Cosmic-ray sum rules

We introduce new sum rules allowing to determine universal properties of the unknown component of the cosmic rays; we show how they can be used to predict the positron fraction at energies not yet explored by current experiments, and to constrain specific models.

Figure 1

Ratio $R(E)$ as a function of the energy $E$ of electrons and positrons and for vales of $r_U=0$, $1/2$, 1, 2, from top to bottom. The shaded region accounts for the one sigma error in PAMELA and FERMI-LAT. Secondaries are estimated according to the expressions in [6, 7].

Figure 2

Model-independent prediction for the positron fraction $P(E)$ as a function of the energy $E$ of electrons and positrons and for vales of $r_U=0$, $1/2$, 1, 2, 4, from top to bottom. Secondaries are estimated according to the expressions in [6, 7] reported in the main text and the derived $N_B$ values: $N_B=0.66$, 0.64, 0.62, 0.58, 0.50.

Figure 3

We display ${\varphi }^U(E)={\varphi }_{\pm }^U(E)$ corresponding to the central shaded region for the whole energy range of the FERMI-LAT experiment. The upper red points are the actual FERMI-LAT data, and the background of electrons is the upper green stripe while the positrons is the lower magenta stripe. See the text for further explanation.