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P. Laguna

Publications and source records attributed to P. Laguna.

16 recordsLinked to original sources
arXiv2008

Binary Black Hole Encounters, Gravitational Bursts and Maximum Final Spin

The spin of the final black hole in the coalescence of nonspinning black holes is determined by the ``residual'' orbital angular momentum of the binary. This residual momentum consists of the orbital angular momentum that the binary is not able to shed in the process of merging. We study the angular momentum radiated, the spin of the final black hole and the gravitational bursts in a series of orbits ranging from almost direct infall to numerous orbits before infall that exhibit multiple bursts of radiation in the merger process. We show that the final black hole gets a maximum spin parameter $a/M_h \le 0.78$, and this maximum occurs for initial orbital angular momentum $L \approx M^2_h$.

gr-qc↗
arXiv2007

Unequal Mass Binary Black Hole Plunges and Gravitational Recoil

We present results from fully nonlinear simulations of unequal mass binary black holes plunging from close separations well inside the innermost stable circular orbit with mass ratios q = M_1/M_2 = {1,0.85,0.78,0.55,0.32}, or equivalently, with reduced mass parameters $η=M_1M_2/(M_1+M_2)^2 = {0.25, 0.248, 0.246, 0.229, 0.183}$. For each case, the initial binary orbital parameters are chosen from the Cook-Baumgarte equal-mass ISCO configuration. We show waveforms of the dominant l=2,3 modes and compute estimates of energy and angular momentum radiated. For the plunges from the close separations considered, we measure kick velocities from gravitational radiation recoil in the range 25-82 km/s. Due to the initial close separations our kick velocity estimates should be understood as a lower bound. The close configurations considered are also likely to contain significant eccentricities influencing the recoil velocity.

gr-qc↗
arXiv2005

Black hole head-on collisions and gravitational waves with fixed mesh-refinement and dynamic singularity excision

We present long-term-stable and convergent evolutions of head-on black hole collisions and extraction of gravitational waves generated during the merger and subsequent ring-down. The new ingredients in this work are the use of fixed mesh-refinement and dynamical singularity excision techniques. We are able to carry out head-on collisions with large initial separations and demonstrate that our excision infrastructure is capable of accommodating the motion of the individual black holes across the computational domain as well as their their merger. We extract gravitational waves from these simulations using the Zerilli-Moncrief formalism and find the ring-down radiation to be, as expected, dominated by the l=2, m=0 quasi-normal mode. The total radiated energy is about 0.1 % of the total ADM mass of the system.

gr-qc↗
arXiv2003

Impact of densitized lapse slicings on evolutions of a wobbling black hole

We present long-term stable and second-order convergent evolutions of an excised wobbling black hole. Our results clearly demonstrate that the use of a densitized lapse function extends the lifetime of simulations dramatically. We also show the improvement in the stability of single static black holes when an algebraic densitized lapse condition is applied. In addition, we introduce a computationally inexpensive approach for tracking the location of the singularity suitable for mildly distorted black holes. The method is based on investigating the fall-off behavior and asymmetry of appropriate grid variables. This simple tracking method allows one to adjust the location of the excision region to follow the coordinate motion of the singularity.

gr-qc↗
arXiv2003

Moving black holes via singularity excision

We present a singularity excision algorithm appropriate for numerical simulations of black holes moving throughout the computational domain. The method is an extension of the excision procedure previously used to obtain stable simulations of single, non-moving black holes. The excision procedure also shares elements used in recent work to study the dynamics of a scalarfield in the background of a single, boosted black hole. The robustness of our excision method is tested with single black-hole evolutions using a coordinate system in which the coordinate location of the black hole, and thus the excision boundary, moves throughout the computational domain.

gr-qc↗
arXiv2000

Approximate Analytical Solutions to the Initial Data Problem of Black Hole Binary Systems

We present approximate analytical solutions to the Hamiltonian and momentum constraint equations, corresponding to systems composed of two black holes with arbitrary linear and angular momentum. The analytical nature of these initial data solutions makes them easier to implement in numerical evolutions than the traditional numerical approach of solving the elliptic equations derived from the Einstein constraints. Although in general the problem of setting up initial conditions for black hole binary simulations is complicated by the presence of singularities, we show that the methods presented in this work provide initial data with $l_1$ and $l_\infty$ norms of violation of the constraint equations falling below those of the truncation error (residual error due to discretization) present in finite difference codes for the range of grid resolutions currently used. Thus, these data sets are suitable for use in evolution codes. Detailed results are presented for the case of a head-on collision of two equal-mass M black holes with specific angular momentum 0.5M at an initial separation of 10M. A straightforward superposition method yields data adequate for resolutions of $h=M/4$, and an "attenuated" superposition yields data usable to resolutions at least as fine as $h=M/8$. In addition, the attenuated approximate data may be more tractable in a full (computational) exact solution to the initial value problem.

gr-qc↗
arXiv1999

The close-limit approximation to Neutron Star Collisions

We develop a close-limit approximation to the head-on collision of two neutron stars similar to that used to treat the merger of black hole binaries . This approximation can serve as a useful benchmark test for future fully nonlinear studies. For neutron star binaries, the close-limit approximation involves assuming that the merged object can be approximated as a perturbed, stable neutron star during the ring-down phase of the coalescence. We introduce a prescription for the construction of initial data sets, discuss the physical plausibility of the various assumptions involved, and briefly investigate the character of the gravitational radiation produced during the merger. The numerical results show that several of the merged objects fluid pulsation modes are excited to a significant level.

gr-qc↗
arXiv1997

Boosted three-dimensional black-hole evolutions with singularity excision

Binary black hole interactions provide potentially the strongest source of gravitational radiation for detectors currently under development. We present some results from the Binary Black Hole Grand Challenge Alliance three- dimensional Cauchy evolution module. These constitute essential steps towards modeling such interactions and predicting gravitational radiation waveforms. We report on single black hole evolutions and the first successful demonstration of a black hole moving freely through a three-dimensional computational grid via a Cauchy evolution: a hole moving ~6M at 0.1c during a total evolution of duration ~60M.

gr-qc↗
arXiv1997

Gravitational wave extraction and outer boundary conditions by perturbative matching

We present a method for extracting gravitational radiation from a three-dimensional numerical relativity simulation and, using the extracted data, to provide outer boundary conditions. The method treats dynamical gravitational variables as nonspherical perturbations of Schwarzschild geometry. We discuss a code which implements this method and present results of tests which have been performed with a three dimensional numerical relativity code.

gr-qc↗
arXiv1997

A Shock-Patching Code for Ultra-Relativistic Fluid Flows

We have developed a one-dimensional code to solve ultra-relativistic hydrodynamic problems, using the Glimm method for an accurate treatment of shocks and contact discontinuities. The implementation of the Glimm method is based on an exact Riemann solver and van der Corput sampling sequence. In order to improve computational efficiency, the Glimm method is replaced by a finite differencing scheme in those regions where the fluid flow is sufficiently smooth. The accuracy and convergence of this hybrid method is investigated in tests involving planar, cylindrically and spherically symmetric flows that exhibit strong shocks and Lorentz factors of up to ~2000. This hybrid code has proven to be successful in simulating the interaction between a thin, ultra-relativistic, spherical shell and a low density stationary medium, a situation likely to appear in Gamma-Ray Bursts, supernovae explosions, pulsar winds and AGNs.

astro-ph↗
arXiv1997

Impact of Relativistic Fireballs on External Matter : Numerical Models of Cosmological Gamma-Ray Bursts

We numerically model the interaction between an expanding fireball and a stationary external medium whose density is either homogeneous or varies with distance as a power-law. The evolution is followed until most of the fireball kinetic energy is converted into internal energy. The density, pressure and flow Lorentz factor profiles are shown at different stages, including shock and rarefaction wave reflections, for a fireball of initial bulk Lorentz factor Gamma = 100, both in the adiabatic and non-adiabatic (radiative) regimes. For cooling times shorter than the dynamic time, bolometric light-curves are computed for values of Gamma = 50, 100 and 200. We compare the numerical light-curves with analytic results, and find that for a homogeneous external medium there is a simple scaling relationship among light-curves obtained for different parameters. The light-curves for power-law external densities are similar in shape to those in the homogeneous case. We discuss the implications of a comparison of the results with observed Gamma-Ray Burst time histories.

astro-ph↗
arXiv1997

Dynamics of perturbations of rotating black holes

We present a numerical study of the time evolution of perturbations of rotating black holes. The solutions are obtained by integrating the Teukolsky equation written as a first-order in time, coupled system of equations, in a form that explicitly captures its hyperbolic structure. We address the numerical difficulties of solving the equation in its original form. We follow the propagation of generic initial data through the burst, quasinormal ringing and power-law tail phases. In particular, we calculate the effects due to the rotation of the black hole on the scattering of incident gravitational wave pulses. These results may help explain how the angular momentum of the black hole affects the gravitational waves that are generated during the final stages of black hole coalescence.

gr-qc↗
arXiv1997

Dynamics of spin-2 fields in Kerr background geometries

We have developed a numerical method for evolving perturbations of rotating black holes. Solutions are obtained by integrating the Teukolsky equation written as a first-order in time, coupled system of equations, in a form that explicitly exhibits the radial characteristic directions. We follow the propagation of generic initial data through the burst, quasi-normal ringing and power-law tail phases. Future results may help to clarify the role of black hole angular momentum on signals produced during the final stages of black hole coalescence.

gr-qc↗
arXiv1996

Dynamics of Scalar Fields in the Background of Rotating Black Holes

A numerical study of the evolution of a massless scalar field in the background of rotating black holes is presented. First, solutions to the wave equation are obtained for slowly rotating black holes. In this approximation, the background geometry is treated as a perturbed Schwarzschild spacetime with the angular momentum per unit mass playing the role of a perturbative parameter. To first order in the angular momentum of the black hole, the scalar wave equation yields two coupled one-dimensional evolution equations for a function representing the scalar field in the Schwarzschild background and a second field that accounts for the rotation. Solutions to the wave equation are also obtained for rapidly rotating black holes. In this case, the wave equation does not admit complete separation of variables and yields a two-dimensional evolution equation. The study shows that, for rotating black holes, the late time dynamics of a massless scalar field exhibit the same power-law behavior as in the case of a Schwarzschild background independently of the angular momentum of the black hole.

gr-qc↗
arXiv1993

Gasdynamics of Relativistically Expanding Gamma-Ray Burst Sources: Kinematics, Energetics, Magnetic Fields and Efficiency

We calculate both analytically and numerically the evolution of a highly relativistic fireball through the stages of free expansion and coasting, and determine the dependence of the thermodynamic and radiation variables in the comoving and laboratory frames. Magnetic fields may have been important in the original impulsive event. We discuss their effect on the fireball dynamics, and consider also their effects on the radiation emitted when the fireball runs into an external medium and is decelerated. The inverse synchro-Compton mechanism can then yield high radiative efficiency in the reverse shock, producing a burst of non-thermal radiation mainly in the MeV to GeV range whose total energy and duration agree with those of typical cosmic gamma ray bursts.

astro-ph↗