The direct observation and characterization of gravitational waves from binary black-hole mergers by LIGO is a testament to the crucial role played by waveform modeling in these discoveries. I will review recent developments in the ﬁeld, discussing both numerical and analytical approaches to the problem of black-hole binaries and their gravitational-wave emission

Taracchini, A.

Scientific Open-access Literature Archive and Repository

DOI 10.1393/ncc/i2017-17122-6Colloquia: SciNeGHE 2016IL NUOVO CIMENTO 40 C (2017) 122Modeling gravitational waves from compact-object binariesA. TaracchiniMax Planck Institute for Gravitational Physics (Albert Einstein Institute)Am Mühlenberg 1, Potsdam 14476, Germanyreceived 14 June 2017Summary. — The direct observation and characterization of gravitational wavesfrom binary black-hole mergers by LIGO is a testament to the crucial role playedby waveform modeling in these discoveries. I will review recent developments inthe field, discussing both numerical and analytical approaches to the problem ofblack-hole binaries and their gravitational-wave emission.1. – Binary black holes in general relativityDuring its first observing run (O1), the Advanced Laser Interferometer Gravitationalwave Observatory (LIGO) detected gravitational waves (GWs) emitted by the coalescenceof two binary black holes (BBHs), GW150914 and GW151226 [1, 2]. A third candidateevent, LVT151012, was also recorded [3], but with not high enough statistical significanceto claim a detection. These discoveries opened the possibility of observing and probingthe most extreme astrophysical objects in the Universe. These first detections and theirdetailed characterization represent the culmination of more than a decade of synergybetween analytical relativity, numerical relativity (NR) and data analysis.The problem of describing the GW signal generated by a pair of BHs that (quasi-circularly) orbit each other and eventually merge into a single BH is challenging becauseof the different dynamical regimes that this process spans. When the binary is wide—say, as compared to the BH horizons— the component objects move at orbital speeds(in the center-of-mass frame) that are small with respect to the speed of light. Duringthis phase of the coalescence, the post-Newtonian (PN) (i.e., slow-motion and weak-field)approximation to general relativity can be employed to model the orbital dynamics andthe associated GW emission (see, e.g., ref. [4] for an extensive review of the currentstatus of PN theory applied to the two-body problem). As the BHs spiral in, plungeand eventually merge, their orbital motion becomes more relativistic and the GW energyflux is stronger. NR techniques are required to obtain highly-accurate waveforms duringthis stage of the process. State-of-the-art codes can now accurately evolve BBHs forseveral tens of orbits (∼ 40–60) in large regions of the parameter space [5-11]: i) at largeCreative Commons Attribution 4.0 License (http://creativecommons.org/licenses/by/4.0) 12 A. TARACCHINImass ratios (∼ 8), but for moderate BH (dimensionless) spin magnitudes (∼ 0.6), andii) at higher BH spin magnitudes, but for comparable masses (∼ 1–3). Shorter simulations(∼ 10) can also be produced for mass ratios ∼ 20 and spin magnitudes ∼ 0.8. The longestNR run to date covers 175 orbits of a nonspinning BBH with mass ratio 7 [12]. Finally,soon after the merger, a distorted remnant BH is born. This relaxes into a stationaryKerr spacetime by radiating GWs that are well described by BH perturbation theory, aswell as by NR.In spite of tremendous progress, a purely NR approach to simulating BBHs for anypossible configuration down to the lower edge of the sensitive frequency band of currentground-based GW detectors is not feasible yet. This motivated the need to develop moresophisticated semi-analytical waveform models [13-17, 19, 20] that, while being cheap tocompute for data analysis, are very good approximations to general relativity.2. – Effective-one-body modelThe effective-one-body (EOB) formalism [21] aims at combining all available resultsthat describe the general-relativistic two-body problem — both analytical and numerical— into a unified description. In the case of a binary composed of BHs, let m1,2 and S1,2be the masses and spins of the two component objects as used in the PN descriptionof the real problem. Let q ≡ m1/m2 ≥ 1 be the mass ratio of the binary. The keyingredient of the EOB model is a resummation of the conservative PN dynamics of ageneric BBH in terms of the conservative dynamics of a test particle with mass μ andspin S∗ in a deformed Kerr metric with mass M and spin SKerr (effective problem),the deformation parameter being μ/M . In analogy with the Newtonian treatment ofa self-gravitating binary, here μ is the reduced mass of the BBH, while M is its totalmass. As to the spins S∗ and SKerr, these are given as functions of m1,2, S1,2 and thedynamical variables [22, 23]. These relationships between mass and spin parameters ofthe real and effective problem are obtained imposing i) a precise energy mapping betweenthe two systems, and ii) requiring that the Hamiltonian describing the effective problemreduces to that of the real problem in the slow-motion, weak-field limit. Concerning thedissipative sector, PN formulae for the inspiral GW modes are employed in a resummedform. The merger and ringdown signal is built independent of an orbital dynamics,namely by a superposition of quasinormal modes of the remnant BH or through fittingformulae. Strong-field information extracted from NR simulations can be incorporatedinto the model by calibrating adjustable parameters that enter the different ingredients ofthe model. The NR-informed versions of the EOB model go under the name of “EOBNRmodels”.3. – Recent results for spin-aligned BBHsIn ref. [20] we build an improved version of the spinning, nonprecessing EOBNRwaveform model that was used for O1 [13, 14], and whose accuracy was recently foundto degrade [24] in some regions of the BBH parameter space, notably large aligned spinsand unequal masses, where the model was extrapolating away from the NR waveformsthat were available at the time of its calibration. The improvements developed in thispaper include: i) the addition of all 4PN terms to the EOB radial potential and of higher-order PN corrections to the polarization modes, ii) a recalibration of the EOBNR modelto a large set of recently produced NR waveforms, which expand the domain of cali-bration towards larger mass ratios and aligned-spin components, and iii) a more robustMODELING GRAVITATIONAL WAVES FROM COMPACT-OBJECT BINARIES 350 100 150 20010–40.0010.0100.1001unfaithfulness(5.0, 0.80, 0.00)(7.0, 0.80, 0.00)(5.0, –0.80, 0.00)(7.0, –0.80, 0.00)(2.0, 0.90, 0.90)(1.3, 0.96, –0.90)othersFig. 1. – Unfaithfulness of the model of ref. [20] against the NR catalog used for its calibration+ 16 additional validation runs for total masses 10 M ≤ M ≤ 200 M, using the AdvancedLIGO design zero-detuned high-power noise PSD and a low-frequency cutoff equal to the initialgeometric frequency of each NR run.description of the merger-ringdown signal. The updated model (SEOBNRv4) has beencoded in the LIGO Algorithm Library, so that it can be employed during the secondobserving (O2) run of Advanced LIGO. One important figure of merit to determine theaccuracy of a waveform model against a numerical-relativity simulation is the unfaith-fulness, that is a frequency-domain overlap integral weighted by the noise power spectraldensity (PSD) of the detector of interest (in this case, zero-detuned high-power AdvancedLIGO), with optimization only on phase and time of coalescence. Figure 1 shows thatSEOBNRv4 has unfaithfulness below 1% against the whole NR catalog used for its calibra-tion, with the addition of 16 validation runs. We compared the improved EOBNR modelto spinning, nonprecessing waveform models that were used in the data analysis of theO1 run of Advanced LIGO, namely SEOBNRv2 [13] and IMRPhenomD [16]. IMRPhenomD isa frequency-domain waveform model that calibrates a phenomenological ansatz to NRwaveforms hybridized with an uncalibrated version of the EOBNR model. We carried outfaithfulness comparisons from 25 Hz with the O1 noise PSD. We found that SEOBNRv4 hasfaithfulness: i) as low as 43% against SEOBNRv2 in the region of large, positive aligned-spin components and spin-asymmetric BBHs, irrespective of the mass ratio, where newNR simulations became available for calibration; ii) as low as 35% against IMRPhenomD inthe region of large, positive aligned-spin components and large mass ratios, where bothmodels are extrapolating away from the respective calibration domain and the number ofGW cycles in band is larger than in any other part of parameter space. The faithfulnessresults against IMRPhenomD waveforms at mass ratios > 4 and aligned-spin components> 0.8 strongly suggest the importance of producing new NR simulations in this regionof the parameter space, so that discrepancies between different ways of extrapolatingwaveform models can be resolved. By contrast, the high effectualness between SEOBNRv4and IMRPhenomD waveform models in almost all parameter space (both for O1 and designnoise curves), suggests that for Advanced LIGO detection purposes the dominant-modemodels do not need to be further improved.4. – Recent results for spin-precessing BBHsWhen the BH spins have generic orientations, both the orbital plane and the spinsundergo precession about the total angular momentum of the binary. For the first time,4 A. TARACCHINIref. [25] proposed a complete EOB model for spinning, precessing BBHs. The idea is touse a precessing frame that tracks the motion of the orbital plane [26]. In this frame,precession-induced amplitude and phase modulations in the waveforms are minimized,thus one employs a nonprecessing EOBNR model calibrated to NR to generate inspiral-plunge modes. The modes are then rotated to the inertial frame that is aligned with thespin of the remnant BH: in this frame, the merger-ringdown modes are generated andsmoothly stitched to the rotated inspiral-plunge modes. Without recalibration of theunderlying nonprecessing EOBNR model [27], the model was compared to two long, pre-cessing NR simulations, finding very good agreement. Currently, the precessing EOBNRmodel is the only waveform model that includes all 15 parameters that characterize aBBH coalescence. In ref. [17], for the first time, we extensively tested the precessingEOBNR model against 70 NR simulations that span mass ratios from 1 to 5, dimension-less spin magnitudes up to 0.5, and generic spin orientations. While we did not recalibratethe inspiral-plunge signal of the underlying nonprecessing model, we improved the de-scription of the merger-ringdown waveform. In particular, we included different QNMsaccording to the prograde/retrograde character of the plunge orbit and we prescribed thetime of onset of the ringdown according to a robust algorithm that minimizes unwantedfeatures in the amplitude of the waveforms around merger. We introduced a sky- andpolarization-averaged unfaithfulness to meaningfully compare precessing waveforms. Wedevised a procedure to identify appropriate initial physical parameters for the modelgiven a precessing NR simulation. We found that for Advanced LIGO the precessingEOBNR model has unfaithfulness within about 3% against the large majority of the70 NR runs when the total mass of the binary varies between 10M and 200M andinclinations ι = 0, π/3, π/2.References [18,15] proposed a precessing inspiral-merger-ringdown frequency-domainmodel based on the nonprecessing phenomenological model of ref. [16]. Similarly to whatis done for the precessing EOBNR model, the inertial-frame waveforms are generated byrotating the nonprecessing modes according to the precessional motion of the orbitalplane. The Euler angles parametrizing the rotation that connects the precessing frameto the observer’s frame are derived from PN theory.The precessing EOBNR model discussed in ref. [17] was one of the waveform mod-els used in the parameter-estimation study of the first GW observation by LIGO,GW150914 [28]. Depending on the region of parameter space, the differences betweenthe two precessing models may or may not be relevant. In particular, in the case ofGW150914 —an almost equal-mass, face-off, non-extremal BBH — ref. [28] showed thatboth approximants give consistent estimations of the parameters of the source.5. – Open problemsThe nonprecessing (precessing) models discussed above only include the dominant(2,2) mode ( = 2 modes) in the GW polarizations h+,×. However, the inclusion ofhigher-order modes is likely to be important to increase our chance of detecting and cor-rectly characterizing binary coalescences in some regions of the parameter space, notablylarge mass ratios [29-31]. Moreover, for spin-precessing binaries, some effects are stillnot accounted for by state-of-the-art models, namely mode asymmetry in the precessingframe [32-34] and the precession of the maximum-radiation direction during the ring-down [32]. Finally, no direct calibration of precessing waveform models to NR has everbeen performed.MODELING GRAVITATIONAL WAVES FROM COMPACT-OBJECT BINARIES 5REFERENCES[1] LIGO Scientific and Virgo Collaborations (Abbott B. P. et al.), Phys. Rev. Lett.,116 (2016) 061102.[2] LIGO Scientific and Virgo Collaborations (Abbott B. P. et al.), Phys. Rev. Lett.,116 (2016) 241103.[3] LIGO Scientific and Virgo Collaborations (Abbott B. P. et al.), Phys. Rev. X, 6(2016) 041015.[4] Blanchet L., Living Rev. Rel., 17 (2014) 2.[5] Mroue A. H. et al., Phys. Rev. Lett., 111 (2013) 241104.[6] Chu T. et al., Class. Quantum Grav., 33 (2016) 165001.[7] Lovelace G., Scheel M. A. and Szilagyi B., Phys. Rev. D, 83 (2011) 024010.[8] Scheel M. A., Giesler M., Hemberger D. A., Lovelace G., Kuper K., Boyle M.,Szilgyi B. and Kidder L. E., Class. Quantum Grav., 32 (2015) 105009.[9] Husa S., Khan S., Hannam M., Pürrer M., Ohme F., Jimnez Forteza X. and BohA., Phys. Rev. D, 93 (2016) 044006.[10] Jani K., Healy J., Clark J. A., London L., Laguna P. and Shoemaker D., Class.Quantum Grav., 33 (2016) 204001.[11] Healy J., Lousto C. O., Zlochower Y. and Campanelli M., arXiv:1703.03423 [gr-qc].[12] Szilgyi B. et al., Phys. Rev. Lett., 115 (2015) 031102.[13] Taracchini A. et al., Phys. Rev. D, 89 (2014) 061502.[14] Pürrer M., Phys. Rev. D, 93 (2016) 064041.[15] Hannam M., Schmidt P., Boh A., Haegel L., Husa S., Ohme F., Pratten G. andPürrer M., Phys. Rev. Lett., 113 (2014) 151101.[16] Khan S., Husa S., Hannam M., Ohme F., Pürrer M., Jimnez Forteza X. and BohA., Phys. Rev. D, 93 (2016) 044007.[17] Babak S., Taracchini A. and Buonanno A., Phys. Rev. D, 95 (2017) 024010.[18] Schmidt P., Ohme F. and Hannam M., Phys. Rev. D, 91 (2015) 024043.[19] Nagar A., Damour T., Reisswig C. and Pollney D., Phys. Rev. D, 93 (2016) 044046.[20] Bohé A. et al., Phys. Rev. D, 95 (2017) 044028.[21] Buonanno A. and Damour T., Phys. Rev. D, 59 (1999) 084006.[22] Barausse E. and Buonanno A., Phys. Rev. D, 81 (2010) 084024.[23] Barausse E. and Buonanno A., Phys. Rev. D, 84 (2011) 104027.[24] Kumar P. et al., Phys. Rev. D, 93 (2016) 104050.[25] Pan Y., Buonanno A., Taracchini A., Kidder L. E., Mrou A. H., Pfeiffer H. P.,Scheel M. A. and Szilgyi B., Phys. Rev. D, 89 (2014) 084006.[26] Buonanno A., Chen Y. b. and Vallisneri M., Phys. Rev. D, 67 (2003) 104025.[27] Taracchini A. et al., Phys. Rev. D, 86 (2012) 024011.[28] LIGO Scientific and Virgo Collaborations (Abbott B. P. et al.), Phys. Rev. X, 6(2016) 041014 doi:10.1103/PhysRevX.6.041014.[29] Capano C., Pan Y. and Buonanno A., Phys. Rev. D, 89 (2014) 102003.[30] Caldern Bustillo J., Laguna P. and Shoemaker D., arXiv:1612.02340 [gr-qc].[31] Varma V. and Ajith P., arXiv:1612.05608 [gr-qc].[32] O’Shaughnessy R., London L., Healy J. and Shoemaker D., Phys. Rev. D, 87 (2013)044038.[33] Pekowsky L., O’Shaughnessy R., Healy J. and Shoemaker D., Phys. Rev. D, 88(2013) 024040.[34] Boyle M., Kidder L. E., Ossokine S. and Pfeiffer H. P., arXiv:1409.4431 [gr-qc].

Modeling gravitational waves from compact-object binaries

http://eprints.bice.rm.cnr.it/19960/1/ncc11436.pdf

Modeling gravitational waves from compact-object binaries

Abstract

Similar works

Full text

Available Versions

Scientific Open-access Literature Archive and Repository