Acceleration Rates and Injection Efficiencies in Oblique Shocks

The rate at which particles are accelerated by the first-order Fermi mechanism in shocks depends on the angle, \teq{\Tbone}, that the upstream magnetic field makes with the shock normal. The greater the obliquity the greater the rate, and in quasi-perpendicular shocks rates can be hundreds of times higher than those seen in parallel shocks. In many circumstances pertaining to evolving shocks (\eg, supernova blast waves and interplanetary traveling shocks), high acceleration rates imply high maximum particle energies and obliquity effects may have important astrophysical consequences. However, as is demonstrated here, the efficiency for injecting thermal particles into the acceleration mechanism also depends strongly on obliquity and, in general, varies inversely with \teq{\Tbone}. The degree of turbulence and the resulting cross-field diffusion strongly influences both injection efficiency and acceleration rates. The test particle \mc simulation of shock acceleration used here assumes large-angle scattering, computes particle orbits exactly in shocked, laminar, non-relativistic flows, and calculates the injection efficiency as a function of obliquity, Mach number, and degree of turbulence. We find that turbulence must be quite strong for high Mach number, highly oblique shocks to inject significant numbers of thermal particles and that only modest gains in acceleration rates can be expected for strong oblique shocks over parallel ones if the only source of seed particles is the thermal background.Comment: 24 pages including 6 encapsulated figures, as a compressed, uuencoded, Postscript file. Accepted for publication in the Astrophysical Journa

Compton Scattering in Ultra-Strong Magnetic Fields: Numerical and Analytical Behavior in the Relativistic Regime

This paper explores the effects of strong magnetic fields on the Compton scattering of relativistic electrons. Recent studies of upscattering and energy loss by relativistic electrons that have used the non-relativistic, magnetic Thomson cross section for resonant scattering or the Klein-Nishina cross section for non-resonant scattering do not account for the relativistic quantum effects of strong fields ($> 4 \times 10^{12}$ G). We have derived a simplified expression for the exact QED scattering cross section for the broadly-applicable case where relativistic electrons move along the magnetic field. To facilitate applications to astrophysical models, we have also developed compact approximate expressions for both the differential and total polarization-dependent cross sections, with the latter representing well the exact total QED cross section even at the high fields believed to be present in environments near the stellar surfaces of Soft Gamma-Ray Repeaters and Anomalous X-Ray Pulsars. We find that strong magnetic fields significantly lower the Compton scattering cross section below and at the resonance, when the incident photon energy exceeds $m_ec^2$ in the electron rest frame. The cross section is strongly dependent on the polarization of the final scattered photon. Below the cyclotron fundamental, mostly photons of perpendicular polarization are produced in scatterings, a situation that also arises above this resonance for sub-critical fields. However, an interesting discovery is that for super-critical fields, a preponderance of photons of parallel polarization results from scatterings above the cyclotron fundamental. This characteristic is both a relativistic and magnetic effect not present in the Thomson or Klein-Nishina limits.Comment: AASTeX format, 31 pages included 7 embedded figures, accepted for publication in The Astrophysical Journa

Magnetic Photon Splitting: the S-Matrix Formulation in the Landau Representation

Calculations of reaction rates for the third-order QED process of photon splitting in strong magnetic fields traditionally have employed either the effective Lagrangian method or variants of Schwinger's proper-time technique. Recently, Mentzel, Berg and Wunner (1994) presented an alternative derivation via an S-matrix formulation in the Landau representation. Advantages of such a formulation include the ability to compute rates near pair resonances above pair threshold. This paper presents new developments of the Landau representation formalism as applied to photon splitting, providing significant advances beyond the work of Mentzel et al. by summing over the spin quantum numbers of the electron propagators, and analytically integrating over the component of momentum of the intermediate states that is parallel to field. The ensuing tractable expressions for the scattering amplitudes are satisfyingly compact, and of an appearance familiar to S-matrix theory applications. Such developments can facilitate numerical computations of splitting considerably both below and above pair threshold. Specializations to two regimes of interest are obtained, namely the limit of highly supercritical fields and the domain where photon energies are far inferior to that for the threshold of single-photon pair creation. In particular, for the first time the low-frequency amplitudes are simply expressed in terms of the Gamma function, its integral and its derivatives. In addition, the equivalence of the asymptotic forms in these two domains to extant results from effective Lagrangian/proper-time formulations is demonstrated.Comment: 19 pages, 3 figures, REVTeX; accepted for publication in Phys. Rev.

Magnetic Photon Splitting: Computations of Proper-time Rates and Spectra

The splitting of photons in the presence of an intense magnetic field has recently found astrophysical applications in polar cap models of gamma-ray pulsars and in magnetar scenarios for soft gamma repeaters. Numerical computation of the polarization-dependent rates of this third order QED process for arbitrary field strengths and energies below pair creation threshold is difficult: thus early analyses focused on analytic developments and simpler asymptotic forms. The recent astrophysical interest spurred the use of the S-matrix approach by Mentzel, Berg and Wunner to determine splitting rates. In this paper, we present numerical computations of a full proper-time expression for the rate of splitting that was obtained by Stoneham, and is exact up to the pair creation threshold. While the numerical results derived here are in accord with the earlier asymptotic forms due to Adler, our computed rates still differ by as much as factors of 3 from the S-matrix re-evaluation of Wilke and Wunner, reflecting the extreme difficulty of generating accurate S-matrix numerics for fields below about \teq{4.4\times 10^{13}}Gauss. We find that our proper-time rates appear very accurate, and exceed Adler's asymptotic specializations significantly only for photon energies just below pair threshold and for supercritical fields, but always by less than a factor of around 2.6. We also provide a useful analytic series expansion for the scattering amplitude valid at low energies.Comment: 13 pages, AASTeX format, including 3 eps figures, ApJ in pres

Magnetars and pulsars: a missing link

There is growing evidence that soft gamma-ray repeaters (SGRs) and anomalous X-ray pulsars (AXPs) are isolated neutron stars with superstrong magnetic fields, i.e., magnetars, marking them a distinguished species from the conventional species of spindown-powered isolated neutron stars, i.e., radio pulsars. The current arguments in favor of the magnetar interpretation of SGR/AXP phenomenology will be outlined, and the two energy sources in magnetars, i.e. a magnetic dissipation energy and a spindown energy, will be reviewed. I will then discuss a missing link between magnetars and pulsars, i.e., lack of the observational evidence of the spindown-powered behaviors in known magnetars. Some recent theoretical efforts in studying such behaviors will be reviewed along with some predictions testable in the near future.Comment: Invited talk at the Sixth Pacific Rim Conference on Stellar Astrophysics, a tribute to Helmut A. Abt, July 11-17, 2002, Xi'an. To appear in the proceedings (eds. K. S. Cheng, K. C. Leung & T. P. Li

Charged-Particle Motion in Electromagnetic Fields Having at Least One Ignorable Spatial Coordinate

We give a rigorous derivation of a theorem showing that charged particles in an arbitrary electromagnetic field with at least one ignorable spatial coordinate remain forever tied to a given magnetic-field line. Such a situation contrasts the significant motions normal to the magnetic field that are expected in most real three-dimensional systems. It is pointed out that, while the significance of the theorem has not been widely appreciated, it has important consequences for a number of problems and is of particular relevance for the acceleration of cosmic rays by shocks.Comment: 7 pages, emulateapj format, including 1 eps figure, to appear in The Astrophysical Journal, Dec. 10 1998 issu

Acceleration of Solar Wind Ions by Nearby Interplanetary Shocks: Comparison of Monte Carlo Simulations with Ulysses Observations

The most stringent test of theoretical models of the first-order Fermi mechanism at collisionless astrophysical shocks is a comparison of the theoretical predictions with observational data on particle populations. Such comparisons have yielded good agreement between observations at the quasi-parallel portion of the Earth's bow shock and three theoretical approaches, including Monte Carlo kinetic simulations. This paper extends such model testing to the realm of oblique interplanetary shocks: here observations of proton and alpha particle distributions made by the SWICS ion mass spectrometer on Ulysses at nearby interplanetary shocks are compared with test particle Monte Carlo simulation predictions of accelerated populations. The plasma parameters used in the simulation are obtained from measurements of solar wind particles and the magnetic field upstream of individual shocks. Good agreement between downstream spectral measurements and the simulation predictions are obtained for two shocks by allowing the the ratio of the mean-free scattering length to the ionic gyroradius, to vary in an optimization of the fit to the data. Generally small values of this ratio are obtained, corresponding to the case of strong scattering. The acceleration process appears to be roughly independent of the mass or charge of the species.Comment: 26 pages, 6 figures, AASTeX format, to appear in the Astrophysical Journal, February 20, 199

Nuclear de-excitation line spectrum of Cassiopeia A

The supernova remnant Cassiopeia A is a prime candidate for accelerating cosmic ray protons and ions. Gamma rays have been observed at GeV and TeV energies, which indicates hadronic interactions, but they could also be caused by inverse-Compton scattering of low-energy photons by accelerated electrons. We seek to predict the flux of nuclear de-excitation lines from Cas A through lower-energy cosmic rays and to compare it with COMPTEL measurements. Assuming a hadronic origin of the high-energy emission, we extrapolate the cosmic ray spectrum down to energies of 10 MeV, taking into account an equilibrium power-law momentum spectrum with a constant slope. We then calculate the nuclear line spectrum of Cassiopeia A, considering the most prominent chemical elements in the MeV band and their abundances as determined by X-ray spectroscopy. We show that the predicted line spectrum is close to the level of the COMPTEL sensitivity and agrees with conservative upper limits.Comment: 4 pages, 1 figure, accepted for publication by A&

Impacts of a power-law non-thermal electron tail on the ionization and recombination rates

We have investigated the effects of a non-thermal electron population on the ionization and recombination rates. The considered electron distribution is defined as a Maxwellian function below a break energy E_b and as a power-law function of index alpha above this energy. We have calculated the collisional (direct and excitation autoionization) ionization coefficient rates as well as the (radiative and dielectronic) recombination rates. Practical methods are given to calculate these rates in order to be easily included in a computer code. The ionization rates are very sensitive to the non-thermal electron population and can be increased by several orders of magnitude depending on the temperature and parameters of the power-law function (E_b and alpha). The non-thermal electrons have a much weaker effect on the (radiative and dielectronic) recombination rates. We have determined the mean electric charge of elements C, N, O, Ne, Mg, Si, S, Ar, Ca, Fe and Ni for different values of the break energy and power-law index. The ionization balance is affected significantly, whereas the effect is smaller in ionizing plasmas.Comment: 16 pages, 19 figures, accepted for publication in A&

Discovery of 5.16s pulsations from the isolated neutron star RBS 1223

The isolated neutron star candidate RBS 1223 was observed with the Advanced CCD Imaging Spectrometer aboard the Chandra X-ray observatory on 2000 June 24. A timing analysis of the data yielded a periodic modulation with a period P=5.1571696^(+1.57*10^(-4) -1.36*10^(-4)s. Using ROSAT HRI archived observations we detected a period P=5.1561274 \pm 4.4*10^(-4)s and determined period derivative dP/dt=(0.7 - 2.0)*10^(-11) s*s^(-1). The detection of this period and dP/dt indicates that RBS 12223 has a ``characteristic'' age of 6000-12000 years and huge magnetic field at the surface (B(dipole)~(1.7- 3.2)*10^(+14) G) typical for anomalous X-ray pulsars (AXPs).Comment: 7 pages, 9 figures, Accepted for publication in Astronomy & Astrophysic