David Eichler

Particle acceleration at astrophysical shocks: A theory of cosmic ray origin

Abstract The theory of first order Fermi acceleration at collisionless astrophysical shock fronts is reviewed. Observations suggest that shock waves in different astrophysical environments accelerate cosmic rays efficiently. In the first order process, high energy particles diffuse through Alfven waves that scatter them and couple them to the background plasma. These particles gain energy, on the average, every time they cross the schock front and bounce off approaching scattering centers. Calculations demonstrate that the distribution function transmitted by a plane shock is roughly a power law in momentum with slope similar to that inferred in galactic cosmic ray sources. The generation of the scattering Alfven waves by the streaming cosmic rays is described and it is argued that the wave amplitude is probably non-linear within sufficiently strong astrophysical shocks. Hydromagnetic scattering can operate on the thermal particles as well, possibly establishing the shock structure. This suggests a model of strong collisionless shocks in which high energy particles are inevitably produced very efficiently. Observable consequences of this model, together with its limitations and some alternatives, are described. Cosmic ray origin and astrophysical shocks can no longer be considered separately.

Cosmic ray drift, shock wave acceleration and the anomalous component of cosmic rays

A model of the anomalous component of the quiet-time cosmic ray flux is presented in which ex-interstellar neutral particles are accelerated continuously in the polar regions of the solar-wind termination shock, and then drift into the equatorial regions of the inner heliosphere. The observed solar-cycle variations, radial gradient, and apparent latitude gradient of the anomalous component are a natural consequence of this model.

A giant γ-ray flare from the magnetar SGR 1806-20

Two classes of rotating neutron stars—soft γ-ray repeaters (SGRs) and anomalous X-ray pulsars—are magnetars, whose X-ray emission is powered by a very strong magnetic field (B ≈ 1015 G). SGRs occasionally become ‘active’, producing many short X-ray bursts. Extremely rarely, an SGR emits a giant flare with a total energy about a thousand times higher than in a typical burst. Here we report that SGR 1806–20 emitted a giant flare on 27 December 2004. The total (isotropic) flare energy is 2 × 1046 erg, which is about a hundred times higher than the other two previously observed giant flares. The energy release probably occurred during a catastrophic reconfiguration of the neutron stars magnetic field. If the event had occurred at a larger distance, but within 40 megaparsecs, it would have resembled a short, hard γ-ray burst, suggesting that flares from extragalactic SGRs may form a subclass of such bursts.1 Los Alamos National Laboratory, Los Alamos, NM, 87545, USA 2 NASA/Goddard Space Flight Center, Greenbelt, MD, 20771, USA 3 NASA/Marshall Space Flight Center, NSSTC, XD-12, 320 Sparkman Dr., Huntsville, AL 35805, USA 4 Department of Physics, Ben Gurion University, POB 653, Beer Sheva 84105, Israel 5 Astronomical Institute “Anton Pannekoek”, University of Amsterdam, Kruislaan 403, 1098 SJ, Amster-

Monte Carlo shock-like solutions to the Boltzmann equation with collective scattering

We present the results of Monte Carlo simulations of steady state shocks generated by a collision operator that isotropizes the particles by means of elastic scattering in some locally defined frame of reference. The simulations include both the back-reaction of accelerated particles on the inflowing plasma and the free escape of high-energy particles from finite shocks. Energetic particles are found to be naturally extracted out of the background plasma by the shock process with an efficiency in good quantitative agreement with (a) an earlier analytic approximation (Eichler 1983, 1984) and (b) observations (Gosling et al. 1981) of the entire particle spectrum at a quasi-parallel interplanetary shock. We use the analytic approximation, which allows a self-consistent determination of the effective adiabatic index of the shocked gas, to calculate the overall acceleration efficiency and particle spectrum for cases where ultrarelativistic energies are obtained. We find that shocks of the strength necessary to produce galactic cosmic rays put approximately 15% of the shock energy into relativistic particles.

An Expanding Radio Nebula Produced by a Giant Flare from the Magnetar SGR 1806-20

Soft γ-ray repeaters (SGRs) are ‘magnetars’, a small class of slowly spinning neutron stars with extreme surface magnetic fields, B ≈ 1015 gauss (refs 1 , 2 –3). On 27 December 2004, a giant flare was detected from the magnetar SGR 1806 - 20 (ref. 2), only the third such event recorded. This burst of energy was detected by a variety of instruments and even caused an ionospheric disturbance in the Earths upper atmosphere that was recorded around the globe. Here we report the detection of a fading radio afterglow produced by this outburst, with a luminosity 500 times larger than the only other detection of a similar source. From day 6 to day 19 after the flare from SGR 1806 - 20, a resolved, linearly polarized, radio nebula was seen, expanding at approximately a quarter of the speed of light. To create this nebula, at least 4 × 1043 ergs of energy must have been emitted by the giant flare in the form of magnetic fields and relativistic particles.

Magnetic Confinement of Jets

The familiar picture of magnetic collimation of jets is critiqued. Solutions are derived that explicity demonstrate the asymptotically parabolic nature of almost all stream lines, more or less consistent with previous discussions. It is then shown that collimation is too slow to be physically relevant when the flow in its uncollimated state is only weakly magnetized. In the alternative and more popular case, where the magnetic field is dynamically significant at all points on the flow, the divergence of field lines to large cylindrical radius implies kink instability

Baryon purity in cosmological gamma-ray bursts as a manifestation of event horizons

The mass-loss rate driven by an electron-positron fireball created in the late stages of an accretion-induced collapse or neutron star merging is calculated. It is shown that the solution connecting the wind regime to the hydrostatic regime has a well-defined mass flux in steady state. Approximately 10 31 g s −1 in baryons is found to be injected if the energy deposition rate below the surface of a neutron star is of order 10 32 ergs s −1 cm −3 , requiring a powerful suppression mechanism of baryon contamination for cosmological GRB models

Energetic particle spectra in finite shocks - The earth's bow shock

Ipavich et al. have reported fast particle spectra near the Earths bow shock that are exponentials in the quantity energy per charge, E/Q. It is shown that this is expected if the fast particles escape the shock via resonant diffusion to unconnected field lines. The calculated e-folding value of E/Q is, to first approximation, independent of the level of turbulence near the shock and is in good agreement with observation. Predictions of this picture and further evidence supporting it are presented. If the model is correct, then the parallel and perpendicular diffusion coefficients can be determined observationally through combined measurements of gradients and spectra, and the Earths bow shock can serve as an accurate laboratory for testing theories of diffusion.

A Compact Fireball Model of Gamma-Ray Bursts

It is proposed that the gamma-ray burst (GRB) photons near the peak of the spectrum at several hundred keV are produced on very compact scales, where photon production is limited by blackbody effects and/or the requirement of energetic quanta (E > 2mec2) for efficient further production. The fast variation of order milliseconds in the time profile is then a natural expectation, given the other observed GRB parameters. Analytic calculations are presented to show that the escape of nonthermal, energetic gamma rays can emerge within 1 s of the thermal photons from a gammasphere of below 1012 cm. The minimum asymptotic bulk Lorentz factor in this model is found to be of order several hundred if the photosphere is of order 3 × 1011 cm and greater for larger or smaller photospheric radii. It is suggested that prompt ultra-high-energy gamma rays might provide a new constraint on the asymptotic Lorentz factor of the outflow.

On the theory of cosmic-ray-mediated shocks with variable compression ratio

Cosmic-ray-mediated shocks may accelerate enough cosmic rays to high enough energies that they escape the shock, carrying an appreciable amount of energy before being convected to downstream infinity. Under such conditions, it is noted, the overall compression ratio cannot be determined from the conservation equations as in conventional hydrodynamic treatments, and the standard equations for shock acceleration admit arbitrarily high compression ratios. A procedure is outlined for obtaining the structure of high Mach number, cosmic-ray-mediated shocks, including their overall compression ratio, around a low Mach number viscous subshock. Analytic solutions are obtained by quadrature for an energy-dependent diffusion coefficient in the limit of extreme sensitivity to energy, which, unlike previous solutions, include the finite thermal pressure of the preshock gas.