Origin of the spectral upturn in the cosmic-ray $\mathrm{C}/\mathrm{Fe}$ and $\mathrm{O}/\mathrm{Fe}$ ratios

The observed spectrum of Galactic cosmic rays has several exciting features such as the rise in the positron fraction above $\sim 10\mathrm{GeV}$ of energy and the spectral hardening of protons and helium at $\gtrsim 300\mathrm{GeV}/\mathrm{n}\mathrm{ucleon}$ of energy. The ATIC-2 experiment has recently reported an unexpected spectral upturn in the elemental ratios involving iron, such as the $\mathrm{C}/\mathrm{Fe}$ or $\mathrm{O}/\mathrm{Fe}$ ratios, at energy $\gtrsim 50\mathrm{GeV}$ per nucleon. It is recognized that the observed positron excess can be explained by pion production processes during diffusive shock acceleration of cosmic-ray hadrons in nearby sources. Recently, it was suggested that a scenario with nearby source dominating the GeV-TeV spectrum may be connected with the change of slope observed in protons and nuclei, which would be interpreted as a flux transition between the local component and the large-scale distribution of Galactic sources. Here I show that, under a two-component scenario with nearby source, the shape of the spectral transition is expected to be slightly different for heavy nuclei, such as iron, because their propagation range is spatially limited by inelastic collisions with the interstellar matter. This enables a prediction for the primary/primary ratios between light and heavy nuclei. From this effect, a spectral upturn is predicted in the $\mathrm{C}/\mathrm{Fe}$ and $\mathrm{O}/\mathrm{Fe}$ ratios in good accordance with the ATIC-2 data.

Figure 1

Energy spectrum of CR protons multiplied by $E^{2.7}$. The solid lines indicate the model calculations. The contribution arising from the nearby SNR (short-dashed lines) and from the Galactic SNR ensemble (long-dashed lines) are shown. The data are from AMS [6], PAMELA [3], ATIC-2 [20], and CREAM [4].

Figure 2

Top: Distribution function (solid line) and cumulative function (dashed line) of Galactic SNRs as function of the distance $d$ from the solar system. Bottom: Fraction of Galactic SNRs contributing to the CR flux of $\mathrm{C}$ (dotted line), $\mathrm{O}$ (solid line), and $\mathrm{Fe}$ (dashed line).

Figure 3

Energy spectra of $\mathrm{O}$ and $\mathrm{Fe}$ multiplied by $E^{2.7}$, and nuclear ratios $\mathrm{C}/\mathrm{Fe}$ and $\mathrm{O}/\mathrm{Fe}$ as function of kinetic energy per nucleon. The solid lines indicate the model calculations. The contributions arising from the nearby source (short-dashed lines) and from the Galactic ensemble (long-dashed lines) are shown. The data are from ATIC-2 [8, 9], CREAM [30], CRN [31], and TRACER [32, 33]. The TRACER data on nuclear ratios are those obtained in Ref. [9]. Standard model predictions are also shown for the $\mathrm{C}/\mathrm{Fe}$ and $\mathrm{O}/\mathrm{Fe}$ ratios (dotted lines).