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

Neutral beam model for the anomalous gamma-ray emission component in GRB 941017

Gonz\'alez et al. (2003) have reported the discovery of an anomalous radiation component from ~ 1 -- 200 MeV in GRB 941017. This component varies independently of and contains > 3 times the energy found in the prompt ~ 50 keV -- 1 MeV radiation component that is well described by the relativistic synchrotron-shock model. Acceleration of hadrons to very high energies can give rise to two additional emission components, one produced inside the GRB blast wave and one associated with an escaping beam of ultra-high energy (UHE; > 10^{14} eV) neutrons, gamma rays, and neutrinos. The first component extending to ~ 100 MeV is from a pair-photon cascade induced by photomeson processes with the internal synchrotron photons coincident with the prompt radiation. The outflowing UHE neutral beam can undergo further interactions with external photons from the backscattered photon field to produce a beam of hyper-relativistic electrons that lose most of their energy during a fraction of a gyroperiod in the assumed Gauss-strength magnetic fields of the circumburst medium. The synchrotron radiation of these electrons has a spectrum with vF_v index equal to +1 that can explain the anomalous component in GRB 941017. This interpretation of the spectrum of GRB 941017 requires a high baryon load of the accelerated particles in GRB blast waves. It implies that most of the radiation associated with the anomalous component is released at > 500 MeV, suitable for observations with GLAST, and with a comparable energy fluence in ~100 TeV neutrinos that could be detected with a km-scale neutrino telescope like IceCube.Comment: 4 pages, 1 figure, minor corrections, Astronomy and Astrophysics Letters, in pres

Efficiency and spectrum of internal gamma-ray burst shocks

We present an analysis of the Internal Shock Model of GRBs, where gamma-rays are produced by internal shocks within a relativistic wind. We show that observed GRB characteristics impose stringent constraints on wind and source parameters. We find that a significant fraction, of order 20 %, of the wind kinetic energy can be converted to radiation, provided the distribution of Lorentz factors within the wind has a large variance and provided the minimum Lorentz factor is higher than 10^(2.5)L_(52)^(2/9), where L=10^(52)L_(52)erg/s is the wind luminosity. For a high, >10 %, efficiency wind, spectral energy breaks in the 0.1 to 1 MeV range are obtained for sources with dynamical time R/c < 1 ms, suggesting a possible explanation for the observed clustering of spectral break energies in this range. The lower limit to wind Lorenz factor and the upper limit, around (R/10^7 cm)^(-5/6) MeV to observed break energies are set by Thomson optical depth due to electron positron pairs produced by synchrotron photons. Natural consequences of the model are absence of bursts with peak emission energy significantly exceeding 1 MeV, and existence of low luminosity bursts with low, 1 keV to 10 keV, break energies.Comment: 10 pages, 5 ps-figures. Expanded discussion of magnetic field and electron energy fraction. Accepted for publication in Astrophysical Journa

Neutrino flux predictions for known Galactic microquasars

It has been proposed recently that Galactic microquasars may be prodigious emitters of TeV neutrinos that can be detected by upcoming km^2 neutrino telescopes. In this paper we consider a sample of identified microquasars and microquasar candiates, for which available data enables rough determination of the jet parameters. By employing the parameters inferred from radio observations of various jet ejection events, we determine the neutrino fluxes that should have been produced during these events by photopion production in the jet. Despite the large uncertainties in our analysis, we demonstrate that in several of the sources considered, the neutrino flux at Earth, produced in events similar to those observed, would exceed the detection threshold of a km^2 neutrino detector. The class of microquasars may contain also sources with bulk Lorentz factors larger than those characteristic of the sample considered here, directed along our line of sight. Such sources, which may be very difficult to resolve at radio wavelengths and hence may be difficult to identify as microqusar candidates, may emit neutrinos with fluxes significantly larger than typically obtained in the present analysis. These sources may eventually be identified through their neutrino and gamma-ray emission.Comment: 17 pages. Submitted to Ap

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

On the Absence of Spurious Eigenstates in an Iterative Algorithm Proposed By Waxman

We discuss a remarkable property of an iterative algorithm for eigenvalue problems recently advanced by Waxman that constitutes a clear advantage over other iterative procedures. In quantum mechanics, as well as in other fields, it is often necessary to deal with operators exhibiting both a continuum and a discrete spectrum. For this kind of operators, the problem of identifying spurious eigenpairs which appear in iterative algorithms like the Lanczos algorithm does not occur in the algorithm proposed by Waxman

No Radio Afterglow from the Gamma-Ray Burst of February 28, 1997

We present radio observations of the gamma-ray burster GRB 970228 made with the Very Large Array (VLA) and the Owens Valley Radio Observatory (OVRO) spanning a range of postburst timescales from one to 300 days. A search for a time-variable radio source was conducted covering an area which included a fading X-ray source and an optical transient, both of which are thought to be the long wavelength counterparts to the gamma-ray burst. At the position of the optical transient sensitive limits between 10 uJy and 1 mJy can be placed on the absence of a radio counterpart to GRB 970228 between 1.4 and 240 GHz. We apply a simple formulation of a fireball model which has been used with some success to reproduce the behavior of the optical and X-ray light curves. Using this model we conclude that the radio non-detections are consistent with the peak flux density of the afterglow lying between 20-40 uJy and it requires that the optical flux peaked between 4 and 16 hours after the burst.Comment: ApJ Let (submitted

Extra galactic sources of high energy neutrinos

The main goal of the construction of large volume, high energy neutrino telescopes is the detection of extra-Galactic neutrino sources. The existence of such sources is implied by observations of ultra-high energy, >10^{19} eV, cosmic-rays (UHECRs), the origin of which is a mystery. The observed UHECR flux sets an upper bound to the extra-Galactic high energy neutrino intensity, which implies that the detector size required to detect the signal in the energy range of 1 TeV to 1 PeV is >=1 giga-ton, and much larger at higher energy. Optical Cerenkov neutrino detectors, currently being constructed under ice and water, are expected to achieve 1 giga-ton effective volume for 1 TeV to 1 PeV neutrinos. Coherent radio Cerenkov detectors (and possibly large air-shower detectors) will provide the >> 1 giga-ton effective volume required for detection at ~10^{19} eV. Detection of high energy neutrinos associated with electromagnetically identified sources will allow to identify the sources of UHECRs, will provide a unique probe of the sources, which may allow to resolve open questions related to the underlying physics of models describing these powerful accelerators, and will provide information on fundamental neutrino properties.Comment: 8 pages, 4 figures; Summary of talk presented at the Nobel Symposium 129: Neutrino Physics, Sweden 200