Implications of long tails in the distribution of mutant effects

Long-tailed distributions possess an in nite variance, yet a nite sample that is drawn from such a distribution has a nite variance. In this work we consider a model of a population subject to mutation, selection and drift. We investigate the implications of a long-tailed distribution of mutant allelic e¤ects on the distribution of genotypic e¤ects in a model with a continuum of allelic e¤ects. While the analysis is confined to asexual populations, it does also have implications for sexual populations. We obtain analytical results for a selectively neutral population as well as one subject to selection. We supplement these analytical results with numerical simulations, to take into account genetic drift. We nd that a long-tailed distribution of mutant e¤ects may a¤ect both the equilibrium and the evolutionary adaptive behaviour of a population

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

High energy cosmic-rays: puzzles, models, and giga-ton neutrino telescopes

The existence of cosmic rays of energies exceeding 10^20 eV is one of the mysteries of high energy astrophysics. The spectrum and the high energy to which it extends rule out almost all suggested source models. The challenges posed by observations to models for the origin of high energy cosmic rays are reviewed, and the implications of recent new experimental results are discussed. Large area high energy cosmic ray detectors and large volume high energy neutrino detectors currently under construction may resolve the high energy cosmic ray puzzle, and shed light on the identity and physics of the most powerful accelerators in the universe.Comment: 12 pages, 7 figures; Summary of review talk, PASCOS 03 (Mumbai, India

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

High Energy Neutrinos from Astrophysical Sources: An Upper Bound

We show that cosmic-ray observations set a model-independent upper bound to the flux of high-energy, > 10^14 eV, neutrinos produced by photo-meson (or p-p) interactions in sources of size not much larger than the proton photo-meson (or pp) mean-free-path. The bound applies, in particular, to neutrino production by either AGN jets or GRBs. This upper limit is two orders of magnitude below the flux predicted in some popular AGN jet models, but is consistent with our predictions from GRB models. We discuss the implications of these results for future km^2 high-energy neutrino detectors.Comment: Added discussion showing bound cannot be evaded by invoking magnetic fields. Accepted Phys Rev

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

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

Implications of the γ\gamma-ray Polarization of GRB 021206

We compare two possible scenarios for the producing of high level of polarization within the prompt emission of a GRB: synchrotron emission from a relativistic jet with a uniform (in space and time) magnetic field and synchrotron emission from a jet with a random magnetic field in the plane of the shock. Somewhat surprisingly we find that both scenarios can produce a comparable level of polarization ($\sim 45-50$% for the uniform field and $\sim 30-35$% for a random field). Uniform time independent field most naturally arises by expansion of the field from the compact object. It requires a $10^{12}$G field at the source and a transport of the field as $\propto R^{-1}$. It {\it does not} imply Poynting flux domination of the energy of the wind. There is a serious difficulty however, within this scenario, accounting for particle acceleration (which requires random magnetic fields) both for Poynting flux and non-Poynting flux domination. Significant polarization can also arise from a random field provided that the observer is located within $1/\Gamma$ orientation from a narrow ($\theta_j \sim 1/\Gamma$) jet. While most jets are wider, the jet of GRB 021206 from which strong polarization was recently observed, was most likely very narrow. GRB 021206 is among the strongest bursts ever. Adopting the energy-angle relation we find an estimated angle of $<1/40$rad or even smaller. Thus, for this particular burst the required geometry is not unusual. We conclude that the RHESSI observations suggest that the prompt emission results from synchrotron radiation. However, in view of the comparable levels of polarizations predicted by both the random field and the homogeneous field scenarios these observations are insufficient to rule out or confirm either one.Comment: 14 pages, 4 figure