A bivariate gamma probability distribution with application to gust modeling

A five-parameter gamma distribution (BGD) having two shape parameters, two location parameters, and a correlation parameter is investigated. This general BGD is expressed as a double series and as a single series of the modified Bessel function. It reduces to the known special case for equal shape parameters. Practical functions for computer evaluations for the general BGD and for special cases are presented. Applications to wind gust modeling for the ascent flight of the space shuttle are illustrated

A new concept for the combination of optical interferometers and high-resolution spectrographs

The combination of high spatial and spectral resolution in optical astronomy enables new observational approaches to many open problems in stellar and circumstellar astrophysics. However, constructing a high-resolution spectrograph for an interferometer is a costly and time-intensive undertaking. Our aim is to show that, by coupling existing high-resolution spectrographs to existing interferometers, one could observe in the domain of high spectral and spatial resolution, and avoid the construction of a new complex and expensive instrument. We investigate in this article the different challenges which arise from combining an interferometer with a high-resolution spectrograph. The requirements for the different sub-systems are determined, with special attention given to the problems of fringe tracking and dispersion. A concept study for the combination of the VLTI (Very Large Telescope Interferometer) with UVES (UV-Visual Echelle Spectrograph) is carried out, and several other specific instrument pairings are discussed. We show that the proposed combination of an interferometer with a high-resolution spectrograph is indeed feasible with current technology, for a fraction of the cost of building a whole new spectrograph. The impact on the existing instruments and their ongoing programs would be minimal.Comment: 27 pages, 9 figures, Experimental Astronomy; v2: accepted versio

Neutrino Interactions in Hot and Dense Matter

We study the charged and neutral current weak interaction rates relevant for the determination of neutrino opacities in dense matter found in supernovae and neutron stars. We establish an efficient formalism for calculating differential cross sections and mean free paths for interacting, asymmetric nuclear matter at arbitrary degeneracy. The formalism is valid for both charged and neutral current reactions. Strong interaction corrections are incorporated through the in-medium single particle energies at the relevant density and temperature. The effects of strong interactions on the weak interaction rates are investigated using both potential and effective field-theoretical models of matter. We investigate the relative importance of charged and neutral currents for different astrophysical situations, and also examine the influence of strangeness-bearing hyperons. Our findings show that the mean free paths are significantly altered by the effects of strong interactions and the multi-component nature of dense matter. The opacities are then discussed in the context of the evolution of the core of a protoneutron star.Comment: 41 pages, 25 figure

Relativistic theory of inverse beta-decay of polarized neutron in strong magnetic field

The relativistic theory of the inverse beta-decay of polarized neutron, $\nu _{e} + n \to p + e ^{-}$, in strong magnetic field is developed. For the proton wave function we use the exact solution of the Dirac equation in the magnetic filed that enables us to account exactly for effects of the proton momentum quantization in the magnetic field and also for the proton recoil motion. The effect of nucleons anomalous magnetic moments in strong magnetic fields is also discussed. We examine the cross section for different energies and directions of propagation of the initial neutrino accounting for neutrons polarization. It is shown that in the super-strong magnetic field the totally polarized neutron matter is transparent for neutrinos propagating antiparallel to the direction of polarization. The developed relativistic approach can be used for calculations of cross sections of the other URCA processes in strong magnetic fields.Comment: 41 pages in LaTex including 11 figures in PostScript, discussion on nucleons AMM interaction with magnetic field is adde

The Effects of Correlations on Neutrino Opacities in Nuclear Matter

Including nucleon-nucleon correlations due to both Fermi statistics and nuclear forces, we have developed a general formalism for calculating the neutral-current neutrino-nucleon opacities in nuclear matter. We derive corrections to the dynamic structure factors due to both density and spin correlations and find that neutrino-nucleon cross sections are suppressed by large factors around and above nuclear density. In addition, we find that the spectrum of energy transfers in neutrino scattering is considerably broadened by the interactions in the medium. An identifiable component of this broadening comes from the absorption and emission of quanta of collective modes akin to the Gamow-Teller and Giant Dipole resonances in nuclei (zero-sound; spin waves), with \v{C}erenkov kinematics. Under the assumption that both the charged-current and the neutral-current cross sections are decreased by many-body effects, we calculate a set of ad hoc protoneutron star cooling models to gauge the potential importance of the new opacities to the supernova itself. We find that after many hundreds of milliseconds to seconds the driving neutrino luminosities might be increased by from 10% to 100%. However, the actual consequences, if any, of these new neutrino opacities remain to be determined.Comment: 39 pages, APS REVTeX format, 11 PostScript figures, submitted to Physical Rev.

Neutrino-Nucleon Interactions in Magnetized Neutron-Star Matter: The Effects of Parity Violation

We study neutrino-nucleon scattering and absorption in a dense, magnetized nuclear medium. These are the most important sources of neutrino opacity governing the cooling of a proto-neutron star in the first tens of seconds after its formation. Because the weak interaction is parity violating, the absorption and scattering cross-sections depend asymmetrically on the directions of the neutrino momenta with respect to the magnetic field. We develop the moment formalism of neutrino transport in the presence of such asymmetric opacities and derive explicit expressions for the neutrino flux and other angular moments of the Boltzmann transport equation. For a given neutrino species, there is a drift flux of neutrinos along the magnetic field in addition to the usual diffusive flux. This drift flux depends on the deviation of the neutrino distribution function from thermal equilibrium. Hence, despite the fact that the neutrino cross-sections are asymmetric throughout the star, asymmetric neutrino flux can be generated only in the outer region of the proto-neutron star where the neutrino distribution deviates significantly from thermal equilibrium. In addition to the asymmetric absorption opacity arising from nucleon polarization, we find the contribution of the electron (or positron) ground state Landau level. For neutrinos of energy less than a few times the temperature, this is the dominant source of asymmetric opacity. Lastly, we discuss the implication of our result to the origin of pulsar kicks: in order to generate kick velocity of a few hundred km/s from asymmetric neutrino emission using the parity violation effect, the proto-neutron star must have a dipole magnetic field of at least $10^{15}-10^{16}$ G.Comment: 35 pages, no figures, submitted to Phys.Rev.

Neutrino propagation and spin zero sound in hot neutron matter with Skyrme interactions

We present microscopic calculations of neutrino propagation in hot neutron matter above nuclear density within the framework of the Random Phase Approximation . Calculations are performed for non- degenerate neutrinos using various Skyrme effective interactions. We find that for densities just above nuclear density, spin zero sound is present at zero temperature for all Skyrme forces considered. However it disappears rapidly with increasing temperature due to a strong Landau damping. As a result the mean-free path is given, to a good approximation, by the mean field value. Because of the renormalization of the bare mass in the mean field, the medium is more transparent as compared to the free case. We find, in contrast, that at several times nuclear density, a new type of behavior sets in due to the vicinity of a magnetic instability. It produces a strong reduction of the mean free path. The corresponding transition density however occurs in a region where inputs from more realistic calculations are necessary for the construction of a reliable Skyrme type parametrization.Comment: 17 pages, 4 figure

Crucial Physical Dependencies of the Core-Collapse Supernova Mechanism

We explore with self-consistent 2D F{\sc{ornax}} simulations the dependence of the outcome of collapse on many-body corrections to neutrino-nucleon cross sections, the nucleon-nucleon bremsstrahlung rate, electron capture on heavy nuclei, pre-collapse seed perturbations, and inelastic neutrino-electron and neutrino-nucleon scattering. Importantly, proximity to criticality amplifies the role of even small changes in the neutrino-matter couplings, and such changes can together add to produce outsized effects. When close to the critical condition the cumulative result of a few small effects (including seeds) that individually have only modest consequence can convert an anemic into a robust explosion, or even a dud into a blast. Such sensitivity is not seen in one dimension and may explain the apparent heterogeneity in the outcomes of detailed simulations performed internationally. A natural conclusion is that the different groups collectively are closer to a realistic understanding of the mechanism of core-collapse supernovae than might have seemed apparent.Comment: 25 pages; 10 figure

The fundamental constants and their variation: observational status and theoretical motivations

This article describes the various experimental bounds on the variation of the fundamental constants of nature. After a discussion on the role of fundamental constants, of their definition and link with metrology, the various constraints on the variation of the fine structure constant, the gravitational, weak and strong interactions couplings and the electron to proton mass ratio are reviewed. This review aims (1) to provide the basics of each measurement, (2) to show as clearly as possible why it constrains a given constant and (3) to point out the underlying hypotheses. Such an investigation is of importance to compare the different results, particularly in view of understanding the recent claims of the detections of a variation of the fine structure constant and of the electron to proton mass ratio in quasar absorption spectra. The theoretical models leading to the prediction of such variation are also reviewed, including Kaluza-Klein theories, string theories and other alternative theories and cosmological implications of these results are discussed. The links with the tests of general relativity are emphasized.Comment: 56 pages, l7 figures, submitted to Rev. Mod. Phy

Control of star formation by supersonic turbulence

Understanding the formation of stars in galaxies is central to much of modern astrophysics. For several decades it has been thought that stellar birth is primarily controlled by the interplay between gravity and magnetostatic support, modulated by ambipolar diffusion. Recently, however, both observational and numerical work has begun to suggest that support by supersonic turbulence rather than magnetic fields controls star formation. In this review we outline a new theory of star formation relying on the control by turbulence. We demonstrate that although supersonic turbulence can provide global support, it nevertheless produces density enhancements that allow local collapse. Inefficient, isolated star formation is a hallmark of turbulent support, while efficient, clustered star formation occurs in its absence. The consequences of this theory are then explored for both local star formation and galactic scale star formation. (ABSTRACT ABBREVIATED)Comment: Invited review for "Reviews of Modern Physics", 87 pages including 28 figures, in pres