Constraining the origin of the rising cosmic ray positron fraction with the boron-to-carbon ratio

The rapid rise in the cosmic ray positron fraction above 10 GeV, as measured by PAMELA and AMS, suggests the existence of nearby primary sources of high energy positrons, such as pulsars or annihilating/decaying dark matter. In contrast, the spectrum of secondary positrons produced through the collisions of cosmic rays in the interstellar medium is predicted to fall rapidly with energy, and thus is unable to account for the observed rise. It has been proposed, however, that secondary positrons could be produced and then accelerated in nearby supernova remnants, potentially explaining the observed rise, without the need of primary positron sources. Yet, if secondary positrons are accelerated in such shocks, other secondary cosmic ray species (such as boron nuclei, and antiprotons) will also be accelerated, leading to rises in the boron-to-carbon and antiproton-to-proton ratios. The measurements of the boron-to-carbon ratio by the PAMELA and AMS collaborations, however, show no sign of such a rise. With this new data in hand, we revisit the secondary acceleration scenario for the rising positron fraction. Assuming that the same supernova remnants accelerate both light nuclei (protons, helium) and heavier cosmic ray species, we find that no more than ~25% of the observed rise in the positron fraction can result from this mechanism (at the 95% confidence level)