1$ TeV; bottom-right: the evolution of DM abundance with the cosmic time $x\equiv m_{\chi}/T$ taking into account the SE corresponding to the models in the bottom-left panel.
• Figure 2: The (relative) fluxes of positrons (left) and antiprotons (right) from DM annihilation for the smooth component (red solid line), the subhalo component with reference configuration (black full circle), and the subhalo component with Moore inner profile (blue empty diamond).
• Figure 3: The boost factors of positrons for the non-resonant SE case, for different model configurations: varying the distribution of subhalo population (top-left); varying the inner property of subhalo (top-right); varying the propagation parameters (bottom-left); and finally the extreme cases with $\alpha_{\rm m}=2.0$, Moore inner profile with B01 concentration model (bottom-right). The errorbars show the variances of the boost factors. For clarity of the plot, we slightly shift the energy axis among different models in one panel.
• Figure 4: The same as Fig. \ref{['fig:pos1']} but for antiprotons.
• Figure 5: The same as Fig. \ref{['fig:pos1']} but for the moderately resonant SE enhancement case with $m_{\phi}=19$ or $1.24$ GeV.