Positron fraction in cosmic rays and models of cosmic-ray propagation

The positron fraction observed by PAMELA and other experiments up to $\sim 100\mathrm{GeV}$ is analyzed in terms of models of cosmic-ray propagation. It is shown that generically we expect the positron fraction to reach $\sim 0.6$ at energies of several TeV, and its energy dependence bears an intimate but subtle connection with that of the boron to carbon ratio in cosmic rays. The observed positron fraction can be fit in a model that assumes a significant fraction of the boron below $\sim 10\mathrm{GeV}$ is generated through spallation of cosmic-ray nuclei in a cocoonlike region surrounding the sources, and the positrons of energy higher than a few GeV are almost exclusively generated through cosmic-ray interactions in the general interstellar medium. Such a model is consistent with the bounds on cosmic-ray anisotropies and other observations.

Figure 1

The positron fraction measured by PAMELA along with the earlier measurements are shown. The effects of gradient drifts in solar modulation may account for some of the difference in the data sets at $E<10\mathrm{GeV}$ [1]. The energy dependence of the positron fraction expected in the M-S model [14] is shown as a solid line and in the nested leaky-box model as a dashed line.

Figure 2

The observed $B/C$ ratio is plotted along with the spectra expected from the M-S model and nested leaky-box model. The $B/C$ data is taken from HEAO3 [50], Dwyer [51], Maehl et al. [52], Chapell and Webber [53], as well as the Tracer [54], CRN [55] and CREAM [56] experiments.

Figure 3

Measurements of the cosmic-ray anisotropy from various compilations [14, 35, 36, 37]. Also plotted are the predictions from models in M-S [14] and the results from Eq. (7), which are labeled as CB. The gray region shows the predicted anisotropy from Eq. (8).

Figure 4

The total electron spectrum $F_t$ measured by various instruments. Also included is a smooth fit to the data used in calculating the positron fraction $R$.