arXiv subjects

Ewald Müller

Publications and source records attributed to Ewald Müller.

27 records · Page 2Linked to original sources

arXiv2013

The Bondi-Sachs metric at the vertex of a null cone: axially symmetric vacuum solutions

In the Bondi-Sachs formulation of General Relativity space-time is foliated via a family of null cones. If these null cones are defined such that their vertices are traced by a regular world-line then the metric tensor has to obey regularity conditions at the vertices. We explore these regularity conditions when the world line is a time-like geodesic. In particular, we solve the Einstein equations for the Bondi-Sachs metric near the vertices for axially symmetric vacuum space- times. The metric is calculated up to third order corrections with respect to a flat metric along the time-like geodesic, as this is the lowest order where non- linear coupling of the metric coefficients occurs. We also determine the boundary conditions of the metric to arbitrary order of these corrections when a linearized and axially symmetric vacuum space-time is assumed. In both cases we find that (i) the initial data on the null cone must have a very rigid angular structure for the vertex to be a regular point, and (ii) the initial data are determined by functions depending only on the time of a geodesic observer tracing the vertex. The latter functions can be prescribed freely, but if the vertex is assumed to be regular they must be finite and have finite derivatives along the geodesic.

gr-qc↗

arXiv2012

Numerical Relativity in Spherical Polar Coordinates: Evolution Calculations with the BSSN Formulation

In the absence of symmetry assumptions most numerical relativity simulations adopt Cartesian coordinates. While Cartesian coordinates have some desirable properties, spherical polar coordinates appear better suited for certain applications, including gravitational collapse and supernova simulations. Development of numerical relativity codes in spherical polar coordinates has been hampered by the need to handle the coordinate singularities at the origin and on the axis, for example by careful regularization of the appropriate variables. Assuming spherical symmetry and adopting a covariant version of the BSSN equations, Montero and Cordero-Carrión recently demonstrated that such a regularization is not necessary when a partially implicit Runge-Kutta (PIRK) method is used for the time evolution of the gravitational fields. Here we report on an implementation of the BSSN equations in spherical polar coordinates without any symmetry assumptions. Using a PIRK method we obtain stable simulations in three spatial dimensions without the need to regularize the origin or the axis. We perform and discuss a number of tests to assess the stability, accuracy and convergence of the code, namely weak gravitational waves, "hydro-without-hydro" evolutions of spherical and rotating relativistic stars in equilibrium, and single black holes.

gr-qc↗

arXiv2012

Fast time variations of supernova neutrino signals from 3-dimensional models

We study supernova neutrino flux variations in the IceCube detector, using 3D models based on a simplified neutrino transport scheme. The hemispherically integrated neutrino emission shows significantly smaller variations compared with our previous study of 2D models, largely because of the reduced SASI activity in this set of 3D models which we interpret as a pessimistic extreme. For the studied cases, intrinsic flux variations up to about 100 Hz frequencies could still be detected in a supernova closer than about 2 kpc.

astro-ph.HE↗

arXiv2012

Magneto-elastic oscillations of neutron stars with dipolar magnetic fields

By means of two dimensional, general-relativistic, magneto-hydrodynamical simulations we investigate the oscillations of magnetized neutron star models (magnetars) including the description of an extended solid crust. The aim of this study is to understand the origin of the QPOs observed in the giant flares of SGRs. We confirm the existence of three different regimes: (a) a weak magnetic field regime B<5 x 10^13 G, where crustal shear modes dominate the evolution; (b) a regime of intermediate magnetic fields 5 x 10^13 G 10^15 G, where magneto-elastic oscillations reach the surface and approach the behavior of purely Alfvén QPOs. When the Alfvén QPOs are confined to the core of the neutron star, we find qualitatively similar QPOs as in the absence of a crust. The lower QPOs associated with the closed field lines of the dipolar magnetic field configuration are reproduced as in our previous simulations without crust, while the upper QPOs connected to the open field lines are displaced from the polar axis. Additionally, we observe a family of edge QPOs. Our results do not leave much room for a crustal-mode interpretation of observed QPOs in SGR giant flares, but can accommodate an interpretation of these observations as originating from Alfvén-like, global, turning-point QPOs in models with dipolar magnetic field strengths in the narrow range of 5 x 10^15 G < B < 1.4 x 10^16 G. This range is somewhat larger than estimates for magnetic field strengths in known magnetars. The discrepancy may be resolved in models including a more complicated magnetic field structure or with models taking superfluidity of the neutrons and superconductivity of the protons in the core into account.

astro-ph.HE↗

arXiv2010

Magneto-elastic torsional oscillations of magnetars

We extend a general-relativistic ideal magneto-hydrodynamical code to include the effects of elasticity. Using this numerical tool we analyse the magneto-elastic oscillations of highly magnetised neutron stars (magnetars). In simulations without magnetic field we are able to recover the purely crustal shear oscillations within an accuracy of about a few per cent. For dipole magnetic fields between 5 x 10^13 and 10^15 G the Alfvén oscillations become modified substantially by the presence of the crust. Those quasi-periodic oscillations (QPOs) split into three families: Lower QPOs near the equator, Edge QPOs related to the last open field line and Upper QPOs at larger distance from the equator. Edge QPOs are called so because they are related to an edge in the corresponding Alfvén continuum. The Upper QPOs are of the same kind, while the Lower QPOs are turning-point QPOs, related to a turning point in the continuous spectrum.

astro-ph.SR↗

arXiv2010

Stationary, Axisymmetric Neutron Stars with Meridional Circulation in General Relativity

We present the first stationary, axisymmetric neutron star models with meridional circulation in general relativity. For that purpose, we developed GRNS, a new code based on a fixed point iteration. We find a two-dimensional set of meridional circulation modes, which differ by the number of vortices in the stream lines of the neutron star fluid. For expected maximal meridional circulation velocities of about 1000 km/s, the vortices cause surface deformations of about a percent. The deformations depend on the shape of the vortices close to the surface and increase with the meridional circulation velocity. We also computed models of rotating neutron stars with meridional circulation, where neither the surface rotates nor does the rotation velocity exceed the circulation velocity.

gr-qc↗

arXiv2010

Magneto-elastic oscillations and the damping of crustal shear modes in magnetars

In a realistic model of magneto-elastic oscillations in magnetars, we find that crustal shear oscillations, often invoked as an explanation of quasi-periodic oscillations (QPOs) seen after giant flares in soft gamma-ray repeaters (SGRs), are damped by resonant absorption on timescales of at most 0.2s, for a lower limit on the dipole magnetic field strength of 5 x 10^13 G. At higher magnetic field strengths (typical in magnetars) the damping timescale is even shorter, as anticipated by earlier toy-models. We have investigated a range of equations of state and masses and if magnetars are dominated by a dipole magnetic field, our findings exclude torsional shear oscillations of the crust from explaining the observed low-frequency QPOs. In contrast, we find that the Alfvén QPO model is a viable explanation of observed QPOs, if the dipole magnetic field strength exceeds a minimum strength of about several times 10^14 G to 10^15 G. Then, Alfvén QPOs are no longer confined to the fluid core, but completely dominate in the crust region and have a maximum amplitude at the surface of the star.

astro-ph.HE↗

arXiv2010

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.

astro-ph.IM↗

arXiv2008

A new general relativistic magnetohydrodynamics code for dynamical spacetimes

We present a new numerical code which solves the general relativistic magneto-hydrodynamics (GRMHD) equations coupled to the Einstein equations for the evolution of a dynamical spacetime within the conformally-flat approximation. This code has been developed with the main objective of studying astrophysical scenarios in which both, high magnetic fields and strong gravitational fields appear, such as the magneto-rotational collapse of stellar cores, the collapsar model of GRBs, and the evolution of neutron stars. The code is based on an existing and thoroughly tested purely hydrodynamics code and on its extension to accommodate weakly magnetized fluids (passive magnetic field approximation). The numerical code we present here is based on high-resolution shock-capturing schemes to solve the GRMHD equations together with the flux constraint transport method to ensure the solenoidal condition of the magnetic field. Since the astrophysical applications envisaged do not deviate much from spherical symmetry, the conformal flatness condition approximation is used for the formulation of the Einstein equations. In addition, the code can handle several equations of state, from simple analytical expressions to microphysical tabulated ones. In this paper we present stringent tests of our new GRMHD numerical code, which show its ability to handle all aspects appearing in the astrophysical scenarios for which the code is intended, namely relativistic shocks, highly magnetized fluids, and equilibrium configurations of magnetized neutron stars. As an application, magneto-rotational core collapse simulations of a realistic progenitor are presented, comparing the results with our previous finding in the passive magnetic field approximation.

astro-ph↗