DIFFUSIVE SHOCK ACCELERATION WITH MAGNETIC FIELD AMPLIFICATION AND ALFVÉNIC DRIFT

Kang, Hyesung The Korean Astronomical Society 2012 Journal of The Korean Astronomical Society Vol.45 No.5

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$\acute{e}$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 ${\xi}$ > $2{\times}10^{-4}$, 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$\acute{e}$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$\acute{e}$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 $20{\leq}M_s{\leq}100$. 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$\acute{e}$nic drift. For shocks with a moderate Alfv$\acute{e}$n Mach number ($M_A$ < 10), the accelerated CR spectrum can become as steep as $E^{-2.1}$ - $E^{-2.3}$, which is more consistent with the observed CR spectrum and gamma-ray photon spectrum of several young supernova remnants.

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

Kang, Hyesung,Jones, T. W.,Edmon, Paul P. IOP Publishing 2013 The Astrophysical journal Vol.777 No.1

<P>We explore nonlinear effects of wave-particle interactions on the diffusive shock acceleration (DSA) process in Type Ia-like supernova remnant (SNR) blast waves by implementing phenomenological models for magnetic field amplification (MFA), Alfvenic drift, and particle escape in time-dependent numerical simulations of nonlinear DSA. For typical SNR parameters, the cosmic-ray (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 Alfvenic drift, it remains somewhat challenging to construct a nonlinear DSA model for SNRs in which of the order of 10% of the supernova explosion energy is converted into 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 emission, we also compute the resulting radio-to-gamma-ray spectra. Nonthermal emission spectra, especially in X-ray and gamma-ray bands, depend on the time-dependent evolution of the CR injection process, MFA, 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 particles that are injected in the very early stages of the blast wave evolution. Thus, it is crucial to better understand the plasma wave-particle interactions associated with collisionless shocks in detailed modeling of nonthermal radiation from SNRs.</P>

Hosting the 31st General Assembly of the International Astronomical Union in the midst of the COVID-19 pandemic

Hyesung Kang 한국천문학회 2022 天文學會報 Vol.47 No.2

DIFFUSIVE SHOCK ACCELERATION AT COSMOLOGICAL SHOCK WAVES

Kang, Hyesung,Ryu, Dongsu IOP Publishing 2013 The Astrophysical journal Vol.764 No.1

<P>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 Alfvenic drift, we perform kinetic DSA simulations for a wide range of sonic and Alfvenic 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 M-s, while the MFA factor depends on the Alfvenic 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 Alfven 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 similar to 20% of the shock ram pressure for strong shocks with M-s greater than or similar to 10. In the test-particle regime (M-s less than or similar to 3), it is expected that the magnetic field is not amplified and the Alfvenic drift effects are insignificant, although relevant plasma physical processes at low Mach number shocks remain largely uncertain.</P>

Self-similar evolution of cosmic-ray-modified quasi-parallel plane shocks

Kang, Hyesung,Jones, T.W. North-Holland 2007 Astroparticle physics Vol.28 No.2

<P><B>Abstract</B></P><P>Using an improved version of the previously introduced Cosmic Ray Acceleration SHock (CRASH) code, we have calculated the time evolution of cosmic-ray (CR) modified quasi-parallel plane shocks for Bohm-like diffusion, including self-consistent models of Alfvén wave drift and dissipation, along with “thermal leakage injection” of CRs. The new simulations follow evolution of the CR distribution to much higher energies than our previous study, providing a better examination of evolutionary and asymptotic behaviors. The postshock CR pressure becomes constant after quick initial adjustment, since the evolution of the CR partial pressure expressed in terms of a momentum similarity variable is self-similar. The shock precursor, which scales as the diffusion length of the highest energy CRs, subsequently broadens approximately linearly with time, independent of diffusion model, so long as CRs continue to be accelerated to ever-higher energies. This means the nonlinear shock structure can be described approximately in terms of the similarity variable, x/(<SUB>us</SUB>t), where <I>u</I><SUB>s</SUB> is the shock speed once the postshock pressure reaches an approximate time asymptotic state. As before, the shock Mach number is the key parameter determining the evolution and the CR acceleration efficiency, although finite Alfvén wave drift and wave energy dissipation in the shock precursor reduce the effective velocity change experienced by CRs. This reduces acceleration efficiency noticeably, thus, providing a second important parameter at low and moderate Mach numbers. For low Mach numbers (<SUB>M0</SUB>≲5) the CR acceleration efficiency depends on the thermal leakage injection rate, the Alfvénic Mach number, and any preexisting CR population. However, these dependences become weak for high shock Mach numbers of <SUB>M0</SUB>>30. To evaluate CR acceleration efficiencies in the simulated shocks we present for a wide range of shock parameters a “CR energy ratio”, Φ(<SUB>M0</SUB>), comparing the time asymptotic volume-integrated energy in CRs to the time-integrated kinetic energy flux through the shock. This ratio asymptotes to roughly 0.5 for sufficiently strong shocks. The postshock CR pressure is also approximately 1/2 the momentum flux through the shock for very high Mach numbers.</P>

Particle Acceleration at Astrophysical Shocks

Hyesung Kang 한국천문학회 2011 天文學會報 Vol.36 No.2

Re-acceleration of Nonthermal Particles at Weak Cosmological Shock Waves

Hyesung Kang,Dongsu Ryu 한국천문학회 2011 天文學會報 Vol.36 No.1

TWO-FLUID CLOSURE PARAMETERS FOR DIFFUSIVE ACCELERATION OF COSMIC RAYS

KANG HYESUNG The Korean Astronomical Society 1993 Journal of The Korean Astronomical Society Vol.26 No.1

In order to explore the time dependence of the closure parameters of the two-fluid calculations for supernova remnants and the terminal shocks of stellar winds, we have considered a simple model in which the time evolution of the cosmic-ray distribution function was followed in the test-particle limit using the Bohm diffusion model. The particles are mostly accelerated to relativistic energy either in the free expansion phase of the SNRs or in the early phase of the stellar winds, so the evolution of the closure parameters during these early stages is substantial and should be followed correctly. We have also calculated the maximum momentum which is limited by either the age or the curvature of these spherical shocks. We found that SNRs expanding into the medium where the gas density decreases with the distance from the explosion center might be necessary to explain the observed power-law distribution of the galactic cosmic rays. The energy loss due to the escaping energetic particles has been estimated for the terminal shocks of the stellar winds.

Efficiency of Nonlinear Particle Acceleration at Cosmic Structure Shocks

Kang, Hyesung,Jones, T. W. IOP Publishing 2005 The Astrophysical journal Vol.620 No.1

NONTHERMAL RADIATION FROM COSMIC-RAY MODIFIED SHOCKS

Kang, Hyesung,Edmon, Paul P.,Jones, T. W. IOP Publishing 2012 The Astrophysical journal Vol.745 No.2

<P>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.</P>