Full calculation of clumpiness boost factors for antimatter cosmic rays in the light of Lambda-CDM N-body simulation results

TL;DR

<3-5 sentence high-level summary> The paper investigates whether dark matter sub-halos can appreciably boost antimatter cosmic ray signals (positrons and anti-protons) in the Milky Way. Using high-resolution N-body-inspired distributions for sub-halos and a semi-analytic propagation framework (complemented by Monte Carlo checks), it quantifies the energy-dependent boost factors and their uncertainties. Across a broad, physically motivated parameter space, the authors find the average clump contribution is negligible compared to the smooth halo, with boost factors near unity and modest variances; only extremely contrived configurations could yield boosts up to a few tens. This result constrains interpretations of upcoming PAMELA/AMS-02 data, and indicates that spectral distortions from clumpiness, rather than large boosts, are the plausible antimatter signatures of dark matter annihilation. All formulas are kept explicit with $D$-style notation where relevant, and the conclusions hold regardless of the specific WIMP scenario within the studied CDM frameworks.

Abstract

Anti-proton and positron Galactic cosmic ray spectra are among the key targets for indirect detection of dark matter. The boost factors, corresponding to an enhancement of the signal and linked to the clumpiness properties of the dark matter distribution, have been taken as high as thousands in the past. The dramatic impact of these boost factors for indirect detection of antiparticles, for instance with the PAMELA satellite or the coming AMS-02 experiment, asks for their detailed calculation. We take into account the results of high resolution N-body dark matter simulations to calculate the most likely energy dependent boost factors linked to the cosmic ray propagation properties, for anti-protons and positrons. Starting from the mass and space distributions of sub-halos, the anti-proton and positron propagators are used to calculate the mean value and the variance of the boost factor for the primary fluxes. We take advantage of the statistical method introduced in Lavalle et al. (2007) and cross-check the results with Monte Carlo computations. By spanning some extreme configurations of sub-halo and propagation properties, we find that the average contribution of the clumps is negligible compared to that of the smooth dark matter component. Sub-halos do not lead to enhancement of the signals, unless they are taken with some extreme (unexpected) properties. This result is independent of the nature of the self-annihilating dark matter candidate considered, and provides precise estimates of the theoretical and the statistical uncertainties of the antimatter flux from dark matter substructures. Spectral distortions can still be expected in antimatter flux measurements, but scenarios invoking large and even mild clumpiness boost factors are strongly disfavoured by our analysis.

Figures (12)

• Figure 1: Mass fraction $f_M$ as a function of _ min$M_{\rm min}$, for different logarithmic slopes _ m$\alpha_{\rm m}$ of the mass distribution (from $2.1$ down to $1.7$---top to bottom curves).
• Figure 2: Same as in Table \ref{['tab:clump_parameters']}. Each parameter is normalised with respect to its maximum value (in the mass range displayed).
• Figure 3: Ratio of the annihilation volume for three benchmark sub-halo models to the reference one, defined as $\xi_r^X\equiv \xi^{\rm x}/\xi^{\rm ref}= B_{\rm}^{\rm x}/B_{\rm cl}^{\rm ref}$. The reference configuration is an inner NFW profile with B01 concentration. The three benchmark configurations are X $=({\rm Moore,B01})$ (upper curve), X $=({\rm Moore,ENS01})$ (middle curve) and X $=({\rm NFW,ENS01})$ (lower curve).
• Figure 4: Differential luminosity (true units in kpc$^3$) of the population of clumps $d{\cal L}_{\rm cl}/d\ln M$ as defined in Eq. (\ref{['eq:lum_cl']}). The curves correspond to the NFW-B01 reference configuration, for various values of ${\alpha{\rm m}$α_ m$}$. The curves for any other configuration may be obtained by multiplying these curves to the ratios shown in Fig. \ref{['fig:clump_parameters2']}.
• Figure 5: Relative luminosity profiles as functions of the galactocentric radius $r$, in units of local luminosity $L_{\odot}$. Luminosities are plotted for the smooth DM contribution and for clumps in logarithmic mass bins of 3-decade width. Top left: reference configuration (ref). Top right: as ref but ${\alpha{\rm m}$α_ m$}=1.8$. Bottom left: as ref but ${\alpha{\rm m}$α_ m$}=2.0$. Bottom right: as ref but for a spatial distribution of clumps $\propto \rho_{\rm sm}(r)$.