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

Nonlinear r-Modes in Neutron Stars: Instability of an unstable mode

We study the dynamical evolution of a large amplitude r-mode by numerical simulations. R-modes in neutron stars are unstable growing modes, driven by gravitational radiation reaction. In these simulations, r-modes of amplitude unity or above are destroyed by a catastrophic decay: A large amplitude r-mode gradually leaks energy into other fluid modes, which in turn act nonlinearly with the r-mode, leading to the onset of the rapid decay. As a result the r-mode suddenly breaks down into a differentially rotating configuration. The catastrophic decay does not appear to be related to shock waves at the star's surface. The limit it imposes on the r-mode amplitude is significantly smaller than that suggested by previous fully nonlinear numerical simulations.Comment: Published in Phys. Rev. D Rapid Comm. 66, 041303(R) (2002

Metal enrichment of the intra-cluster medium over a Hubble time for merging and relaxed galaxy clusters

We investigate the efficiency of galactic mass loss, triggered by ram-pressure stripping and galactic winds of cluster galaxies, on the chemical enrichment of the intra-cluster medium (ICM). We combine N-body and hydrodynamic simulations with a semi-numerical galaxy formation model. By including simultaneously different enrichment processes, namely ram-pressure stripping and galactic winds, in galaxy-cluster simulations, we are able to reproduce the observed metal distribution in the ICM. We find that the mass loss by galactic winds in the redshift regime z>2 is ~10% to 20% of the total galactic wind mass loss, whereas the mass loss by ram-pressure stripping in the same epoch is up to 5% of the total ram-pressure stripping mass loss over the whole simulation time. In the cluster formation epochs z<2 ram-pressure stripping becomes more dominant than galactic winds. We discuss the non-correlation between the evolution of the mean metallicity of galaxy clusters and the galactic mass losses. For comparison with observations we present two dimensional maps of the ICM quantities and radial metallicity profiles. The shape of the observed profiles is well reproduced by the simulations in the case of merging systems. In the case of cool-core clusters the slope of the observed profiles are reproduced by the simulation at radii below ~300 kpc, whereas at larger radii the observed profiles are shallower. We confirm the inhomogeneous metal distribution in the ICM found in observations. To study the robustness of our results, we investigate two different descriptions for the enrichment process interaction.Comment: 11 pages, 13 figures, accepted for publication in A&A, high resolution version can be found at <http://astro.uibk.ac.at/~wolfgang/kapferer.pdf

Towards a Realistic Neutron Star Binary Inspiral: Initial Data and Multiple Orbit Evolution in Full General Relativity

This paper reports on our effort in modeling realistic astrophysical neutron star binaries in general relativity. We analyze under what conditions the conformally flat quasiequilibrium (CFQE) approach can generate ``astrophysically relevant'' initial data, by developing an analysis that determines the violation of the CFQE approximation in the evolution of the binary described by the full Einstein theory. We show that the CFQE assumptions significantly violate the Einstein field equations for corotating neutron stars at orbital separations nearly double that of the innermost stable circular orbit (ISCO) separation, thus calling into question the astrophysical relevance of the ISCO determined in the CFQE approach. With the need to start numerical simulations at large orbital separation in mind, we push for stable and long term integrations of the full Einstein equations for the binary neutron star system. We demonstrate the stability of our numerical treatment and analyze the stringent requirements on resolution and size of the computational domain for an accurate simulation of the system.Comment: 22 pages, 18 figures, accepted to Phys. Rev.

Metal enrichment of the intra-cluster medium by thermally and cosmic-ray driven galactic winds

We investigate the efficiency and time-dependence of thermally and cosmic ray driven galactic winds for the metal enrichment of the intra-cluster medium (ICM) using a new analytical approximation for the mass outflow. The spatial distribution of the metals are studied using radial metallicity profiles and 2D metallicity maps of the model clusters as they would be observed by X-ray telescopes like XMM-Newton. Analytical approximations for the mass loss by galactic winds driven by thermal and cosmic ray pressure are derived from the Bernoulli equation and implemented in combined N-body/hydrodynamic cosmological simulations with a semi-analytical galaxy formation model. Observable quantities like the mean metallicity, metallicity profiles, and 2D metal maps of the model clusters are derived from the simulations. We find that galactic winds alone cannot account for the observed metallicity of the ICM. At redshift $z=0$ the model clusters have metallicities originating from galactic winds which are almost a factor of 10 lower than the observed values. For massive, relaxed clusters we find, as in previous studies, a central drop in the metallicity due to a suppression of the galactic winds by the pressure of the ambient ICM. Combining ram-pressure stripping and galactic winds we find radial metallicity profiles of the model clusters which agree qualitatively with observed profiles. Only in the inner parts of massive clusters the observed profiles are steeper than in the simulations. Also the combination of galactic winds and ram-pressure stripping yields too low values for the ICM metallicities. The slope of the redshift evolution of the mean metallicity in the simulations agrees reasonably well with recent observations.Comment: 9 pages, 6 figures, accepted by A&

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

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.

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