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 $10^{20}{\rm eV}$ 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 $\geq50{\rm yr}$. 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 $\gtrsim5{\rm Mpc}$ and field weaker than $10^{-15}{\rm G}$. 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 $\sim4\times10^{-11}{\rm G}$ 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 $100{\rm Mpc}$ is $\sim100{\rm yr}$, and the fluence of secondary photons above $10{\rm GeV}$ on hour--day time scales is $I(>E)\sim10^{-6}E_{\rm TeV}^{-1}{\rm cm}^{-2}$. This fluence is close to the detection threshold of current high-energy $\gamma$-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 $>10^{19}eV$ originate in the same cosmological objects producing gamma-ray bursts (GRB's). Inter-galactic magnetic fields $\gtrsim 10^{-12} G$ 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 $E_{crit} \simeq2\times10^{20}$~eV with very weak sensitivity to the inter-galactic magnetic field strength. Below $E_{crit}$, a very large number of sources is expected, consistent with observations. Above $E_{crit}$, 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