Development of high-order realizable finite-volume schemes for quadrature-based moment method

Kinetic equations containing terms for spatial transport, gravity, fluid drag and particle-particle collisions can be used to model dilute gas-particle flows. However, the enormity of independent variables makes direct numerical simulation of these equations almost impossible for practical problems. A viable alternative is to reformulate the problem in terms of moments of velocity distribution. Recently, a quadrature-based moment method was derived by Fox for approximating solutions to kinetic equation for arbitrary Knudsen number. Fox also described 1st- and 2nd-order finite-volume schemes for solving the equations. The success of the new method is based on a moment-inversion algorithm that is used to calculate non-negative weights and abscissas from moments. The moment-inversion algorithm does not work if the moments are non-realizable, meaning they do not correspond to a distribution function. Not all the finite-volume schemes lead to realizable moments. Desjardins et al. showed that realizability is guaranteed with the 1 st-order finite-volume scheme, but at the expense of excess numerical diffusion. In the present work, the nonrealizability of the standard 2 nd-order finite-volume scheme is demonstrated and a generalized idea for the development of high-order realizable finite-volume schemes for quadrature-based moment methods is presented. This marks a significant improvement in the accuracy of solutions using the quadrature-based moment method as the use of 1st-order scheme to guarantee realizability is no longer a limitation

Ultracold neutrons, quantum effects of gravity and the Weak Equivalence Principle

We consider an extension of the recent experiment with ultracold neutrons and the quantization of its vertical motion in order to test the Weak Equivalence Principle. We show that an improvement on the energy resolution of the experiment may allow to establish a modest limit to the Weak Equivalence Principle and on the gravitational screening constant. We also discuss the influence of a possible new interaction of Nature.Comment: Revtex4, 4 pages. Discussion on the equivalence principle altered. Bound is improve

Cosmological Hydrodynamics with Adaptive Mesh Refinement: a new high resolution code called RAMSES

A new N-body and hydrodynamical code, called RAMSES, is presented. It has been designed to study structure formation in the universe with high spatial resolution. The code is based on Adaptive Mesh Refinement (AMR) technique, with a tree based data structure allowing recursive grid refinements on a cell-by-cell basis. The N-body solver is very similar to the one developed for the ART code (Kravtsov et al. 97), with minor differences in the exact implementation. The hydrodynamical solver is based on a second-order Godunov method, a modern shock-capturing scheme known to compute accurately the thermal history of the fluid component. The accuracy of the code is carefully estimated using various test cases, from pure gas dynamical tests to cosmological ones. The specific refinement strategy used in cosmological simulations is described, and potential spurious effects associated to shock waves propagation in the resulting AMR grid are discussed and found to be negligible. Results obtained in a large N-body and hydrodynamical simulation of structure formation in a low density LCDM universe are finally reported, with 256^3 particles and 4.1 10^7 cells in the AMR grid, reaching a formal resolution of 8192^3. A convergence analysis of different quantities, such as dark matter density power spectrum, gas pressure power spectrum and individual haloes temperature profiles, shows that numerical results are converging down to the actual resolution limit of the code, and are well reproduced by recent analytical predictions in the framework of the halo model.Comment: 21 pages and 13 low resolution JPEG images. Accepted for publication in A&

Nonlinear r-modes in Rapidly Rotating Relativistic Stars

The r-mode instability in rotating relativistic stars has been shown recently to have important astrophysical implications (including the emission of detectable gravitational radiation, the explanation of the initial spins of young neutron stars and the spin-distribution of millisecond pulsars and the explanation of one type of gamma-ray bursts), provided that r-modes are not saturated at low amplitudes by nonlinear effects or by dissipative mechanisms. Here, we present the first study of nonlinear r-modes in isentropic, rapidly rotating relativistic stars, via 3-D general-relativistic hydrodynamical evolutions. Our numerical simulations show that (1) on dynamical timescales, there is no strong nonlinear coupling of r-modes to other modes at amplitudes of order one -- unless nonlinear saturation occurs on longer timescales, the maximum r-mode amplitude is of order unity (i.e., the velocity perturbation is of the same order as the rotational velocity at the equator). An absolute upper limit on the amplitude (relevant, perhaps, for the most rapidly rotating stars) is set by causality. (2) r-modes and inertial modes in isentropic stars are predominantly discrete modes and possible associated continuous parts were not identified in our simulations. (3) In addition, the kinematical drift associated with r-modes, recently found by Rezzolla, Lamb and Shapiro (2000), appears to be present in our simulations, but an unambiguous confirmation requires more precise initial data. We discuss the implications of our findings for the detectability of gravitational waves from the r-mode instability.Comment: 4 pages, 4 eps figures, accepted in Physical Review Letter

Neutrino oscillations in curved spacetime: an heuristic treatment

We discuss neutrino oscillations in curved spacetime. Our heuristic approach can accomodate matter effects and gravitational contributions to neutrino spin precession in the presence of a magnetic field. By way of illustration, we perform explicit calculations in the Schwarzschild geometry. In this case, gravitational effects on neutrino oscillations are intimately related to the redshift. We discuss how spacetime curvature could affect the resonance position and adiabaticity of matter-enhanced neutrino flavor conversion.Comment: 7 pages, REVTeX and 1 included style file. Submitted to Phys. Rev.

Three-dimensional general relativistic hydrodynamics II: long-term dynamics of single relativistic stars

This is the second in a series of papers on the construction and validation of a three-dimensional code for the solution of the coupled system of the Einstein equations and of the general relativistic hydrodynamic equations, and on the application of this code to problems in general relativistic astrophysics. In particular, we report on the accuracy of our code in the long-term dynamical evolution of relativistic stars and on some new physics results obtained in the process of code testing. The tests involve single non-rotating stars in stable equilibrium, non-rotating stars undergoing radial and quadrupolar oscillations, non-rotating stars on the unstable branch of the equilibrium configurations migrating to the stable branch, non-rotating stars undergoing gravitational collapse to a black hole, and rapidly rotating stars in stable equilibrium and undergoing quasi-radial oscillations. The numerical evolutions have been carried out in full general relativity using different types of polytropic equations of state using either the rest-mass density only, or the rest-mass density and the internal energy as independent variables. New variants of the spacetime evolution and new high resolution shock capturing (HRSC) treatments based on Riemann solvers and slope limiters have been implemented and the results compared with those obtained from previous methods. Finally, we have obtained the first eigenfrequencies of rotating stars in full general relativity and rapid rotation. A long standing problem, such frequencies have not been obtained by other methods. Overall, and to the best of our knowledge, the results presented in this paper represent the most accurate long-term three-dimensional evolutions of relativistic stars available to date.Comment: 19 pages, 17 figure

Instabilities in the Ionization Zones Around the First Stars

We consider the evolution of the ionization zone around Population III stars with $M_*\sim 25-200 M_\odot$ in protogalaxies with $M\sim 10^7 M_\odot$ at redshifts $z = 12$, assuming that the dark matter profile is a modified isothermal sphere. We study the conditions for the growth of instabilities in the ionization zones. The Rayleigh-Taylor and thermal instabilities develop efficiently in the ionization zones around 25-40 $M_\odot$ stars, while this efficiency is lower for stars with $\sim 120 M_\odot$. For more massive stars ($\sim 200 M_\odot$), the flux of ionizing photons is strong enough to considerably reduce the gas density in the ionization zone, and the typical lifetimes of stars ($\sim 2$ Myr) are insufficient for the growth of instabilities. The gas in a protogalaxy with $M\sim 10^7 M_\odot$ with a 200 $M_\odot$ central star is completely ionized by the end of the star's lifetime; in the case of a 120 $M_\odot$ central star, only one-third of the total mass of gas is ionized. Thus, ionizing photons from stars with M_*\simlt 120 M_\odot cannot leave protogalaxies with M\simgt 10^7 M_\odot. If the masses of the central stars are 25 and 40 $M_\odot$, the gas in protogalaxies of this mass remains essentially neutral. We discuss the consequences of the evolution of the ionization zones for the propagation of the envelope after the supernova explosions of the stars and the efficiency of enrichment of the intergalactic medium in heavy elements.Comment: 11 pages, 4 figure

The neutron and its role in cosmology and particle physics

Experiments with cold and ultracold neutrons have reached a level of precision such that problems far beyond the scale of the present Standard Model of particle physics become accessible to experimental investigation. Due to the close links between particle physics and cosmology, these studies also permit a deep look into the very first instances of our universe. First addressed in this article, both in theory and experiment, is the problem of baryogenesis ... The question how baryogenesis could have happened is open to experimental tests, and it turns out that this problem can be curbed by the very stringent limits on an electric dipole moment of the neutron, a quantity that also has deep implications for particle physics. Then we discuss the recent spectacular observation of neutron quantization in the earth's gravitational field and of resonance transitions between such gravitational energy states. These measurements, together with new evaluations of neutron scattering data, set new constraints on deviations from Newton's gravitational law at the picometer scale. Such deviations are predicted in modern theories with extra-dimensions that propose unification of the Planck scale with the scale of the Standard Model ... Another main topic is the weak-interaction parameters in various fields of physics and astrophysics that must all be derived from measured neutron decay data. Up to now, about 10 different neutron decay observables have been measured, much more than needed in the electroweak Standard Model. This allows various precise tests for new physics beyond the Standard Model, competing with or surpassing similar tests at high-energy. The review ends with a discussion of neutron and nuclear data required in the synthesis of the elements during the "first three minutes" and later on in stellar nucleosynthesis.Comment: 91 pages, 30 figures, accepted by Reviews of Modern Physic