An axis-free overset grid in spherical polar coordinates for simulating 3D self-gravitating flows

A type of overlapping grid in spherical coordinates called the Yin-Yang grid is successfully implemented into a 3D version of the explicit Eulerian grid-based code PROMETHEUS including self-gravity. The modified code successfully passed several standard hydrodynamic tests producing results which are in very good agreement with analytic solutions. Moreover, the solutions obtained with the Yin-Yang grid exhibit no peculiar behaviour at the boundary between the two grid patches. The code has also been successfully used to model astrophysically relevant situations, namely equilibrium polytropes, a Taylor-Sedov explosion, and Rayleigh-Taylor instabilities. According to our results, the usage of the Yin-Yang grid greatly enhances the suitability and efficiency of 3D explicit Eulerian codes based on spherical polar coordinates for astrophysical flows.Comment: 15 pages, 17 figures, 2 tables, 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

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

Mind to Market: A Cautionary Tale

The excitement of discovery and invention is unusual in the academic setting. The opportunity of applying for a patent related to one’s teaching is not something that is taught in professional school. However, with the innovation now required to meet the needs of students at a distance and the use of technology, it might be a valuable asset. The focus of this article is to give an overview about the patent process and copyright law to prevent mistakes that can stop the opportunity. It is possible to violate the process before you are even aware that you might be able to secure a patent

Hydrodynamic simulations of merging clusters of galaxies

We present the results of high-resolution AP3M+SPH simulations of merging clusters of galaxies. We find that the compression and shocking of the core gas during a merger can lead to large increases in bolometric X-ray luminosities and emission-weighted temperatures of clusters. Cooling flows are completely disrupted during equal-mass mergers, with the mass deposition rate dropping to zero as the cores of the clusters collide. The large increase in the cooling time of the core gas strongly suggests that cooling flows will not recover from such a merger within a Hubble time. Mergers with subclumps having one eighth of the mass of the main cluster are also found to disrupt a cooling flow if the merger is head-on. However, in this case the entropy injected into the core gas is rapidly radiated away and the cooling flow restarts within a few Gyr of the merger. Mergers in which the subcluster has an impact parameter of 500 kpc do not disrupt the cooling flow, although the mass deposition rate is reduced by ∼30 per cent. Finally, we find that equal mass, off-centre mergers can effectively mix gas in the cores of clusters, while head on mergers lead to very little mixing. Gas stripped from the outer layers of subclumps results in parts of the outer layers of the main cluster being well mixed, although they have little effect on the gas in the core of the cluster. None of the mergers examined here resulted in the intracluster medium being well mixed globally

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

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

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

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