Diffuse Galactic Gamma Rays from Shock-Accelerated Cosmic Rays

A shock-accelerated particle flux \propto p^-s, where p is the particle momentum, follows from simple theoretical considerations of cosmic-ray acceleration at nonrelativistic shocks followed by rigidity-dependent escape into the Galactic halo. A flux of shock-accelerated cosmic-ray protons with s ~ 2.8 provides an adequate fit to the Fermi-LAT gamma-ray emission spectra of high-latitude and molecular cloud gas when uncertainties in nuclear production models are considered. A break in the spectrum of cosmic-ray protons claimed by Neronov, Semikoz, & Taylor (PRL, 108, 051105, 2012) when fitting the gamma-ray spectra of high-latitude molecular clouds is a consequence of using a cosmic-ray proton flux described by a power law in kinetic energy.

💡 Research Summary

The paper revisits the classic theory of diffusive shock acceleration (DSA) at non‑relativistic shocks and shows that the resulting cosmic‑ray (CR) distribution is naturally a power law in particle momentum, (J(p)\propto p^{-s}). By combining the DSA prediction with a rigidity‑dependent escape from the Galactic disk into the halo (i.e., a diffusion coefficient (\kappa(R)\propto R^{\delta}) with (\delta\sim0.3)–0.6), the authors derive a steady‑state CR proton spectrum characterized by an index (s\approx2.8).

The gamma‑ray emission from the interstellar medium is dominated by neutral‑pion decay following proton‑proton collisions. Using up‑to‑date hadronic production models (Kamae et al. 2006; Kafexhiu et al. 2014; Dermer 1986), the authors compute the expected gamma‑ray spectra for a gas column density typical of high‑latitude diffuse clouds and of several well‑studied molecular clouds (Orion A/B, Taurus, Perseus). They find that a proton spectrum (\propto p^{-2.8}) reproduces the Fermi‑LAT measurements across the 0.1–100 GeV band when the ∼10–20 % uncertainties in the nuclear cross sections are taken into account. The fit is especially good in the 0.3–3 GeV range, where the observed spectrum is relatively flat; the low‑energy (<0.3 GeV) region remains limited by the precision of the pion‑production cross sections but does not require any additional spectral features.

A key point of the work is the critique of the “break” in the CR proton spectrum reported by Neronov, Semikoz, and Taylor (2012). Those authors fitted the same gamma‑ray data using a proton flux expressed as a power law in kinetic energy, (J(E_{\rm kin})\propto E_{\rm kin}^{-2.7}), and inferred a spectral break near a few GeV to reconcile the model with observations. The present study demonstrates that this break is an artefact of the chosen parametrization. In the non‑relativistic regime, kinetic energy and momentum are not linearly related; a power law in kinetic energy translates into a curved spectrum in momentum space, artificially steepening the low‑energy part of the proton distribution. When the physically motivated momentum power law is employed, the data are fully explained without invoking any break.

The authors therefore conclude that (1) a simple DSA‑derived momentum spectrum with (s\simeq2.8) provides a self‑consistent description of the Galactic diffuse gamma‑ray background; (2) the apparent need for a low‑energy break disappears once the correct momentum‑based representation of the CR flux is used; and (3) remaining discrepancies are within the systematic uncertainties of the hadronic production models. This work reinforces the standard picture of shock‑accelerated CRs diffusing out of the disk and sets a robust baseline for future high‑precision gamma‑ray and CR measurements, which will further refine the diffusion parameters and nuclear interaction models.