Advances and Challenges in Waveform Modeling for Gravitational-Wave Observations Alessandra Buonanno Max Planck Institute for Gravitational Physics (Albert Einstein Institute, AEI) Department of Physics, University of Maryland Advances & Challenges in Computational Relativity”, ICERM, Brown U Sep 14, 2020
Outline • Observing gravitational waves and inferring astrophysical/physical information hinges on our ability to make precise predictions of two- body dynamics and gravitational radiation. • How do we build the hundred-thousand accurate and efficient waveform models employed in LIGO/Virgo searches and inference studies ? • Success of interplay between analytical and numerical relativity . • State-of-the-art waveform models for binary black holes. • Are current observations dominated by systematics due to modeling? • What are the highest modeling priorities toward the era of high- precision GW astrophysics?
GW observations by LIGO & Virgo so far
Solving two-body problem in General Relativity bound orbits: v 2 /c 2 ~ GM/rc 2 4 10 • GR is non-linear theory . (AB & Sathyaprakash 14) 3 Post-Newtonian theory 10 Perturbation 2 /GM • Einstein’s field equations can theory 2 10 Effective one-body theory be solved: gravitational r c self-force Numerical 1 - approximately, but analytically 10 Relativity ( fast way) 0 - “ exactly” , but numerically on 10 0 1 2 3 4 5 10 10 10 10 10 10 supercomputers ( slow way) m 1 / m 2 • Synergy between analytical and numerical relativity is crucial.
Analytical Relativity • Post-Newtonian (PN) (large separation, • Post-Minkowskian (PM) (large and slow motion, bound motion , i.e., separation, unbound motion , i.e., early inspiral ) scattering ) • Small mass-ratio (gravitational self- • Perturbation theory ( ringdown force, i.e., early to late inspiral ) of final object, tides ) • Effective-one-body (EOB) (combines results from all methods, i.e., entire coalescence )
Numerical Relativity 1 . 0 precessing runs non-precessing runs • Einstein’s equations solved numerically 0 . 8 new precessing runs primary spin 0 . 6 | χ 1 | 0 . 4 0 . 2 • 376 GW cycles , zero spins & mass-ratio 7 0 . 0 (8 months, few millions CPU-h) 2 4 6 8 10 mass ratio q (Szilagyi, Blackman, AB, Taracchini et al. 15) • Public SXS NR catalog (Boyle et 0.1 0.0 al. 19) plus non-public SXS NR -0.1 D L /M Re( h 22 ) 0 20000 40000 60000 80000 100000 waveforms (Ossokine et al. 20) . 0.1 0.0 -0.1 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 • Other NR catalogs 0.1 0.0 -0.1 (Husa et al. 15, Jani et al. 17, 100000 101000 102000 103000 104000 105000 ( t − r * ) / M Healy et al. 17, 19, 20)
The effective-one-body approach in a nutshell Real description Effective description µ m 2 m M ap • Two-body dynamics is mapped 1 into dynamics of one-effective body moving in deformed black- hole spacetime , deformation being the mass ratio. g g eff µ ν µ ν m m 1 2 • Some key ideas of EOB theory E E eff real were inspired by quantum field theory when describing energy of J N J N real comparable-mass charged bodies. eff eff real (AB & Damour 19 99 )
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