108 research outputs found
Numerical Integration of Nonlinear Wave Equations for General Relativity
A second-order numerical implementation is given for recently derived
nonlinear wave equations for general relativity. The Gowdy T cosmology is
used as a test bed for studying the accuracy and convergence of simulations of
one-dimensional nonlinear waves. The complete freedom in space-time slicing in
the present formulation is exploited to compute in the Gowdy line-element.
Second-order convergence is found by direct comparison of the results with
either analytical solutions for polarized waves, or solutions obtained from
Gowdy's reduced wave equations for the more general unpolarized waves. Some
directions for extensions are discussed.Comment: 19 pages (LaTex), 3 figures (ps
Gravitational radiation from gamma-ray bursts as observational opportunities for LIGO and VIRGO
Gamma-ray bursts are believed to originate in core-collapse of massive stars.
This produces an active nucleus containing a rapidly rotating Kerr black hole
surrounded by a uniformly magnetized torus represented by two counter-oriented
current rings. We quantify black hole spin-interactions with the torus and
charged particles along open magnetic flux-tubes subtended by the event
horizon. A major output of Egw=4e53 erg is radiated in gravitational waves of
frequency fgw=500 Hz by a quadrupole mass-moment in the torus. Consistent with
GRB-SNe, we find (i) Ts=90s (tens of s, Kouveliotou et al. 1993), (ii)
aspherical SNe of kinetic energy Esn=2e51 erg (2e51 erg in SN1998bw, Hoeflich
et al. 1999) and (iii) GRB-energies Egamma=2e50 erg (3e50erg in Frail et al.
2001). GRB-SNe occur perhaps about once a year within D=100Mpc. Correlating
LIGO/Virgo detectors enables searches for nearby events and their spectral
closure density 6e-9 around 250Hz in the stochastic background radiation in
gravitational waves. At current sensitivity, LIGO-Hanford may place an upper
bound around 150MSolar in GRB030329. Detection of Egw thus provides a method
for identifying Kerr black holes by calorimetry.Comment: to appear in PRD, 49
An -frequency dynamics algorithm for gravitational waves
Coalescence of low mass compact binaries of neutron stars and black holes are
primary burst sources for LIGO and VIRGO.Of importance in the early stages of
observations will be the classification of candidate detections by source-type.
The diversity in source parameters and serendipity in any new window of
observations suggest to consider model-independent detection algorithms. Here a
frequency dynamics algorithm is described which extracts a trajectory in the
-plane from the noisy signal. The algorithm is studied in simulated
binary coalescence. Robust results are obtained with experimental noise data.
Experiments show the method to be superior to matched filtering in the presence
of model imperfections.Comment: to appear in Rapid Commun, Phys Rev
Non-vanishing Magnetic Flux through the Slightly-charged Kerr Black Hole
In association with the Blanford-Znajek mechanism for rotational energy
extraction from Kerr black holes, it is of some interest to explore how much of
magnetic flux can actually penetrate the horizon at least in idealized
situations. For completely uncharged Kerr hole case, it has been known for some
time that the magnetic flux gets entirely expelled when the hole is
maximally-rotating. In the mean time, it is known that when the rotating hole
is immersed in an originally uniform magnetic field surrounded by an ionized
interstellar medium (plasma), which is a more realistic situation, the hole
accretes certain amount of electric charge. In the present work, it is
demonstrated that as a result of this accretion charge small enough not to
disturb the geometry, the magnetic flux through this slightly charged Kerr hole
depends not only on the hole's angular momentum but on the hole's charge as
well such that it never vanishes for any value of the hole's angular momentum.Comment: 33pages, 1 figure, Revtex, some comments added, typos correcte
Extending the lifetime of 3D black hole computations with a new hyperbolic system of evolution equations
We present a new many-parameter family of hyperbolic representations of
Einstein's equations, which we obtain by a straightforward generalization of
previously known systems. We solve the resulting evolution equations
numerically for a Schwarzschild black hole in three spatial dimensions, and
find that the stability of the simulation is strongly dependent on the form of
the equations (i.e. the choice of parameters of the hyperbolic system),
independent of the numerics. For an appropriate range of parameters we can
evolve a single 3D black hole to -- , and are
apparently limited by constraint-violating solutions of the evolution
equations. We expect that our method should result in comparable times for
evolutions of a binary black hole system.Comment: 11 pages, 2 figures, submitted to PR
Energy Norms and the Stability of the Einstein Evolution Equations
The Einstein evolution equations may be written in a variety of equivalent
analytical forms, but numerical solutions of these different formulations
display a wide range of growth rates for constraint violations. For symmetric
hyperbolic formulations of the equations, an exact expression for the growth
rate is derived using an energy norm. This expression agrees with the growth
rate determined by numerical solution of the equations. An approximate method
for estimating the growth rate is also derived. This estimate can be evaluated
algebraically from the initial data, and is shown to exhibit qualitatively the
same dependence as the numerically-determined rate on the parameters that
specify the formulation of the equations. This simple rate estimate therefore
provides a useful tool for finding the most well-behaved forms of the evolution
equations.Comment: Corrected typos; to appear in Physical Review
Magnetic Reconnection in Extreme Astrophysical Environments
Magnetic reconnection is a basic plasma process of dramatic rearrangement of
magnetic topology, often leading to a violent release of magnetic energy. It is
important in magnetic fusion and in space and solar physics --- areas that have
so far provided the context for most of reconnection research. Importantly,
these environments consist just of electrons and ions and the dissipated energy
always stays with the plasma. In contrast, in this paper I introduce a new
direction of research, motivated by several important problems in high-energy
astrophysics --- reconnection in high energy density (HED) radiative plasmas,
where radiation pressure and radiative cooling become dominant factors in the
pressure and energy balance. I identify the key processes distinguishing HED
reconnection: special-relativistic effects; radiative effects (radiative
cooling, radiation pressure, and Compton resistivity); and, at the most extreme
end, QED effects, including pair creation. I then discuss the main
astrophysical applications --- situations with magnetar-strength fields
(exceeding the quantum critical field of about 4 x 10^13 G): giant SGR flares
and magnetically-powered central engines and jets of GRBs. Here, magnetic
energy density is so high that its dissipation heats the plasma to MeV
temperatures. Electron-positron pairs are then copiously produced, making the
reconnection layer highly collisional and dressing it in a thick pair coat that
traps radiation. The pressure is dominated by radiation and pairs. Yet,
radiation diffusion across the layer may be faster than the global Alfv\'en
transit time; then, radiative cooling governs the thermodynamics and
reconnection becomes a radiative transfer problem, greatly affected by the
ultra-strong magnetic field. This overall picture is very different from our
traditional picture of reconnection and thus represents a new frontier in
reconnection research.Comment: Accepted to Space Science Reviews (special issue on magnetic
reconnection). Article is based on an invited review talk at the
Yosemite-2010 Workshop on Magnetic Reconnection (Yosemite NP, CA, USA;
February 8-12, 2010). 30 pages, no figure
Relativistic Hydrodynamic Evolutions with Black Hole Excision
We present a numerical code designed to study astrophysical phenomena
involving dynamical spacetimes containing black holes in the presence of
relativistic hydrodynamic matter. We present evolutions of the collapse of a
fluid star from the onset of collapse to the settling of the resulting black
hole to a final stationary state. In order to evolve stably after the black
hole forms, we excise a region inside the hole before a singularity is
encountered. This excision region is introduced after the appearance of an
apparent horizon, but while a significant amount of matter remains outside the
hole. We test our code by evolving accurately a vacuum Schwarzschild black
hole, a relativistic Bondi accretion flow onto a black hole, Oppenheimer-Snyder
dust collapse, and the collapse of nonrotating and rotating stars. These
systems are tracked reliably for hundreds of M following excision, where M is
the mass of the black hole. We perform these tests both in axisymmetry and in
full 3+1 dimensions. We then apply our code to study the effect of the stellar
spin parameter J/M^2 on the final outcome of gravitational collapse of rapidly
rotating n = 1 polytropes. We find that a black hole forms only if J/M^2<1, in
agreement with previous simulations. When J/M^2>1, the collapsing star forms a
torus which fragments into nonaxisymmetric clumps, capable of generating
appreciable ``splash'' gravitational radiation.Comment: 17 pages, 14 figures, submitted to PR
Search for Gravitational Waves Associated with Gamma-Ray Bursts Detected by Fermi and Swift during the LIGO-Virgo Run O3b
We search for gravitational-wave signals associated with gamma-ray bursts (GRBs) detected by the Fermi and Swift satellites during the second half of the third observing run of Advanced LIGO and Advanced Virgo (2019 November 1 15:00 UTC-2020 March 27 17:00 UTC). We conduct two independent searches: A generic gravitational-wave transients search to analyze 86 GRBs and an analysis to target binary mergers with at least one neutron star as short GRB progenitors for 17 events. We find no significant evidence for gravitational-wave signals associated with any of these GRBs. A weighted binomial test of the combined results finds no evidence for subthreshold gravitational-wave signals associated with this GRB ensemble either. We use several source types and signal morphologies during the searches, resulting in lower bounds on the estimated distance to each GRB. Finally, we constrain the population of low-luminosity short GRBs using results from the first to the third observing runs of Advanced LIGO and Advanced Virgo. The resulting population is in accordance with the local binary neutron star merger rate. © 2022. The Author(s). Published by the American Astronomical Society
Narrowband Searches for Continuous and Long-duration Transient Gravitational Waves from Known Pulsars in the LIGO-Virgo Third Observing Run
Isolated neutron stars that are asymmetric with respect to their spin axis are possible sources of detectable continuous gravitational waves. This paper presents a fully coherent search for such signals from eighteen pulsars in data from LIGO and Virgo's third observing run (O3). For known pulsars, efficient and sensitive matched-filter searches can be carried out if one assumes the gravitational radiation is phase-locked to the electromagnetic emission. In the search presented here, we relax this assumption and allow both the frequency and the time derivative of the frequency of the gravitational waves to vary in a small range around those inferred from electromagnetic observations. We find no evidence for continuous gravitational waves, and set upper limits on the strain amplitude for each target. These limits are more constraining for seven of the targets than the spin-down limit defined by ascribing all rotational energy loss to gravitational radiation. In an additional search, we look in O3 data for long-duration (hours-months) transient gravitational waves in the aftermath of pulsar glitches for six targets with a total of nine glitches. We report two marginal outliers from this search, but find no clear evidence for such emission either. The resulting duration-dependent strain upper limits do not surpass indirect energy constraints for any of these targets. © 2022. The Author(s). Published by the American Astronomical Society
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