Phys. Rev. D 89, 043013 (2014) - Constraining the origin of the rising cosmic ray positron fraction with the boron-to-carbon ratio

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

Ilias Cholis and Dan Hooper

Phys. Rev. D 89, 043013 – Published 24 February 2014

Abstract

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 $\sim 25 %$ of the observed rise in the positron fraction can result from this mechanism (at the 95% confidence level).

Received 19 December 2013

DOI:https://doi.org/10.1103/PhysRevD.89.043013

Authors & Affiliations

Ilias Cholis^1,* and Dan Hooper^1,2,†

¹Fermi National Accelerator Laboratory, Center for Particle Astrophysics, Batavia, Illinois 60510, USA
²Department of Astronomy and Astrophysics, University of Chicago, Chicago, Illinois 60637, USA

^*cholis@fnal.gov
^†dhooper@fnal.gov

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Vol. 89, Iss. 4 — 15 February 2014

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Figure 1
The ratio of the secondary cosmic ray acceleration term to the primary cosmic ray acceleration term in Eqs. (7) and (8), as a function of momentum per nucleon. The impact of including the acceleration of secondary cosmic rays produced inside and around the supernova shock front is most important at high energies and for lighter species. For ${}^{10}B$ B the ratio is significantly higher since $f_{{}^{10}B}^{- \infty}$ is suppressed. As in Ref. [26], we have adopted optimistic values for $K_{B}$ , $B$ , $n_{gas}^{-}$ , $v^{-}$ and $r$ (see text for more details).
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Figure 2
The cosmic ray boron-to-carbon ratio predicted for various parameter choices. In each frame, the black dotted curves represent the prediction without any contribution from the acceleration of secondary CRs in SNR shocks. In the left frames, this is calculated according to Eq. (8) with $q_{i}^{-} = 0$ , whereas in the right frames we have used GALPROP (see text for details). The other curves include contributions from accelerated secondaries. In the upper frames, we consider different values of $K_{B}$ , and set $n_{gas}^{-} = 2 {cm}^{- 3}$ . In the lower frames, we set $K_{B} = 40$ and vary the value of $n_{gas}^{-}$ . In all frames, we set $B = 1$ , $μ G$ , $v^{-} = 0.5 \times 10^{8} cm s^{- 1}$ and $r = 4$ . In each frame, the solid blue, dashed green, and dashed-dotted brown curves represent parameter choices that are incompatible with the measured boron-to-carbon spectrum at the 95%, 99%, and 99.9% confidence levels, respectively (using the combination of data from AMS and PAMELA; HEAO 3 data is shown only for comparison). We also include in each frame the prediction for an even more extreme parameter value ( $K_{B} = 40$ , $n_{gas}^{-} = 2.0 {cm}^{- 3}$ ) for comparison with Ref. [26].
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Figure 3
The cosmic ray antiproton-to-proton ratio predicted for some of the same parameter choices used in Fig. 2. See text for details.
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Figure 4
The cosmic ray positron fraction predicted for the parameter choices used in Figs. 2 and 3. The dotted black line denotes the prediction from secondary positrons produced in the interstellar medium [see Eqs. (14) and (15)], without any contribution from positrons accelerated in the shocks of supernova remnants. In the left frame, we set $n_{gas}^{-} = 2 {cm}^{- 3}$ and vary the value of $K_{B}$ . In the right frame, we set $K_{B} = 40$ and consider a range of values for $n_{gas}^{-}$ . In both frames, we take $B = 1 μ G$ , $v^{-} = 0.5 \times 10^{8} cm s^{- 1}$ and $r = 4$ up to the highest energies. We also take $E_{\max} = 10 TeV$ (see Fig. 5). Although the measured positron fraction can be accommodated by a model with $K_{B} = 40$ and $n_{gas}^{-} = 2 {cm}^{- 3}$ , such a scenario is highly incompatible with the measured boron-to-carbon ratio (and, to a lesser degree, with the antiproton-to-proton ratio). If we limit ourselves to parameter choices that are compatible with boron-to-carbon at the 95% confidence level, we find that the acceleration of secondary positrons in SNRs can account for only $\sim 25 %$ of the excess positrons observed above 30 GeV.
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Figure 5
The impact of varying the value of the maximum energy to which $e^{\pm}$ are accelerated inside of supernova remnants. See text for details.
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Physical Review D

covering particles, fields, gravitation, and cosmology

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

Ilias Cholis and Dan Hooper

Phys. Rev. D 89, 043013 – Published 24 February 2014

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Physical Review D

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

Ilias Cholis and Dan Hooper

Phys. Rev. D 89, 043013 – Published 24 February 2014

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