The Cosmic-Ray Positron Excess, Recounted: A Budget Audit of the AMS-02 Positron Fraction

The Alpha Magnetic Spectrometer (AMS-02) measured a positron fraction that rises from 0.052 at 10 GeV to 0.155 at 300 GeV, where calculations in which positrons are produced only as secondaries of cosmic-ray collisions predict a falling fraction. This paper recounts that measurement as a budget: it states how much positron flux the secondary-only account is missing at representative energies, how much energy the surplus positrons carry locally, and what power each proposed source must supply to pay for them. Using the published AMS-02 anchor values and the collaboration's two-component fit, whose added source term has a cutoff energy of 810 GeV, the secondary-only prediction falls short of the measured fraction by a factor of 5.26 at 100 GeV and 11.6 at 300 GeV; the added source must supply 81.0% of the positrons at 100 GeV and 91.4% at 300 GeV. The surplus positrons above 10 GeV carry a local energy density of 9.22 x 10^-14 GeV cm^-3. Against synchrotron and inverse-Compton losses with an effective loss time of 2 x 10^5 years, maintaining that density requires an injection power density of 2.34 x 10^-29 erg cm^-3 s^-1. A pulsar population can pay this bill only at substantial pair-production efficiency, and a single Geminga-like pulsar at its present spin-down power falls short of the local (1 kpc) bill by a factor of about 90. Dark-matter annihilation at a representative mass of 800 GeV requires an annihilation cross section of 1.30 x 10^-22 cm^3 s^-1 in this accounting, a factor of 4330 above the thermal-relic value of 3 x 10^-26 cm^3 s^-1; with the longest plausible loss time the requirement falls to a factor of 866. The excess is therefore a measured surplus with a definite price, and each candidate source can be judged by whether it can pay that price.