Nonlinear Diffusive Shock Acceleration Research Articles

Nonlinear diffusive shock acceleration of cosmic rays: quasi-thermal and non-thermal particle distributions

Nonlinear diffusive shock acceleration of cosmic rays: quasi-thermal and non-thermal particle distributions

Hadronic versus Leptonic Origin of Gamma-Ray Emission from Supernova Remnants

GeV and TeV emission from the forward shocks of supernova remnants (SNRs) indicates that they are capable particle accelerators, making them promising sources of Galactic cosmic rays (CRs). However, it remains uncertain whether this γ-ray emission arises primarily from the decay of neutral pions produced by very-high-energy hadrons, or from inverse-Compton and/or bremsstrahlung emission from relativistic leptons. By applying a semi-analytic approach to non-linear diffusive shock acceleration, and calculating the particle and photon spectra produced in different environments, we parameterize the relative strength of hadronic and leptonic emission. We show that even if CR acceleration is likely to occur in all SNRs, the observed photon spectra may primarily reflect the environment surrounding the SNR: the emission is expected to look hadronic unless the ambient density is particularly low (with proton number density ≲0.1 cm−3) or the photon background is enhanced with respect to average Galactic values (with radiation energy density u rad ≳ 10 eV cm−3). We introduce a hadronicity parameter to characterize how hadronic or leptonic we expect a source to look based on its environment, which can be used to guide the interpretation of current γ-ray observations and the detection of high-energy neutrinos from SNRs.

Possible hadronic origin of TeV photon emission from SNR G106.3+2.7

Context. Recently, HAWC, ASγ, and LHAASO experiments have reported the gamma-ray spectrum of supernova remnant (SNR) G106.3+2.7 above 40 TeV, indicating that SNR G106.3+2.7 is a promising PeVatron candidate. However, the origin of the gamma-ray spectrum is still debated. Thus, a dedicated theoretical model with self-consistent descriptions is required to decipher the properties of the gamma-ray spectrum for this specific source. Aims. We construct a theoretical model to explain the multiband photon emission from the PeVatron SNR G106.3+2.7. Methods. 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 solving the hydrodynamic equations numerically for gas density, gas velocity, and gas pressure and the equation for the quasi-isotropic particle momentum distribution. The consequent multiband nonthermal emission stems from two different regions, namely the acceleration region and the escaping region. Results. Our model is capable of explaining the multiband photon emission via the dominant synchrotron radiation of the electrons accelerated inside the SNR. The photons with energy of ≳GeV are naturally produced by the protons inside and outside the SNR. Moreover, photons in the energy range of ~1−~ 100 TeV are due to the interaction of escaped protons with dense molecular clouds. Conclusions. For photons with energy Eγ ≳ 1 GeV from SNR G106.3+2.7, our results here favor a hadronic origin, where the photons in the energy range of ~1G eV to ~1 TeV are produced inside the SNR through proton-proton interaction, while photons with Eγ ≳ 1 TeV originate from the interaction of escaped protons with a dense molecular cloud.

Steep Cosmic-Ray Spectra with Revised Diffusive Shock Acceleration

Abstract 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 nonlinear DSA, we investigate the implications that these results have on the phenomenology of a wide range of SNRs. By accounting for the motion of magnetic structures in the downstream, we produce CR energy distributions that are substantially steeper than E −2 and consistent with observations. Our formalism reproduces both modestly steep spectra of Galactic SNRs (∝E −2.2) and the very steep spectra of young radio supernovae (∝E −3).

Modeling of Cosmic-Ray Production and Transport and Estimation of Gamma-Ray and Neutrino Emissions in Starburst Galaxies

Abstract Starburst galaxies (SBGs) with copious massive stars and supernova (SN) explosions are the sites of active cosmic-ray production. Based on the predictions of nonlinear diffusive shock acceleration theory, we model the cosmic-ray proton (CRP) production by both pre-SN stellar winds (SWs) and supernova remnants (SNRs) from core-collapse SNe inside the starburst nucleus. Adopting different models for the transport of CRPs, we estimate the γ-ray and neutrino emissions due to pp collisions from nearby SBGs such as M82, NGC 253, and Arp 220. We find that with the current γ-ray observations by Fermi-LAT, Veritas, and H.E.S.S., it would be difficult to constrain CRP production and transport models. Yet, the observations are better reproduced with (1) the combination of a single power-law (PL) momentum distribution for SNR-produced CRPs and a diffusion model in which the CRP diffusion is mediated by the strong Kolmogorov-type turbulence of δ B / B ∼ 1 , and (2) the combination of a double-PL model for SNR-produced CRPs and a diffusion model in which the scattering of CRPs is controlled mostly by self-excited waves rather than the preexisting turbulence. The contribution of SW-produced CRPs could be substantial in Arp 220, where the star formation rate is higher and the slope of the initial mass function would be flatter. We suggest that M82 and NGC 253 might be detectable as point sources of high-energy neutrinos in the upcoming KM3NET and IceCube-Gen2, when optimistic models are applied. Future observations of neutrinos, as well as γ-rays, would provide constraints for the production and diffusion of CRPs in SBGs.

Non-linear diffusive shock acceleration: A recipe for injection of electrons

Prescriptions for electron injection into the diffusive shock acceleration process are required in many practical considerations of cosmic-ray astrophysics, particularly in modeling of the synchrotron emission of astrophysical sources. In particle-in-cell simulations of quasi-parallel magnetized collisionless shocks, we analyse the evolution of particle spectra. We find that in the later stages of shock evolution, the initially strong suprathermal part in the ion spectra fades, thus leaving the spectra composed of a Maxwellian and a power law. Once the electron and ion spectra flatten and become parallel, we find that the amounts of cosmic ray ions and electrons become similar. We make the step towards relating the micro and macro-scale physics by applying this injection rule to Blasi’s semi-analytical model of non-linear diffusive shock acceleration, in order to obtain the particle spectra and electron-to-proton ratio Kep at high energies. By using shock jump conditions that include the electron heating, we find Kep as a function of Mach number. For Mach number ∼ 100, our model finely reproduce the typically observed ratio for Galactic cosmic-rays Kep∼ 1:100 in the test particle regime.

Radio emission from interstellar shocks: Young type Ia supernova remnants and the case of N 103B in the Large Magellanic Cloud

Here we present a radio continuum study based on new and archival data from the Australia Telescope Compact Array towards N 103B, a young (<=1000 yrs) spectroscopically confirmed type Ia SNR in the Large Magellanic Cloud (LMC) and proposed to have originated from a single degenerate progenitor. The radio morphology of this SNR is asymmetrical with two bright regions towards the north-west and south-west of the central location as defined by radio emission. N 103B identified features include: a radio spectral index of -0.75+-0.01 (consistent with other young type Ia SNRs in the Galaxy); a bulk SNR expansion rate as in X-rays; morphology and polarised electrical field vector measurements where we note radial polarisation peak towards the north-west of the remnant at both 5500 and 9000 MHz. The spectrum is concave-up and the most likely reason is the non-linear diffusive shock acceleration effects or presence of two different populations of ultra-relativistic electrons. We also note unpolarized clumps near the south-west region which is in agreement with this above scenario. We derive a typical magnetic field strength for N 103B, of 16.4 microG for an average rotation measurement of 200 rad m^-2. However, we estimate the equipartition field to be of the order of ~235 microG with an estimated minimum energy of Emin=6.3*10^48 erg. The close (~0.5 degree) proximity of N 103B to the LMC mid-plane indicates that an early encounter with dense interstellar medium may have set an important constrain on SNR evolution. Finally, we compare features of N 103B, to six other young type Ia SNRs in the LMC and Galaxy, with a range of proposed degeneracy scenarios to highlight potential differences due to a different models. We suggest that the single degenerate scenario might point to morphologically asymmetric type Ia supernova explosions.

Spectrum of Electrons Accelerated in Supernova Remnants.

Using a semianalytic model of nonlinear diffusive shock acceleration, we model the total spectrum of cosmic ray (CR) electrons accelerated by supernova remnants (SNRs). Because electrons experience synchrotron losses in the amplified magnetic fields characteristic of SNRs, they exhibit substantially steeper spectra than protons. In particular, we find that the difference between the electron and proton spectral index (power law slope) ranges from 0.1 to 0.4. Our findings must be reckoned with theories of Galactic CR transport, which often assume that electrons and protons are injected with the same slope, and may especially have implications for the observed "positron excess".

Spectral hardening of cosmic ray protons and helium nuclei in supernova remnant shocks * * Supported by the National Natural Science Foundation of China (11433004, U1738211, 11563009), the Yunnan Applied Basic Research Projects (2015FB103, 2016FB001, 2018FY001 (-003)), and National Key R&D Program of China (2018YFA0404204)

The observed hardening of the spectra of cosmic ray protons and helium nuclei is studied within the model of nonlinear diffusive shock acceleration of supernova remnants (SNRs). In this model, the injected particles with energies below the spectral " knee” are assumed to be described by two populations with different spectral indexes around 200 GeV. The high-energy population is dominated by the particles with energies above 200 GeV released upstream of the shock of SNR, and the low-energy population is attributed to the particles with energies below 200 GeV released downstream of the shock of SNR. In this scenario, the spectral hardening of cosmic ray protons and helium nuclei observed by PAMELA, AMS-02, and CREAM experiments can be reproduced.

Shock Acceleration of Electrons and Synchrotron Emission from the Dynamical Ejecta of Neutron Star Mergers

Abstract Neutron star mergers (NSMs) eject energetic subrelativistic dynamical ejecta into circumbinary media. Analogous to supernovae and supernova remnants, the NSM dynamical ejecta are expected to produce nonthermal emission by electrons accelerated at a shock wave. In this paper, we present the expected radio and X-ray signals by this mechanism, taking into account nonlinear diffusive shock acceleration (DSA) and magnetic field amplification. We suggest that the NSM is unique as a DSA site, where the seed relativistic electrons are abundantly provided by the decays of r-process elements. The signal is predicted to peak at a few 100–1000 days after the merger, determined by the balance between the decrease of the number of seed electrons and the increase of the dissipated kinetic energy, due to the shock expansion. While the resulting flux can ideally reach the maximum flux expected from near-equipartition, the available kinetic energy dissipation rate of the NSM ejecta limits the detectability of such a signal. It is likely that the radio and X-ray emission are overwhelmed by other mechanisms (e.g., an off-axis jet) for an observer placed in a jet direction (i.e., for GW170817). However, for an off-axis observer, to be discovered once a number of NSMs are identified, the dynamical ejecta component is predicted to dominate the nonthermal emission. While the detection of this signal is challenging even with near-future facilities, this potentially provides a robust probe of the creation of r-process elements in NSMs.

On the Foundation of Equipartition in Supernova Remnants

Abstract A widely accepted paradigm is that equipartition (eqp) between the energy density of cosmic rays (CRs) and the energy density of the magnetic field cannot be sustained in supernova remnants (SNRs). However, our 3D hydrodynamic supercomputer simulations, coupled with a nonlinear diffusive shock acceleration model, provide evidence that eqp may be established at the end of the Sedov phase of evolution in which most SNRs spend the longest portions of their lives. We introduce the term “constant partition” for any constant ratio between the CR energy density and the energy density of the magnetic field in an SNR, while the term “equipartition” should be reserved for the case of approximately the same values of the energy density (also, it is constant partition in the order of magnitude) of ultra-relativistic electrons only (or CRs in total) and the energy density of the magnetic field. Our simulations suggest that this approximate constant partition exists in all but the youngest SNRs. We speculate that since evolved SNRs at the end of the Sedov phase of evolution can reach eqp between CRs and magnetic fields, they may be responsible for initializing this type of eqp in the interstellar medium. Additionally, we show that eqp between the electron component of CRs and the magnetic field may be used for calculating the magnetic field strength directly from observations of synchrotron emission from SNRs. The values of magnetic field strengths in SNRs given here are approximately 2.5 times lower than values calculated by Arbutina et al.

A possible explanation of the knee of cosmic light component spectrum from 100 TeV to 3 PeV**Supported by the National Natural Science Foundation of China (11433004, 11363006, 11103016, 11173020), Top Talents Program of Yunnan Province (2015HA030) and the Natural Science Foundation of Yunnan Province(2015FB103)

A mixed hydrogen and helium (H + He) spectrum with a clear steepening at ∼ 700 TeV has been detected by the ARGO-YBJ experiments. In this paper, we demonstrate that the observed H + He spectrum can be reproduced well with a model of cosmic rays escaping from the supernova remnants (SNRs) in our Galaxy. In this model, particles are accelerated in a SNR through a non-linear diffusive shock acceleration mechanism. Three components of high energy light nuclei escaped from the SNR are considered. It should be noted that the proton spectrum observed by KASCADE can be also explained by this model given a higher acceleration efficiency.

Hydrodynamical and radio evolution of young supernova remnant G1.9+0.3 based on the model of diffusive shock acceleration

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 1051 erg and ejecta mass 1.4 M⊙, the non-thermal continuum radio emission is calculated. The main purpose of this paper is to explain radio flux brightening measured over recent decades and also predict its future temporal evolution. We estimate that the SNR is now ∼120 yr old, expanding in an ambient density of 0.02 cm−3, and explain its steep radio spectral index only by means of efficient non-linear diffusive shock acceleration (NLDSA). We also make comparison between simulations and observations of this young SNR, in order to test the models and assumptions suggested. Our model prediction of a radio flux density increase of ∼1.8 per cent yr−1 during the past two decades agrees well with the measured values. We synthesize the synchrotron spectrum from radio to X-ray and it fits well the Very Large Array, Molonglo Observatory Synthesis Telescope, Effelsberg, Chandra and NuSTAR measurements. We also propose a simplified evolutionary model of the SNR in gamma rays and suggest it may be a promising target for gamma-ray observations at TeV energies with the future generation of instruments like Cherenkov Telescope Array. SNR G1.9+0.3 is the only known Galactic SNR with the increasing flux density and we present here the prediction that the flux density will start to decrease approximately 500 yr from now. We conclude that this is a general property of SNRs in the free expansion phase.

Spectra of accelerated particles at supernova shocks in the presence of neutral hydrogen: the case of Tycho

The presence of neutral hydrogen in the shock proximity changes the structure of the shock and affects the spectra of particles accelerated through the first-order Fermi mechanism. This phenomenon has profound implications for the interpretation of the multifrequency spectra of radiation from supernova remnants. Neutrals that undergo charge exchange with hot ions downstream of the shock may result in fast neutrals moving towards the upstream gas, where they can suffer additional charge exchange or ionisation reactions, thereby depositing energy and momentum upstream. Here we discuss the implications of this neutral return flux, which was already predicted in our previous work on neutral mediated supernova shocks, and show how the spectra of accelerated particles turn out to be appreciably steeper than $p^{-4}$, thereby affecting the gamma ray spectra from supernova remnants in general and from Tycho specifically. The theory that describes non-linear diffusive shock acceleration in the presence of neutral hydrogen has been developed in recent years. Here we use a semi-analytical theory developed in previous work and specialise our predictions to the case of the Tycho supernova shock, where there is evidence that the spectrum of the accelerated cosmic rays is steeper than expected from the traditional theory of diffusive shock acceleration. We show that, if the fraction of neutral hydrogen in the vicinity of the Tycho supernova shock is, as suggested by observations, ~70-90, then spectra of accelerated protons steeper than $p^{-4}$ may be a natural consequence of charge exchange reactions and the associated neutral return flux. The spectral shape is affected by this phenomenon for particles with energies below ~100-1000 GeV, for which the diffusion length is less than or at most comparable to the pathlength of charge exchange and ionisation upstream of the shock.

Type IIn supernovae as sources of high energy astrophysical neutrinos

It is shown that high-energy astrophysical neutrinos observed in the IceCube experiment can be produced by protons accelerated in extragalactic Type IIn supernova remnants by shocks propagating in the dense circumstellar medium. The nonlinear diffusive shock acceleration model is used for description of particle acceleration. We calculate the neutrino spectrum produced by an individual Type IIn supernova and the spectrum of neutrino background produced by IIn supernovae in the expanding Universe. We also found that the arrival direction of one Icecube neutrino candidate (track event 47) is at 1.35° from Type IIn supernova 2005bx.

PARTICLE ACCELERATION IN SUPERNOVA REMNANTS

Most high energy cosmic rays (CRs) are thought to be produced by diffusive shock acceleration (DSA) in supernova remnants (SNRs) within the Galaxy. Plasma and MHD simulations have shown that the self-excitation of MHD waves and amplification of magnetic fields via plasma instabilities are an integral part of DSA for strong collisionless shocks. In this study we explore how plasma processes such as plasma instabilities and wave-particle interactions can affect the energy spectra of CR protons and electrons, using time-dependent DSA simulations of SNR shocks. We demonstrate that the time-dependent evolution of the shock dynamics, the self-amplified magnetic fields and Alfvenic drift govern the highest energy end of the CR energy spectra. As a result, the spectral cutoffs in nonthermal X-ray and γ-ray radiation spectra are regulated by the evolution of the highest energy particles, which are injected at the early phase of SNRs. We also find that the maximum energy of CR protons can be boosted significantly only if the scale height of the magnetic field precursor is long enough to contain the diffusion lengths of the particles of interests. Thus, detailed understandings of nonlinear wave-particle interactions and time-dependent DSA simulations are crucial for understanding the nonthermal radiation from CR acceleration sources.

MODELING BRIGHTγ-RAY AND RADIO EMISSION AT FAST CLOUD SHOCKS

Recent observations by the Large Area Telescope (LAT) onboard the Fermi satellite have revealed bright gamma-ray emission from middle-aged supernova remnants (SNRs) inside our Galaxy. These remnants, which also possess bright non-thermal radio shells, are often found to be interacting directly with surrounding gas clouds. We explore the non-thermal emission mechanism at these dynamically evolved SNRs by constructing a hydrodynamical model. Two scenarios of particle acceleration, either a re-acceleration of Galactic cosmic rays (CRs) or an efficient nonlinear diffusive shock acceleration (NLDSA) of particles injected from downstream, are considered. Using parameters inferred from observations, our models are contrasted with the observed spectra of SNR W44. For the re-acceleration case, we predict a significant enhancement of radio and GeV emission as the SNR undergoes a transition into the radiative phase. If sufficiently strong magnetic turbulence is present in the molecular cloud, the re-acceleration scenario can explain the observed broadband spectral properties. The NLDSA scenario also succeeds in explaining the $\gamma$-ray spectrum but fails to reproduce the radio spectral index. Efficient NLDSA also results in a significant post-shock non-thermal pressure that limits the compression during cooling and prevents the formation of a prominent dense shell. Some other interesting differences between the two models in hydrodynamical behavior and resulting spectral features are illustrated.

On the escape and propagation of high-energy protons near young supernova remnants

The escape and propagation of high-energy protons near young supernova remnants (SNRs) are investigated in the frame of non-linear diffusive shock acceleration (NLDSA) model by using two methods. In the first method, the particle diffusion is assumed to be different inside and outside the absorbing boundary of the particles accelerated in the SNR shock, and the proton spectra at a given distance of the outer region and corresponding pi(0) decay gamma-ray spectra can be calculated if a molecular cloud is assumed to be at the distance. In the second method, the total spectrum of high-energy protons escaping from an absorbing boundary during the SNR evolution time is treated as injection rate of the protons and the proton spectrum is calculated in the accumulative diffusion model. Our results show that (1) the spectrum of high-energy protons escaping from a young SNR does not have a power-law form and the protons concentrate on high-energy region and (2) the escaping proton spectra and corresponding pi(0) decay gamma-ray spectra predicted in both methods are different, indicating that the second method overestimates the propagation effect. We may conclude that the first method is a more realistic description of the escape and propagation of high-energy protons near SNRs.

Electron Acceleration in Supernovae and Millimeter Perspectives

Supernovae launch a strong shock wave by the interaction of the expanding ejecta and surrounding circumstellar matter (CSM). At the shock, electrons are accelerated to relativistic speed, creating observed synchrotron emissions in radio wavelengths. In this paper, I suggest that SNe (i.e., &amp;lt; 1 year since the explosion) provide a unique site to study the electron acceleration mechanism. I argue that the eciency of the acceleration at the young SN shock is much lower than conventionally assumed, and that the electrons emitting in the&lt;em&gt; cm&lt;/em&gt; wavelengths are &lt;em&gt;not&lt;/em&gt; fully in the Diffusive Shock Acceleration (DSA) regime. Thus radio emissions from young SNe record information on the yet-unresolved 'injection' mechanism. I also present perspectives of millimeter (&lt;em&gt;mm&lt;/em&gt;) observations of SNe - this will provide opportunities to uniquely determine the shock physics and the acceleration efficiency, to test the non-linear DSA mechanism and provide a characteristic electron energy scale with which the DSA start dominating the electron acceleration.

COSMIC RAY ACCELERATION AT PERPENDICULAR SHOCKS IN SUPERNOVA REMNANTS

Supernova remnants (SNRs) are believed to accelerate particles up to high energies through the mechanism of diffusive shock acceleration (DSA). Except for direct plasma simulations, all modeling efforts must rely on a given form of the diffusion coefficient, a key parameter that embodies the interactions of energetic charged particles with the magnetic turbulence. The so-called Bohm limit is commonly employed. In this paper we revisit the question of acceleration at perpendicular shocks, by employing a realistic model of perpendicular diffusion. Our coefficient reduces to a power-law in momentum for low momenta (of index $\alpha$), but becomes independent of the particle momentum at high momenta (reaching a constant value $\kappa_{\infty}$ above some characteristic momentum $p_{\rm c}$). We first provide simple analytical expressions of the maximum momentum that can be reached at a given time with this coefficient. Then we perform time-dependent numerical simulations to investigate the shape of the particle distribution that can be obtained when the particle pressure back-reacts on the flow. We observe that, for a given index $\alpha$ and injection level, the shock modifications are similar for different possible values of $p_{\rm c}$, whereas the particle spectra differ markedly. Of particular interest, low values of $p_{\rm c}$ tend to remove the concavity once thought to be typical of non-linear DSA, and result in steep spectra, as required by recent high-energy observations of Galactic SNRs.