Rough Equipartition Research Articles

TeV Neutrinos and Hard X-Rays from Relativistic Reconnection in the Corona of NGC 1068

The recent discovery of astrophysical neutrinos from the Seyfert galaxy NGC 1068 suggests the presence of nonthermal protons within a compact “coronal” region close to the central black hole. The acceleration mechanism of these nonthermal protons remains elusive. We show that a large-scale magnetic reconnection layer, of the order of a few gravitational radii, may provide such a mechanism. In such a scenario, rough energy equipartition between magnetic fields, X-ray photons, and nonthermal protons is established in the reconnection region. Motivated by recent 3D particle-in-cell simulations of relativistic reconnection, we assume that the spectrum of accelerated protons is a broken power law, with the break energy being constrained by energy conservation (i.e., the energy density of accelerated protons is at most comparable to the magnetic energy density). The proton spectrum is dnp/dEp∝Ep−1 below the break and dnp/dEp∝Ep−s above the break, with IceCube neutrino observations suggesting s ≃ 3. Protons above the break lose most of their energy within the reconnection layer via photohadronic collisions with the coronal X-rays, producing a neutrino signal in good agreement with the recent observations. Gamma rays injected in photohadronic collisions are cascaded to lower energies, sustaining the population of electron–positron pairs that makes the corona moderately Compton thick.

Effects of Magnetic Fields on Gas Dynamics and Star Formation in Nuclear Rings

Nuclear rings at the centers of barred galaxies are known to be strongly magnetized. To explore the effects of magnetic fields on star formation in these rings and nuclear gas flows, we run magnetohydrodynamic simulations in which there is a temporally constant magnetized inflow to the ring, representing a bar-driven inflow. The mass inflow rate is 1M ⊙ yr−1, and we explore models with a range of field strength in the inflow. We adopt the TIGRESS framework developed by Kim & Ostriker to handle radiative heating and cooling, star formation, and resulting supernova (SN) feedback. We find that magnetic fields are efficiently amplified in the ring due to rotational shear and SN feedback. Within a few 100 Myr, the turbulent component B trb in the ring saturates at ∼35 μG (in rough equipartition with the turbulent kinetic energy density), while the regular component B reg exceeds 50 μG. Expanding superbubbles created by clustered SN explosions vertically drag predominantly toroidal fields from near the midplane to produce poloidal fields in high-altitude regions. The growth of magnetic fields greatly suppresses star formation at late times. Simultaneously, strong magnetic tension in the ring drives radially inward accretion flows from the ring to form a circumnuclear disk in the central region; this feature is absent in the unmagnetized model.

Interplasmoid Compton scattering and the Compton dominance of BL Lacs

ABSTRACT Blazar emission models based on magnetic reconnection succeed in reproducing many observed spectral and temporal features, including the short-duration luminous flaring events. Plasmoids, a self-consistent by-product of the tearing instability in the reconnection layer, can be the main source of blazar emission. Kinetic simulations of relativistic reconnection have demonstrated that plasmoids are characterized by rough energy equipartition between their radiating particles and magnetic fields. This is the main reason behind the apparent shortcoming of plasmoid-dominated emission models to explain the observed Compton ratios of BL Lac objects. Here, we demonstrate that the radiative interactions among plasmoids, which have been neglected so far, can assist in alleviating this contradiction. We show that photons emitted by large, slow-moving plasmoids can be a potentially important source of soft photons to be then upscattered, via inverse Compton, by small fast-moving, neighbouring plasmoids. This interplasmoid Compton scattering process can naturally occur throughout the reconnection layer, imprinting itself as an increase in the observed Compton ratios from those short and luminous plasmoid-powered flares within BL Lac sources, while maintaining energy equipartition between radiating particles and magnetic fields.

Rayleigh–Taylor Instability in Interacting Supernovae: Implications for Synchrotron Magnetic Fields

Abstract Synchrotron emission from a supernova (SN) necessitates a magnetic field, but it is unknown how strong the relevant magnetic fields are, and what mechanism generates them. In this study, we perform high-resolution numerical gas dynamics calculations in axisymmetry to determine the growth of turbulence due to Rayleigh–Taylor (RT) instability, and the resulting kinetic energy in turbulent fluctuations, as a means of inferring how strong magnetic fields can become when amplified by this turbulence. Assuming rough equipartition between kinetic and magnetic energy in the turbulence, we find that RT instability may produce turbulent fluctuations strong enough to amplify magnetic fields to a few percent of equipartition with the thermal energy. This turbulence stays concentrated near the reverse shock, but averaging this magnetic energy throughout the shocked region (weighting by emissivity) sets the magnetic fields at a minimum of 0.3 percent of equipartition. This line of argument predicts a minimum effective magnetic field strength ( ) that should be present in all interacting SNe. This provides a prediction for what should be found in highly resolved, three-dimensional magnetohydrodynamics calculations. The strength and spatial distribution of turbulently generated magnetic fields would have implications for the shape and luminosity of SN radio light curves.

A hadronic minute-scale GeV flare from quasar 3C 279?

Abstract The flat spectrum radio quasar 3C 279 is a known γ-ray variable source that has recently exhibited minute-scale variability at energies >100 MeV. One-zone leptonic models for blazar emission are severely constrained by the short time-scale variability that implies a very compact emission region at a distance of hundreds of Schwarzschild radii from the central black hole. Here, we investigate a hadronic scenario where GeV γ-rays are produced via proton synchrotron radiation. We also take into account the effects of the hadronically initiated electromagnetic cascades (EMC). For a γ-ray emitting region in rough equipartition between particles and kG magnetic fields, located within the broad-line region (BLR), the development of EMC redistributes the γ-ray luminosity to softer energy bands and eventually leads to broad-band spectra that differ from the observed ones. Suppression of EMC and energy equipartition are still possible, if the γ-ray emitting region is located beyond the BLR, is fast moving with Doppler factor (>70) and contains strong magnetic fields (>100 G). Yet, these conditions cannot be easily met in parsec-scale jets, thus disfavouring a proton synchrotron origin of the Fermi-LAT flare.

Plasmoids in relativistic reconnection, from birth to adulthood: first they grow, then they go

Blobs, or quasi-spherical emission regions containing relativistic particles and magnetic fields, are often assumed ad hoc in emission models of relativistic astrophysical jets, yet their physical origin is still not well understood. Here, we employ a suite of large-scale two-dimensional particle-in-cell simulations in electron-positron plasmas to demonstrate that relativistic magnetic reconnection can naturally account for the formation of quasi-spherical plasmoids filled with high-energy particles and magnetic fields. Our simulations extend to unprecedentedly long temporal and spatial scales, so we can capture the asymptotic physics independently of the initial setup. We characterize the properties of the plasmoids that are continuously generated as a self-consistent by-product of the reconnection process: they are in rough energy equipartition between particles and magnetic fields; the upper energy cutoff of the plasmoid particle spectrum is proportional to the plasmoid width w, corresponding to a Larmor radius ~0.2 w; the plasmoids grow in size at ~0.1 of the speed of light, with most of the growth happening while they are still non-relativistic (first they grow); their growth is suppressed once they get accelerated to relativistic speeds by the field line tension, up to the Alfven speed (then they go). The largest plasmoids, whose typical recurrence interval is ~2.5 L/c, reach a characteristic size w ~ 0.2 L independently of the system length L, they have nearly isotropic particle distributions and they contain the highest energy particles, whose Larmor radius is ~0.03 L. The latter can be regarded as the Hillas criterion for relativistic reconnection. We briefly discuss the implications of our results for the high-energy emission from relativistic jets and pulsar winds.

Relativistic jets shine through shocks or magnetic reconnection?

Observations of gamma-ray-bursts and jets from active galactic nuclei reveal that the jet flow is characterized by a high radiative efficiency and that the dissipative mechanism must be a powerful accelerator of non-thermal particles. Shocks and magnetic reconnection have long been considered as possible candidates for powering the jet emission. Recent progress via fully-kinetic particle-in-cell simulations allows us to revisit this issue on firm physical grounds. We show that shock models are unlikely to account for the jet emission. In fact, when shocks are efficient at dissipating energy, they typically do not accelerate particles far beyond the thermal energy, and vice versa. In contrast, we show that magnetic reconnection can deposit more than 50 per cent of the dissipated energy into non-thermal leptons as long as the energy density of the magnetic field in the bulk flow is larger than the rest-mass energy density. The emitting region, i.e. the reconnection downstream, is characterized by a rough energy equipartition between magnetic fields and radiating particles, which naturally accounts for a commonly observed property of blazar jets.

THE DOMINANCE OF NEUTRINO-DRIVEN CONVECTION IN CORE-COLLAPSE SUPERNOVAE

Multi-dimensional instabilities have become an important ingredient in core-collapse supernova (CCSN) theory. Therefore, it is necessary to understand the driving mechanism of the dominant instability. We compare our parameterized three-dimensional CCSN simulations with other buoyancy-driven simulations and propose scaling relations for neutrino-driven convection. Through these comparisons, we infer that buoyancy-driven convection dominates post-shock turbulence in our simulations. In support of this inference, we present four major results. First, the convective fluxes and kinetic energies in the neutrino-heated region are consistent with expectations of buoyancy-driven convection. Second, the convective flux is positive where buoyancy actively drives convection, and the radial and tangential components of the kinetic energy are in rough equipartition (i.e. K_r ~ K_{\theta} + K_{\phi}). Both results are natural consequences of buoyancy-driven convection, and are commonly observed in simulations of convection. Third, buoyant driving is balanced by turbulent dissipation. Fourth, the convective luminosity and turbulent dissipation scale with the driving neutrino power. In all, these four results suggest that in neutrino-driven explosions, the multi-dimensional motions are consistent with neutrino-driven convection.

Simulations of Dynamo Action in Fully Convective Stars

We present three-dimensional nonlinear magnetohydrodynamic simulations of the interiors of fully convective M dwarfs. Our models consider 0.3 solar-mass stars using the Anelastic Spherical Harmonic code, with the spherical computational domain extending from 0.08 to 0.96 times the overall stellar radius. Like previous authors, we find that fully convective stars can generate kG-strength magnetic fields (in rough equipartition with the convective flows) without the aid of a tachocline of shear. Although our model stars are everywhere unstably stratified, the amplitudes and typical pattern sizes of the convective flows vary strongly with radius, with the outer regions of the stars hosting vigorous convection and field amplification while the deep interiors are more quiescent. Modest differential rotation is established in hydrodynamic calculations, but—unlike in some prior work—strongly quenched in MHD simulations because of the Maxwell stresses exerted by the dynamo-generated magnetic fields. Despite the lack of strong differential rotation, the magnetic fields realized in the simulations possess significant mean (axisymmetric) components, which we attribute partly to the strong influence of rotation on the slowly overturning flows.

GRB 060218: The Nature of the Optical‐UV Component

The optical-UV component in GRB 060218 is assumed to be due to optically thick cyclotron emission. The key aspect of this model is the high temperature of the absorbing electrons. The heat input derives from nuclei accelerated in semirelativistic internal shocks, like in ordinary gamma-ray bursts. Coulomb collisions transfer part of that energy to electrons. Inverse Compton cooling on the X-ray photons leads to electron temperatures around ~100 keV. Such a high brightness temperature for the optical-UV emission implies an emitting area roughly equal to that of the thermal X-ray component. This suggests a model in which the radio, optical-UV, and thermal X-ray emission are closely related. Although the optical-UV and thermal X-ray emission are two separate spectral components, it is argued that they both come from the photosphere of a quasi-spherical, continuous outflow, whose interaction with the circumstellar medium gives rise to the radio emission. The properties of GRB 060218, as measured in the comoving frame, are similar to those of ordinary gamma-ray bursts; i.e., the main difference is the much lower value of the bulk Lorentz factor in GRB 060218. The cyclotron absorption implies a magnetic field in rough equipartition with the matter energy density in the outflow. Hence, the magnetic field could have a dynamically important role, possibly with a magnetar as the central engine.

Nonlinear evolution of the magnetohydrodynamic Rayleigh-Taylor instability

We study the nonlinear evolution of the magnetic Rayleigh-Taylor instability using three-dimensional magnetohydrodynamic simulations. We consider the idealized case of two inviscid, perfectly conducting fluids of constant density separated by a contact discontinuity perpendicular to the effective gravity g, with a uniform magnetic field B parallel to the interface. Modes parallel to the field with wavelengths smaller than λc=B∙B∕(ρh−ρl)g are suppressed (where ρh and ρl are the densities of the heavy and light fluids, respectively), whereas modes perpendicular to B are unaffected. We study strong fields with λc varying between 0.01 and 0.36 of the horizontal extent of the computational domain. Even a weak field produces tension forces on small scales that are significant enough to reduce shear (as measured by the distribution of the amplitude of vorticity), which in turn reduces the mixing between fluids, and increases the rate at which bubbles and finger are displaced from the interface compared to the purely hydrodynamic case. For strong fields, the highly anisotropic nature of unstable modes produces ropes and filaments. However, at late time flow along field lines produces large scale bubbles. The kinetic and magnetic energies transverse to gravity remain in rough equipartition and increase as t4 at early times. The growth deviates from this form once the magnetic energy in the vertical field becomes larger than the energy in the initial field. We comment on the implications of our results to Z-pinch experiments, and a variety of astrophysical systems.

Disc-jet coupling in black hole accretion systems - I. General relativistic magnetohydrodynamical models

General relativistic numerical simulations of magnetized accretion flows around black holes show a disordered electromagnetic structure in the disk and corona and a highly relativistic, Poynting-dominated funnel jet in the polar regions. The polar jet is nearly consistent with the stationary paraboloidal Blandford-Znajek model of an organized field threading the polar regions of a rotating black hole. How can a disordered accretion disk and corona lead to an ordered jet? We show that the polar jet is associated with a strikingly simple angular-integrated toroidal current distribution $dI_\phi/dr \propto r^{-5/4}$, where $I_\phi(r)$ is the toroidal current enclosed inside radius $r$. We demonstrate that the poloidal magnetic field in the simulated jet agrees well with the force-free field solution for a non-rotating thin disk with an $r^{-5/4}$ toroidal current, suggesting rotation leads to negligible self-collimation. We find that the polar field is confined/collimated by the corona. The electromagnetic field in the disk also scales as $r^{-5/4}$, which is consistent with some Newtonian accretion models that assume rough equipartition between magnetic and gas pressure. However, the agreement is accidental since toward the black hole the magnetic pressure increases faster than the gas pressure. This field dominance near the black hole is associated with magnetic stresses that imply a large effective viscosity parameter $\alpha\sim 1$, whereas the typically assumed value of $\alpha\sim 0.1$ holds far from the black hole.[abridged]

Magnetic field in galaxies, galaxy clusters, and intergalactic space

Magnetic fields of unknown origin appear to permeate the Universe on all large scales. We suggest that the winds and cosmic rays, which are produced by the spherical ejecta and jets from supernova explosions, magnetize the interstellar medium in galaxies, the intracluster medium in galaxy clusters, and the intergalactic space. We show that, if the cosmic rays generate magnetic fields in rough energy equipartition with the cosmic rays, the predicted magnetic-field strengths coincide with the ones observed.

Relativistic Magnetohydrodynamics with Application to Gamma‐Ray Burst Outflows. I. Theory and Semianalytic Trans‐Alfvenic Solutions

We present a general formulation of special-relativistic magnetohydrodynamics and derive exact radially self-similar solutions for axisymmetric outflows from strongly magnetized, rotating compact objects. We generalize previous work by including thermal effects and analyze in detail the various forces that guide, accelerate, and collimate the flow. We demonstrate that, under the assumptions of a quasi-steady poloidal magnetic field and of a highly relativistic poloidal velocity, the equations become effectively time-independent and the motion can be described as a frozen pulse. We concentrate on trans-Alfvenic solutions and consider outflows that are super-Alfvenic throughout in the companion paper. Our results are applicable to relativistic jets in gamma-ray burst (GRB) sources, active galactic nuclei, and microquasars, but our discussion focuses on GRBs. We envision the outflows in this case to initially consist of a hot and optically thick mixture of baryons, electron-positron pairs, and photons. We show that the flow is at first accelerated thermally but that the bulk of the acceleration is magnetic, with the asymptotic Lorentz factor corresponding to a rough equipartition between the Poynting and kinetic-energy fluxes (i.e., \~50% of the injected total energy is converted into baryonic kinetic energy). The electromagnetic forces also strongly collimate the flow, giving rise to an asymptotically cylindrical structure.

Relativistic Magnetohydrodynamics with Application to Gamma‐Ray Burst Outflows. II. Semianalytic Super‐Alfvenic Solutions

We present exact radially self-similar solutions of special-relativistic magnetohydrodynamics representing ``hot'' super-Alfvenic outflows from strongly magnetized, rotating compact objects. We argue that such outflows can plausibly arise in gamma-ray burst (GRB) sources and demonstrate that, just as in the case of the trans-Alfvenic flows considered in the companion paper, they can attain Lorentz factors that correspond to a rough equipartition between the Poynting and kinetic-energy fluxes and become cylindrically collimated on scales compatible with GRB observations. As in the trans-Alfvenic case, the initial acceleration is thermal, but, in contrast to the solutions presented in Paper I, part of the enthalpy flux is transformed into Poynting flux during this phase. The subsequent, magnetically dominated acceleration can be significantly less rapid than in trans-Alfvenic flows.

UHECR production by a compact black hole dynamo: application to Sgr A *

The possibility that the excess cosmic ray (CR) flux near 10 18 eV, reported recently by the AGASA group, is due to a compact black hole dynamo associated with the Sgr A * source is considered. Under the assumption that the Galactic center black hole rotates with nearly maximal spin, and that the magnetic field threading the horizon is in rough equipartition with matter accreted by the hole, the spectra and total fluxes of accelerated CRs and their associated curvature emission depend only on accretion rate. For the accretion rate estimated on the basis of observations of stellar winds near Sgr A * (∼10 −3 Eddington), the maximum proton energy achievable by this mechanism is of the order of 10 18 eV, and the corresponding CR power is ∼10 41α CR erg s −1 , where α CR≪1 is the CR production efficiency. The corresponding spectrum of curvature photons peaks at around 100 GeV, with a total luminosity comparable to the CR power released. For much lower accretion rates both the CR and gamma-ray fluxes predicted are completely insignificant. Upcoming gamma-ray experiments, such as CANGAROO, HESS and GLAST, can be used to probe the parameters of this system.

Nonlinear Dynamics in the Relativistic Plasma of Astrophysical High‐Energy Sources

Relativistic plasmas are interesting media for particle acceleration, especially when their kinetic pressure is in rough equipartition with the magnetic pressure. Indeed, when in rough equipartition, these relativistic plasmas have generalized Alfven waves that propagate at velocities close to the velocity of light, which makes the acceleration process more efficient than usual. With this in mind, we have investigated some properties that are of interest to several issues in high-energy astrophysics, such as the source of high-energy cosmic rays, the origin of the high-energy emission of blazars and microquasars, the synchrotron radiation of jets, and the gamma-ray bursts of cosmic fireballs. Three types of relativistic plasmas are considered: plasma dominated by the relativistic proton component (high-energy cosmic rays), plasma dominated by highly relativistic electrons (the protons being nonrelativistic), and plasma dominated by relativistic electron-positron pairs. Electron or pair-dominated plasmas are interesting on the one hand because of their fast dynamics, and on other hand because the energy of magnetic perturbations goes directly into the radiative particles. The energy transfer from the electromagnetic perturbations to the particles depends on the nonlinear dynamics. We derive the nonlinear systems that govern the dynamics of these relativistic plasmas close to equipartition. We discuss the possibility of self-modulation instability and soliton formation and demonstrate the existence of a transition at equipartition that has remarkable mathematical properties. We show that particle acceleration in a pair plasma is efficient only when the plasma pressure is below the equipartition value. We give intuitive arguments that this would also be true for the other plasmas, but we do not yet have firm proof. Thus, a pair plasma has a regulation mechanism toward equipartition, since radiation cooling is not efficiently balanced above equipartition. This is an interesting issue for nonthermal radio sources. We have also devised a new kind of collisionless quasi-parallel relativistic shock when a relativistic pair cloud pervades an ambient medium. The proton backstream in the relativistic front drives a monochromatic wave responsible for strong nonlinearities that heat the relativistic plasma. The instability is quenched when the relativistic plasma has been sufficiently heated.

A Comparison between Markovian and Non‐Markovian Closures in Simulations of Nonlinear Dynamos with Application to the Protogalactic Dynamo

Nonhelical magnetohydrodynamic (MHD) turbulence and the nonlinear dynamo are investigated numerically using two statistical closures: the direct interaction approximation, or DIA (Kraichnan), and the realizable Markovian closure, or RMC (Bowman et al.). The RMC is an approximate version of the DIA that can be used to simulate wider ranges of wavenumbers for longer stretches of time. In a controlled numerical experiment, it is found that the DIA and RMC lead to comparable results in simulations of the nonlinear dynamo. This helps justify the use of the RMC and other Markovian closures for the dynamo problem, thereby supporting the result of Pouquet, Frisch, & Leorat that an initially weak magnetic field grows up to rough equipartition with the kinetic energy on all scales. The result obtained by Pouquet, Frisch, & Leorat is also reproduced directly with a numerical DIA calculation. A separate DIA calculation produces k-3/2 spectra for steady state isotropic MHD turbulence, in accord with the physical arguments of Kraichnan. A rough preliminary calculation based upon the RMC suggests that the magnetic energy grows to approximately 6% of the kinetic energy during the collapse of the protogalaxy in the theory of Kulsrud et al. In a technical aside, a geometric algorithm is presented for calculating wavenumber-bin volume factors in three-dimensional closure calculations.

A Turbulent Model for the Interstellar Medium. II. Magnetic Fields and Rotation

view Abstract Citations (156) References (56) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS A Turbulent Model for the Interstellar Medium. II. Magnetic Fields and Rotation Passot, Thierry ; Vazquez-Semadeni, Enrique ; Pouquet, Annick Abstract We present results from two-dimensional numerical simulations of a supersonic turbulent flow with parameters characteristic of the interstellar medium at the 1 kpc scale in the plane of the Galactic disk, incorporating shear, thresholded and discrete star formation (SF), self-gravity, rotation, and magnetic fields. A test of the model in the linear regime supports the results of the linear theory presented by Elmegreen in 1991. At low shear, a weak azimuthal magnetic field stabilizes the medium by opposing collapse of radial perturbations, while a strong field is destabilizing by preventing Coriolis spin-up of azimuthal perturbations (magnetic braking). At high shear, azimuthal perturbations are sheared into the radial direction before they have time to collapse, and the magnetic field becomes stabilizing again. In the fully nonlinear turbulent regime, while some results of the linear theory persist, new effects also emerge. The production of turbulent density fluctuations appears to be affected by the magnetic field as in the linear regime: moderate field strengths cause a decrease in the time-integrated star formation rate, while larger values cause an increase. A result not predicted by the linear theory is that, for very large field strengths, a decrease in the integrated SFR obtains again, indicating a "rigidization" of the medium due to the magnetic field. Other exclusively nonlinear effects are the following: (1) Even though there is no dynamo in two dimensions, the simulations are able to maintain or increase their net magnetic energy in the presence of a seed uniform azimuthal component. (2) A well-defined power-law magnetic spectrum and an inverse magnetic cascade are observed in the simulations, indicating full MHD turbulence. Thus, magnetic field energy is generated in regions of SF and cascades up to the largest scales. (3) The field has a slight but noticeable tendency to be aligned with density features. This appears to be as much a consequence of the gas pushing on the magnetic field as due to constraints on gas motions because of the presence of the magnetic field. (4) A "pressure-cooker" effect is observed in which the magnetic field prevents H ii regions from expanding freely, as in the recent results of Slavin and Cox. (5) The orientation of the large-scale azimuthal field appears to follow that of the large-scale Galactic shear. (6) A tendency to exhibit less filamentary structures at stronger values of the uniform component of the magnetic field is present in several magnetic runs. Possible mechanisms that may lead to this result are discussed. (7) For fiducial values of the parameters, the flow in general appears to be in rough equipartition between magnetic and kinetic energy. There is no clear domination of either the magnetic or the inertial forces. (8) A median value of the magnetic field strength within clouds is ∼12 μG, while for the intercloud medium a value of ∼3 μG is found. Maximum contrasts of up to a factor of ∼10 are observed. Publication: The Astrophysical Journal Pub Date: December 1995 DOI: 10.1086/176603 arXiv: arXiv:astro-ph/9601182 Bibcode: 1995ApJ...455..536P Keywords: ISM: CLOUDS; ISM: MAGNETIC FIELDS; INSTABILITIES; TURBULENCE; HYDRODYNAMICS; ISM: KINEMATICS AND DYNAMICS; Astrophysics E-Print: Plain TeX file, 25 pages. Gzipped, tarred set of Tex file plus 17 figures and 3 tables (Postscript) available at ftp://kepler.astroscu.unam.mx/incoming/enro/papers/mhdgturb.tar.gz full text sources arXiv | ADS | Related Materials (2) Part 1: 1995ApJ...441..702V Part 3: 1999ApJ...518..748G

Nonlinear shock acceleration. III - Finite wave velocity, wave pressure, and entropy generation via wave damping

The nonlinear theory of shock acceleration developed in earlier papers, which treated the waves as being completely frozen into the fluid, is generalized to include wave dynamics. In the limit where damping keeps the wave amplitude small, it is found that a finite phase velocity (V sub ph) of the scattering waves through the background fluid, tempers the acceleration generated by high Mach number shocks. Asymptotic spectra proportional to 1/E sq are possible only when the ratio of wave velocity to shock velocity is less than 0.13. For a given asymptotic spectrum, the efficiency of relativistic particle production is found to be practically independent of the value of V sub ph, so that earlier results concerning its value remain valid for finite V sub ph. In the limit where there is no wave damping, it is shown that for modest Alfven Mach numbers, approximately greater than 4 and less than 6, the magnetic field is amplified by the energetic particles to the point of being in rough equipartition with them, as models of synchrotron emission frequently take the field to be. In this case, the disordering and amplification of field energy may play a major role in the shock transition.