Ringdown Phases Research Articles

Solar diffraction of LIGO-band gravitational waves

We show that chirping gravitational waves in the LIGO frequency band f = 1–5000 Hz can be gravitationally diffracted by the Sun, due to the coincidence of its Fresnel length rF ∝ √1 AU/f and the solar radius r ⊙. This solar diffraction is potentially detectable through its frequency-dependent amplification of the wave. The detection rate with Einstein Telescope is estimated to be ∼ 1/1000 per year, with the optical depth ∝ (solar angular area on the sky)/4π. High-frequency regimes of merger and ringdown phases are found to be crucial. In addition to the discovery, we advocate that solar diffraction allows probing the inner solar density profile, as rF sweeps a range of solar radius during the chirping. These physics are captured by a formalism in terms of convergence and shear, which allows much easier estimation and more intuitive understanding. Solar diffraction can be a new opportunity with ongoing and future LIGO-band missions.

Simulating gravitational waves passing through the spacetime of a black hole

We investigate how GWs pass through the spacetime of a Schwarzschild black hole using time-domain numerical simulations. Our work is based on the perturbed $3+1$ Einstein's equations up to the linear order. We show explicitly that our perturbation equations are covariant under infinitesimal coordinate transformations. Then we solve a symmetric second-order hyperbolic wave equation with a spatially varying wave speed. As the wave speed in our wave equation vanishes at the horizon, our formalism can naturally avoid boundary conditions at the horizon. Our formalism also does not contain coordinate singularities and, therefore, does not need regularity conditions. Then, based on our code, we simulate both finite and continuous initially plane-fronted wave trains passing through the Schwarzschild black hole. We find that for the finite wave train, the wave zone of GWs is wildly twisted by the black hole. While for the continuous wave train, unlike geometric optics, GWs cannot be sheltered by the black hole. A strong beam and an interference pattern appear behind the black hole along the optical axis. Moreover, we find that the back-scattering due to the interaction between GWs and the background curvature is strongly dependent on the direction of the propagation of the trailing wavefront relative to the black hole. Finally, for a realistic input waveform generated by binary black holes, we find that the lensed waveform in the merger and ringdown phases is much longer than that of the input waveform due to the effect of back-scattering.

Deep learning model based on a bidirectional gated recurrent unit for the detection of gravitational wave signals

The application of deep learning to the detection of gravitational wave (GW) signals has attracted much attention in recent years, and nearly all of the existing deep learning-based GW detection algorithms are based on the convolutional neural network (CNN), which can be used to identify the GW merger moment and produce responding triggers. However, current CNN-based models are not best optimized tools in modeling the causal logic of sequential data in the time dimension to incorporate the information of the inspiral, merger and ringdown phases of the GW waveform. To address this issue we propose a deep learning model designed based on the bidirectional gated recurrent unit (BiGRU), a variant of the recurrent neural network (RNN) that is sensitive to the sequential logic of GW data. We train the neural network and implement the GW detection task by using the data obtained during the first, second and third observation runs (O1/O2/O3) of the LIGO-VIGRO scientific collaboration. We find that our BiGRU model achieves a false alarm probability (FAP) of $4.88\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ (corresponding false alarm rate is about 1 per 18.2 hours) and maintains a detection ratio of about 89.6%. We also construct a model ensemble containing two independently trained BiGRU models and find it does not trigger any false alarm events on our testing dataset. Meanwhile, our BiGRU model not only recovers all the reported GW events of O1-O2 runs, including the unique (as of today) confident (with observed electromagnetic counterparts) GW event originating from a binary neutron star (BNS) merger (GW170817), but also achieves a detection ratio of about 80% of the O3 run. By calculating and comparing the receiver operator characteristic (ROC) curves we demonstrate the superiority of the BiGRU model over traditional CNN-based models, and show that the BiGRU model, being optimized to deal with GW waveform that sequentially contains the inspiral, merger and ringdown phases, is a potentially powerful tool to study the GW data in the future.

Footprints of Population III Stars in the Gravitational-wave Background

We investigate detection prospects of the gravitational-wave background (GWB) that originates from the merging of compact objects formed by the collapse of Population III stars. Younger Population I/II stars lead to a GWB in the LIGO/Virgo frequency band at the inspiral phase, while Population III stars would likely show up at the later merger and ringdown phases. We show that, using a network of third-generation detectors, we may be able to separate a Population I/II signal from a Population III one, provided we can subtract individual coalescence events. A detection of a Population III GWB could reveal important information, such as the average redshifted total mass.

Numerical-relativity simulations of the quasicircular inspiral and merger of nonspinning, charged black holes: Methods and comparison with approximate approaches

We present fully general relativistic simulations of the quasi-circular inspiral and merger of charged, non-spinning, binary black holes with charge-to-mass ratio $\lambda \le 0.3$. We discuss the key features that enabled long term and stable evolutions of these binaries. We also present a formalism for computing the angular momentum carried away by electromagnetic waves, and the electromagnetic contribution to black-hole horizon properties. We implement our formalism and present the results for the first time in numerical-relativity simulations. In addition, we compare our full non-linear solutions with existing approximate models for the inspiral and ringdown phases. We show that Newtonian models based on the quadrupole approximation have errors of 20 % - 100 % in key gauge-invariant quantities. On the other hand, for the systems considered, we find that estimates of the remnant black hole spin based on the motion of test particles in Kerr-Newman spacetimes agree with our non-linear calculations to within a few percent. Finally, we discuss the prospects for detecting black hole charge by future gravitational-wave detectors using either the inspiral-merger-ringdown signal or the ringdown signal alone.

Deep learning model on gravitational waveforms in merging and ringdown phases of binary black hole coalescences

The waveform templates of the matched filtering-based gravitational-wave search ought to cover wide range of parameters for the prosperous detection. Numerical relativity (NR) has been widely accepted as the most accurate method for modeling the waveforms. Still, it is well-known that NR typically requires a tremendous amount of computational costs. In this paper, we demonstrate a proof-of-concept of a novel deterministic deep learning (DL) architecture that can generate gravitational waveforms from the merger and ringdown phases of the non-spinning binary black hole coalescence. Our model takes ${\cal O}$(1) seconds for generating approximately $1500$ waveforms with a 99.9\% match on average to one of the state-of-the-art waveform approximants, the effective-one-body. We also perform matched filtering with the DL-waveforms and find that the waveforms can recover the event time of the injected gravitational-wave signals.

Scope Out Multiband Gravitational-Wave Observations of GW190521-Like Binary Black Holes with Space Gravitational Wave Antenna B-DECIGO

The gravitational wave event, GW190521, is the most massive binary black hole merger observed by ground-based gravitational wave observatories LIGO/Virgo to date. While the observed gravitational wave signal is mainly in the merger and ringdown phases, the inspiral gravitational wave signal of the GW190521-like binary will be more visible to space-based detectors in the low-frequency band. In addition, the ringdown gravitational wave signal will be louder in the next generation (3G) of ground-based detectors in the high-frequency band, displaying the great potential of multiband gravitational wave observations. In this paper, we explore the scientific potential of multiband observations of GW190521-like binaries with a milli-Hz gravitational wave observatory: LISA; a deci-Hz observatory: B-DECIGO; and (next generation of) hecto-Hz observatories: aLIGO and ET. In the case of quasicircular evolution, the triple-band observations of LISA, B-DECIGO, and ET will provide parameter estimation errors of the masses and spin amplitudes of component black holes at the level of order of 1–10%. This would allow consistency tests of general relativity in the strong field at an unparalleled precision, particularly with the “B-DECIGO + ET” observation. In the case of eccentric evolution, the multiband signal-to-noise ratio found in “B-DECIGO + ET” observation would be larger than 100 for a five-year observation prior to coalescence, even with high final eccentricities.

Hybrid geometric-random template-placement algorithm for gravitational wave searches from compact binary coalescences

Astrophysical compact binary systems consisting of neutron stars and blackholes are an important class of gravitational wave (GW) sources for advanced LIGO detectors. Accurate theoretical waveform models from the inspiral, merger and ringdown phases of such systems, are used to filter detector data under the template based matched filtering paradigm. An efficient grid over the parameter space at a fixed minimal match has a direct impact on the overall time taken by these searches. We present a new hybrid geometric-random template placement algorithm for signals described by two masses and one spin magnitude parameters. Such template banks could potentially be used in GW searches from binary neutron stars and neutron star-blackhole systems. The template placement is robust and is able to automatically accommodate curvature and boundary effects with no fine tuning. We also compare these banks against vanilla-stochastic template banks and show that while both are equally efficient in the fitting-factor sense, the bank sizes are $\sim 25 \%$ larger in the stochastic method. Further, we show that the generation of the proposed hybrid banks can be sped-up by nearly an order of magnitude over the stochastic bank. Generic issues related to optimal implementation are discussed in detail. These improvements are expected to directly reduce the computational cost of gravitational wave searches.

Enhanced Gravitational Wave Science with LISA and gLISA.

The geosynchronous Laser Interferometer Space Antenna (gLISA) is a space-based gravitational wave (GW) mission that, for the past five years, has been under joint study at the Jet Propulsion Laboratory, Stanford University, the National Institute for Space Research (I.N.P.E., Brazil), and Space Systems Loral. With an arm length of 73,000 km, gLISA will display optimal sensitivity over a frequency region that is exactly in between those accessible by LISA and LIGO. Such a GW frequency band is characterized by the presence of a very large ensemble of coalescing black-hole binaries (BHBs) similar to those first observed by LIGO and with masses that are 10 to 100 times the mass of the Sun. gLISA will detect thousands of such signals with good signal-to-noise ratio (SNR) and enhance the LIGO science by measuring with high precision the parameters characterizing such signals (source direction, chirp parameter, time to coalescence, etc.) well before they will enter the LIGO band. This valuable information will improve LIGO’s ability to detect these signals and facilitate its study of the merger and ring-down phases not observable by space-based detectors. If flown at the same time as the LISA mission, the two arrays will deliver a joint sensitivity that accounts for the best performance of both missions in their respective parts of the milliHertz band. This simultaneous operation will result in an optimally combined sensitivity curve that is “white” from about 3 × 10−3 Hz to 1 Hz, making the two antennas capable of detecting, with high signal-to-noise ratios (SNRs), BHBs with masses in the range (10 − 107)M⊙. Their ability of jointly tracking, with enhanced SNR, signals similar to that observed by the Advanced Laser Interferometer Gravitational Wave Observatory (aLIGO) on September 14, 2015 (the GW150914 event) will result in a larger number of observable small-mass binary black-holes and an improved precision of the parameters characterizing these sources. Together, LISA, gLISA and aLIGO will cover, with good sensitivity, the (10−4 − 103) Hz frequency band.

Possible golden events for ringdown gravitational waves

There is a forbidden region in the parameter space of quasinormal modes of black holes in general relativity. Using both inspiral and ringdown phases of gravitational waves from binary black holes, we propose two methods to test general relativity. We also evaluate how our methods will work when we apply them to Pop III black-hole binaries with typical masses. Adopting the simple mean of the estimated range of the event rate, we have the expected rate of $500\text{ }\text{ }{\mathrm{yr}}^{\ensuremath{-}1}$. Then, the rates of events with signal-to-noise ratios greater than 20 and greater than 50 are $32\text{ }\text{ }{\mathrm{yr}}^{\ensuremath{-}1}$ and $2\text{ }\text{ }{\mathrm{yr}}^{\ensuremath{-}1}$, respectively. Therefore, there is a good chance to confirm (or refute) the Einstein theory in the strong gravity region by observing the expected quasinormal modes.

Parameter estimation on compact binary coalescences with abruptly terminating gravitational waveforms

Gravitational-wave (GW) astronomy seeks to extract information about astrophysical systems from the GW signals they emit. For coalescing compact-binary sources this requires accurate model templates for the inspiral and, potentially, the subsequent merger and ringdown. Models with frequency-domain waveforms that terminate abruptly in the sensitive band of the detector are often used for parameter-estimation studies. We show that the abrupt waveform termination contains significant information that affects parameter-estimation accuracy. If the sharp cutoff is not physically motivated, this extra information can lead to misleadingly good accuracy claims. We also show that using waveforms with a cutoff as templates to recover complete signals can lead to biases in parameter estimates. We evaluate when the information content in the cutoff is likely to be important in both cases. We also point out that the standard Fisher matrix formalism, frequently employed for approximately predicting parameter-estimation accuracy, cannot properly incorporate an abrupt cutoff that is present in both signals and templates; this observation explains some previously unexpected results found in the literature. These effects emphasize the importance of using complete waveforms with accurate merger and ringdown phases for parameter estimation.

Intermediate-mass-ratio inspirals in the Einstein Telescope. I. Signal-to-noise ratio calculations

The Einstein Telescope (ET) is a proposed third-generation ground-based interferometric gravitational wave detector, for which the target is a sensitivity that is a factor of 10 better than Advanced LIGO and a frequency range that extends down to $\ensuremath{\sim}1\text{ }\text{ }\mathrm{Hz}$. Such a third-generation interferometer will provide opportunities to test Einstein's theory of relativity in the strong field and will realize precision gravitational wave astronomy with a thousandfold increase in the expected number of events over the advanced ground-based detectors. A design study for ET is currently underway, so it is timely to assess the science that could be done with such an instrument. This paper is the first in a series that will carry out a detailed study of intermediate-mass-ratio inspirals (IMRIs) for ET. In the context of ET, an IMRI is the inspiral of a neutron star or stellar-mass black hole into an intermediate mass black hole (IMBH). In this paper we focus on the development of IMRI waveform models for circular and equatorial inspirals. We consider two approximations for the waveforms, which both incorporate the inspiral, merger, and ringdown phases in a consistent way. One approximation, valid for IMBHs of arbitrary spin, uses the transition model of Ori and Thorne [A. Ori and K. S. Thorne, Phys. Rev. D 62, 124022 (2000).] to describe the merger, and this is then matched smoothly onto a ringdown waveform. The second approximation uses the effective one body approach to model the merger phase of the waveform and is valid for nonspinning IMBHs. In this paper, we use both waveform models to compute signal-to-noise ratios for IMRI sources detectable by ET. At a redshift of $z=1$, we find typical signal-to-noise ratios for IMRI systems with masses $1.4{M}_{\ensuremath{\bigodot}}+100{M}_{\ensuremath{\bigodot}}$, $10{M}_{\ensuremath{\bigodot}}+100{M}_{\ensuremath{\bigodot}}$, $1.4{M}_{\ensuremath{\bigodot}}+500{M}_{\ensuremath{\bigodot}}$ and $10{M}_{\ensuremath{\bigodot}}+500{M}_{\ensuremath{\bigodot}}$ of $\ensuremath{\sim}10--25$, $\ensuremath{\sim}40--80$, $\ensuremath{\sim}3--15$, and $\ensuremath{\sim}10--60$, respectively. We also find that the two models make predictions for nonspinning inspirals that are consistent to about 10%.

Intermediate-mass-ratio inspirals in the Einstein Telescope. II. Parameter estimation errors

We explore the precision with which the Einstein Telescope (ET) will be able to measure the parameters of intermediate-mass-ratio inspirals (IMRIs). We calculate the parameter estimation errors using the Fisher Matrix formalism and present results of a Monte Carlo simulation of these errors over choices for the extrinsic parameters of the source. These results are obtained using two different models for the gravitational waveform which were introduced in paper I of this series. These two waveform models include the inspiral, merger and ringdown phases in a consistent way. One of the models, based on the transition scheme of Ori & Thorne [1], is valid for IMBHs of arbitrary spin, whereas the second model, based on the Effective One Body (EOB) approach, has been developed to cross-check our results in the non-spinning limit. In paper I of this series, we demonstrated the excellent agreement in both phase and amplitude between these two models for non-spinning black holes, and that their predictions for signal-to-noise ratios (SNRs) are consistent to within ten percent. We now use these models to estimate parameter estimation errors for binary systems with masses 1.4+100, 10+100, 1.4+500 and 10+500 solar masses (SMs), and various choices for the spin of the central intermediate-mass black hole (IMBH). Assuming a detector network of three ETs, the analysis shows that for a 10 SM compact object (CO) inspiralling into a 100 SM IMBH with spin q=0.3, detected with an SNR of 30, we should be able to determine the CO and IMBH masses, and the IMBH spin magnitude to fractional accuracies of 0.001, 0.0003, and 0.001, respectively. We also expect to determine the location of the source in the sky and the luminosity distance to within 0.003 steradians, and 10%, respectively. We also assess how the precision of parameter determination depends on the network configuration.

Systematic errors in measuring parameters of non-spinning compact binary coalescences with post-Newtonian templates

We study the astrophysical impact of inaccurate and incomplete modeling of the gravitational waveforms from compact binary coalescences (CBCs). We do so by the matched filtering of phenomenological inspiral-merger-ringdown (IMR) signals with a bank of inspiral-phase templates modeled on the 3.5 post-Newtonian TaylorT1 approximant. The rationale for the choice of the templates is threefold. (1) The inspiral phase of the phenomenological IMR signals, which are an example of complete IMR signals, is modeled on the same TaylorT1 approximant. (2) In the low-mass limit, where the merger and ringdown phases are much shorter than the inspiral phase, the errors should tend to vanishingly small values and, thus, provide an important check on the numerical aspects of our simulations. (3) Since the binary black hole signals are not yet known for mass ratios above ten and since signals from CBCs involving neutron stars are affected by uncertainties in the knowledge of their equation of state, inspiral templates are still in use in searches for those signals. The results from our numerical simulations are compared with analytical calculations of the systematic errors using the Fisher matrix on the template parameter space. We find that the loss in signal-to-noise ratio (SNR) can be as large as 45% even for binary black holes with component masses m1 = 10 M⊙ and m2 = 40 M⊙. Also the estimated total mass for the same pair can be off by as much as 20%. Both of these are worse for some higher mass combinations. Even the estimation of the symmetric mass ratio η suffers a nearly 20% error for this example and can be worse than 50% for the mass ranges studied here. These errors significantly dominate their statistical counterparts (at a nominal SNR of 10). It may, however, be possible to mitigate the loss in SNR by allowing for templates with unphysical values of η.

Gravitational-wave data analysis overview of compact binary searches using waveforms inspired by numerical relativity

Binary black holes with total masses between ∼20 and 200 M⊙ require numerical relativity to describe the detectable signal in ground-based, gravitational-wave detectors. The time–frequency properties of the signals suggest that both modeled, matched filter searches and unmodeled, burst searches can expect to detect high mass binary signals. This paper presents a comparison of a matched filter pipeline and two unmodeled burst pipelines on the inspiral, merger and ring-down phases of compact binary coalescence by evaluating the sensitivity to binaries with total masses between 25 and 100 M⊙ at a fixed false alarm rate. All three algorithms provided an average range of ∼250 Mpc for a 50,50 M⊙ binary at 10−7 Hz false alarm rate.

Simulations of binary black hole mergers using spectral methods

Several improvements in numerical methods and gauge choice are presented that make it possible now to perform simulations of the merger and ringdown phases of "generic" binary black-hole evolutions using the pseudo-spectral evolution code SpEC. These improvements include the use of a new damped-wave gauge condition, a new grid structure with appropriate filtering that improves stability, and better adaptivity in conforming the grid structures to the shapes and sizes of the black holes. Simulations illustrating the success of these new methods are presented for a variety of binary black-hole systems. These include fairly ``generic'' systems with unequal masses (up to 2:1 mass ratios), and spins (with magnitudes up to 0.4 M^2) pointing in various directions.

Long-term general relativistic simulation of binary neutron stars collapsing to a black hole

General relativistic simulations for the merger of binary neutron stars are performed as an extension of a previous work [M. Shibata and K. Taniguchi, Phys. Rev. D 73, 064027 (2006).]. We prepare binary neutron stars with a large initial orbital separation and employ the moving-puncture formulation, which enables one to follow merger and ringdown phases for a long time, even after black hole formation. For modeling inspiraling neutron stars, which should be composed of cold neutron stars, the Akmal-Pandharipande-Ravenhall (APR) equation of state (EOS) is adopted. After the onset of merger, the hybrid-type EOS is used; i.e., the cold and thermal parts are given by the APR and {gamma}-law EOSs, respectively. Three equal-mass binaries, each with mass 1.4M{sub {center_dot}}, 1.45M{sub {center_dot}}, and 1.5M{sub {center_dot}}, and two unequal-mass binaries with mass, 1.3 vs 1.6M{sub {center_dot}} and 1.35 vs 1.65M{sub {center_dot}}, are prepared. We focus primarily on the black hole formation case, and explore mass and spin of the black hole, mass of disks which surround the black hole, and gravitational waves emitted during the black hole formation. We find that (i) the black hole is promptly formed if total mass of the system initially satisfies m{sub 0} > or approx. 2.9M{submore » {center_dot}}; (ii) for the systems of m{sub 0}=2.9-3.0M{sub {center_dot}} and of mass ratio {approx_equal}0.8, the mass of disks which surround the formed black hole is 0.006-0.02M{sub {center_dot}}; (iii) the spin of the formed black hole is 0.78{+-}0.02 when a black hole is formed after the merger in the dynamical time scale. This value depends weakly on the total mass and mass ratio, and is about 0.1 larger than that of a black hole formed from nonspinning binary black holes; (iv) for the black hole formation case, Fourier spectrum shape of gravitational waves emitted in the merger and ringdown phases has a universal qualitative feature irrespective of the total mass and mass ratio, but quantitatively, the spectrum reflects the parameters of the binary neutron stars.« less

Searching for numerically simulated signals from black-hole binaries with a phenomenological template family

Recent progress in numerical relativity now allows computation of the binary black-hole merger, whereas post-Newtonian and perturbative techniques can be used to model the inspiral and ringdown phases. So far, most gravitational-wave searches have made use of various post-Newtonian-inspired templates to search for signals arising from the coalescence of compact binary objects. Ajith et al have produced hybrid waveforms for non-spinning binary black-hole systems which include the three stages of the coalescence process, and constructed from them phenomenological templates which capture the features of these waveforms in a parametrized form. As a first step towards extending the present inspiral searches to higher-mass binary black-hole systems, we have used these phenomenological waveforms in a search for numerically simulated signals injected into synthetic LIGO data as part of the NINJA project.

Gravitational wave burst search in the Virgo C7 data

A search for gravitational wave burst events has been performed with the Virgo C7 commissioning run data that have been acquired in September 2005 over 5 days. It focused on unmodeled short duration signals in the frequency range 150 Hz to 2 kHz. A search aimed at detecting the GW emission from the merger and ring-down phases of binary black hole coalescences was also carried out. An extensive understanding of the data was required to be able to handle a burst search using the output of only one detector. A 90% confidence level upper limit on the number of expected events given the Virgo C7 sensitivity curve has been derived as a function of the signal strength, for unmodeled gravitational wave searches. The sensitivity of the analysis presented is, in terms of the root sum square strain amplitude, hrss ≃ 10−20 Hz−1/2. This can be interpreted in terms of a frequentist upper limit on the rate of detectable gravitational wave bursts at the level of 1.1 events per day at a 90% confidence level. From the binary black hole search, we obtained the distance reach at 50% and 90% efficiency as a function of the total mass of the final black hole. The maximal detection distance for non-spinning high and equal mass black hole binary system obtained by this analysis in C7 data is ≃2.9 ± 0.1 Mpc for a detection efficiency of 50% for a binary of total mass 80 M⊙.

Gravitational-wave memory revisited: Memory from the merger and recoil of binary black holes

Gravitational-wave memory refers to the permanent displacement of the test masses in an idealized (freely-falling) gravitational-wave interferometer. Inspiraling binaries produce a particularly interesting form of memory—the Christodoulou memory. Although it originates from nonlinear interactions at 2.5 post-Newtonian order, the Christodoulou memory affects the gravitational-wave amplitude at leading (Newtonian) order. Previous calculations have computed this non-oscillatory amplitude correction during the inspiral phase of binary coalescence. Using an "effective-one-body" description calibrated with the results of numerical relativity simulations, the evolution of the memory during the inspiral, merger, and ringdown phases, as well as the memory's final saturation value, are calculated. Using this model for the memory, the prospects for its detection are examined, particularly for supermassive black hole binary coalescences that LISA will detect with high signal-to-noise ratios. Coalescing binary black holes also experience center-of-mass recoil due to the anisotropic emission of gravitational radiation. These recoils can manifest themselves in the gravitational-wave signal in the form of a "linear" memory and a Doppler shift of the quasi-normal-mode frequencies. The prospects for observing these effects are also discussed.