26 research outputs found
Gravitational-wave detectability of equal-mass black-hole binaries with aligned spins
Binary black-hole systems with spins aligned or anti-aligned to the orbital
angular momentum provide the natural ground to start detailed studies of the
influence of strong-field spin effects on gravitational wave observations of
coalescing binaries. Furthermore, such systems may be the preferred end-state
of the inspiral of generic supermassive binary black-hole systems. In view of
this, we have computed the inspiral and merger of a large set of binary systems
of equal-mass black holes with spins parallel to the orbital angular momentum
but otherwise arbitrary. Our attention is particularly focused on the
gravitational-wave emission so as to quantify how much spin effects contribute
to the signal-to-noise ratio, to the horizon distances, and to the relative
event rates for the representative ranges in masses and detectors. As expected,
the signal-to-noise ratio increases with the projection of the total black hole
spin in the direction of the orbital momentum. We find that equal-spin binaries
with maximum spin aligned with the orbital angular momentum are more than
"three times as loud" as the corresponding binaries with anti-aligned spins,
thus corresponding to event rates up to 30 times larger. We also consider the
waveform mismatch between the different spinning configurations and find that,
within our numerical accuracy, binaries with opposite spins S_1=-S_2 cannot be
distinguished whereas binaries with spin S_1=S_2 have clearly distinct
gravitational-wave emissions. Finally, we derive a simple expression for the
energy radiated in gravitational waves and find that the binaries always have
efficiencies E_rad/M > 3.6%, which can become as large as E_rad/M = 10% for
maximally spinning binaries with spins aligned with the orbital angular
momentum.Comment: 18 pages, 11 figures, matches published versio
A numerical study of the quasinormal mode excitation of Kerr black holes
We present numerical results from three-dimensional evolutions of scalar perturbations of Kerr black holes. Our simulations make use of a high-order accurate multi-block code which naturally allows for fixed adaptivity and smooth inner (excision) and outer boundaries. We focus on the quasinormal ringing phase, presenting a systematic method for extraction of the quasinormal mode frequencies and amplitudes and comparing our results against perturbation theory. The amplitude of each mode depends exponentially on the starting time of the quasinormal regime, which is not defined unambiguously. We show that this time-shift problem can be circumvented by looking at appropriately chosen relative mode amplitudes. From our simulations we extract the quasinormal frequencies and the relative and absolute amplitudes of corotating and counterrotating modes (including overtones in the corotating case). We study the dependence of these amplitudes on the shape of the initial perturbation, the angular dependence of the mode and the black hole spin, comparing against results from perturbation theory in the so-called asymptotic approximation. We also compare the quasinormal frequencies from our numerical simulations with predictions from perturbation theory, finding excellent agreement. Finally we study under what conditions the relative amplitude between given pairs of modes gets maximally excited and present a quantitative analysis of rotational mode-mode coupling. The main conclusions and techniques of our analysis are quite general and, as such, should be of interest in the study of ringdown gravitational waves produced by astrophysical gravitational wave sources
High accuracy binary black hole simulations with an extended wave zone
We present results from a new code for binary black hole evolutions using the
moving-puncture approach, implementing finite differences in generalised
coordinates, and allowing the spacetime to be covered with multiple
communicating non-singular coordinate patches. Here we consider a regular
Cartesian near zone, with adapted spherical grids covering the wave zone. The
efficiencies resulting from the use of adapted coordinates allow us to maintain
sufficient grid resolution to an artificial outer boundary location which is
causally disconnected from the measurement. For the well-studied test-case of
the inspiral of an equal-mass non-spinning binary (evolved for more than 8
orbits before merger), we determine the phase and amplitude to numerical
accuracies better than 0.010% and 0.090% during inspiral, respectively, and
0.003% and 0.153% during merger. The waveforms, including the resolved higher
harmonics, are convergent and can be consistently extrapolated to
throughout the simulation, including the merger and ringdown. Ringdown
frequencies for these modes (to ) match perturbative
calculations to within 0.01%, providing a strong confirmation that the remnant
settles to a Kerr black hole with irreducible mass and spin $S_f/M_f^2 = 0.686923 \pm 10\times10^{-6}
Inspiral-merger-ringdown waveforms for black-hole binaries with non-precessing spins
We present the first analytical inspiral-merger-ringdown gravitational
waveforms from binary black holes (BBHs) with non-precessing spins, that is
based on a description of the late-inspiral, merger and ringdown in full
general relativity. By matching a post-Newtonian description of the inspiral to
a set of numerical-relativity simulations, we obtain a waveform family with a
conveniently small number of physical parameters. These waveforms will allow us
to detect a larger parameter space of BBH coalescence, including a considerable
fraction of precessing binaries in the comparable-mass regime, thus
significantly improving the expected detection rates.Comment: To appear in Phys. Rev. Lett. Significant new results. One figure
removed due to page limitatio
Initial data transients in binary black hole evolutions
We describe a method for initializing characteristic evolutions of the
Einstein equations using a linearized solution corresponding to purely outgoing
radiation. This allows for a more consistent application of the characteristic
(null cone) techniques for invariantly determining the gravitational radiation
content of numerical simulations. In addition, we are able to identify the {\em
ingoing} radiation contained in the characteristic initial data, as well as in
the initial data of the 3+1 simulation. We find that each component leads to a
small but long lasting (several hundred mass scales) transient in the measured
outgoing gravitational waves.Comment: 18 pages, 4 figure
The [N II] Kinematics of R Aquarii
We report a kinematic study of the symbiotic star system R Aqr derived from [N H]lambda 6584 emission observations with a Fabry-Perot imaging spectrometer. The [N II] spatial structure of the R Aqr jet, first observed circa 1977, and surrounding hourglass-shaped nebulosity, due to an explosion approximately 660 years ago, are derived from 41 velocity planes spaced at approximately 12 km/s intervals. Fabry-Perot imagery shows the elliptical nebulosity comprising the waist of the hourglass shell is consistent with a circular ring expanding radially at 55 km/s as seen at an inclination angle, i approximately 70 deg. Fabry-Perot imagery shows the two-sided R Aqr jet is collimated flow in opposite directions. The intensity-velocity structure of the strong NE jet component is shown in contrast to the amorphous SW jet component. We offer a idealized schematic model for the R Aqr jet motion which results in a small-scale helical structure forming around a larger-scale helical path. The implications of such a jet model are discussed. We present a movie showing a side-by-side comparison of the spatial structure of the model and the data as a function of the 41 velocity planes
Effective source approach to self-force calculations
Numerical evaluation of the self-force on a point particle is made difficult
by the use of delta functions as sources. Recent methods for self-force
calculations avoid delta functions altogether, using instead a finite and
extended "effective source" for a point particle. We provide a review of the
general principles underlying this strategy, using the specific example of a
scalar point charge moving in a black hole spacetime. We also report on two new
developments: (i) the construction and evaluation of an effective source for a
scalar charge moving along a generic orbit of an arbitrary spacetime, and (ii)
the successful implementation of hyperboloidal slicing that significantly
improves on previous treatments of boundary conditions used for
effective-source-based self-force calculations. Finally, we identify some of
the key issues related to the effective source approach that will need to be
addressed by future work.Comment: Invited review for NRDA/Capra 2010 (Theory Meets Data Analysis at
Comparable and Extreme Mass Ratios), Perimeter Institute, June 2010, CQG
special issue - 22 pages, 8 figure
Matching post-Newtonian and numerical relativity waveforms: systematic errors and a new phenomenological model for non-precessing black hole binaries
We present a new phenomenological gravitational waveform model for the
inspiral and coalescence of non-precessing spinning black hole binaries. Our
approach is based on a frequency domain matching of post-Newtonian inspiral
waveforms with numerical relativity based binary black hole coalescence
waveforms. We quantify the various possible sources of systematic errors that
arise in matching post-Newtonian and numerical relativity waveforms, and we use
a matching criteria based on minimizing these errors; we find that the dominant
source of errors are those in the post-Newtonian waveforms near the merger. An
analytical formula for the dominant mode of the gravitational radiation of
non-precessing black hole binaries is presented that captures the phenomenology
of the hybrid waveforms. Its implementation in the current searches for
gravitational waves should allow cross-checks of other inspiral-merger-ringdown
waveform families and improve the reach of gravitational wave searches.Comment: 22 pages, 11 figure
Numerical relativity with characteristic evolution, using six angular patches
The characteristic approach to numerical relativity is a useful tool in
evolving gravitational systems. In the past this has been implemented using two
patches of stereographic angular coordinates. In other applications, a
six-patch angular coordinate system has proved effective. Here we investigate
the use of a six-patch system in characteristic numerical relativity, by
comparing an existing two-patch implementation (using second-order finite
differencing throughout) with a new six-patch implementation (using either
second- or fourth-order finite differencing for the angular derivatives). We
compare these different codes by monitoring the Einstein constraint equations,
numerically evaluated independently from the evolution. We find that, compared
to the (second-order) two-patch code at equivalent resolutions, the errors of
the second-order six-patch code are smaller by a factor of about 2, and the
errors of the fourth-order six-patch code are smaller by a factor of nearly 50.Comment: 12 pages, 5 figures, submitted to CQG (special NFNR issue
Characteristic extraction in numerical relativity: binary black hole merger waveforms at null infinity
The accurate modeling of gravitational radiation is a key issue for
gravitational wave astronomy. As simulation codes reach higher accuracy,
systematic errors inherent in current numerical relativity wave-extraction
methods become evident, and may lead to a wrong astrophysical interpretation of
the data. In this paper, we give a detailed description of the
Cauchy-characteristic extraction technique applied to binary black hole
inspiral and merger evolutions to obtain gravitational waveforms that are
defined unambiguously, that is, at future null infinity. By this method we
remove finite-radius approximations and the need to extrapolate data from the
near zone. Further, we demonstrate that the method is free of gauge effects and
thus is affected only by numerical error. Various consistency checks reveal
that energy and angular momentum are conserved to high precision and agree very
well with extrapolated data. In addition, we revisit the computation of the
gravitational recoil and find that finite radius extrapolation very well
approximates the result at \scri. However, the (non-convergent) systematic
differences to extrapolated data are of the same order of magnitude as the
(convergent) discretisation error of the Cauchy evolution hence highlighting
the need for correct wave-extraction.Comment: 41 pages, 8 figures, 2 tables, added references, fixed typos. Version
matches published version