Challenges for numerical relativity and gravitational-wave source - PowerPoint PPT Presentation

Challenges for numerical relativity and gravitational-wave source modeling Emanuele Berti, Johns Hopkins University ICERM Workshop “Advances and challenges in computational relativity” September 14 2020

Focus of this talk: what improvements in numerical relativity do we need to test GR with binary black hole mergers? “The binary black hole problem has been solved 15 years ago” In general relativity, for comparable-mass nonspinning nonprecessing noneccentric binaries (and I won’t talk about neutron stars…)

What keeps me up at night: Systematic errors in GR: not good enough for LISA/CE/ET spectroscopy tests sky localization Identifying “best” beyond-GR theories: specific theories vs. parametrization Punchline: NR may guide theoretical work

Group GWIC prize 2016 GWIC prize 2017

Black hole spectroscopy: a null test

B/XicbVDLSsNAFJ3UV42v+Ni5CRbBVUmqoIsuim6 s4J9QBPCZDp h85kwsxEqKH4K25cKOLW/3Dn3zhps9DWA5d7O de5s4JE0qkcpxvo7Syura+Ud40t7Z3dves/YO 5KlAuI045aIXQokpiXFbEUVxLxEYspDibji+yf3uAxaS8PheTRLsMziMSUQ VFoKrCOn7nG h7DOvNu8B03TDKyKU3VmsJeJW5AK NAKrC9vwFHKcKwQhVL2XSdRfgaFIojiqemlEicQjeEQ9zWNIcPSz2bXT+1TrQzsiAtdsbJn6u+ND IpJyzUkwyqkVz0cvE/r5+q6MrPSJykCsdo/lCU ltxO4/CHhCBkaIT SASRN9qoxEUECkdWB6Cu/jlZdKpVd3zau3uotK4LuIog2NwAs6ACy5BAzRBC7QBAo/gGbyCN+PJeDHejY/5aMkodg7BHxifP3uJk/E=</latexit> <latexit sha1_base64="jYfVTIpELl6Vbm+ImvxJeEbWqUs=">A Quasinormal (and superradiant) modes Ergo-region Barrier Potential Well region Exponential growth region “Mirror” at r~1/µ Potential [Arvanitaki+Dubovsky, 1004.3558] Black Hole Horizon r * Quasinormal modes: Massive scalar field: • Ingoing waves at the horizon, • Superradiance: black hole bomb when outgoing waves at infinity [Press-Teukolsky 1972] 0 < ω < m Ω H • Spectrum of damped modes (“ringdown”) • Hydrogen-like, unstable bound states [EB+, 0905.2975] [Detweiler 1980, Zouros+Eardley, Dolan…]

Schwarzschild and Kerr quasinormal mode spectrum • One mode fixes mass and spin – and the whole spectrum! • N modes: N tests of GR dynamics… if they can be measured • Needs SNR>50 or so for a comparable mass, nonspinning binary merger [Berti-Cardoso-Will, gr-qc/0512160; EB+, gr-qc/0707.1202]

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Earth vs. space-based: ringdown detections and black hole spectroscopy 10 6 10 3 Q3nod 4L Q3nod 4L M3 M3 Q3d 4L Q3d 4L 10 5 M10 M10 PopIII 4L PopIII 4L M1 M1 Q3nod 6L Q3nod 6L ρ > ρ GLRT 10 4 ρ > 8 Q3d 6L Q3d 6L PopIII 6L PopIII 6L ρ > 8 ρ > ρ GLRT 10 3 10 2 10 2 events/year events/year 10 1 10 0 10 1 10 − 1 10 − 2 10 − 3 10 0 1 2 O + + t r X B 1 w n 1 2 5 1 2 5 r e O O E 2 A A A A A A G A + V D T 2 g E C E a 1 1 1 2 2 2 T E I A C y N N N N N N L C E o d V A [EB+, 1605.09286]

Multi-mode detectability: mass ratio and spin dependence Strongest spin dependence: [Baibhav+, 1710.02156]

How many modes? Depends on spin. Best/worst case scenarios in LISA [Baibhav+EB, 1809.03500]

SNR

Including overtones is crucial, even in linear perturbation theory Leaver (1986): Green’s function in Schwarzschild. Overtones: agreement well before peak Zhang+: extension to Kerr (here for an ultrarelativistic infall along the z axis) 20 20 l=2, j=0 l=2, j=0.98 Numerical Numerical 15 15 n=0 n=0 n=1 n=1 n=2 n=2 Re(X l )/(m 0 E) Re(X l )/(m 0 E) n=3 10 n=3 10 5 5 0 0 -5 -5 -10 -15 -10 -5 0 5 10 15 20 25 -15 -10 -5 0 5 10 15 20 25 t-r * t-r * [Zhang+, 1710.02156] “Excitation factors” in Kerr known “Excitation coefficients” depend on initial data: difficult, unsolved problem for comparable-mass mergers [Leaver, PRD, 1986] [EB+Cardoso, gr-qc/0605118]

Systematic errors on QNM frequencies/mass+spin from SXS/PP waveforms 10 0 Top: N = 1 real part (thick) N = 2 10 − 1 N = 3 imaginary part (thin) 10 − 2 δω / ω 1% determination of 10 − 3 needs one overtone 10 − 4 (better if two or three) SXS, q = 1 SXS, q = 3 Point Particle 10 − 5 0 5 10 15 20 5 10 15 20 5 10 15 20 t 22 0 − t 22 t 22 0 − t 22 t 22 0 − t 22 peak peak peak Bottom: spin (thick) mass (thin) 1% determination of mass and spin needs at least two modes [Baibhav+, 1710.02156]

Systematic errors on mass and spin from fitting SXS waveforms Overtones improve quality of consistency tests for GW150914, not a “genuine” spectroscopy test: 10 0 1 . 0 N = 0 10 − 1 N = 1 N = 2 0 . 8 10 − 2 N = 3 N = 4 10 − 3 0 . 6 N = 5 M N = 6 χ f 10 − 4 IMR IMR N = 7 0 . 4 ∆ t 0 = 0 ms 10 − 5 N = 0 0 . 2 10 − 6 N = 1 N = 2 10 − 7 0 . 0 − 20 − 10 0 10 20 30 40 50 50 60 70 80 90 100 t 0 − t peak [ M ] M f [ M � ] [Giesler+, 1903.08284; Isi+, 1905.00869]

Mass and spin measurement with multiple modes

Median errors on mass and spin combining multiple modes

Sky localization and distance determination Amplitudes: Amplitude ratio: Phase difference: Relative antenna and polarization power:

Sky localization: the eightfold way and higher harmonics Assume inclination is known. Main observables: Ignoring errors, these give contours of constant Degenerate positions witout orbital modulation and higher harmonics – but can do do better with better waveform models/PE [Baibhav+, 2001.10011] [Marsat+, 2003.00357]

Beyond GR: specific theories

A guiding principle to modified GR: Lovelock’s theorem In four spacetime dimensions the only divergence-free (WEP) symmetric rank-2 Higher dimensions WEP violations Higher dimensions WEP violations tensor constructed solely from the metric and its derivatives up to 2nd order, and preserving diffeomorphism invariance, Lovelock Lovelock theorem theorem is the Einstein tensor plus L . Extra fields Diff-invar. violations Diff-invar. violations Extra fields Generic modifications introduce additional fields (simplest: scalars) Dynamical fields Dynamical fields Minimal requirements: Massive gravity Lorentz-violations Nondynamical fields Massive gravity Lorentz-violations Nondynamical fields (SEP violations) (SEP violations) Action principle • dRGT theory Einstein-Aether Palatini f(R) Well-posed • Massive bimetric Horava-Lifshitz Eddington-Born-Infeld gravity n-DBI • Testable predictions • Black holes, neutron stars Scalars Vectors Tensors Cosmologically viable • [Sotiriou+, 0707.2748] Scalar-tensor, Metric f(R) Einstein-Aether TeVeS Horndeski, galileons Horava-Lifshitz Bimetric gravity [EB+, 1501.07274] Quadratic gravity, n-DBI