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All sourcesNASA NTRSDOE OSTI
NASA NTRS2010

Numerical Relativity Simulations for Black Hole Merger Astrophysics

Massive black hole mergers are perhaps the most energetic astronomical events, establishing their importance as gravitational wave sources for LISA, and also possibly leading to observable influences on their local environments. Advances in numerical relativity over the last five years have fueled the development of a rich physical understanding of general relativity's predictions for these events. Z will overview the understanding of these event emerging from numerical simulation studies. These simulations elucidate the pre-merger dynamics of the black hole binaries, the consequent gravitational waveform signatures ' and the resulting state, including its kick velocity, for the final black hole produced by the merger. Scenarios are now being considered for observing each of these aspects of the merger, involving both gravitational-wave and electromagnetic astronomy.

Baker, John G.↗
NASA NTRS2009

Merging Black Holes, Gravitational Waves, and Numerical Relativity

The final merger of two black holes will emit more energy than all the stars in the observable universe combined. This energy will come in the form of gravitational waves, which are a key prediction of Einstein's general relativity and a new tool for exploring the universe. Observing these mergers with gravitational wave detectors, such as the ground-based LIGO and the space-based LISA, requires knowledge of the radiation waveforms. Since these mergers take place in regions of extreme gravity, we need to solve Einstein's equations of general relativity on a computer. For more than 30 years, scientists have tried to compute black hole mergers using the methods of numerical relativity. The resulting computer codes were long plagued by instabilities, causing them to crash well before the black holes in the binary could complete even a single orbit. Within the past few years, however, this situation has changed dramatically, with a series of remarkable breakthroughs. This talk will focus on new simulations that are revealing the dynamics and w ae~fo rms of binary black hole mergers, and their applications in gravitational wave detection, testing general relativity, and astrophysics.

Centrella, Joan M.↗
NASA NTRS2007

Binary Black Holes, Gravitational Waves, and Numerical Relativity

Massive black hole (MBH) binaries are found at the centers of most galaxies. MBH mergers trace galaxy mergers and are strong sources of gravitational waves. Observing these sources with gravitational wave detectors requires that we know the radiation waveforms they emit. Since these mergers take place in regions of very strong gravitational fields, we need to solve Einstein's equations of general relativity on a computer in order to calculate these waveforms. For more than 30 years, scientists have tried to compute these waveforms using the methods of numerical relativity. The resulting computer codes have been plagued by instabilities. causing them to crash well before the black hole:, in the binary could complete even a single orbit. Recently this situation has changed dramatically, with a series of amazing breakthroughs. This presentation shows how a spacetime is constructed on a computer to build a simulation laboratory for binary black hole mergers. Focus is on the recent advances that that reveal these waveforms, and the potential for discoveries that arises when these sources are observed by LIGO and LISA.

Centrella, Joan↗
NASA NTRS2007

Binary Black Holes, Gravitational Waves, and Numerical Relativity

The final merger of two black holes is expected to be the strongest gravitational wave source for ground-based interferometers such as LIGO, VIRGO, and GE0600, as well as the space-based interferometer LISA. Observing these sources with gravitational wave detectors requires that we know the radiation waveforms they emit. Since these mergers take place in regions of extreme gravity, we need to solve Einstein's equations of general relativity on a computer in order to calculate these waveforms. For more than 30 years, scientists have tried to compute black hole mergers using the methods of numerical relativity. The resulting computer codes have been plagued by instabilities, causing them to crash well before the black holes in the binary could complete even a single orbit. Within the past few years, however, this situation has changed dramatically, with a series of remarkable breakthroughs. This talk will focus on new simulations that are revealing the dynamics and waveforms of binary black hole mergers, and their applications in gravitational wave detection, data analysis, and astrophysics.

Centrella, John↗
NASA NTRS2010

Black-Hole Binaries, Gravitational Waves, and Numerical Relativity

Understanding the predictions of general relativity for the dynamical interactions of two black holes has been a long-standing unsolved problem in theoretical physics. Black-hole mergers are monumental astrophysical events ' releasing tremendous amounts of energy in the form of gravitational radiation ' and are key sources for both ground- and spacebased gravitational wave detectors. The black-hole merger dynamics and the resulting gravitational waveforms can only he calculated through numerical simulations of Einstein's equations of general relativity. For many years, numerical relativists attempting to model these mergers encountered a host of problems, causing their codes to crash after just a fraction of a binary orbit cnuld be simulated. Recently ' however, a series of dramatic advances in numerical relativity has ' for the first time, allowed stable / robust black hole merger simulations. We chronicle this remarkable progress in the rapidly maturing field of numerical relativity, and the new understanding of black-hole binary dynamics that is emerging. We also discuss important applications of these fundamental physics results to astrophysics, to gravitationalwave astronomy, and in other areas.

Kelly, Bernard J.↗
NASA NTRS2011

Numerical Relativity for Space-Based Gravitational Wave Astronomy

In the next decade, gravitational wave instruments in space may provide high-precision measurements of gravitational-wave signals from strong sources, such as black holes. Currently variations on the original Laser Interferometer Space Antenna mission concepts are under study in the hope of reducing costs. Even the observations of a reduced instrument may place strong demands on numerical relativity capabilities. Possible advances in the coming years may fuel a new generation of codes ready to confront these challenges.

Baker, John G.↗
DOE OSTI2026

Axisymmetric hydrodynamics in numerical relativity: treating coordinate singularity, artificial heating and modeling MHD instabilities

Two-dimensional axisymmetric simulations of binary neutron star (BNS) merger remnant are a cheap alternative to 3D simulations. To maintain realism for secular timescales, simulations must avoid accumulated errors from drifts in conserved quantities and artificial heating, and they must model turbulent transport in a way that remains plausible throughout the evolution. It is also crucial to avoid numerical artifacts due to the polar coordinate axis singularity. Methods that behave well near the axis often break flux-conservative form of the hydrodynamic equations, resulting in significant drifts in conserved quantities. We present a flux-conservative scheme that maintains smoothness near the axis without sacrificing conservative formulation of the equations or incurring drifts in conserved global quantities. We compare the numerical performance of different treatments of the hydrodynamic equations when evolving a hypermassive neutron star resembling the remnant of a BNS merger. These simulations demonstrate that the new scheme combines the axis smoothness of non-conservative methods with the mass and angular momentum conservation of other conservative methods on $\sim 10^2$ ms timescales of viscous and neutrino-driven evolution. Because fluid profiles remain smooth in the remnant interior, it is possible to remove artificial heating by evolving the entropy density. We show how physical heating and cooling terms can be easily calculated from source terms of the conservative evolution variables and demonstrate our implementation. Finally, we discuss and implement improvements to the effective viscosity scheme to better model the effect of magnetohydrodynamic instabilities as the remnant evolves.

axisymmetry↗
NASA NTRS2006

Consistency of Post-Newtonian Waveforms with Numerical Relativity

General relativity predicts the gravitational radiation signatures of mergers of compact binaries, such as coalescing binary black hole systems. Derivations of waveform predictions for such systems are required for optimal scientific analysis of observational gravitational wave data, and have so far been achieved primarily with the aid of the post-Newtonian (PN) approximation. The quality of this treatment is unclear, however, for the important late inspiral portion. We derive late-inspiral waveforms via a complementary approach, direct numerical simulation of Einstein's equations, which has recently matured sufficiently for such applications. We compare waveform phasing from simulations covering the last approximately 14 cycles of gravitational radiation from an equal-mass binary system of nonspinning black holes with the corresponding 3PN and 3.5PN orbital phasing. We find agreement consistent with internal error estimates based on either approach at the level of one radian over approximately 10 cycles. The result suggests that PN waveforms for this system are effective roughly until the system reaches its last stable orbit just prior to the final merger/

Baker, John G.↗
NASA NTRS2007

Consistency of Post-Newtonian Waveforms with Numerical Relativity

General relativity predicts the gravitational radiation signatures of mergers of compact binaries,such as coalescing binary black hole systems. Derivations of waveform predictions for such systems are required for optimal scientific analysis of observational gravitational wave data, and have so far been achieved primarily with the aid of the post-Newtonian (PN) approximation. The quaIity of this treatment is unclear, however, for the important late inspiral portion. We derive late-inspiral wave forms via a complementary approach, direct numerical simulation of Einstein's equations, which has recently matured sufficiently for such applications. We compare waveform phasing from simulations covering the last approximately 14 cycles of gravitational radiation from an equal-mass binary system of nonspinning black holes with corresponding 3PN and 3.5PN waveforms. We find phasing agreement consistent with internal error estimates based in either approach, at the level of one radian over approximately 10 cycles. The result suggests that PN waveforms for this system are effective roughly until the system reaches its last stable orbit just prior to the final merger.

Baker, John G.↗
NASA NTRS1986

Analysis of coaxial spray combustion flames and related numerical issues

An approach to the simulation of strongly coupled multiphase flows in combustion hardware is sketched and its unique requirements highlighted. An example of a successful application to a coaxial injector flame is presented. Furthermore, several numerical issues that tend to interact with the physics of the problem are discussed with special regard to their potential impact on the choices of numerical parameters by the analyst. These include the issues of stability, numerical diffusivity, stiffness, and boundary conditions. The theme of this paper focuses on the intriguing relationships among the grid, the solution algorithm, and the actual physical mechanisms themselves.

Liang, P. Y.↗
NASA NTRS2007

Binary Black Holes, Numerical Relativity, and Gravitational Waves

The final merger of two black holes releases a tremendous amount of energy, more than the combined light from all the stars in the visible universe. This energy is emitted in the form of gravitational waves, and observing these sources with gravitational wave detectors such as LISA requires that we know the pattern or fingerprint of the radiation emitted. Since black hole mergers take place in regions of extreme gravitational fields, we need to solve Einstein's equations of general relativity on a computer in order to calculate these wave patterns. For more than 30 years, scientists have tried to compute these wave patterns. However, their computer codes have been plagued by problems that caused them to crash. This situation has changed dramatically in the past 2 years, with a series of amazing breakthroughs. This talk will take you on this quest for these gravitational wave patterns, showing how a spacetime is constructed on a computer to build a simulation laboratory for binary black hole mergers. We will focus on the recent advances that are revealing these waveforms, and the dramatic new potential for discoveries that arises when these sources will be observed by LISA

Centrella, Joan↗
NASA NTRS2011

Results from Numerical General Relativity

For several years numerical simulations have been revealing the details of general relativity's predictions for the dynamical interactions of merging black holes. I will review what has been learned of the rich phenomenology of these mergers and the resulting gravitational wave signatures. These wave forms provide a potentially observable record of the powerful astronomical events, a central target of gravitational wave astronomy. Asymmetric radiation can produce a thrust on the system which may accelerate the single black hole resulting from the merger to high relative velocity.

Baker, John G.↗
NASA NTRS2005

Simulating Gravitational Radiation from Binary Black Holes Mergers as LISA Sources

A viewgraph presentation on the simulation of gravitational waves from Binary Massive Black Holes with LISA observations is shown. The topics include: 1) Massive Black Holes (MBHs); 2) MBH Binaries; 3) Gravitational Wavws from MBH Binaries; 4) Observing with LISA; 5) How LISA sees MBH binary mergers; 6) MBH binary inspirals to LISA; 7) Numerical Relativity Simulations; 8) Numerical Relativity Challenges; 9) Recent Successes; 10) Goddard Team; 11) Binary Black Hole Simulations at Goddard; 12) Goddard Recent Advances; 13) Baker, et al.:GSFC; 13) Starting Farther Out; 14) Comparing Initial Separation; 15) Now with AMR; and 16) Conclusion.

Baker, John↗
NASA NTRS2008

Observing Mergers of Nonspinning Black Hole Binaries with LISA

Recent advances in the field of numerical relativity now make it possible to calculate the final, most powerful merger phase of binary black hole coalescence. We present the application of nonspinning numerical relativity waveforms to the search for and precision measurement of black hole binary coalescences using LISA. In particular, we focus on the advances made in moving beyond the equal mass, nonspinning case into other regions of parameter space, focusing on the case of nonspinning holes with ever-increasing mass ratios. We analyze the available unequal mass merger waveforms from numerical relativity, and compare them to two models, both of which use an effective one body treatment of the inspiral, but which use fundamentally different approaches to the treatment of the merger-ringdown. We confirm the expected mass ratio scaling of the merger, and investigate the changes in waveform behavior and their observational impact with changing mass ratio. Finally, we investigate the potential contribution from the merger portion of the waveform to measurement uncertainties of the binary's parameters for the unequal mass case.

McWilliams S.↗
NASA NTRS1990

Reliable algorithm for modal decomposition

This paper describes a reliable, general algorithm for modal decomposition in real arithmetic and its use in analyzing and synthesizing control logic for linear dynamic systems. The numerical difficulties are described associated with computing the Jordan canonical form when the system has repeated, or nearly repeated, eigenvalues. A new algorithm is described that satisfactorily solves these numerical difficulties. The relation and extension to related numerical analysis research are discussed to clarify the reliability of the techniques. Finally, its implementation as a practical modal decomposition method for efficiently computing the matrix exponential, transfer functions, and frequency response is also described.

Walker, Robert A.↗
NASA NTRS1987

Numerical experiments related to the summer 1980 U.S. heat wave

The NASA Goddard Laboratory for Atmospheres fourth-order GCM was used in a series of medium-range numerical forecast experiments in order to improve understanding of the severe summer 1980 heat wave over the U.S. The results show that the derived soil moisture anomalies in the summer of 1980 contributed positively to the model's simulation of the heat wave maintenance, and suggest that once a region of reduced soil moisture is established, it tends to persist and maintain warmer and drier conditions. The lower soil moisture values resulted in reduced evaporation, higher ground temperatures, increased sensible heat flux from ground to air, higher surface air temperature, lower sea-level pressure, and higher 500-mb height. The effects of North Pacific sea-surface-temperature anomalies were mostly opposite to those of the soil-moisture anomalies: enhanced northerly flow of cooler drier air, increased evaporation, lower ground and air temperature, higher sea level pressure, and lower 500 mb heights over the Great Plains.

Wolfson, N.↗
DOE OSTI2026

Anti-Ultralocality and Plateau Models of Inflation

Anti-ultralocality refers to the growth of spatial gradient terms relative to velocity terms in the coupled Einstein--scalar field equations. It is a characteristic feature of decelerated expansion before the onset of inflation. Previous numerical relativity studies have shown that anti-ultralocality prevents the onset of inflation in models with power-law inflaton potentials. In this paper, we show that models with plateau-shaped inflaton potentials, which are considered to be the simplest way to generate a tensor-to-scalar ratio below current observational upper limits, are especially vulnerable to anti-ultralocality effects. The reasons are the flatness of the plateau and the energy density gap of $\sim 10$ orders of magnitude between the Planck density and the plateau potential energy. To study the problem, we develop a protocol for assessing the viability of inflationary models in general, and we apply it to a plateau potential using a previously validated numerical relativity code. We find that, starting from generic initial conditions, the growth of gradient terms in the Einstein equations relative to non-gradient terms either prevents inflation from lasting for enough $e$-folds or triggers a phase of quantum runaway. We show that the fine-tuning of initial conditions necessary to avoid these issues becomes more severe as the energy scale of inflation is made smaller, disfavoring common approaches for reducing the tensor-to-scalar ratio.

FOS: Physical sciences↗
NASA NTRS2007

Accurate Waveforms for Non-spinning Binary Black Holes using the Effective-one-body Approach

Using numerical relativity as guidance and the natural flexibility of the effective-one-body (EOB) model, we extend the latter so that it can successfully match the numerical relativity waveforms of non-spinning binary black holes during the last stages of inspiral, merger and ringdown. Here, by successfully, we mean with phase differences < or approx. 8% of a gravitational-wave cycle accumulated until the end of the ringdown phase. We obtain this result by simply adding a 4 post-Newtonian order correction in the EOB radial potential and determining the (constant) coefficient by imposing high-matching performances with numerical waveforms of mass ratios m1/m2 = 1,2/3,1/2 and = 1/4, m1 and m2 being the individual black-hole masses. The final black-hole mass and spin predicted by the numerical simulations are used to determine the ringdown frequency and decay time of three quasi-normal-mode damped sinusoids that are attached to the EOB inspiral-(plunge) waveform at the light-ring. The accurate EOB waveforms may be employed for coherent searches of gravitational waves emitted by non-spinning coalescing binary black holes with ground-based laser-interferometer detectors.

Buonanno, Alessandra↗