606 research outputs found
Resonant Inverse Compton Scattering Spectra from Highly-magnetized Neutron Stars
Hard, non-thermal, persistent pulsed X-ray emission extending between 10 keV
and keV has been observed in nearly ten magnetars. For
inner-magnetospheric models of such emission, resonant inverse Compton
scattering of soft thermal photons by ultra-relativistic charges is the most
efficient production mechanism. We present angle-dependent upscattering spectra
and pulsed intensity maps for uncooled, relativistic electrons injected in
inner regions of magnetar magnetospheres, calculated using collisional
integrals over field loops. Our computations employ a new formulation of the
QED Compton scattering cross section in strong magnetic fields that is
physically correct for treating important spin-dependent effects in the
cyclotron resonance, thereby producing correct photon spectra. The spectral
cut-off energies are sensitive to the choices of observer viewing geometry,
electron Lorentz factor, and scattering kinematics. We find that electrons with
energies MeV will emit most of their radiation below 250 keV,
consistent with inferred turnovers for magnetar hard X-ray tails. More
energetic electrons still emit mostly below 1 MeV, except for viewing
perspectives sampling field line tangents. Pulse profiles may be singly- or
doubly-peaked dependent upon viewing geometry, emission locale, and observed
energy band. Magnetic pair production and photon splitting will attenuate
spectra to hard X-ray energies, suppressing signals in the Fermi-LAT band. The
resonant Compton spectra are strongly polarized, suggesting that hard X-ray
polarimetry instruments such as X-Calibur, or a future Compton telescope, can
prove central to constraining model geometry and physics.Comment: 43 pages, 12 figures; accepted for publication in ApJ; v3 fixes typos
and updates some reference
Resonant Compton Upscattering in High Field Neutron Stars
The extremely efficient process of resonant Compton upscattering by
relativistic electrons in high magnetic fields is believed to be a leading
emission mechanism of high field pulsars and magnetars in the production of
intense X-ray radiation. New analytic developments for the Compton scattering
cross section using Sokolov & Ternov (S&T) states with spin-dependent resonant
widths are presented. These new results display significant numerical
departures from both the traditional cross section using spin-averaged widths,
and also from the spin-dependent cross section that employs the Johnson &
Lippmann (J&L) basis states, thereby motivating the astrophysical deployment of
this updated resonant Compton formulation. Useful approximate analytic forms
for the cross section in the cyclotron resonance are developed for S&T basis
states. These calculations are applied to an inner magnetospheric model of the
hard X-ray spectral tails in magnetars, recently detected by RXTE and INTEGRAL.
Relativistic electrons cool rapidly near the stellar surface in the presence of
intense baths of thermal X-ray photons. We present resonant Compton cooling
rates for electrons, and the resulting photon spectra at various magnetospheric
locales, for magnetic fields above the quantum critical value. These
demonstrate how this scattering mechanism has the potential to produce the
characteristically flat spectral tails observed in magnetars.Comment: 2 pages, no figures, The proceedings from the Pulsar Conference:
Electromagnetic Radiation from Pulsars and Magnetars will be published in the
Astronomical Society of the Pacific Conference Serie
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
Formal Verification of a Geometry Algorithm: A Quest for Abstract Views and Symmetry in Coq Proofs
This extended abstract is about an effort to build a formal description of a
triangulation algorithm starting with a naive description of the algorithm
where triangles, edges, and triangulations are simply given as sets and the
most complex notions are those of boundary and separating edges. When
performing proofs about this algorithm, questions of symmetry appear and this
exposition attempts to give an account of how these symmetries can be handled.
All this work relies on formal developments made with Coq and the mathematical
components library
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 ( 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 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
Gradual Certified Programming in Coq
Expressive static typing disciplines are a powerful way to achieve
high-quality software. However, the adoption cost of such techniques should not
be under-estimated. Just like gradual typing allows for a smooth transition
from dynamically-typed to statically-typed programs, it seems desirable to
support a gradual path to certified programming. We explore gradual certified
programming in Coq, providing the possibility to postpone the proofs of
selected properties, and to check "at runtime" whether the properties actually
hold. Casts can be integrated with the implicit coercion mechanism of Coq to
support implicit cast insertion a la gradual typing. Additionally, when
extracting Coq functions to mainstream languages, our encoding of casts
supports lifting assumed properties into runtime checks. Much to our surprise,
it is not necessary to extend Coq in any way to support gradual certified
programming. A simple mix of type classes and axioms makes it possible to bring
gradual certified programming to Coq in a straightforward manner.Comment: DLS'15 final version, Proceedings of the ACM Dynamic Languages
Symposium (DLS 2015
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