1,990 research outputs found
Improving the Convergence of an Iterative Algorithm Proposed By Waxman
In the iterative algorithm recently proposed by Waxman for solving eigenvalue
problems, we point out that the convergence rate may be improved. For many
non-singular symmetric potentials which vanish asymptotically, a simple
analytical relationship between the coupling constant of the potential and the
ground state eigenvalue is obtained which can be used to make the algorithm
more efficient
Towards a Model for the Progenitors of Gamma-Ray Bursts
We consider models for gamma-ray bursts in which a collimated jet expands
either into a homogeneous medium or into a stellar wind environment, and
calculate the expected afterglow temporal behavior. We show that (i) following
a break and a faster decay, afterglows should exhibit a flattening, which may
be detectable in both the radio and optical bands; (ii) Only observations at
times much shorter than a day can clearly distinguish between a fireball
interacting with a homogeneous medium and one interacting with a stellar wind.
Using our results we demonstrate that constraints can be placed on progenitor
models. In particular, existing data imply that while some long duration bursts
may be produced by collapses of massive stars, it is almost certain that not
all long duration bursts are produced by such progenitors.Comment: 13 pages; Submitted to Ap
Rex E. Lee Conference on the Office of the Solicitor General of the United States: Panel for Former Solicitors General
I agree entirely that the chain of command is clear and that the Framers managed to make it all the way through all the articles of the Constitution without even conceiving of a solicitor general, let alone bothering to mention an attorney general. It is important nonetheless to distinguish between those things the solicitor general does pursuant to the longstanding notice-and-comment regulation, and the other things a solicitor general may do pursuant to his (and, someday, her!) statutory obligation to be of general assistance to the attorney general
New direction for gamma-rays
The origin of energetic gamma-ray bursts is still unknown. But the detection
of polarization of gamma-rays provides fresh insight into the mechanism driving
these powerful explosions.Comment: Nature "News & Views", RE Coburn & Boggs (astro-ph/0305377
GeV Photons from Ultra High Energy Cosmic Rays accelerated in Gamma Ray Bursts
Gamma-ray bursts are produced by the dissipation of the kinetic energy of a
highly relativistic fireball, via the formation of a collisionless shock. When
this happens, Ultra High Energy Cosmic Rays up to 10^20 eV are produced. I show
in this paper that these particles produce, via synchrotron emission as they
cross the acceleration region, photons up to 300 GeV which carry away a small,
~0.01, but non-negligible fraction of the total burst energy. I show that, when
the shock occurs with the interstellar medium, the optical depth to
photon-photon scattering, which might cause energy degradation of the photons,
is small. The burst thusly produced would be detected at Earth simultaneoulsy
with the parent gamma-ray burst, although its duration may differ significantly
from that of the lower energy photons. The expected fluences, ~10^{-5}-10^{-6}
erg/cm^2 are well within the range of planned detectors. A new explanation for
the exceptional burst GRB 940217 is discussed.Comment: Accepted for publication in The Physical Review Letters. 4 pages,
RevTeX needed, no figure
Delayed GeV--TeV Photons from Gamma-Ray Bursts Producing High-Energy Cosmic Rays
A scenario in which cosmic rays (CRs) above are produced by
cosmological gamma-ray bursts (GRBs) is consistent with observations provided
that deflections by the inter-galactic magnetic field (IGMF) delay and spread
the arrival time of the CRs over . The energy lost by the CRs
as they propagate and interact with the microwave background is transformed by
cascading into secondary GeV-TeV photons. We show that a significant fraction
of these photons can arrive with delays much smaller than the CR delay if much
of inter-galactic space is occupied by large-scale magnetic ``voids'', regions
of size and field weaker than . Such voids
might be expected, for example, in models where a weak primordial field is
amplified in shocked, turbulent regions of the intergalactic medium during the
formation of large-scale structure. For a field strength
in the high field regions, the value required to
account for observed galactic fields if the IGMF were frozen in the
protogalactic plasma, the delay of CRs produced by a burst at a distance of
is , and the fluence of secondary photons above
on hour--day time scales is . This fluence is close to the detection threshold of current
high-energy -ray experiments. Detection of the delayed flux would
support the GRB-CR association and would also provide information on the IGMF
structure.Comment: ApJ Letters in press; 10 pages (LaTeX file, 2 PostScript figures,
aaspp4.sty style file, tar'ed, gzip'ed and uuencoded
The Gradient Expansion for the Free-Energy of a Clean Superconductor
We describe a novel method for obtaining the gradient expansion for the free
energy of a clean BCS superconductor. We present explicit results up to fourth
order in the gradients of the order parameter.Comment: 33 pages, Late
Signatures of the Origin of High-Energy Cosmic Rays in Cosmological Gamma-Ray Bursts
We derive observational consequences of the hypothesis that cosmic rays
(CR's) of energy originate in the same cosmological objects
producing gamma-ray bursts (GRB's). Inter-galactic magnetic fields are required in this model to allow CR's to be observed
continuously in time by producing energy dependent delays in the CR arrival
times. This results in individual CR sources having very narrow observed
spectra, since at any given time only those CR's having a fixed time delay are
observed. Thus, the brightest CR sources should be different at different
energies. The average number of sources contributing to the total CR flux
decreases with energy much more rapidly than in a model of steady CR sources,
dropping to one at ~eV with very weak
sensitivity to the inter-galactic magnetic field strength. Below , a
very large number of sources is expected, consistent with observations. Above
, a source may be observed with a flux considerably higher than the
time-averaged CR flux from all sources, if a nearby GRB occurred recently. If
such a source is present, its narrow spectrum may produce a ``gap'' in the
total spectrum. These signatures should be detectable by the planned ``Auger''
CR experiment.Comment: Submitted to the ApJ Letters; 10 pages (LaTeX file, 3 PostScript
figures, aaspp4.sty style file, tar'ed, gzip'ed and uuencoded
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