34 pages, 10 figures. To appear in "Foundations of Cosmic Ray Astrophysics", Proceedings of the International School of Physics "Enrico Fermi", Course 208, Varenna, 24-29 June 2022, edited by F. Aharonian, E. Amato, and P. Blasi
Massive stars blow powerful winds and eventually explode as supernovae. By doing so, they inject energy and momentum in the circumstellar medium, which is pushed away from the star and piles up to form a dense and expanding shell of gas. The effect is larger when many massive stars are grouped together in bound clusters or associations. Large cavities form around clusters as a result of the stellar feedback on the ambient medium. They are called superbubbles and are characterised by the presence of turbulent and supersonic gas motions. This makes star clusters ideal environments for particle acceleration, and potential contributors to the observed Galactic cosmic ray intensity.
This paper discusses the relation between the study of the fluxes of cosmic rays, gamma rays and neutrinos, and the connection of these observations with the newly born field of gravitational wave astronomy.
The $γ$-ray emission observed in several classes of Galactic and extragalactic astrophysical sources appears to be linked to accreting black holes and rotational powered neutron stars. These systems are prodigious cosmic accelerators, and are also potential sources of the UHE cosmic rays detected by several experiments and VHE neutrinos. We review a recent progress in our understanding of these objects, and demonstrate how recent and future observations can be employed to probe the conditions in the sources.
Combined data from gamma-ray telescopes and cosmic-ray detectors have produced some new surprising insights regarding intergalactic and galactic magnetic fields, as well as extragalactic background light. We review some recent advances, including a theory explaining the hard spectra of distant blazars and the measurements of intergalactic magnetic fields based on the spectra of distant sources. Furthermore, we discuss the possible contribution of transient galactic sources, such as past gamma-ray bursts and hypernova explosions in the Milky Way, to the observed flux of ultrahigh-energy cosmic-…
This white paper describes the contributions of the VERITAS gamma-ray telescope array to the CF6-A subgroup of the 'Cosmic Frontier' working group, part of the Snowmass Community Summer Study 2013.
We will review the main channels of gamma ray emission due to the acceleration and propagation of cosmic rays, discussing the cases of both galactic and extra-galactic cosmic rays and their connection with gamma rays observations.
The PeV gamma ray background produced in the interactions of ultra high energy cosmic rays with the ambient matter and radiations during their propagation in the Milky Way has been calculated in this paper. If the primary ultra high energy cosmic rays are produced from Galactic point sources then those point sources are also emitting PeV gamma rays. We discuss that the detection of galactocentric PeV gamma rays in the future would be a signature of the presence of EeV cosmic accelerators in the Milky Way.
This paper deals with the cosmic-ray penetration into molecular clouds and with the related gamma--ray emission. High energy cosmic rays interact with the dense gas and produce neutral pions which in turn decay into two gamma rays. This makes molecular clouds potential sources of gamma rays, especially if they are located in the vicinity of a powerful accelerator that injects cosmic rays in the interstellar medium. The amplitude and duration in time of the cosmic--ray overdensity around a given source depend on how quickly cosmic rays diffuse in the turbulent galactic magnetic field. For these…
The observation of neutrinos from cosmic accelerators will be revolutionary. High energy neutrinos are closely connected to ultrahigh energy cosmic rays and their sources. Cosmic ray sources are likely to produce neutrinos and the propagation of ultrahigh cosmic rays from distant sources can generate PeV to ZeV neutrinos. We briefly review recent progress on the observations of ultrahigh energy cosmic rays and their implications for the future detections of high energy neutrinos.
After a hundred years of searching for the origin of cosmic rays, where and how they are made has finally become clear. Here we briefly trace that odyssey through both astronomical observations and cosmic ray measurements.
In this paper we review the status of the search for high-energy neutrinos from outside the solar system and discuss the implications for the origin and propagation of cosmic rays. Connections between neutrinos and gamma-rays are also discussed.
The properties of galactic cosmic rays are investigated with the KASCADE-Grande experiment in the energy range between $10^{14}$ and $10^{18}$ eV. Recent results are discussed. They concern mainly the all-particle energy spectrum and the elemental composition of cosmic rays.
We examine the effects of streaming cosmic rays upstream of a strong, parallel collisionless shock. We include explicitly the inertia of the cosmic rays in our analysis, which was neglected in previous work. For parameters relevant to the acceleration of cosmic rays at a supernova blast wave, we find no MHD fluid instability that would lead to the amplification of the magnetic field above that given by the compression at the shock. We show how to recover, from our own analysis, the cosmic-ray-driven MHD fluid instability found by previous authors. We conclude that including the inertia and dyn…
The study of the gamma-ray radiation produced by cosmic rays that escape their accelerators is of paramount importance for (at least) two reasons: first, the detection of those gamma-ray photons can serve to identify the sources of cosmic rays and, second, the characteristics of that radiation give us constraints on the way in which cosmic rays propagate in the interstellar medium. This paper reviews the present status of the field.
Auger Collaboration has reported a large-scale anisotropy in the arrival directions of cosmic rays above 8 EeV. The dipole direction, at 125$^\circ$ from the Galactic center, is taken as an indication of an extragalactic origin of these cosmic rays. We show, both theoretically and by direct numerical simulations, that this is not necessarily true. Intermediate mass nuclei originating in the Galaxy and diffusing in the Galactic magnetic field can have a dipole anisotropy pointing away from the Galactic center. Our theory predicts a quadrupole anisotropy of the same order of magnitude as the dip…
We demonstrate that cosmic rays form filamentary structures in the precursors of supernova remnant shocks due to their self-generated magnetic fields. The cosmic-ray filamentation results in the growth of a long wavelength instability, and naturally couples the rapid non-linear amplification on small scales to larger length scales. Hybrid magnetohydrodynamics--particle simulations are performed to confirm the effect. The resulting large scale magnetic field may facilitate the scattering of high energy cosmic rays as required to accelerate protons beyond the knee in the cosmic-ray spectrum at s…
Observations of molecular clouds in the gamma ray domain provide us with a tool to study the distribution of cosmic rays in the Galaxy. This is because cosmic rays can penetrate molecular clouds, undergo hadronic interactions in the dense gas, and produce neutral pions that in turn decay into gamma rays. The detection of this radiation allows us to estimate the spectrum and intensity of cosmic rays at the cloud's position. Remarkably, this fact can be used to constrain the cosmic ray diffusion coefficient at specific locations in the Galaxy.
The arrival directions of Galactic cosmic rays exhibit anisotropies up to the level of one per-mille over various angular scales. Recent observations of TeV-PeV cosmic rays show that the dipole anisotropy has a strong energy dependence with a phase-flip around 100 TeV. We argue that this behavior can be well understood by the combination of various effects: the anisotropic diffusion of cosmic rays, the presence of nearby sources, the Compton-Getting effect from our relative motion and the reconstruction bias of ground-based observatories.
The upper limit on the flux of ultra high energy neutrinos from gamma-ray bursts (GRBs) that was reported recently by the IceCube collaboration contradicts predictions based on the Fireball model of GRBs, but does not exclude GRBs as a main source of ultra-high energy cosmic rays.
We briefly review sources of cosmic rays, their composition and spectra as well as their propagation in the galactic and extragalactic magnetic fields, both regular and fluctuating. A special attention is paid to the recent results of the X-ray and gamma-ray observations that shed light on the origin of the galactic cosmic rays and the challenging results of Pierre Auger Observatory on the ultra high energy cosmic rays. The perspectives of both high energy astrophysics and cosmic-ray astronomy to identify the sources of ultra high energy cosmic rays, the mechanisms of particle acceleration, to…
The maximum cosmic ray energy achievable by acceleration by a relativistic blast wave is derived. It is shown that forward shocks from long GRB in the interstellar medium are powerful enough to produce the Galactic cosmic-ray component up to the ankle at $4\times 10^{18}$eV, as per an earlier suggestion (Levinson and Eichler, 1993). It is further argued that, were extragalactic long GRB responsible for the component {\it above} the ankle as well, the contribution from an occasional Galactic GRB within the solar circle would yield more than the observational limits on the outward flux from the …
It has been suggested that hypernova remnants, with a substantial amount of energy in semi-relativistic ejecta, can accelerate intermediate mass or heavy nuclei to ultra-high energies and provide sufficient amount of energy in cosmic rays to account for the observed flux. We here calculate the expected energy spectrum and chemical composition of ultra-high energy cosmic rays from such semi-relativistic hypernovae. With a chemical composition equal to that of the hypernova ejecta and a flat or hard spectrum for cosmic rays at the sources, the spectrum and composition of the propagated cosmic ra…
Progress reported during the XV International Symposium on Very High-Energy Cosmic-Ray Interactions is summarized. Emphasize is given to experimental work. The actual status, recent results, and their implications on the present understanding of the origin of high-energy cosmic-rays and their interactions are discussed.
The High-Altitude Water Cherenkov Observatory, or HAWC, is carrying out an unbiased survey of cosmic rays and gamma rays from the Northern Hemisphere between 100 GeV and 100 TeV. HAWC is currently the only high-uptime wide-field TeV observatory in operation, and has a robust program to search for flares and other transient sources of gamma rays. The detector is also well suited to observe spatially extended regions of gamma-ray emission and cosmic-ray anisotropy. HAWC recently concluded its first year of data taking with the complete detector. The results include not only observations of many …
It is shown that the relativistic jets associated with the growth and past activity of the supermassive black hole in the Andromeda galaxy could be the main source of cosmic rays with energies above $10^{15}$ eV. Most of the cosmic ray energy is related to a bow shock of the jet that produces multi-PeV cosmic rays with light composition. The highest energy cosmic rays with heavy composition are produced in the jet itself. The spectra of energetic particles produced in Andromeda galaxy and propagated to the Earth are calculated and compared with observations.
An analysis of arrival directions of extensive air showers generated by cosmic rays in the PeV energy range and registered with the EAS MSU and EAS-1000 Prototype arrays reveals a considerable number of regions of excessive flux of cosmic rays. We present results of comparative analysis of regions found in the two data sets, estimate probabilities of their appearance, and discuss correlation of their locations with coordinates of possible astrophysical sources of PeV cosmic rays.
High-energy cosmic rays, impinging on the atmosphere of the Earth initiate cascades of secondary particles, the extensive air showers. The electrons and positrons in the air shower emit electromagnetic radiation. This emission is detected with the LOFAR radio telescope in the frequency range from 10 to 240 MHz. The data are used to determine the properties of the incoming cosmic rays. The radio technique is now routinely used to measure the arrival direction, the energy, and the particle type (atomic mass) of cosmic rays in the energy range from $10^{17}$ to $10^{18}$ eV. This energy region is…
Results are presented that were obtained by analysing the arrival directions of E0 > 8x10**18 eV primary cosmic rays recorded at the Yakutsk array over the period between 1974 and 2003 and at the SUGAR array (Australia). The greatest primary cosmic ray flux is shown to arrive from the region of visible intersection of the planes of the Galaxy and the Supergalaxy (local supercluster of galaxies) at a galactic longitude of about 137 degres. On a global scale, the lowest temperature of the cosmic microwave background is typical of this region.
After the discovery of Fermi Bubbles and the excess of gamma-ray emission, the Galactic Centre has received increasing attention with the aim to understand its role in the origin and acceleration of primary cosmic rays (CRs). Based on a diffusion/re-acceleration model, we use the GALPROP software to solve the diffusion equation for the cosmic rays and compare the results with the CRs spectrum, motivated by relationship between several energetic sources at the Galactic Centre and the generated diffuse GeV-TeV gamma-rays. We calculate the cosmic ray distribution, gamma-ray flux from Galactic Cen…
In this paper we note that the spectral intensities of antiprotons observed in Galactic cosmic rays in the energy range ~ 1-100 GeV by BESS, PAMELA and AMS instruments display nearly the same spectral shape as that generated by primary cosmic rays through their interaction with matter in the interstellar medium, without any significant modifications. More importantly, a constant residence time of ~ 2.5 +/-0.7 million years in the Galactic volume, independent of the energy of cosmic rays, matches the observed intensities. A small additional component of secondary antiprotons in the energy below…
The arguments surrounding the Galactic component of the cosmic rays, the energy budget, questions of composition, spectral features, anisotropy, sources etc, will be critically examined. We are moving into a new phase in the study of the Galactic cosmic rays where it is becoming clear that precision measurements are revealing new, and in some cases unexpected, features which are forcing us to develop more sophisticated models for their production and propagation. The fundamental concepts however appear to be quite solid and have changed remarkably little in the more than fifty years since Ginz…
This review summarizes recent developments in the understanding of high-energy cosmic rays. It focuses on galactic and presumably extragalactic particles in the energy range from the knee (10^15 eV) up to the highest energies observed (>10^20 eV). Emphasis is put on observational results, their interpretation, and the global picture of cosmic rays that has emerged during the last decade.
In over two years of operation Fermi-LAT has revolutionized our knowledge of the gamma-ray sky. Interstellar gamma rays are part of this new era and allow unprecedented tests for models of cosmic rays in the Galaxy. The extension to lower energies with INTEGRAL/SPI data is also evolving. The global multiwavelength luminosity of the Milky Way has been derived, with implications for the Galactic energy balance and the radio-FIR correlation.
In this paper, we used the Monte Carlo code CRPropa version 2.0 to simulate the propagation of UHE cosmic rays. In the simulation, uniform cosmic ray sources with spectral indices of α = 1.4, α = 2 and Emax = 1021 eV for pure iron composition at the source position are assumed. We obtained the logarithmic average mass of cosmic rays as a function of energy and compared it with the experimental values in the ankle, and we demonstrated how the mass composition changes before and after the ankle.
We study general implications of the IceCube observations in the energy range from $10^{6}$ GeV to $10^{10}$ GeV for the origin of extragalactic ultrahigh energy cosmic rays assuming that high energy neutrinos are generated by the photomeson production of protons in the extragalactic universe. The PeV-energy neutrino flux observed by IceCube gives strong bounds on the photomeson-production optical depth of protons in their sources and the intensity of the proton component of extragalactic cosmic rays. The neutrino flux implies that extragalactic cosmic-ray sources should have the optical depth…
While there is some level of consensus on a Galactic origin of cosmic rays up to the knee ($E_{k}\sim 3\times 10^{15}$ eV) and on an extragalactic origin of cosmic rays with energy above $\sim 10^{19}$ eV, the debate on the genesis of cosmic rays in the intermediate energy region has received much less attention, mainly because of the ambiguity intrinsic in defining such a region. The energy range between $10^{17}$ eV and $\sim 10^{19}$ eV is likely to be the place where the transition from Galactic to extragalactic cosmic rays takes place. Hence the origin of these particles, though being of …
The measurement of ultra-high energy cosmic rays is an unique way to study article interactions at energies which are well above the capability of current accelerators. Significant progress in this field has occurred during last years, particularly due to the measurements made at the Pierre Auger Observatory. The important results which were achieved during last years are described here. Also future plans for the study of cosmic rays are presented.
Recent high energy gamma-ray observations of both single supernova remnants and superbubbles, together with observations of supernovae, star formation regions, and local cosmic ray composition, now provide an integrated framework tying together the sources, injection, acceleration and propagation of the cosmic rays, so that it is possible to determine their relative contributions to cosmic ray acceleration for all but the very highest energies.
The cores of Arp 220, the closest ultra-luminous infrared starburst galaxy, provide an opportunity to study interactions of cosmic rays under extreme conditions. In this paper, we model the populations of cosmic rays produced by supernovae in the central molecular zones of both starburst nuclei. We find that ~65 - 100% of cosmic rays are absorbed in these regions due to their huge molecular gas contents, and thus, the nuclei of Arp 220 nearly complete proton calorimeters. As the cosmic ray protons collide with the interstellar medium, they produce secondary electrons that are also contained wi…
Galaxies at high redshifts with strong star formation are sources of high-energy cosmic rays. These cosmic rays interact with the baryon and radiation fields of the galactic environment via photo-pair, photo-pion and proton-proton processes to produce charged and neutral pions, neutrons and protons. The cosmic rays thereby deposit energy into the interstellar medium (ISM) as they propagate. We show how energy transport and deposition by ultra high-energy cosmic rays is regulated by the evolution of the galaxy, in particular by the development of the galactic magnetic field. We show how the par…
The effect of cosmic rays on the Parker-Jeans instability in magnetized self-gravitating gaseous disks is studied by three-dimensional magnetohydrodynamic (MHD) simulations with cosmic rays taken as a massless fluid with notable pressure. Cosmic ray diffusion along the magnetic field is taken into account in the simulation. The initial configuration of the disk is a magnetized cold gas slab sandwiched between hot corona (on top and bottom). We show that cosmic rays play an important role in the formation of filaments or clumps in some parameter regimes. In a certain range of the thickness of t…
The galactic cosmic rays are generally believed to be originated in supernova remnants (SNRs), produced in diffusive shock acceleration (DSA) process in supernova blast waves driven by expanding SNRs. One of the key unsettled issue in SNR origin of cosmic ray model is the maximum attainable energy by a cosmic ray particle in the supernova shock. Recently it has been suggested that an amplification of effective magnetic field strength at the shock may take place in young SNRs due to growth of magnetic waves induced by accelerated cosmic rays and as a result the maximum energy achieved by cosmic…
I review here some of the physics we are learning and expect to learn in the near future through the observation of cosmic rays. The study of cosmic rays involves a combination of data from accelerators, ground arrays, atmospheric fluorescence detectors and balloon and satellite experiments. I will discuss the data of the Pierre Auger Observatory, PAMELA, ATIC and FST among other experiments.
The High-Altitude Water Cherenkov (HAWC) Observatory, located 4100 m above sea level near Sierra Negra (19$^\circ$ N) in Mexico, is sensitive to gamma rays and cosmic rays at TeV energies. The arrival direction distribution of cosmic rays at these energies shows significant anisotropy on several angular scales, with a relative intensity ranging between 10$^{-3}$ and 10$^{-4}$. We present the results of a study of cosmic-ray anisotropy based on more than 86 billion cosmic-ray air showers recorded with HAWC since June 2013. The HAWC cosmic-ray sky map, which has a median energy of 2 TeV, exhibit…
We briefly review the main channels of gamma ray and neutrino production due to the propagation of ultra high energy cosmic rays. We show how the observations of these secondary radiations are of paramount importance in tagging mass composition and sources of ultra high energy cosmic rays.
This is a review of the most resent results from the investigation of the Ultrahigh Energy Cosmic Rays, particles of energy exceeding 10$^{18}$ eV. After a general introduction to the topic and a brief review of the lower energy cosmic rays and the detection methods, the two most recent experiments, the High Resolution Fly's Eye (HiRes) and the Southern Auger Observatory are described. We then concentrate on the results from these two experiments on the cosmic ray energy spectrum, the chemical composition of these cosmic rays and on the searches for their sources. We conclude with a brief anal…
We study the escape of cosmic-ray protons accelerated at a supernova remnant (SNR). We are interested in their propagation in interstellar medium (ISM) after they leave the shock neighborhood where they are accelerated, but when they are still near the SNR with their energy density higher than that in the average ISM. Using Monte-Carlo simulations, we found that the cosmic-rays with energies of <~TeV excite Alfven waves around the SNR on a scale of the SNR itself if the ISM is highly ionized. Thus, even if the cosmic-rays can leave the shock, scattering by the waves prevents them from moving f…
We present the main results on the energy spectrum and composition of the highest energy cosmic rays of energy exceeding 10$^{18}$ eV obtained by the High Resolution Fly's Eye and the Southern Auger Observatory. The current results are somewhat contradictory and raise interesting questions about the origin and character of these particles.
The role of cosmic rays generated by supernovae and young stars has very recently begun to receive significant attention in studies of galaxy formation and evolution due to the realization that cosmic rays can efficiently accelerate galactic winds. Microscopic cosmic ray transport processes are fundamental for determining the efficiency of cosmic ray wind driving. Previous studies focused on modeling of cosmic ray transport either via constant diffusion coefficient or via streaming proportional to the Alfven speed. However, in predominantly cold, neutral gas, cosmic rays can propagate faster t…
Cosmic rays are a sample of solar, galactic and extragalactic matter. Their origin and properties are one of the most intriguing question in modern astrophysics. The most energetic events and active objects in the Universe: supernovae explosion, pulsars, relativistic jets, active galactic nuclei, have been proposed as sources of cosmic rays although unambiguous evidences have still to be found. Electrons, while comprising ~1% of the cosmic radiation, have unique features providing important information regarding the origin and propagation of cosmic rays in the Galaxy that is not accessible fro…
It is widely believe that galactic cosmic rays are originated in supernova remnants (SNRs) where they are accelerated by diffusive shock acceleration process at supernova blast waves driven by expanding SNRs. In recent theoretical developments of the diffusive shock acceleration theory in SNRs, protons are expected to accelerate in SNRs at least up to the knee energy. If SNRs are true generator of cosmic rays, they should accelerate not only protons but also heavier nuclei with right proportion and the maximum energy of heavier nuclei should be atomic mass (Z) times that of protons. In this wo…
The wealth of data collected in the last few years thanks to the Pierre Auger Observatory and recently to the Telescope Array made the problem of the origin of ultra high energy cosmic rays a genuinely experimental/observational one. The apparently contradictory results provided by these experiments in terms of spectrum, chemical composition and anisotropies do not allow to reach any final conclusions as yet. Here I will discuss some of the theoretical challenges imposed by these data: in particular I will discuss some issues related to the transition from Galactic to extragalactic cosmic rays…
We present a linear perturbation analysis of the magnetorotational instability in the presence of the cosmic rays. Dynamical effects of the cosmic rays are considered by a fluid description and the diffusion of cosmic rays is only along the magnetic field lines. We show an enhancement in the growth rate of the unstable mode because of the existence of cosmic rays. But as the diffusion of cosmic rays increases, we see that the growth rate decreases. Thus, cosmic rays have a destabilizing role in the magnetorotational instability of the accretion discs.
Cosmic rays and related measurements: IceTop overview; IceTop calibration; Cosmic ray composition; Air shower measurements; Studies of cosmic ray muons; Studies of PeV gamma rays; Cosmic ray anisotropy; Forbush decrease; Submitted papers to the 32nd International Cosmic Ray Conference, Beijing 2011.
Recent direct measurements of Galactic cosmic ray spectra by balloon/space-borne detectors reveal spectral hardenings of all major nucleus species at rigidities of a few hundred GV. The all-sky diffuse gamma-ray emissions measured by the Fermi Large Area Telescope also show spatial variations of the intensities and spectral indices of cosmic rays. These new observations challenge the traditional simple acceleration and/or propagation scenario of Galactic cosmic rays. In this work we propose a spatially-dependent diffusion scenario to explain all these phenomena. The diffusion coefficient is as…
It is known from some time that to explain some apparently {\it exotic events} observed in cosmic ray experiments, a deeply penetrating component in cosmic rays is needed, which, in turn, leads frequently to the nonexponential distributions of some observables. We argue that such unexpected behavior of some cosmic rays data can be most naturally explained by attributing them to the possible fluctuations of cross sections.
The Hubble Space Telescope (HST) has been operational for over 30 years and throughout that time it has been bombarded by high energy charged particles colloquially referred to as cosmic rays. In this paper, we present a comprehensive study of more than 1.2 billion cosmic rays observed with HST using a custom written python package, \texttt{HSTcosmicrays}, that is available to the astronomical community. We analyzed $75,908$ dark calibration files taken as part of routine calibration programs for five different CCD imagers with operational coverage of Solar Cycle 23 and 24. We observe the expe…
We study the change in cosmic-ray pressure, the change in cosmic-ray density, and the level of cosmic-ray induced heating via Alfven-wave damping when cosmic rays move from a hot ionized plasma to a cool cloud embedded in that plasma. The general analysis method outlined here can apply to diffuse clouds in either the ionized interstellar medium or in galactic winds. We introduce a general-purpose model of cosmic-ray diffusion building upon the hydrodynamic approximation for cosmic rays (from McKenzie & Voelk and Breitschwerdt and collaborators). Our improved method self-consistently derives th…
We show that the observed fluxes, spectra and sky distributions of the high energy diffuse backgrounds of astronomical neutrinos, gamma rays and cosmic ray positrons satisfy simple relations expected from their common production in hadronic collisions of high energy cosmic rays (CRs) with diffuse matter. This provides compelling evidence that the high energy neutrino, gamma ray, and positron backgrounds have a common origin - hadronic meson production by cosmic rays in our Galaxy and in external galaxies rather than through the decay/annihilation of dark matter particles.
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 …
