What can we really learn from positron flux 'anomalies'?

We present a critical analysis of the observational constraints on, and of the theoretical modelling of, aspects of cosmic ray (CR) generation and propagation in the Galaxy, which are relevant for the interpretation of recent positron and antiproton measurements. We give simple, analytic, model-independent expressions for the secondary (p) over bar flux, and an upper limit for the secondary e(+) flux, obtained by neglecting e(+) radiative losses, e(+)/(e(+) + e(-)) < 0.2 +/- 0.1 up to similar to 300 GeV. These expressions are completely determined by the rigidity-dependent grammage, which is measured from stable CR secondaries up to similar to 150 GeV nucleon(-1), and by nuclear cross-sections measured in the laboratory. <(p)over bar> and e(+) measurements, available up to similar to 100 GeV, are consistent with these estimates, implying that there is no need for new, non-secondary, (p) over bar p or e(+) sources. The radiative loss suppression factor f(s,e+) of the e(+) flux depends on the e(+) propagation in the Galaxy, which is not understood theoretically. A rough, model-independent estimate of f(s,e+) similar to 1/3 can be obtained at a single energy, epsilon similar to 20 GeV, from unstable secondary decay and is found to be consistent with e(+) measurements, including the positron fraction measured by Payload for Antimatter Matter Exploration and Light-nuclei Astrophysics (PAMELA). We show that specific detailed models, that agree with compositional CR data, agree with our simple expressions for the e(+) and (p) over bar flux, and that the claims that the positron fraction measured by PAMELA requires new primary e(+) sources are based on assumptions, that are not supported by observations. If PAMELA results are correct, they suggest that f(s,e+) (epsilon) is slightly increasing with energy, which provides an interesting constraint on CR propagation models. We argue that measurements of the e(+) to (p) over bar ratio are more useful for challenging secondary production models than the e(+)/(e(+) + e(-)) fraction.