Towards Understanding the Origin of Cosmic-Ray Positrons

Precision measurements of cosmic ray positrons are presented up to 1 TeV based on 1.9 million positrons collected by the Alpha Magnetic Spectrometer on the International Space Station. The positron flux exhibits complex energy dependence. Its distinctive properties are (a) a significant excess starting from $25.2\pm 1.8\mathrm{GeV}$ compared to the lower-energy, power-law trend, (b) a sharp dropoff above $284_{-64}^{+91}\mathrm{GeV}$, (c) in the entire energy range the positron flux is well described by the sum of a term associated with the positrons produced in the collision of cosmic rays, which dominates at low energies, and a new source term of positrons, which dominates at high energies, and (d) a finite energy cutoff of the source term of $E_s=810_{-180}^{+310}\mathrm{GeV}$ is established with a significance of more than $4\sigma$. These experimental data on cosmic ray positrons show that, at high energies, they predominantly originate either from dark matter annihilation or from other astrophysical sources.

Figure 1

For display purposes, the positron flux, ${\mathrm{\Phi }}_{e^{+}}$ is traditionally presented scaled by ${\tilde{E}}^3$. The resulting AMS positron spectrum, ${\tilde{E}}^3{\mathrm{\Phi }}_{e^{+}}$, (red data points) is shown as a function of energy $\tilde{E}$. The time variation of the flux at low energies due to solar modulation [3] is indicated by the red band. To guide the eye, the vertical color bands indicate the energy ranges corresponding to changing behavior of the spectrum: flattening, rising, and falling spectrum (see text).

Figure 2

The AMS positron spectrum (${\tilde{E}}^3{\mathrm{\Phi }}_{e^{+}}$) together with earlier measurements from PAMELA [26], Fermi-LAT [27], MASS [28], CAPRICE [29], AMS-01 [30], and HEAT [31].

Figure 3

(a) The spectral index of the AMS positron flux in nonoverlapping energy intervals (red data points). The spectral index has complex energy dependence with a significant decrease towards higher energies. (b),(c) A double power-law fit of Eq. (3) to the flux in the energy ranges [7.10–55.58] and [55.58–1000] GeV, respectively. The red data points are the measured positron flux values scaled by ${\tilde{E}}^3$. The fitted functions are represented by the blue lines. The vertical dashed lines and the bands correspond to the value and the error of the energies $E_0$ where the changes of the spectral index occur. The dashed blue lines are the extrapolations of the power law below $E_0$ into the higher-energy regions. $\mathrm{\Delta }\gamma$ is the magnitude of the spectral index change, see Eq. (3). The green band in (a) represents the 68% C.L. interval of the minimal model fit of Eq. (4) to the positron flux (see text).

Figure 4

The fit of Eq. (4) (green line) to the positron flux in the energy range [0.5–1000] GeV together with the 68% C.L. interval (green band). The exponential cutoff of the source term is determined to be $810_{-180}^{+310}\mathrm{GeV}$ from the fit. The red data points represent the measured positron flux values scaled by ${\tilde{E}}^3$. The source term contribution is represented by the magenta area and the diffuse term contribution by the gray area. The insert shows projections of the regions of $1\sigma$ (green contour), $2\sigma$ (black contour), $3\sigma$ (blue contour), and $4\sigma$ (red contour) significance of the $1/E_s$ measurement onto the plane of parameters $1/E_s-C_s$ (see text).