Photon Splitting in Magnetar Models of Soft Gamma Repeaters

The recent association of soft gamma repeaters (SGRs) with counterparts in other wavebands has sparked much interest in these sources. One of the recent models for these objects is that they originate in the environs of neutron stars with fields much stronger than the quantum critical field \teq{B_{cr}=4.413\times 10^{13}} Gauss. Near such neutron stars, dubbed magnetars, the exotic quantum process of magnetic photon splitting becomes prolific. Its principal effect is to degrade photon energies and thereby soften gamma-ray spectra from neutron stars; it has recently been suggested that splitting may be responsible for limiting the hardness of emission in SGRs, if these sources originate in neutron stars with supercritical surface fields. Seed photons in supercritical fields efficiently generate soft gamma-ray spectra, typical of repeaters. In this paper, the influence of the curved dipole field geometry of a neutron star magnetosphere on the photon splitting rate is investigated. The dependence of the attenuation length on the location and angular direction of the seed photons is explored.Comment: 5 pages including 3 encapsulated figures, as a compressed, uuencoded, Postscript file. To appear in Proc. of the 1995 La Jolla workshop ``High Velocity Neutron Stars and Gamma-Ray Bursts'' eds. Rothschild, R. et al., AIP, New Yor

Photon Splitting and Pair Conversion in Strong Magnetic Fields

The magnetospheres of neutron stars provide a valuable testing ground for as-yet unverified theoretical predictions of quantum electrodynamics (QED) in strong electromagnetic fields. Exhibiting magnetic field strengths well in excess of a TeraGauss, such compact astrophysical environments permit the action of exotic mechanisms that are forbidden by symmetries in field-free regions. Foremost among these processes are single-photon pair creation, where a photon converts to an electron-positron pair, and magnetic photon splitting, where a single photon divides into two of lesser energy via the coupling to the external field. The pair conversion process is exponentially small in weak fields, and provides the leading order contribution to vacuum polarization. In contrast, photon splitting possesses no energy threshold and can operate in kinematic regimes where the lower order pair conversion is energetically forbidden. This paper outlines some of the key physical aspects of these processes, and highlights their manifestation in neutron star magnetospheres. Anticipated observational signatures include profound absorption turnovers in pulsar spectra at gamma-ray wavelengths. The shapes of these turnovers provide diagnostics on the possible action of pair creation and the geometrical locale of the photon emission region. There is real potential for the first confirmation of strong field QED with the new GLAST mission, to be launched by NASA in 2008. Suppression of pair creation by photon splitting and its implications for pulsars is also discussed.Comment: 18 pages, 3 embedded figures, invited review, to appear in Proc. CASYS '07 Conference "Computing Anticipatory Systems," eds. D. Dubois, et al. (AIP Conf. Proc., New York, 2008

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

Photon splitting in soft gamma repeaters

The exotic quantum process of photon splitting has great potential to explain the softness of emission in soft gamma repeaters (SGRs) if they originate in neutron stars with surface fields above the quantum critical field B_{\rm cr}=4.413\times 10^{13}Gauss. Splitting becomes prolific at such field strengths: its principal effect is to degrade photon energies, initiating a cascade that softens gamma-ray spectra. Uniform field cascade calculations have demonstrated that emission could be softened to the observed SGR energies for fields exceeding about 10^{14}Gauss. Recently, we have determined splitting attenuation lengths and maximum energies for photon escape in neutron star environments including the effects of magnetospheric dipole field geometry. Such escape energies \erg_{esc} suitably approximate the peak energy of the emergent spectrum, and in this paper we present results for \erg_{esc} as a function of photon emission angles for polar cap and equatorial emission regions. The escape energy is extremely insensitive to viewing perspective for equatorial emission, arguing in favour of such a site for the origin of SGR activity

Hard X-ray Quiescent Emission in Magnetars via Resonant Compton Upscattering

Non-thermal quiescent X-ray emission extending between 10 keV and around 150 keV has been seen in about 10 magnetars by RXTE, INTEGRAL, Suzaku, NuSTAR and Fermi-GBM. For inner magnetospheric models of such hard X-ray signals, inverse Compton scattering is anticipated to be the most efficient process for generating the continuum radiation, because the scattering cross section is resonant at the cyclotron frequency. We present hard X-ray upscattering spectra for uncooled monoenergetic relativistic electrons injected in inner regions of pulsar magnetospheres. These model spectra are integrated over bundles of closed field lines and obtained for different observing perspectives. The spectral turnover energies are critically dependent on the observer viewing angles and electron Lorentz factor. We find that electrons with energies less than around 15 MeV will emit most of their radiation below 250 keV, consistent with the turnovers inferred in magnetar hard X-ray tails. Electrons of higher energy still emit most of the radiation below around 1 MeV, except for quasi-equatorial emission locales for select pulse phases. Our spectral computations use a new state-of-the-art, spin-dependent formalism for the QED Compton scattering cross section in strong magnetic fields.Comment: 5 pages, 2 figures, to appear in Proc. "Physics of Neutron Stars - 2017," Journal of Physics: Conference Series, eds. G. G. Pavlov, et al., held in Saint Petersburg, Russia, 10-14 July, 201

Photon Splitting Cascades in Gamma-Ray Pulsars and the Spectrum of PSR1509-58

Magnetic photon splitting, a QED process that becomes important only in magnetic fields approaching the quantum critical value, B_cr = 4.41 X 10^13 Gauss, is investigated as a mechanism for attenuation of gamma-rays emitted near the surface of strongly-magnetized pulsars. We model photon splitting attenuation and subsequent splitting cascades in gamma-ray pulsars, including the dipole field and curved spacetime geometry of the neutron star magnetosphere. We focus specifically on PSR1509-58, which has the highest surface magnetic field of all the gamma-ray pulsars (B_0 = 3 X 10^13 Gauss). We find that splitting will not be important for most gamma-ray pulsars, i.e. those with B_0 <~ 0.2 B_cr, but will be important for gamma-ray pulsars having B_0 >~ 0.3 B_cr, where the splitting attenuation lengths and escape energies become comparable to or less than those for pair production. We compute Monte Carlo spectral models for PSR1509-58. We find that photon splitting, or combined splitting and pair production, can explain the unusually low cutoff energy (between 2 and 30 MeV) of PSR1509-58, and that the model cascade spectra, which display strong polarization, are consistent with the observed spectral points and upper limits for polar cap emission at a range of magnetic colatitudes up to ~ 25 degrees.Comment: 39 pages, 14 embedded figures, AASTEX To appear in ApJ, January 20, 199

Prompt GeV-TeV Emission of Gamma-Ray Bursts Due to High-Energy Protons, Muons and Electron-Positron Pairs

In the framework of the internal shock scenario, we model the broadband prompt emission of gamma-ray bursts (GRBs) with emphasis on the GeV-TeV bands, utilizing Monte Carlo simulations that include various processes associated with electrons and protons accelerated to high energies. While inverse Compton emission from primary electrons is often dominant, different proton-induced mechanisms can also give rise to distinct high-energy components, such as synchrotron emission from protons, muons or secondary electrons/positrons injected via photomeson interactions. In some cases, they give rise to double spectral breaks that can serve as unique signatures of ultra-high-energy protons. We discuss the conditions favorable for such emission, and how they are related to the production of ultra-high-energy cosmic rays and neutrinos in internal shocks. Ongoing and upcoming observations by {\it GLAST}, atmospheric Cerenkov telescopes and other facilities will test these expectations and provide important information on the physical conditions in GRB outflows.Comment: 11 pages, 8 figures and 14 appendix figures, accepted for publication in ApJ vol. 671 with minor revision

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.

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