Small-scale clumps in the galactic halo and dark matter annihilation

TL;DR

The paper analyzes the production, survival, and impact of small-scale DM clumps in the Galactic halo within the standard cosmological model and an inflationary power spectrum. It develops a hierarchical clustering framework that includes tidal destruction, diffusion, and free streaming to predict the minimal clump mass $M_{min}$ and core formation, and it quantifies how clumpiness enhances DM annihilation signals via the factor $\eta=(I_{cl}+I_{hom})/I_{hom}$. The results show that even a tiny surviving clump fraction substantially boosts the annihilation rate, with typical boosts of $\eta\approx2-5$ for $n_p\approx1$, while modest increases in $n_p$ can lead to much larger enhancements, especially for clumps with $M\sim M_{min}$ and $\nu\sim2.5$. The work provides concrete predictions for clump mass, radius, core size, and spatial distribution in the halo, with implications for interpreting gamma-ray and cosmic-ray signals from DM annihilation.

Abstract

Production of small-scale DM clumps is studied in the standard cosmological scenario with an inflation-produced primeval fluctuation spectrum. Special attention is given to three following problems: (i) The mass spectrum of small-scale clumps with $M \lesssim 10^3 M_{\odot}$ is calculated with tidal destruction of the clumps taken into account within the hierarchical model of clump structure. Only 0.1 - 0.5% of small clumps survive the stage of tidal destruction in each logarithmic mass interval $Δ\ln M\sim1$. (ii) The mass distribution of clumps has a cutoff at $M_{\rm min}$ due to diffusion of DM particles out of a fluctuation and free streaming at later stage. $M_{\rm min}$ is a model dependent quantity. In the case the neutralino, considered as a pure bino, is a DM particle, $M_{\rm min} \sim 10^{-8} M_{\odot}$. (iii) The evolution of density profile in a DM clump does not result in the singularity because of formation of the core under influence of tidal interaction. The radius of the core is $R_c \sim 0.1 R$, where $R$ is radius of the clump. The applications for annihilation of DM particles in the Galactic halo are studied. The number density of clumps as a function of their mass, radius and distance to the Galactic center is presented. The enhancement of annihilation signal due to clumpiness, valid for arbitrary DM particles, is calculated. In spite of small survival probability, the annihilation signal in most cases is dominated by clumps. For observationally preferable value of index or primeval fluctuation spectrum $n_p \approx 1$, the enhancement of annihilation signal is described by factor 2 - 5 for different density profiles in a clump.

Figures (7)

• Figure 1: Function $f(\delta_{\text{eq}})$ defined by Eq. (\ref{['f1']}). The ratio of the core radius to the clump radius in typical case $\simeq0.3\nu^{-2}f(\delta_{\text{eq}})$.
• Figure 2: Function $y(\nu)$ from Eq. (\ref{['psiitog']}) obtained by the numerical integration of (\ref{['phiin']}). This curve is valid with good accuracy for all $\beta$ from the interval $1 \leq \beta \leq 2$.
• Figure 3: The global enhancement $\eta$ of the annihilation signal from Eq. (\ref{['itogexpr']}) as a function of the minimal clump mass $M_{\text{min}}$, for clump density profile with index $\beta=1$ and for different indices $n_p$ of primeval perturbation spectrum. The curves are marked by the values of $n_p$.
• Figure 4: The same as Fig. \ref{['bet1l']} but for $\beta=1.5$.
• Figure 5: The same as Fig. \ref{['bet1l']} but for $\beta=1.8$.