We study the 0509-67.5 supernova remnant in the Large Magellanic Cloud with the VLT/FORS2 spectrograph. We detect a broad component in the H-alpha emission with a FWHM of 2680 \pm 70 km/s and 3900 \pm 800 km/s for the southwest (SW) and northeast (NE) shocks respectively. For the SW, the proton temperature appears to be too low for the shock velocity, which we attribute to a cosmic-ray pressure behind the shock front of at least 20% of the total pressure. For the NE, the post-shock proton temperature and the shock velocity are compatible, only if the plasma behind the shock front has a degree of thermal equilibrium of over 20%, which is at odds with current models for temperature equilibration behind fast shocks, which do not accelerate cosmic rays. If we assume the electron temperature to be less than 10% of the proton temperature, we find a post-shock cosmic-ray pressure of at least 7%.
We review the basic features of particle acceleration theory around collisionless shocks in supernova remnants (SNRs). We show how non linear effects induced by the back reaction of accelerated particles onto the shock dynamics are of paramount importance to support the hipotesys that SNRs are the factories of Galactic cosmic rays. Recent developments in the modeling of the mechanism of diffusive shock acceleration are discussed, with emphasis on the role of magnetic field amplification and the presence of neutrals in the circumstellar environment. Special attention will be devoted to observat…
We consider diffusive shock acceleration in supernova remnants throughout their evolution including a radiative stage. It is found that a more efficient acceleration and fast exit of particles at the radiative stage results in the hardening of the source cosmic ray proton and electron spectra at energies $\sim 100-500$ GeV. The effect is stronger for cosmic ray electrons.
A new numerical model of the nonlinear diffusive shock acceleration is presented. It is used for modeling of particle acceleration in supernova remnants. The model contains coupled spherically symmetric hydrodynamic equations and the transport equations for energetic protons, ions and electrons. The forward and reverse shocks are included in the consideration. The spectra of cosmic rays released into interstellar medium from a supernova remnant are determined. The role of the reverse shock in the production of CR ions and positrons is discussed.
Stochastic acceleration of charged particles due to their interactions with plasma waves may be responsible for producing superthermal particles in a variety of astrophysical systems. This process can be described as a diffusion process in the energy space with the Fokker-Planck equation. In this paper, a time-dependent numerical code is used to solve the reduced Fokker-Planck equation involving only time and energy variables with general forms of the diffusion coefficients. We also propose a self-similar model for particle acceleration in Sedov explosions and use the TeV SNR RX J1713.7-3946 a…
We present a library of numerical models of cosmic-ray accelerating supernova remnants (SNRs) evolving through a homogeneous ambient medium. We analyse distributions of the different energy components and diffusive shock acceleration time-scales for the models in various conditions. The library comprises a variety of SNR evolutionary scenarios and is used to map remnants with sufficiently known properties. This mapping constrains the respective ambient medium properties and the acceleration efficiency. Employing the library, we derive the ambient medium density, ambient magnetic field strength…
Collisionless shocks are loosely defined as shocks where the transition between pre-and post-shock states happens on a length scale much shorter than the collisional mean free path. In the absence of collision to enforce thermal equilibrium post-shock, electrons and ions need not have the same temperatures. While the acceleration of electrons for injection into shock acceleration processes to produce cosmic rays has received considerable attention, the related problem of the shock heating of quasi-thermal electrons has been relatively neglected. In this paper we review that state of our knowle…
Over the past decade, $γ$-ray observations of supernova remnants (SNRs) and accurate cosmic-ray (CR) spectral measurements have significantly advanced our understanding of particle acceleration in SNRs. In combination with multiwavelength observations of a large sample of SNRs, it has been proposed that the highest energy particles are mostly accelerated in young remnants, and the maximum energy that middle-age and old SNRs can accelerate particles to decreases rapidly with the decrease in shock speed. If SNRs dominate the CR flux observed at Earth, a large number of particles need to be accel…
Supernova Remnants (SNRs) are broadly accepted as the main accelerators of Galactic cosmic rays (GCRs) with energies up to the knee region. Recent measurements of pion bumps in IC 443 and W 44 by Fermi-LAT show indirect evidence of the acceleration of hadronic particles in SNRs. But, whether SNRs are the powerhouses for GCR acceleration all the way up to the knee region still remains an unsolved question. Tycho is a promising target for this study because it has been widely studied in multi-wavelength observations from IR to TeV and it is a young type Ia SNR located in a relatively clean envir…
We analyze the GeV gamma-ray emission data from the vicinity of the supernova remnant (SNR) HB9 (G160.9+2.6) from the \textit{Fermi}-LAT 12-year observations to quantify the evolution of diffusive shock acceleration (DSA) in the SNR. In the vicinity of HB9, there are molecular clouds whose locations do not coincide with the SNR shell in the line of sight. We detect significant gamma-ray emissions above 1~GeV spatially coinciding with the two prominent cloud regions, as well as a emission from the SNR shell, the latter of which is consistent with the results of previous studies. The energy spec…
We analyse the model of stochastic re-acceleration of electrons, which are emitted by supernova remnants (SNRs) in the Galactic Disk and propagate then into the Galactic halo, in order to explain the origin on nonthermal (radio and gamma-ray) emission from the Fermi Bubbles (FB). We assume that the energy for re-acceleration in the halo is supplied by shocks generated by processes of star accretion onto the central black hole. Numerical simulations show that regions with strong turbulence (places for electron re-acceleration) are located high up in the Galactic Halo about several kpc above the…
Estimating the cosmic-ray acceleration efficiency $ ε$ in supernova remnants (SNRs) through observations is a challenging task in general. Based on the Rankine-Hugoniot shock conditions, we find an anticorrelation between $ ε$ and the power-law spectral index $ α$ of relativistic particle distribution produced via diffusive particle acceleration by nonrelativistic shocks, implying more efficient acceleration in older SNRs with harder radio spectra. Then $ ε$ may be estimated from some hard radio spectral index measurements. Assuming the particle distribution in downstream of strong shocks to b…
Recent gamma-ray observations of middle-aged supernova remnants revealed a mysterious broken power-law spectrum. Using three-dimensional magnetohydrodynamics simulations, we show that the interaction between a supernova blast wave and interstellar clouds formed by thermal instability generates multiple reflected shocks. The typical Mach numbers of the reflected shocks are shown to be M ~ 2 depending on the density contrast between the diffuse intercloud gas and clouds. These secondary shocks can further energize cosmic-ray particles originally accelerated at the blast-wave shock. This "two-ste…
Cutoff energy in a synchrotron radiation spectrum of a supernova remnant (SNR) contains a key parameter of ongoing particle acceleration. We systematically analyze 11 young SNRs, including all historical SNRs, to measure the cutoff energy, thus shedding light on the nature of particle acceleration at the early stage of SNR evolution. The nonthermal (synchrotron) dominated spectra in filament-like outer rims are selectively extracted and used for spectral fitting because our model assumes that accelerated electrons are concentrated in the vicinity of the shock front due to synchrotron cooling. …
Context. Supernova remnants (SNRs) are thought to be the primary candidates for the sources of Galactic cosmic rays. According to the diffusive shock acceleration theory, SNR shocks produce a power-law spectrum with an index of s = 2, perhaps nonlinearly modified to harder spectra at high energy. Observations of SNRs often indicate particle spectra that are softer than that and show features not expected from classical theory. Known drawbacks of the standard approach are the assumption that SNRs evolve in a uniform environment, and that the reverse shock does not accelerate particles. Relaxing…
Context: Observation of Balmer lines from the region around the forward shock of supernova remnants may provide precious information on the shock dynamics and on the efficiency of particle acceleration at the shock. Aims: We calculate the Balmer line emission and the shape of the broad Balmer line for parameter values suitable for SNR 0509-67.5, as a function of the cosmic ray acceleration efficiency and of the level of thermal equilibration between electrons and protons behind the shock. This calculation aims at using the width of the broad Balmer line emission to infer the cosmic ray acceler…
Synchrotron X-ray emission in young supernova remnants (SNRs) is a powerful diagnostic tool to study the population of high energy electrons accelerated at the shock front and the acceleration process. We performed a spatially resolved spectral analysis of NuSTAR and XMM-Newton observations of the young Kepler's SNR, aiming to study in detail its non-thermal emission in hard X-rays. We selected a set of regions all around the rim of the shell and extracted the corresponding spectra. The spectra were analyzed by adopting a model of synchrotron radiation in the loss-limited regime, to constrain …
We have developed an inversion method for determination of the characteristics of the acceleration mechanism directly and non-parametrically from observations, in contrast to the usual forward fitting of parametric model variables to observations. In two recent papers (Petrosian & Chen 2010, Chen & Petrosian 2013), we demonstrate the efficacy of this inversion method by its application to acceleration of electrons in solar flares based on stochastic acceleration by turbulence. Here we explore its application for determining the characteristics of shock acceleration in supernova remnants (SNRs)…
We discuss the prospects for a progress to be brought by ASTRO-H in the understanding of the physics of particle acceleration in astrophysical environments. Particular emphasis will be put on the synergy with gamma-ray astronomy, in the context of the rapid developments of recent years. Selected topics include: shock acceleration in supernova remnants (SNRs) and in clusters of galaxies, and the extreme particle acceleration seen in gamma-ray binaries. Since the hydrodynamics and thermal properties of shocks in these objects are covered in other white papers, we focus on the aspects related to …
Recent gamma-ray observations show that middle aged supernova remnants (SNRs) interacting with molecular clouds (MCs) can be sources of both GeV and TeV emission. Based on the MC association, two scenarios have been proposed to explain the observed gamma-ray emission. In one, energetic cosmic ray (CR) particles escape from the SNR and then illuminate nearby MCs, producing gamma-ray emission, while the other involves direct interaction between the SNR and MC. In the direct interaction scenario, re-acceleration of pre-existing CRs in the ambient medium is investigated while particles injected fr…
We study cosmic-ray acceleration in a supernova remnant (SNR) and the escape from it. We model nonthermal particle and photon spectra for the hidden SNR in the open cluster Westerlund 2, and the old-age mixed-morphology SNR W 28. We assume that the SNR shock propagates in a low-density cavity, which is created and heated through the activities of the progenitor stars and/or previous supernova explosions. We indicate that the diffusion coefficient for cosmic-rays around the SNRs is less than ~1% of that away from them. We compare our predictions with the gamma-ray spectra of molecular clouds il…
Galactic cosmic ray (CR) acceleration to the knee in the spectrum at a few PeV is only possible if the magnetic field ahead of a supernova remnant (SNR) shock is strongly amplified by CR escaping the SNR. A model formulated in terms of the electric charge carried by escaping CR predicts the maximum CR energy and the energy spectrum of CR released into the surrounding medium. We find that historical SNR such as Cas A, Tycho and Kepler may be expanding too slowly to accelerate CR to the knee at the present time.
The spectrum of cosmic rays (CRs) is affected by their escape from an acceleration site. This may have been observed not only in the gamma-ray spectrum of young supernova remnants (SNRs) such as RX J1713.7-3946, but also in the spectrum of CRs showering on the Earth. The escape-limited model of cosmic-ray acceleration is studied in general. We discuss the spectrum of CRs running away from the acceleration site. The model may also constrain the spectral index at the acceleration site and the ansatz with respect to the unknown injection process into the particle acceleration. We apply our model …
We present results of semi-analytic calculations which show clear evidence for changes in the non-equilibrium ionization behind a supernova remnant forward shock undergoing efficient diffusive shock acceleration (DSA). The efficient acceleration of particles (i.e., cosmic rays) lowers the shock temperature and raises the density of the shocked gas, thus altering the ionization state of the plasma in comparison to the test particle approximation where cosmic rays gain an insignificant fraction of the shock energy. The differences between the test particle and efficient acceleration cases are su…
The radio evolution of, so far the youngest known, Galactic supernova remnant (SNR) G1.9+0.3 is investigated by using three-dimensional (3D) hydrodynamic modelling and non-linear kinetic theory of cosmic ray (CR) acceleration in SNRs. We include consistent numerical treatment of magnetic field amplification (MFA) due to resonant streaming instability. Under the assumption that SNR G1.9+0.3 is the result of a Type Ia supernova explosion located near the Galactic Centre, using widely accepted values for explosion energy 10$^{51}$ erg and ejecta mass 1.4 $M_{\odot}$, the non-thermal continuum rad…
The mechanism for acceleration of cosmic rays in supernova remnants (SNRs) is an outstanding question in the field. We model a sample of 32 axisymmetric SNRs using the quasi-perpendicular and quasi-parallel cosmic-ray-electron (CRE) acceleration cases. The axisymmetric sample is defined to include SNRs with a double-sided, bilateral morphology, and also those with a one-sided morphology where one limb is much brighter than the other. Using a coordinate transformation technique, we insert a bubble-like model SNR into a model of the Galactic magnetic field. Since radio emission of SNRs is domina…
The existence of a "knee" at energy ~1 PeV in the cosmic-ray spectrum suggests the presence of Galactic PeV proton accelerators called "PeVatrons". Supernova Remnant (SNR) G106.3+2.7 is a prime candidate for one of these. The recent detection of very high energy (0.1-100 TeV) gamma rays from G106.3+2.7 may be explained either by the decay of neutral pions or inverse Compton scattering by relativistic electrons. We report an analysis of 12 years of Fermi-LAT gamma-ray data which shows that the GeV-TeV gamma-ray spectrum is much harder and requires a different total electron energy than the radi…
Supernova remnants (SNRs) are believed to be the major contributors to Galactic cosmic rays. The detection of non-thermal emission from SNRs demonstrates the presence of energetic particles, but direct signatures of protons and other ions remain elusive. If these particles receive a sizeable fraction of the explosion energy, the morphological and spectral evolution of the SNR must be modified. To assess this, we run 3D hydrodynamic simulations of a remnant coupled with a non-linear acceleration model. We obtain the time-dependent evolution of the shocked structure, impacted by the Rayleigh-Tay…
Tycho's supernova remnant (SNR) is well-established as a source of particle acceleration to very high energies. Constraints from numerous studies indicate that the observed gamma-ray emission results primarily from hadronic processes, providing direct evidence of highly relativistic ions that have been accelerated by the SNR. Here we present an investigation of the dynamical and spectral evolution of Tycho's SNR by carrying out hydrodynamical simulations that include diffusive shock acceleration of particles in the amplified magnetic field at the forward shock of the SNR. Our simulations provi…
The shocks of several young supernova remnants (SNR) are often associated with very thin optical filaments dominated by Balmer emission resulting from charge-exchange and collisional excitation between neutral Hydrogen from the interstellar medium and shocked protons and electrons. Optical lines are a direct probe of the conditions at the shock, in particular the width of the narrow and broad components reflect the temperature upstream and downstream of the shock, respectively. When the shock accelerate efficiently non-thermal particles, the shock structure changes producing anomalous Balmer l…
In our model, the acceleration and propagation of particles from the Bohm-like diffusion region inside the SNR to the Galactic diffusion region outside the SNR are described through nonlinear diffusive shock acceleration (NLDSA). The main content of our NLDSA model is to solve the hydrodynamic equations numerically for gas density, gas velocity, gas pressure as well as the equation for the quasi-isotropic particle momentum distribution. The consequent multi-band non-thermal emission is from two different regions, namely the acceleration region and the escaping region. Our model is capable of e…
Galactic cosmic rays (CRs) are accelerated at the forward shocks of supernova remnants (SNRs) via diffusive shock acceleration (DSA), an efficient acceleration mechanism that predicts power-law energy distributions of CRs. However, observations of nonthermal SNR emission imply CR energy distributions that are generally steeper than $E^{-2}$, the standard DSA prediction. Recent results from kinetic hybrid simulations suggest that such steep spectra may arise from the drift of magnetic structures with respect to the thermal plasma downstream of the shock. Using a semi-analytic model of non-linea…
It has been known for over 50 years that the radio emission from shell supernova remnants (SNRs) indicates the presence of electrons with energies in the GeV range emitting synchrotron radiation. The discovery of nonthermal X-ray emission from supernova remnants is now 30 years old, and its interpretation as the extension of the radio synchrotron spectrum requires electrons with energies of up to 100 TeV. SNRs are now detected at GeV and TeV photon energies as well. Strong suggestions of the presence of energetic ions exist, but conclusive evidence remains elusive. Several arguments suggest th…
Context. Supernova remnants (SNRs) are thought to be the main source of Galactic cosmic rays (CRs) up to the "knee" in CR spectrum. During the evolution of a SNR, the bulk of the CRs are confined inside the SNR shell. The highest-energy particles leave the system continuously, while the remaining adiabatically cooled particles are released when the SNR has expanded sufficiently and decelerated so that the magnetic field at the shock is no longer able to confine them. Particles escaping from the parent system may interact with nearby molecular clouds, producing $γ$-rays in the process via pion …
To better model the efficient production of cosmic rays (CRs) in supernova remnants (SNRs) with the associated coupling between CR production and SNR dynamics, we have generalized an existing cr-hydro-NEI code (i.e., Ellison et al. 2012) to include the following processes: (1) an explicit calculation of the upstream precursor structure including the position dependent flow speed, density, temperature, and magnetic field strength; (2) a momentum and space dependent CR diffusion coefficient; (3) an explicit calculation of magnetic field amplification (MFA); (4) calculation of the maximum CR mome…
We present new models for the forward and reverse shock thermal X-ray emission from core-collapse and Type Ia supernova remnants (SNRs) which include the efficient production of cosmic rays via non-linear diffusive shock acceleration (DSA). Our CR-hydro-NEI code takes into account non-equilibrium ionization (NEI), hydrodynamic effects of efficient CR production on the SNR evolution, and collisional temperature equilibration among heavy ions and electrons in both the shocked supernova (SN) ejecta and the shocked circumstellar material. While X-ray emission is emphasized here, our code self-cons…
Supernova Remnants and Pulsar Wind Nebulae are among the most significant sources of non-thermal X-rays in the sky, and the closest laboratories where relativistic plasma dynamics and particle acceleration can be investigated. Being strong synchrotron emitters, they are ideal candidates for X-ray polarimetry, and indeed the Crab nebula is up to present the only object where X-ray polarization has been detected with a high level of significance. Future polarimetric measures will likely provide us crucial informations on the level of turbulence that is expected at the particle acceleration sites…
Synchrotron X-rays can be a useful tool to investigate electron acceleration at young supernova remnants (SNRs). At present, since the magnetic field configuration around the shocks of SNRs is uncertain, it is not clear whether electron acceleration is limited by SNR age, synchrotron cooling, or even escape from the acceleration region. We study whether the acceleration mechanism can be constrained by the cutoff shape of the electron spectrum around the maximum energy. We derive analytical formulae of the cutoff shape in each case where the maximum electron energy is determined by SNR age, syn…
Precise measurements of galactic cosmic rays revealed a significant difference between the rigidity spectral indices of protons and helium ions. This finding is a notable contrast to the commonly accepted theoretical prediction that supernova remnant (SNR) shocks accelerate protons and helium ions with the same rigidity alike. Most of the earlier explanations for the "paradox" appealed to SNR environmental factors, such as inhomogeneous $p$/He mixes in the shock upstream medium, variable ionization states of He, or a multi-SNR origin of the observed spectra. The newest observations, however, a…
We study cosmic-ray acceleration in young Type Ia Supernova Remnants (SNRs) by means of test-particle diffusive shock acceleration theory and 1-D hydrodynamical simulations of their evolution. In addition to acceleration at the forward shock, we explore the particle acceleration at the reverse shock in the presence of a possible substantial magnetic field, and consequently the impact of this acceleration on the particle spectra in the remnant. We investigate the time evolution of the spectra for various time-dependent profiles of the magnetic field in the shocked region of the remnant. We test…
Supernova remnants (SNRs) have long been considered as one of the most promising sources of Galactic cosmic rays. In the SNR paradigm, petaelectronvolt (PeV) proton acceleration may only be feasible at the early evolution stage, lasting a few hundred years, when the SNR shock speed is high. While evidence supporting the acceleration of PeV protons in young SNRs has yet to be discovered, X-ray synchrotron emission is an important indicator of fast shock. We here report the first discovery of X-ray synchrotron emission from the possibly middle-aged SNR G106.3+2.7, implying that this SNR is still…
Supernova remnants (SNRs) are believed to be the most important acceleration sites for cosmic rays (CRs) below $\sim10^{15}$ eV in the Galaxy. High energy photons, either directly from the shocks of the SNRs or indirectly from the interaction between SNRs and the nearby clouds, are crucial probes for the CR acceleration. Big progresses on observations of SNRs have been achieved by space- and ground-based $γ$-ray facilities. However, whether $γ$-rays come from accelerated hadrons or not, as well as their connection with the CRs observed at Earth, remains in debate. Large High Altitude Air Showe…
Distributions of nonthermal surface brightness of supernova remnants (SNRs) contain important information about the properties of magnetic field and acceleration of charged particles. In the present paper, the synchrotron radio, X-ray, and inverse-Compton (IC) gamma-ray maps of adiabatic SNRs in uniform interstellar medium and interstellar magnetic field are modeled and their morphology is analyzed, with particular emphasis to comparison of azimuthal and radial variations of brightness in radio, X-rays, and gamma-rays. Approximate analytical formulae for the azimuthal and radial profiles of th…
The theoretical fundamentals of formation of the supernova remnant (SNR) continuum radio spectra are presented in this review. Mainly based on the Fermi 1 theory - also known as diffuse shock acceleration (DSA) - the different shapes (linear or curved in log-log scale) of SNR radio spectra are predicted for both young and evolved SNRs. On the other hand, some particular forms of spectra of older SNRs can be predicted by including the additional processes such as Fermi 2 acceleration mechanism or thermal bremsstrahlung radiation. Also, all of these theoretically predicted forms of radio spectra…
Galactic cosmic rays (CRs) are accelerated by astrophysical shocks, primarily supernova remnants (SNRs), via diffusive shock acceleration (DSA), an efficient mechanism that predicts power-law energy distributions of CRs. However, observations of both nonthermal SNR emission and Galactic CRs imply CR spectra that are steeper than the standard DSA prediction, $\propto E^{-2}$. Recent kinetic hybrid simulations suggest that such steep spectra may be the result of a "postcursor", or drift of CRs and magnetic structures with respect to the thermal plasma behind the shock. Using a semi-analytic mode…
Until now, providing an experimental unambiguous proof of Cosmic Ray (CR) origin has been elusive. The SuperNova Remnant (SNR) study showed an increasingly complex scenario with a continuous elaboration of theoretical models. The middle-aged supernova remnant (SNR) W44 has recently attracted attention because of its relevance regarding the origin of Galactic cosmic-rays. The gamma-ray missions AGILE and Fermi have established, for the first time for a SNR, the spectral continuum below 200 MeV which can be attributed to neutral pion emission. Our work is focused on a global re-assessment of all…
On the acceleration of cosmic rays at the post-adiabatic shocks of supernova remnants
INAF - Osservatorio Astronomico di Palermo（意大利国家天体物理研究所巴勒莫天文台）；Institute for Applied Problems in Mechanics and Mathematics, National Academy of Sciences of Ukraine（乌克兰国家科学院应用力学与数学问题研究所）；INAF - Osservatorio Astrofisico di Arcetri（意大利国家天体物理研究所阿切特里天文台）；Institute of Physics and Astronomy, University of Potsdam（波茨坦大学物理与天文学研究所）；INAF - Osservatorio Astrofisico di Catania（意大利国家天体物理研究所卡塔尼亚天文台）
Supernova remnants (SNRs) are believed to produce the majority of galactic cosmic rays (CRs). SNRs harbor non-relativistic collisionless shocks responsible for acceleration of CRs via diffusive shock acceleration (DSA), in which particles gain their energies via repeated interactions with the shock front. As the DSA theory involves pre-existing mildly energetic particles, a means of pre-acceleration is required, especially for electrons. Electron injection remains one of the most troublesome and still unresolved issues and our physical understanding of it is essential to fully comprehend the p…
Context. Observation of Balmer lines from the region around the forward shock of supernova remnants (SNR) may provide valuable information on the shock dynamics and the efficiency of particle acceleration at the shock. Aims. We calculated the Balmer line emission and the shape of the broad Balmer line for parameter values suitable for SNR RCW 86 (G315.4-2.3) as a function of the cosmic-ray (CR) acceleration efficiency and of the level of thermal equilibration between electrons and protons behind the shock. This calculation aims at using the width of the broad Balmer-line emission to infer the …
We compare the $γ$-ray spectra from 10 middle-aged supernova remnants (SNRs), which are interacting with molecular clouds (MCs), with the model prediction from widely used escaping scenario and direct interaction scenario. It is found that the $γ$-ray data is inconsistent with the escaping scenario statistically, as it predicts a diversity of spectral shape which is not observed. The inconsistency suggests that the free escape boundary adopted in the escaping model is not a good approximation, which challenges our understanding of cosmic ray (CR) escaping in SNRs. In addition, we show that amb…
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…
