Axisymmetric core collapse simulations using characteristic numerical relativity

We present results from axisymmetric stellar core collapse simulations in general relativity. Our hydrodynamics code has proved robust and accurate enough to allow for a detailed analysis of the global dynamics of the collapse. Contrary to traditional approaches based on the 3+1 formulation of the gravitational field equations, our framework uses a foliation based on a family of outgoing light cones, emanating from a regular center, and terminating at future null infinity. Such a coordinate system is well adapted to the study of interesting dynamical spacetimes in relativistic astrophysics such as stellar core collapse and neutron star formation. Perhaps most importantly this procedure allows for the unambiguous extraction of gravitational waves at future null infinity without any approximation, along with the commonly used quadrupole formalism for the gravitational wave extraction. Our results concerning the gravitational wave signals show noticeable disagreement when those are extracted by computing the Bondi news at future null infinity on the one hand and by using the quadrupole formula on the other hand. We have strong indication that for our setup the quadrupole formula on the null cone does not lead to physical gravitational wave signals. The Bondi gravitational wave signals extracted at infinity show typical oscillation frequencies of about 0.5 kHz.Comment: 17 pages, 18 figures, submitted to Phys. Rev.

Tectono-metamorphic evolution of the Wadi Hafafit Culmination (central Eastern Desert, Egypt). Implication for Neoproterozoic core complex exhumation in NE Africa

The Neoproterozoic rock assemblages in the Wadi Hafafit Culmination (WHC) can be subdivided into two main units which are separated by the Nugrus Thrust. The structurally higher Nugrus unit is mainly composed of low grade micaschists, metavolcanic, serpentinites, and metagabbros. The overthrusted Hafafit unit forms the Hafafit domes and is composed of ortho- and para-gneisses associated with amphibolite and ultramafic rocks. Mineral chemistry and thermobarometry indicate that the WHC was affected by two main metamorphic phases. The first metamorphic phase (M1), observed in the micaschists of the Nugrus unit, is characterized by greenschist- facies conditions. Garnet-biotite and garnet-muscovite geothermometry, as well as temperatures calculated by means of the TWEEQU program yield temperatures of 400°–550°C, whereas the white mica geobarometer reveals pressure of 3.7-4.9 kbar for this metamorphic phase (M1). The second metamorphic phase (M2), observed in gneisses and amphibolites of the Hafafit unit, is characterized by amphibolite-facies conditions. Garnet-biotite, garnet-amphibole and amphibole-plagioclase geothermometry yield temperatures of 600°–750°C, whereas the garnet-hornblende-plagioclase-quartz geobarometer indicates pressures of 6-8 kbar for the second metamorphic phase (M2). Sm-Nd and Rb-Sr whole rock-mineral isochron ages around 590 Ma for gneisses and amphibolites probably represent cooling from the metamorphic thermal peak which was attained around 600 Ma or slightly earlier. A 3-stage geologic evolution model is proposed for the tectonic evolution of the WHC. The first stage started earlier than 680 Ma ago with rifting and ocean floor spreading at a time which is as yet unspecified. It was followed by a second stage of subduction and emplacement of subduction-related granitoids around 620-640 Ma. At this time, the Hafafit region has become an active margin with the production of large amounts of calc-alkaline subduction-related volcanic and plutonic sequences. Subduction was terminated by collision and NW-ward Nugrus Nappe thrusting under greenschist-facies conditions (M1) around 620-640 Ma. At this stage, rocks of Hafafit unit were subjected to intense deformation and metamorphism in amphibolite facies (M2). Next came the third stage of late-orogenic extension and crustal thinning that was controlled by the Najd transform faults (620-580 my) and that resulted in exhumation of the Hafafit domes through a combination of transpression and lateral extrusion

On the Effect of Constraint Enforcement on the Quality of Numerical Solutions in General Relativity

In Brodbeck et al 1999 it has been shown that the linearised time evolution equations of general relativity can be extended to a system whose solutions asymptotically approach solutions of the constraints. In this paper we extend the non-linear equations in similar ways and investigate the effect of various possibilities by numerical means. Although we were not able to make the constraint submanifold an attractor for all solutions of the extended system, we were able to significantly reduce the growth of the numerical violation of the constraints. Contrary to our expectations this improvement did not imply a numerical solution closer to the exact solution, and therefore did not improve the quality of the numerical solution.Comment: 14 pages, 9 figures, accepted for publication in Phys. Rev.

Tethered subsatellite study

The results are presented of studies performed relating to the feasibility of deploying a subsatellite from the shuttle by means of a tether. The dynamics, the control laws, the aerodynamics, the heating, and some communication considerations of the tethered subsatellite system are considered. Nothing was found that prohibits the use of a subsatellite joined to the shuttle by a long (100 km) tether. More detailed studies directed at specific applications are recommended

First-order quasilinear canonical representation of the characteristic formulation of the Einstein equations

We prescribe a choice of 18 variables in all that casts the equations of the fully nonlinear characteristic formulation of general relativity in first--order quasi-linear canonical form. At the analytical level, a formulation of this type allows us to make concrete statements about existence of solutions. In addition, it offers concrete advantages for numerical applications as it now becomes possible to incorporate advanced numerical techniques for first order systems, which had thus far not been applicable to the characteristic problem of the Einstein equations, as well as in providing a framework for a unified treatment of the vacuum and matter problems. This is of relevance to the accurate simulation of gravitational waves emitted in astrophysical scenarios such as stellar core collapse.Comment: revtex4, 7 pages, text and references added, typos corrected, to appear in Phys. Rev.

Tectono-metamorphic evolution of the Wadi Hafafit Culmination (central Eastern Desert, Egypt). Implication for Neoproterozoic core complex exhumation in NE Africa

The Neoproterozoic rock assemblages in the Wadi Hafafit Culmination (WHC) can be subdivided into two main units which are separated by the Nugrus Thrust. The structurally higher Nugrus unit is mainly composed of low grade micaschists, metavolcanic, serpentinites, and metagabbros. The overthrusted Hafafit unit forms the Hafafit domes and is composed of ortho- and para-gneisses associated with amphibolite and ultramafic rocks. Mineral chemistry and thermobarometry indicate that the WHC was affected by two main metamorphic phases. The first metamorphic phase (M1), observed in the micaschists of the Nugrus unit, is characterized by greenschist-facies conditions. Garnet-biotite and garnet-muscovite geothermometry, as well as temperatures calculated by means of the TWEEQU program yield temperatures of 400°-550°C, whereas the white mica geobarometer reveals pressure of 3.7-4.9 kbar for this metamorphic phase (M1). The second metamorphic phase (M2), observed in gneisses and amphibolites of the Hafafit unit, is characterized by amphibolite-facies conditions. Garnet-biotite, garnet-amphibole and amphibole-plagioclase geothermometry yield temperatures of 600°-750°C, whereas the garnet-hornblende-plagioclase-quartz geobarometer indicates pressures of 6-8 kbar for the second metamorphic phase (M2). Sm-Nd and Rb-Sr whole rock-mineral isochron ages around 590 Ma for gneisses and amphibolites probably represent cooling from the metamorphic thermal peak which was attained around 600 Ma or slightly earlier. A 3-stage geologic evolution model is proposed for the tectonic evolution of the WHC. The first stage started earlier than 680 Ma ago with rifting and ocean floor spreading at a time which is as yet unspecified. It was followed by a second stage of subduction and emplacement of subduction-related granitoids around 620-640 Ma. At this time, the Hafafit region has become an active margin with the production of large amounts of calc-alkaline subduction-related volcanic and plutonic sequences. Subduction was terminated by collision and NW-ward Nugrus Nappe thrusting under greenschist-facies conditions (M1) around 620-640 Ma. At this stage, rocks of Hafafit unit were subjected to intense deformation and metamorphism in amphibolite facies (M2). Next came the third stage of late-orogenic extension and crustal thinning that was controlled by the Najd transform faults (620-580 my) and that resulted in exhumation of the Hafafit domes through a combination of transpression and lateral extrusion

Small-x Dipole Evolution Beyond the Large-N_c Limit

We present a method to include colour-suppressed effects in the Mueller dipole picture. The model consistently includes saturation effects both in the evolution of dipoles and in the interactions of dipoles with a target in a frame-independent way. When implemented in a Monte Carlo simulation together with our previous model of energy--momentum conservation and a simple dipole description of initial state protons and virtual photons, the model is able to reproduce to a satisfactory degree both the gamma*-p cross sections as measured at HERA as well as the total p-p cross section all the way from ISR energies to the Tevatron and beyond

Bondian frames to couple matter with radiation

A study is presented for the non linear evolution of a self gravitating distribution of matter coupled to a massless scalar field. The characteristic formulation for numerical relativity is used to follow the evolution by a sequence of light cones open to the future. Bondian frames are used to endow physical meaning to the matter variables and to the massless scalar field. Asymptotic approaches to the origin and to infinity are achieved; at the boundary surface interior and exterior solutions are matched guaranteeing the Darmois--Lichnerowicz conditions. To show how the scheme works some numerical models are discussed. We exemplify evolving scalar waves on the following fixed backgrounds: A) an atmosphere between the boundary surface of an incompressible mixtured fluid and infinity; B) a polytropic distribution matched to a Schwarzschild exterior; C) a Schwarzschild- Schwarzschild spacetime. The conservation of energy, the Newman--Penrose constant preservation and other expected features are observed.Comment: 20 pages, 6 figures; to appear in General Relativity and Gravitatio

Advantages of modified ADM formulation: constraint propagation analysis of Baumgarte-Shapiro-Shibata-Nakamura system

Several numerical relativity groups are using a modified ADM formulation for their simulations, which was developed by Nakamura et al (and widely cited as Baumgarte-Shapiro-Shibata-Nakamura system). This so-called BSSN formulation is shown to be more stable than the standard ADM formulation in many cases, and there have been many attempts to explain why this re-formulation has such an advantage. We try to explain the background mechanism of the BSSN equations by using eigenvalue analysis of constraint propagation equations. This analysis has been applied and has succeeded in explaining other systems in our series of works. We derive the full set of the constraint propagation equations, and study it in the flat background space-time. We carefully examine how the replacements and adjustments in the equations change the propagation structure of the constraints, i.e. whether violation of constraints (if it exists) will decay or propagate away. We conclude that the better stability of the BSSN system is obtained by their adjustments in the equations, and that the combination of the adjustments is in a good balance, i.e. a lack of their adjustments might fail to obtain the present stability. We further propose other adjustments to the equations, which may offer more stable features than the current BSSN equations.Comment: 10 pages, RevTeX4, added related discussion to gr-qc/0209106, the version to appear in Phys. Rev.

Gravitational waves from axisymmetrically oscillating neutron stars in general relativistic simulations

Gravitational waves from oscillating neutron stars in axial symmetry are studied performing numerical simulations in full general relativity. Neutron stars are modeled by a polytropic equation of state for simplicity. A gauge-invariant wave extraction method as well as a quadrupole formula are adopted for computation of gravitational waves. It is found that the gauge-invariant variables systematically contain numerical errors generated near the outer boundaries in the present axisymmetric computation. We clarify their origin, and illustrate it possible to eliminate the dominant part of the systematic errors. The best corrected waveforms for oscillating and rotating stars currently contain errors of magnitude $\sim 10^{-3}$ in the local wave zone. Comparing the waveforms obtained by the gauge-invariant technique with those by the quadrupole formula, it is shown that the quadrupole formula yields approximate gravitational waveforms besides a systematic underestimation of the amplitude of $O(M/R)$ where $M$ and $R$ denote the mass and the radius of neutron stars. However, the wave phase and modulation of the amplitude can be computed accurately. This indicates that the quadrupole formula is a useful tool for studying gravitational waves from rotating stellar core collapse to a neutron star in fully general relativistic simulations. Properties of the gravitational waveforms from the oscillating and rigidly rotating neutron stars are also addressed paying attention to the oscillation associated with fundamental modes