Gravitational Wave Energy Research Articles

Confusion noise from LISA capture sources

Captures of compact objects (COs) by massive black holes (MBHs) in galactic nuclei will be an important source for LISA, the space-based gravitational-wave (GW) detector. However, a large fraction of captures will not be individually resolvable--either because they are too distant, have unfavorable orientation, or have too many years to go before final plunge--and so will constitute a source of ``confusion noise,'' obscuring other types of sources. Here we estimate the shape and overall magnitude of the spectrum of confusion noise from CO captures. The overall magnitude depends on the capture rates, which are rather uncertain, so we present results for a plausible range of rates. We show that the impact of capture confusion noise on the total LISA noise curve ranges from insignificant to modest, depending on these rates. Capture rates at the high end of estimated ranges would raise LISA's overall (effective) noise level by at most a factor \sim 2. While this slightly elevated noise level would somewhat decrease LISA's sensitivity to other classes of sources, overall, this would be a pleasant problem for LISA to have: It would also imply that detection rates for CO captures were at nearly their maximum possible levels (given LISA's baseline design). This paper includes several other results that should be useful in further studies of LISA capture sources, including (i) a calculation of the total GW energy output from generic inspirals into Kerr MBHs, and (ii) an approximate GW energy spectrum for a typical capture.

Massive black hole remnants of the first stars - III. Observational signatures from the past

The first stars forming in minihaloes at redshifts greater than 20 may have been very massive and could have left behind massive black hole (MBH) remnants. In previous papers we investigated the hierarchical merging of these `seed' MBHs and their associated haloes, using a semi-analytical approach consisting of a hierarchical merger tree algorithm and explicit prescriptions for the dynamics of merged substructure inside a larger host halo following a merger. We also estimated accretion luminosities for these MBHs and found them to be consistent with observations of ultra-luminous X-ray point sources. Here we compute the strength of gravitational wave events as MBHs merge to grow from seed mass MBH at high redshifts to those that we predict to reside in galaxy haloes today. If MBHs merge efficiently we predict that some 10^4 - 10^5 events per year could be observed, that fall just within the sensitivity limits of the proposed LISA gravitational wave observatory. The collapse of the first massive stars to form MBHs may be accompanied by gamma ray bursts (GRBs). If this is the case and GRBs are in principle observable out to the redshifts of first star formation, we find that about 10^5 - 10^6 GRBs per year could be detected. As merging MBH binaries reach their last stable orbits before final coalescence a fraction of the gravitational wave energy may be released as a pulse of gamma rays (for instance, through interaction with material enveloping a merging MBH binary). This fraction has to be in the range between 10^{-14} - 10^{-10} for MBH mergers to be less luminous than GBRs, yet detectable out to cosmological distances with upcoming GRB detector missions.

Analysis of first LIGO science data for stochastic gravitational waves

We present the analysis of between 50 and 100 h of coincident interferometric strain data used to search for and establish an upper limit on a stochastic background of gravitational radiation. These data come from the first LIGO science run, during which all three LIGO interferometers were operated over a 2-week period spanning August and September of 2002. The method of cross correlating the outputs of two interferometers is used for analysis. We describe in detail practical signal processing issues that arise when working with real data, and we establish an observational upper limit on a f^-3 power spectrum of gravitational waves. Our 90% confidence limit is Ω0h100(^2)<~23±4.6 in the frequency band 40–314 Hz, where h100 is the Hubble constant in units of 100 km/sec/Mpc and Ω0 is the gravitational wave energy density per logarithmic frequency interval in units of the closure density. This limit is approximately 104 times better than the previous, broadband direct limit using interferometric detectors, and nearly 3 times better than the best narrow-band bar detector limit. As LIGO and other worldwide detectors improve in sensitivity and attain their design goals, the analysis procedures described here should lead to stochastic background sensitivity levels of astrophysical interest.

Self-phase modulation of spherical gravitational waves

Self-phase modulation of spherical gravitational wavepackets propagating in a flat space-time in the presence of a tenuous distribution of matter is considered. Analogies with respect to similar effects in nonlinear optics are explored. Self phase modulation of waves emitted from a single source can eventually lead to an efficient energy dilution of the gravitational wave energy over an increasingly large spectral range. An explicit criterium for the occurrence of a significant spectral energy dilution is established.

Correlation between gamma ray bursts and gravitational wave bursts: the AURIGA complete data analysis

A widely accepted paradigm for astrophysical models of gamma ray bursts (GRB) prescribes a compact ‘central engine’ dominated by gravitational interactions, and therefore a concurrent emission of GRBs and gravitational wave bursts is likely to occur. Consequently, we have tested a novel and reliable method for searching for time correlation in the AURIGA and BATSE complete dataset. The analysis covers the period 1997–1999. The obtained upper limit on the averaged gravitational wave energy released in a neighbourhood of 300 s around the GRB triggers is hRMS = 1.8 × 10−18 at 95% confidence level. We also estimate the minimum statistical coverage of confidence levels for a frequentist interpretation of our upper limit.

Detection methods for non-Gaussian gravitational wave stochastic backgrounds

A gravitational wave stochastic background can be produced by a collection of independent gravitational wave events. There are two classes of such backgrounds, one for which the ratio of the average time between events to the average duration of an event is small (i.e., many events are on at once), and one for which the ratio is large. In the first case the signal is continuous, sounds something like a constant $hiss,$ and has a Gaussian probability distribution. In the second case, the discontinuous or intermittent signal sounds something like popcorn popping, and is described by a non-Gaussian probability distribution. In this paper we address the issue of finding an optimal detection method for such a non-Gaussian background. As a first step, we examine the idealized situation in which the event durations are short compared to the detector sampling time, so that the time structure of the events cannot be resolved, and we assume white, Gaussian noise in two collocated, aligned detectors. For this situation we derive an appropriate version of the maximum likelihood detection statistic. We compare the performance of this statistic to that of the standard cross-correlation statistic both analytically and with Monte Carlo simulations. In general the maximum likelihood statistic performs better than the cross-correlation statistic when the stochastic background is sufficiently non-Gaussian, resulting in a gain factor in the minimum gravitational-wave energy density necessary for detection. This gain factor ranges roughly between 1 and 3, depending on the duty cycle of the background, for realistic observing times and signal strengths for both ground and space based detectors. The computational cost of the statistic, although significantly greater than that of the cross-correlation statistic, is not unreasonable. Before the statistic can be used in practice with real detector data, further work is required to generalize our analysis to accommodate separated, misaligned detectors with realistic, colored, non-Gaussian noise.

Gravitational optics: Self-phase modulation and harmonic cascades

Nonlinear wave interaction of low amplitude gravitational waves in flat space-time is considered. Analogy with optics is established. It is shown that the flat metric space-time is equivalent to a centro-symmetric optical medium, with no second order susceptibility. The lowest order nonlinear effects are those due to the third order nonlinearity and include self-phase modulation and high harmonic generation. These processes lead to an efficient energy dilution of the gravitational wave energy over an increasingly large spectral range.

Measuring neutron-star radii with gravitational-wave detectors.

Coalescing binary neutron stars (NS) are expected to be an important source of gravitational waves (GW) detectable by laser interferometers. We present here a simple method for determining the compactness ratio M/R of NS based on the observed deviation of the GW energy spectrum from point-mass behavior at the end of inspiral. Our method is based on the properties of quasiequilibrium binary NS sequences and does not require the computation of the full GW signal h(t). Combined with the measurement of the NS masses during inspiral, the determination of M/R will allow very strong constraints to be placed on the equation of state of dense nuclear matter.

A note on gravitational wave lensing

In a recent paper (Rua 1999) it was proposed that the massive black hole at the Galactic center may act as a gravitational lens focusing gravitational wave energy to the Earth. Considering the gravitational wave signal emitted by galactic spinning pulsars, an enhancement in the gravitational wave intensity by a factor of a few thousand is found. For galactic and extra-galactic sources the intensity enhancement can be as high as 4000 and 17 000, respectively. In this note we consider the probability of significant signal enhancement from galactic and extra-galactic pulsars by the proposed mechanism and find that it is actually negligible. The lensing eect due to a possible companion object (a star or the galactic center black hole) of the gravitational wave source is also investigated in the framework of the classical microlensing theory.

Wave — Jet Converters

The possibilities of conversion of the energy of gravitational surface waves in liquid into a constant reactive flow due to special nonlinear mechanical floating devices (wave-jet converters) are investigated. The last ensure rectification of wave pressure and the effect of wave traction. Physical problems of radiation and scattering wave pressure rectification are considered separately using the examples of concrete devices. A ship model of special construction has been designed and tested. This model effectively converts ship's pitching immediately into a constant jet flow without using any external sources of energy. The ship's motion is characterized by an average Froude number Fr=0.14 and average forward velocity exceeding the velocities of liquid particles in the wave field. This ship presents a uniflow wave jet propulsive device.

Comparing initial-data sets for binary black holes

We compare the results of constructing binary black hole initial data with three different decompositions of the constraint equations of general relativity. For each decomposition we compute the initial data using a superposition of two Kerr-Schild black holes to fix the freely specifiable data. We find that these initial-data sets differ significantly, with the ADM energy varying by as much as 5% of the total mass. We find that all initial-data sets currently used for evolutions might contain unphysical gravitational radiation of the order of several percent of the total mass. This is comparable to the amount of gravitational-wave energy observed during the evolved collision. More astrophysically realistic initial data will require more careful choices of the freely specifiable data and boundary conditions for both the metric and extrinsic curvature. However, we find that the choice of extrinsic curvature affects the resulting data sets more strongly than the choice of conformal metric.

Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries.

The article reviews the current status of a theoretical approach to the problem of the emission of gravitational waves by isolated systems in the context of general relativity. Part A of the article deals with general post-Newtonian sources. The exterior field of the source is investigated by means of a combination of analytic post-Minkowskian and multipolar approximations. The physical observables in the far-zone of the source are described by a specific set of radiative multipole moments. By matching the exterior solution to the metric of the post-Newtonian source in the near-zone we obtain the explicit expressions of the source multipole moments. The relationships between the radiative and source moments involve many nonlinear multipole interactions, among them those associated with the tails (and tails-of-tails of gravitational waves. Part B of the article is devoted to the application to compact binary systems. We present the equations of binary motion, and the associated Lagrangian and Hamiltonian, at the third post-Newtonian (3PN) order beyond the Newtonian acceleration. The gravitational-wave energy flux, taking consistently into account the relativistic corrections in the binary moments as well as the various tail effects, is derived through 3.5PN order with respect to the quadrupole formalism. The binary’s orbital phase, whose prior knowledge is crucial for searching and analyzing the signals from inspiralling compact binaries, is deduced from an energy balance argument.

Gravitational waves from rotating strained neutron stars

In this review we examine the dynamics and gravitational wave detectability of rotating strained neutron stars. The discussion is divided into two halves: triaxial stars and precessing stars. We summarize recent studies on how crustal strains and magnetic fields can sustain triaxiality, and suggest that Magnus forces connected with pinned superfluid vortices might contribute to deformation also. The conclusions that could be drawn following the successful gravitational wave detection of a triaxial star are discussed, and areas requiring further study identified. The latest ideas regarding free precession are then outlined, and the recent suggestion of Middleditch et al (Middleditch et al 2000 New Astronomy 5 243; 2000 Preprint astro-ph/0010044) that the remnant of SN1987A contains a freely precessing star, spinning down by gravitational wave energy loss, is examined critically. We describe what we would learn about neutron stars should the gravitational wave detectors prove this hypothesis to be correct.

Tidal interaction in binary-black-hole inspiral.

Tidal torque may lead to important effects in the strong field interaction at the end point of the inspiral of two rapidly rotating black holes. We point out here that in such a case the exchange of spin and orbital angular momentum may significantly affect the energy and waveform of late stage gravitational waves, and may play an important role in the shedding of excess angular momentum. We argue that numerical relativity, the only tool for determining the importance of tidal torque, should be more specifically focused on binary configurations with aligned, large, angular momenta.

Gravitational waves from a spinning particle scattered by a relativistic star: Axial mode case

We study gravitational waves from a spinning test particle scattered by a relativistic star using a perturbation method. The present analysis is restricted to axial modes. By calculating the energy spectrum, the waveforms and the total energy and angular momentum of gravitational waves, we analyze the dependence of the emitted gravitational waves on a particle spin. For a normal neutron star, the energy spectrum has one broad peak whose characteristic frequency corresponds to the angular velocity at the turning point (a periastron). Since the turning point is determined by the orbital parameter, there exists the dependence of the gravitational wave on a particle spin. We find that the total energy of $l = 2$ gravitational waves gets larger as the spin increases in the anti-parallel direction to the orbital angular momentum. For an ultracompact star, in addition to such an orbital contribution, we find the quasi-normal modes exited by a scattered particle, whose excitation rate to gravitational waves depends on the particle spin. We also discuss the ratio of the total angular momentum to the total energy of gravitational waves and explain its spin dependence.

Statistics of the detection rates for tensor and scalar gravitational waves from the Local Galaxy universe

We use data on the local 3-dimensional galaxy distribution for studying the statistics of the detection rates of gravitational waves (GW) coming from supernova explosions. We consider both tensor and scalar grav- itational waves which are possible in a wide range of relativistic and quantum gravity theories. We show that statistics of GW events as a function of sidereal time can be used for distinction between scalar and tensor gravi- tational waves because of the anisotropy of spatial galaxy distribution. For calculation of the expected amplitudes of GW signals we use the values of the released GW energy, frequency and duration of GW pulse which are consistent with existing scenarios of SN core collapse. The amplitudes of the signals produced by Virgo and the Great Attractor clusters of galaxies is expressed as a function of the sidereal time for resonant bar detectors oper- ating now (IGEC) and for forthcoming laser interferometric detectors (VIRGO). Then, we calculate the expected number of GW events as a function of sidereal time produced by all the galaxies within 100 Mpc. In the case of axisymmetric rotational core collapse which radiates a GW energy of 10 9 Mc 2 , only the closest explosions can be detected. However, in the case of nonaxisymmetric supernova explosion, due to such phenomena as centrifugal hangup, bar and lump formation, the GW radiation could be as strong as that from a coalescing neutron-star binary. For radiated GW energy higher than 10 6 Mc 2 and sensitivity of detectors at the level h 10 23 it is possible to detect Virgo cluster and Great Attractor, and hence to use the statistics of GW events for testing gravity theories.

Energy flows of gravitational waves

The problem of the energy transfer produced by weak gravitational waves on a static background is solved by using the Killing vectors without introducing the momentum-energy pseudotensor. The Lagrangian, which is of the second order in metric excitations and which determines the flow and density of the energy of gravitational waves on a static spherically symmetrical space-time background, is derived. Integration over angular variables in the action integral thus reduces the problem to a two-dimensional effective problem. Energy flows on the Schwarzschild metric background are calculated.

Gravitational Lensing of Gravitational Waves

The concentrated mass at the Galactic center is considered as a gravitational lens that focuses gravitational-wave energy to the Earth. It is found that 60 Hz gravitational waves from a rotating neutron star outside our Galaxy are focused onto a region having an approximate radius of 1.1×1011 m (assuming that the concentrated mass has the form of a supermassive black hole). The increase in intensity (which is proportional to the square of the increase in strain amplitude h) is by a factor of approximately 17,000. Sources within our Galaxy lead to increases in intensity by a factor that can exceed 4000.

Matter flows around black holes and gravitational radiation

We develop and calibrate a new method for estimating the gravitational radiation emitted by complex motions of matter sources in the vicinity of black holes. We compute numerically the linearized curvature perturbations induced by matter fields evolving in fixed black hole backgrounds, whose evolution we obtain using the equations of relativistic hydrodynamics. The current implementation of the proposal concerns Schwarzschild black holes and axisymmetric hydrodynamical motions. As first applications we study (i) dust shells falling onto the black hole isotropically from finite distance, (ii) initially spherical layers of material falling onto a moving black hole, and (iii) anisotropic collapse of shells. We focus on the dependence of the total gravitational wave energy emission on the flow parameters, in particular shell thickness, velocity and degree of anisotropy. The gradual excitation of the black hole quasi-normal mode frequency by sufficiently compact shells is demonstrated and discussed. A new prescription for generating physically reasonable initial data is discussed, along with a range of technical issues relevant to numerical relativity.

Two Kerr black holes with axisymmetric spins: head-on collision and gravitational radiation

We present a semi-analytical approach to the interaction of two (originally) Kerr black holes through a head-on collision process. An expression for the rate of emission of gravitational radiation is derived from an exact solution to Einstein's field equations. The total amount of gravitational radiation emitted in the process is calculated. We find that the spin-spin interaction increases the emission of gravitational wave energy by up to 0.2% of the total rest mass. We also discuss the possibility of spin exchange between the holes.