Nonlinear Diffusive Shock Acceleration Research Articles

REVERSE AND FORWARD SHOCK X-RAY EMISSION IN AN EVOLUTIONARY MODEL OF SUPERNOVA REMNANTS UNDERGOING EFFICIENT DIFFUSIVE SHOCK ACCELERATION

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-consistently determines both thermal and non-thermal broadband emission from radio to TeV energies. We include Doppler broadening of the spectral lines by thermal motions of the ions and by the remnant expansion. We study, in general terms, the roles which the ambient environment, progenitor models, temperature equilibration, and processes related to DSA have on the thermal and non-thermal spectra. The study of X-ray line emission from young SNRs is a powerful tool for determining specific SN elemental contributions, and for providing critical information that helps to understand the type and energetics of the explosion, the composition of the ambient medium in which the SN exploded, and the ionization and dynamics of the hot plasma in the shocked SN ejecta and interstellar medium. With the approaching launch of the next-generation X-ray satellite Astro-H, observations of spectral lines with unprecedented high resolution will become a reality. Our self-consistent calculations of the X-ray spectra from various progenitors will help interpret future observations of SNRs.

Sharp knee phenomenon of primary cosmic ray energy spectrum

Primary energy spectral models are tested in the energy range of 1-200 PeV using standardized extensive air shower responses from BASJE-MAS, Tibet, GAMMA and KASCADE scintillation shower arrays. Results point towards the two-component origin of observed cosmic ray energy spectra in the knee region (GAPS spectral model) consisting of a pulsar component superimposed upon rigidity-dependent power law diffuse galactic flux. The two-component energy spectral model accounts for both the sharp knee shower spectral phenomenon and observed irregularity of all-particle energy spectrum in the region of 50-100 PeV. Alternatively, tested multi-population primary energy spectra predicted by non-linear diffusive shock acceleration (DSA) models describe observed shower spectra in the knee region provided that the cutoff magnetic rigidities of accelerating particles are 6.0+/-0.3 PV and 45+/-2 PV for the first two populations respectively. Both tested spectral models confirm the predominant H-He primary nuclei origin of observed shower spectral knee. The parameters of tested energy spectra are evaluated using solutions of inverse problem on the basis of the corresponding parameterizations of energy spectra for primary H, He, O-like and Fe-like nuclei, standardized shower size spectral responses in the 550-1085 g/cm^2 atmospheric slant depth range and near vertical muon truncated size spectra detected by the GAMMA array.

THE RELATIONSHIP BETWEEN THE PARTICLE INJECTION RATE AND THE DISPERSION OF THE SCATTERING ANGULAR DISTRIBUTION

Although non-linear diffusive shock acceleration could be simulated by some well-established models, the particle injection rate is a priori assumed to proceed from thermal particles to the superthermal population in some models that use numerical simulations. In order to investigate the effect of anisotropy in particle scattering on the particle injection rate, we present a dynamical Monte Carlo simulation of a bow shock from Earth with different dispersions in the pitch-angle scattering. Since the particle injection rate is intrinsically defined by the prescribed scattering law in a Monte Carlo approach, we can directly study the relationship between the particle injection rate and the dispersion of the particle scattering angular distribution. As a result, we find that the particle injection rate increases as the dispersion of the scattering angular distribution increases. The shock energy spectrum also becomes harder as the scattering angular distribution varies from a situation with anisotropy to one with isotropy. If the particle injection rate can dominate the shock strength, that may imply that a low-speed coronal mass ejection (CME) could drive a strong shock and a high-speed CME could drive a weak shock.

NONTHERMAL RADIATION FROM SUPERNOVA REMNANTS: EFFECTS OF MAGNETIC FIELD AMPLIFICATION AND PARTICLE ESCAPE

We explore nonlinear effects of wave-particle interactions on the diffusive shock acceleration (DSA) process in Type Ia-like, SNR blast waves, by implementing phenomenological models for magnetic field amplification, Alfv'enic drift, and particle escape in time-dependent numerical simulations of nonlinear DSA. For typical SNR parameters the CR protons can be accelerated to PeV energies only if the region of amplified field ahead of the shock is extensive enough to contain the diffusion lengths of the particles of interest. Even with the help of Alfv'enic drift, it remains somewhat challenging to construct a nonlinear DSA model for SNRs in which order of 10 % of the supernova explosion energy is converted to the CR energy and the magnetic field is amplified by a factor of 10 or so in the shock precursor, while, at the same time, the energy spectrum of PeV protons is steeper than E^{-2}. To explore the influence of these physical effects on observed SNR emissions, we also compute resulting radio-to-gamma-ray spectra. Nonthermal emission spectra, especially in X-ray and gamma-ray bands,depend on the time dependent evolution of CR injection process, magnetic field amplification, and particle escape, as well as the shock dynamic evolution. This result comes from the fact that the high energy end of the CR spectrum is composed of the particles that are injected in the very early stages of blast wave evolution. Thus it is crucial to understand better the plasma wave-particle interactions associated with collisionless shocks in detail modeling of nonthermal radiation from SNRs.

Nonthermal Radiation from Supernova Remnant Shocks

Most of high energy cosmic rays (CRs) are thought to be produced by diffusive shock acceleration (DSA) at supernova remnants (SNRs) within the Galaxy. Fortunately, nonthermal emissions from CR protons and electrons can provide direct observational evidence for such a model and place strong constraints on the complex nonlinear plasma processes in DSA theory. In this study we calculate the energy spectra of CR protons and electrons in Type Ia SNRs, using time-dependent DSA simulations that incorporate phenomenological models for some wave-particle interactions. We demonstrate that the time-dependent evolution of the self-amplified magnetic fields, Alfvnic drift, and escape of the highest energy particles affect the energy spectra of accelerated protons and electrons, and so resulting nonthermal radiation spectrum. Especially, the spectral cutoffs in X-ray and -ray emission spectra are regulated by the evolution of the highest energy particles, which are injected at the early phase of SNRs. Thus detailed understandings of nonlinear wave-particle interactions and time-dependent DSA simulations of SNRs are crucial in testing the SNR hypothesis for the origin of Galactic cosmic rays.

ACR-HYDRO-NEIMODEL OF MULTI-WAVELENGTH EMISSION FROM THE VELA JR. SUPERNOVA REMNANT (SNR RX J0852.0–4622)

Based largely on energy budget considerations and the observed cosmic-ray (CR) ionic composition, supernova remnant (SNR) blast waves are the most likely sources of CR ions with energies at least up to the "knee" near 3 PeV. Shocks in young shell-type TeV-bright SNRs are surely producing TeV particles, but the emission could be dominated by ions producing neutral pion-decay emission or electrons producing inverse-Compton gamma-rays. Unambiguously identifying the GeV-TeV emission process in a particular SNR will not only help pin down the origin of CRs, it will add significantly to our understanding of the diffusive shock acceleration (DSA) mechanism and improve our understanding of supernovae and the impact SNRs have on the circumstellar medium. In this study, we investigate the Vela Jr. SNR, an example of TeV-bright non-thermal SNRs. We perform hydrodynamic simulations coupled with non-linear DSA and non-equilibrium ionization near the forward shock (FS) to confront currently available multi-wavelength data. We find, with an analysis similar to that used earlier for SNR RX J1713.7-3946, that self-consistently modeling the thermal X-ray line emission with the non-thermal continuum in our one-dimensional model strongly constrains the fitting parameters, and this leads convincingly to a leptonic origin for the GeV-TeV emission for Vela Jr. This conclusion is further supported by applying additional constraints from observation, including the radial brightness profiles of the SNR shell in TeV gamma-rays, and the spatial variation of the X-ray synchrotron spectral index. We will discuss implications of our models on future observations by the next-generation telescopes.

EFFECTS OF WAVE-PARTICLE INTERACTIONS ON DIFFUSIVE SHOCK ACCELERATION AT SUPERNOVA REMNANTS

Nonthermal radiation from supernova remnants (SNRs) provides observational evidence and constraints on the diffusive shock acceleration (DSA) hypothesis for the origins of Galactic cosmic rays (CRs). Recently it has been recognized that a variety of plasma wave-particle interactions operate at astrophysical shocks and the detailed outcomes of DSA are governed by their complex and nonlinear interrelationships. Here we calculate the energy spectra of CR protons and electrons accelerated at Type Ia SNRs, using time-dependent, DSA simulations with phenomenological models for magnetic field amplification due to CR streaming instabilities, Alf<TEX>$\acute{e}$</TEX>enic drift, and free escape boundary. We show that, if scattering centers drift with the Alf<TEX>$\acute{e}$</TEX>en speed in the amplified magnetic fields, the CR energy spectrum is steepened and the acceleration efficiency is significantly reduced at strong CR modified SNR shocks. Even with fast Afv<TEX>$\acute{e}$</TEX>nic drift, DSA can still be efficient enough to develop a substantial shock precursor due to CR pressure feedback and convert about 20-30% of the SN explosion energy into CRs. Since the high energy end of the CR proton spectrum is composed of the particles that are injected in the early stages, in order to predict nonthermal emissions, especially in X-ray and <TEX>${\gamma}-ray$</TEX> bands, it is important to follow the time dependent evolution of the shock dynamics, CR injection process, magnetic field amplification, and particle escape. Thus it is crucial to understand the details of these plasma interactions associated with collisionless shocks in successful modeling of nonlinear DSA.

DIFFUSIVE SHOCK ACCELERATION AT COSMOLOGICAL SHOCK WAVES

We reexamine nonlinear diffusive shock acceleration (DSA) at cosmological shocks in the large scale structure of the Universe, incorporating wave-particle interactions that are expected to operate in collisionless shocks. Adopting simple phenomenological models for magnetic field amplification (MFA) by cosmic-ray (CR) streaming instabilities and Alfv'enic drift, we perform kinetic DSA simulations for a wide range of sonic and Alfv'enic Mach numbers and evaluate the CR injection fraction and acceleration efficiency. In our DSA model the CR acceleration efficiency is determined mainly by the sonic Mach number Ms, while the MFA factor depends on the Alfv'enic Mach number and the degree of shock modification by CRs. We show that at strong CR modified shocks, if scattering centers drift with an effective Alfv'en speed in the amplified magnetic field, the CR energy spectrum is steepened and the acceleration efficiency is reduced significantly, compared to the cases without such effects. As a result, the postshock CR pressure saturates roughly at ~ 20 % of the shock ram pressure for strong shocks with Ms>~ 10. In the test-particle regime (Ms<~ 3), it is expected that the magnetic field is not amplified and the Alfv'enic drift effects are insignificant, although relevant plasma physical processes at low Mach number shocks remain largely uncertain.

DIFFUSIVE SHOCK ACCELERATION WITH MAGNETIC FIELD AMPLIFICATION AND ALFVÉNIC DRIFT

We explore how wave-particle interactions affect diffusive shock acceleration (DSA) at astrophysical shocks by performing time-dependent kinetic simulations, in which phenomenological models for magnetic field amplification (MFA), Alfv<TEX>$\acute{e}$</TEX>nic drift, thermal leakage injection, Bohm-like diffusion, and a free escape boundary are implemented. If the injection fraction of cosmic-ray (CR) particles is <TEX>${\xi}$</TEX> > <TEX>$2{\times}10^{-4}$</TEX>, for the shock parameters relevant for young supernova remnants, DSA is efficient enough to develop a significant shock precursor due to CR feedback, and magnetic field can be amplified up to a factor of 20 via CR streaming instability in the upstream region. If scattering centers drift with Alfv<TEX>$\acute{e}$</TEX>n speed in the amplified magnetic field, the CR energy spectrum can be steepened significantly and the acceleration efficiency is reduced. Nonlinear DSA with self-consistent MFA and Alfv<TEX>$\acute{e}$</TEX>nic drift predicts that the postshock CR pressure saturates roughly at ~10 % of the shock ram pressure for strong shocks with a sonic Mach number ranging <TEX>$20{\leq}M_s{\leq}100$</TEX>. Since the amplified magnetic field follows the flow modification in the precursor, the low energy end of the particle spectrum is softened much more than the high energy end. As a result, the concave curvature in the energy spectra does not disappear entirely even with the help of Alfv<TEX>$\acute{e}$</TEX>nic drift. For shocks with a moderate Alfv<TEX>$\acute{e}$</TEX>n Mach number (<TEX>$M_A$</TEX> < 10), the accelerated CR spectrum can become as steep as <TEX>$E^{-2.1}$</TEX> - <TEX>$E^{-2.3}$</TEX>, which is more consistent with the observed CR spectrum and gamma-ray photon spectrum of several young supernova remnants.

Strong evidence for hadron acceleration in Tycho’s supernova remnant

Very recent gamma-ray observations of G120.1+1.4 (Tycho's) supernova remnant (SNR) by Fermi-LAT and VERITAS provided new fundamental pieces of information for understanding particle acceleration and non-thermal emission in SNRs. We want to outline a coherent description of Tycho's properties in terms of SNR evolution, shock hydrodynamics and multi-wavelength emission by accounting for particle acceleration at the forward shock via first order Fermi mechanism. We adopt here a quick and reliable semi-analytical approach to non-linear diffusive shock acceleration which includes magnetic field amplification due to resonant streaming instability and the dynamical backreaction on the shock of both cosmic rays (CRs) and self-generated magnetic turbulence. We find that Tycho's forward shock is accelerating protons up to at least 500 TeV, channelling into CRs about the 10 per cent of its kinetic energy. Moreover, the CR-induced streaming instability is consistent with all the observational evidences indicating a very efficient magnetic field amplification (up to ~300 micro Gauss). In such a strong magnetic field the velocity of the Alfv\'en waves scattering CRs in the upstream is expected to be enhanced and to make accelerated particles feel an effective compression factor lower than 4, in turn leading to an energy spectrum steeper than the standard prediction {\propto} E^-2. This latter effect is crucial to explain the GeV-to-TeV gamma-ray spectrum as due to the decay of neutral pions produced in nuclear collisions between accelerated nuclei and the background gas. The self-consistency of such an hadronic scenario, along with the fact that the concurrent leptonic mechanism cannot reproduce both the shape and the normalization of the detected the gamma-ray emission, represents the first clear and direct radiative evidence that hadron acceleration occurs efficiently in young Galactic SNRs.

NONTHERMAL RADIATION FROM COSMIC-RAY MODIFIED SHOCKS

We calculate nonthermal radiation from cosmic-ray (CR) protons and electrons accelerated at CR modified plane and spherical shocks, using time-dependent, diffusive shock acceleration (DSA) simulations that include radiative losses of CR electrons. Strong non-relativistic shocks with physical parameters relevant for young supernova remnants (SNRs) are considered in both the plane-parallel and spherically symmetric geometries, and compared at times when their dynamical and CR properties are concordant. A thermal leakage injection model and a Bohm-like diffusion coefficient are adopted. After DSA energy gains balance radiative losses, the electron spectrum at the plane shock approaches a time-asymptotic spectrum with a super-exponential cutoff above the equilibrium momentum. The postshock electron spectrum cuts off at a progressively lower momentum downstream from the shock due to the energy losses. That results in the steepening of the volume integrated electron energy spectrum by one power of the particle energy. These features evolve toward lower energies in the spherical, SNR shocks. In a CR modified shock, pion decay gamma-ray emission reveals distinct signatures of nonlinear DSA due to the concave proton momentum spectrum. Although the electron momentum spectrum has a much weaker concavity, the synchrotron spectral slope at the shock may flatten by about 0.1-0.3 between radio and X-ray bands. The slope of the volume integrated emission spectrum behaves nonlinearly around the break frequency.

CORE-COLLAPSE MODEL OF BROADBAND EMISSION FROM SNR RX J1713.7–3946 WITH THERMAL X-RAYS AND GAMMA RAYS FROM ESCAPING COSMIC RAYS

We present a spherically symmetric, core-collapse model of SNR RX J1713.7-3946 that includes a hydrodynamic simulation of the remnant evolution coupled to the efficient production of cosmic rays (CRs) by nonlinear diffusive shock acceleration (DSA). High-energy CRs that escape from the forward shock (FS) are propagated in surrounding dense material that simulates either a swept-up, pre-supernova shell or a nearby molecular cloud. The continuum emission from trapped and escaping CRs, along with the thermal X-ray emission from the shocked heated ISM behind the FS, integrated over the remnant, is compared against broadband observations. Our results show conclusively that, overall, the GeV-TeV emission is dominated by inverse-Compton from CR electrons if the supernova is isolated regardless of its type, i.e., not interacting with a >>100 Msun shell or cloud. If the SNR is interacting with a much larger mass >10^4 Msun, pion-decay from the escaping CRs may dominate the TeV emission, although a precise fit at high energy will depend on the still uncertain details of how the highest energy CRs are accelerated by, and escape from, the FS. Based on morphological and other constraints, we consider the 10^4 Msun pion-decay scenario highly unlikely for SNR RX J1713.7-3946 regardless of the details of CR escape. Importantly, even though CR electrons dominate the GeV-TeV emission, the efficient production of CR ions is an essential part of our leptonic model.

Numerical simulations of diffusive shock acceleration in SNRs

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 cosmic ray ions and positrons is discussed.

X-RAY STRIPES IN TYCHO'S SUPERNOVA REMNANT: SYNCHROTRON FOOTPRINTS OF A NONLINEAR COSMIC-RAY-DRIVEN INSTABILITY

High-resolution Chandra observations of Tycho's SNR have revealed several sets of quasi-steady, high-emissivity, nearly-parallel X-ray stripes in some localized regions of the SNR. These stripes are most likely the result of cosmic-ray (CR) generated magnetic turbulence at the SNR blast wave. However, for the amazingly regular pattern of these stripes to appear requires the simultaneous action of a number of shock-plasma phenomena and is not predicted by most models of magnetic field amplification. A consistent explanation of these stripes yields information on the complex nonlinear plasma processes connecting efficient CR acceleration and magnetic field fluctuations in strong collisionless shocks. The nonlinear diffusive shock acceleration (NL-DSA) model described here, which includes magnetic field amplification from a cosmic-ray current driven instability, does predict stripes consistent with the synchrotron emission observations of Tycho's SNR. We argue that the local ambient mean magnetic field geometry determines the orientation of the stripes and therefore it can be reconstructed with the high resolution X-ray imaging. The estimated maximum energy of the CR protons responsible for the stripes is $\sim 10^{15}$\,eV. Furthermore, the model predicts that a specific X-ray polarization pattern, with a polarized fraction ~ 50%, accompanies the stripes, which can be tested with future X-ray polarimeter missions.

THE IMPACT OF EFFICIENT PARTICLE ACCELERATION ON THE EVOLUTION OF SUPERNOVA REMNANTS IN THE SEDOV-TAYLOR PHASE

We investigate the effects of the efficient production of cosmic rays on the evolution of supernova remnants (SNRs) in the adiabatic Sedov-Taylor phase. We model the SNR by coupling the hydrodynamic evolution with nonlinear diffusive shock acceleration (DSA), and track self-consistently the ionization state of the shock-heated plasma. Using a plasma emissivity code and the results of the model, we predict the thermal X-ray emission and combine it with the non-thermal component in order to obtain the complete spectrum in this energy range. Hence, we study how the interpretation of thermal X-ray observations is affected by the efficiency of the DSA process, and find that, compared to test particle cases, the efficient DSA example yields a smaller shock radius and speed, a larger compression ratio, and lower intensity X-ray thermal emission. We also find that a model where the shock is not assumed to produce CRs can fit the X-ray observational properties of an example with efficient particle acceleration, with a different set of input parameters, and in particular a much lower explosion energy. Additionally, we model the broadband non-thermal emission, and investigate what signatures result from the acceleration of particles.

Non-thermal radiation from Type Ia supernova remnants

We present calculations of expected continuum emissions from Sedov-Taylor phase Type Ia supernova remnants (SNRs), using the energy spectra of cosmic ray (CR) electrons and protons from nonlinear diffusive shock acceleration (DSA) simulations. A new, general-purpose radiative process code, Cosmicp, was employed to calculate the radiation expected from CR electrons and protons and their secondary products. These radio, X-ray and gamma-ray emissions are generally consistent with current observations of Type Ia SNRs. The emissions from electrons in these models dominate the radio through X-ray bands. Decays of \pi^0 s from p-p collisions mostly dominate the gamma-ray range, although for a hot, low density ISM case (n_{ISM}=0.003 cm^{-3}), the pion decay contribution is reduced sufficiently to reveal the inverse Compton contribution to TeV gamma-rays. In addition, we present simple scalings for the contributing emission processes to allow a crude exploration of model parameter space, enabling these results to be used more broadly. We also discuss the radial surface brightness profiles expected for these model SNRs in the X-ray and gamma-ray bands.

ENERGY SPECTRUM OF NONTHERMAL ELECTRONS ACCELERATED AT A PLANE SHOCK

We calculate the energy spectra of cosmic ray (CR) protons and electrons at a plane shock with quasi-parallel magnetic fields, using time-dependent, diffusive shock acceleration (DSA) simulations, including energy losses via synchrotron emission and Inverse Compton (IC) scattering. A thermal leakage injection model and a Bohm type diffusion coeffcient are adopted. The electron spectrum at the shock becomes steady after the DSA energy gains balance the synchrotron/IC losses, and it cuts off at the equilibrium momentum peq. In the postshock region the cutoff momentum of the electron spectrum decreases with the distance from the shock due to the energy losses and the thickness of the spatial distribution of electrons scales as p?¹. Thus the slope of the downstream integrated spectrum steepens by one power of p for p br ＜ p ＜ p eq , where the break momentum decreases with the shock age as p br χ t?¹. In a CR modified shock, both the proton and electron spectrum exhibit a concave curvature and deviate from the canonical test-particle power-law, and the upstream integrated electron spectrum could dominate over the downstream integrated spectrum near the cutoff momentum. Thus the spectral shape near the cutoff of X-ray synchrotron emission could reveal a signature of nonlinear DSA.

GAMMA-RAY EMISSION OF ACCELERATED PARTICLES ESCAPING A SUPERNOVA REMNANT IN A MOLECULAR CLOUD

We present a model of gamma-ray emission from core-collapse supernovae originating from the explosions of massive young stars. The fast forward shock of the supernova remnant (SNR) can accelerate particles by diffusive shock acceleration (DSA) in a cavern blown by a strong, pre-supernova stellar wind. As a fundamental part of nonlinear DSA, some fraction of the accelerated particles escape the shock and interact with a surrounding massive dense shell producing hard photon emission. To calculate this emission, we have developed a new Monte Carlo technique for propagating the cosmic rays (CRs) produced by the forward shock of the SNR, into the dense, external material. This technique is incorporated in a hydrodynamic model of an evolving SNR which includes the nonlinear feedback of CRs on the SNR evolution, the production of escaping CRs along with those that remain trapped within the remnant, and the broad-band emission of radiation from trapped and escaping CRs. While our combined CR-hydro-escape model is quite general and applies to both core collapse and thermonuclear supernovae, the parameters we choose for our discussion here are more typical of SNRs from very massive stars whose emission spectra differ somewhat from those produced by lower mass progenitors directly interacting with a molecular cloud.

MULTIBAND NONTHERMAL EMISSION FROM THREE TeV SHELL-TYPE SUPERNOVA REMNANTS

Nonthermal radiative properties of three TeV shell-type supernova remnants (SNRs) RX J1713.7?3946, RX?J0852.0?4622, and RCW 86, argued to be expanding into low-density hot bubbles created by the wind of the massive progenitor stars, are investigated based on a semi-analytical solution to diffusive acceleration at nonlinear shocks. In the model, a free-escape boundary upstream of the shock is used to mimic the escape of cosmic rays from the SNR, with the dynamic reaction of the self-generated magnetic field via resonant streaming instability on the shock taken into account. Origins of the ?-rays from the three remnants are studied with appropriate parameters, and consistent results with the multiband observed fluxes are obtained within the nonlinear diffusive shock acceleration regime. The order of the resulting downstream magnetic field strength for the three SNRs is between 60 and 100 ?G, and the observed TeV ?-rays are mainly produced via the decay of neutral ? mesons produced from the hadronic collisions.

X-Ray and Gamma-Ray Emission of the Shell-Type Supernova Remnant RX J1713.7−3946

To study possible origins of high-energy gamma-ray emission from shell-type supernova remnants, RX J1713.7$-$3946, we model their nonthermal photon spectra from X-ray to very high energy (VHE) gamma-ray bands in the frame of non-linear diffusive shock acceleration, respectively. In our modeling, the accelerated proton spectrum is calculated based on a semi-analytical solution of the problem of particle acceleration at non-linear shock waves with a free escape boundary at some location upstream, and the accelerated electron spectrum is similar to the proton's spectrum when the electron's momentum is much less than its maximum momentum, which is determined by equating the synchrotron loss time with the acceleration time, and the cutoff shapes are assumed to be an super-exponential. In the one-zone model, we calculated the non-thermal photon spectra of the supernova remnants (SNR) for both leptonic and hadronic cases, and found out that the spectra calculated for both cases can reproduce the observed data by Suzaku, Fermi LAT, and HESS under reasonable model parameters. However, high-energy gamma-ray emission would have a hadronic origin if the observed thickness of the X-ray filament of the SNR is taken into account.