Advances and Challenges in Waveform Modeling for Gravitational-Wave - - PowerPoint PPT Presentation

Alessandra Buonanno

Max Planck Institute for Gravitational Physics (Albert Einstein Institute, AEI) Department of Physics, University of Maryland

Advances and Challenges in Waveform Modeling for Gravitational-Wave Observations

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

10 10

1

10

2

10

3

10

4

10

5

m1/m2 10 10

1

10

2

10

3

10

4

r c

2/GM

Effective one-body theory

Numerical Relativity Post-Newtonian theory Perturbation theory gravitational self-force

(AB & Sathyaprakash 14) bound orbits: v2/c2 ~ GM/rc2

• GR is non-linear theory.
• Einstein’s field equations can

be solved:

• Synergy between analytical and numerical relativity is crucial.
• approximately, but analytically

(fast way)

• “exactly”, but numerically on

supercomputers (slow way)

Analytical Relativity

• Post-Newtonian (PN) (large separation,

and slow motion, bound motion, i.e., early inspiral)

• Perturbation theory (ringdown
• f final object, tides)
• Post-Minkowskian (PM) (large

separation, unbound motion, i.e., scattering)

• Small mass-ratio (gravitational self-

force, i.e., early to late inspiral)

• Effective-one-body (EOB)

(combines results from all methods, i.e., entire coalescence)

2 4 6 8 10

q

0.0 0.2 0.4 0.6 0.8 1.0

|χ1| precessing runs non-precessing runs new precessing runs

• Public SXS NR catalog (Boyle et
• al. 19) plus non-public SXS NR

waveforms (Ossokine et al. 20).

• Other NR catalogs

(Husa et al. 15, Jani et al. 17, Healy et al. 17, 19, 20)

Numerical Relativity

20000 40000 60000 80000 100000

• 0.1

0.0 0.1 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

• 0.1

0.0 0.1 100000 101000 102000 103000 104000 105000

(t − r*) / M

• 0.1

0.0 0.1

DL/M Re(h22)

• 376 GW cycles, zero spins & mass-ratio 7

(8 months, few millions CPU-h)

(Szilagyi, Blackman, AB, Taracchini et al. 15)

• Einstein’s equations solved numerically

mass ratio primary spin

1

m

2

m

1

m

2

m

µν

g

real

E Eeff

real

J Nreal

eff

J

eff

N

Real description

µν

g eff

Effective description µ

The effective-one-body approach in a nutshell

• Two-body dynamics is mapped

into dynamics of one-effective body moving in deformed black- hole spacetime, deformation being the mass ratio.

• Some key ideas of EOB theory

were inspired by quantum field theory when describing energy of comparable-mass charged bodies.

Map

(AB & Damour 1999 )

EOB Hamiltonian: resummed conservative dynamics

• Real Hamiltonian
• Effective Hamiltonian
• EOB Hamiltonian:
• Dynamics condensed Aν(r) and Bν(r)
• Aν(r), which encodes the energetics of circular orbits, is quite simple:

Aν(r) = 1 − 2M r +2M 3ν r3 + ✓94 3 − 41 32π2 ◆ M 4ν r4 + a5(ν) + alog

5 (ν) log(r)

r5 + a6(ν) r6 + · · ·

5PN

EOB conservative spin resummed dynamics

S = S1 + S2

S∗ = m2 m1 S1 + m1 m2 S2

• What is

when compact objects carry spin? Mapping is not unique, variants of exist.

Hν

eff

Hν

eff

HEOB

real

= M s 1 + 2ν ✓Hν

eff

µ − 1 ◆

(credit: Hinderer)

(Damour 01, Damour, Jaranowski & Schäfer 08; Damour & Nagar 14; Rettegno et al. 20)

• Test mass (TM):

Hν

eff = H

Kerr-orb,ν

eff

+ [GS(r, p) S + GS∗(r, p), S∗] pϕ

(TEOBResumS)

(Barausse, Racine & AB 10; Barausse & AB 11, 12; Vines et al. 16; Khalil et al. 20)

• Test spin (TS):

Hν

eff = H

Kerr-orb,ν

eff

+ [gν

S(r, p) S + gν S∗(r, p) S∗] pϕ + HSS,ν eff

(SEOBNR)

0.30 0.35 0.40

• 0.07
• 0.06
• 0.05
• 0.04

2 3 4 5 10 0.30 0.35 0.40 0.00 0.02 0.04 0.06 0.08 0.10 0.12 2 3 4 5 10

Comparison between 4PN EOB and NR binding energies

(Khalil, … AB 20) non-spinning non-spinning

χ1 = S1/m2

1

q = m1/m2 χ2 = S2/m2

2

0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.00 0.05 0.10 0.15 1 2 3 4 5 10 20 40 0.30 0.35 0.40 0.45 0.50 0.55 1 2 3 4 5 10 20 40 0.26 0.28 0.30 0.32 0.34 0.36 2 3 4 5 10 20

spinning spinning spinning (see also Rettegno et al. 20) SEOB is uncalibrated

(SEOB curves are for “circular” orbits)

EOB conservative spin dynamics & waveforms

(credit: Hinderer)

• EOB equations of motion (AB et al. 00, 05; Damour et al. 09):
• EOB waveforms (AB et al. 00; Damour et al. 09, 11; Pan, AB et al. 11):

• 0.2
• 0.1

0.1 0.2 0.3 gravitational waveform inspiral-plunge merger-ringdown

• 250
• 200
• 150
• 100
• 50

50 c3t/GM 0.1 0.2 0.3 0.4 0.5 frequency: GMω/c3 2 x orbital freq inspiral-plunge GW freq merger-ringdown GW freq

(AB & Damour 00)

light ring

(credit: Hinderer)

H2

real = m2 1 + m2 2 + 2m1m2

✓Heff µ ◆

• By solving Hamilton equations with appropriate (resummed) radiation-reaction

force, we obtain orbital motion and gravitational waveform.

EOB inspiral-merger-ringdown analytic waveform

• EOB merger-ringdown signal is a

superposition of quasi-normal modes, including overtones.

• To improve stability, recent models

use fits to merger-ringdown from NR simulations.

(AB & Damour 00, AB et al. 07, Damour & Nagar 07) (Del Pozzo & Nagar 17, Bohé et al. 17 )

light ring

Completing EOB waveforms using NR/perturbation theory information

(credit: Taracchini)

• 2
• 1

1 2 R/µ Re(h22

Teuk)

20600 20800 21000 21200 21400 21600 21800 22000 (t − r*) / M 0.4 0.6 0.8 Mω22

Teuk

2MΩ a / M = 0.99, (2,2) mode ISCO LR tmatch

22

• We calibrate to merger-ringdown waveforms

in test-body limit. (Taracchini, AB et al.13, 14)

(credit: Taracchini)

58 56 57 59 60 61 62 6364 gravitational-wave cycles

• 0.3

0.3 DL/M Reh22

• 0.3

0.3 DL/M Reh22 11500 11550 11600 11650 11700 11750 11800 11850 (t − R*) / M

• 0.3

0.3 DL/M Reh22

NR EOB

Calibration, no NQC corrections No calibration, no NQC corrections Calibration + NQC corrections

• We calibrate to inspiral-merger-ringdown

NR waveforms.

141 SXS simulations

0.00 0.05 0.10 0.15 0.20 0.25

• 1.0
• 0.5

0.0 0.5 1.0 ν χeff

SEOBNRv4 SEOBNRv2 Teukolsky validation

(Bohé et al. 17) (Pan, AB et al. 13, Taracchini, AB, Pan, Hinderer & SXS 14, Pürrer 15) (Bohé, Shao, Taracchini, AB & SXS 17, Babak et al. 16; Cotesta et al. 18, 20, Ossokine et al. 20) (see also Damour & Nagar 14, Nagar et

• al. 18, Nagar, Messina et al. 19, Nagar,

Pratten et al. 20, Nagar, Riemenschneider et al. 20)

Calibration of SEOBNR for O2-O3 searches and follow-up

Phenomenological waveforms used in O1-O3 follow-up analyses

• Fast, frequency-domain waveform model hybridizing EOB & NR

waveforms, and then fitting (Schmidt et al.12; Hannam et al. 13; Khan et al. 15; Husa et

• al. 15; Khan et al. 18-19; García-Quíros et al. 20, Pratten et al. 20)
• First works in mid-late 2000 (Ajith et al. 07, Pan et al. 07, Santamaria, Ohme et al. 10)

(If PN were used instead, accuracy will degrade, because of “gap” between PN and NR)

−(dϕ/df )

| ˜ h|

M f M f

(IMRPhenom)

Surrogate models using NR simulations

• NR surrogate models are built directly by interpolating NR simulations,

which are selected in parameter space using analytical waveform models.

• Highly accurate, but limited in binary’s parameter space and length (~20 orbits).

(Varma et al. 19)

(Field, Galley, Tiglio; Blackman, Varma, Scheel, …)

NR surrogate

• First works in late 2000

(Abbott et al. PRL 116 (2016) 241103)

Template bank for modeled search & possible systematics

(Dal Canton & Harry 17)

325,000 EOBNR templates for BBHs & NSBHs 75,000 PN templates for BNSs

• Systematics due to

modeling were smaller than statistical errors for GW events observed in O1 & O2 runs.

(Abbott et al. CQG 34 (2017) 104002, Abbott et al. PRX 9 (2019) 031040) (Ossokine, AB & SXS project) (visualization credit: Dietrich, Haas @AEI)

GW151226 GW151226

• Matched filtering employed

(Abbott et al. PRL 116 (2016) 241103)

O2/O3

eccentricity eEOBNRv2 a l i g n e d s p i n s SEOBNRv4 aligned spins + higher-order modes SEOBNRv4HM precessing spins S E O B N R v 4 P precessing spins + higher-order modes SEOBNRv4PHM aligned spins + higher-order modes + parametrised merger-ringdown pSEOBNRv4HM aligned spins + tides SEOBNRv4T non-spinning

Family tree of EOBNR waveforms

Ever more physics in waveform models

(credit: Cotesta)

Other family trees for IMRPhenom, TEOBResumS, NRSurrogate

Importance of higher harmonics: varying mass ratio

(Cotesta, AB et al. 18)

h+(t; Θ, ϕ) − i h×(t; Θ, ϕ) =

∞

X

`=2 `

X

m=−` −2Y`m(Θ, ϕ) h`m(t)

1 2 3 4 5 6 7 8 9 10

q

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

|h`m(t`m

peak)|/|h22(t22 peak)|

χ1 = χ2 = 0

(3, 3) (2, 1) (5, 5) (4, 3) (4, 4) (3, 2)

(see also Mehta et al. 17, London et al. 17, Varma et al. 19, García-Quíros et al. 20, Nagar et al. 2020)

−100 −75 −50 −25 25 50 75 100

(t −t22

peak)/M

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14

Dashed: SEOBNRv4HM Solid: NR

|h22| 2×|h21| 2×|h33| 3×|h44| 4×|h55|

q = 8, χ1 = −0.5, χ2 = 0

Θ (credit: Cotesta)

Importance of higher harmonics: varying spins

(Cotesta, AB et al. 18)

h+(t; Θ, ϕ) − i h×(t; Θ, ϕ) =

∞

X

`=2 `

X

m=−` −2Y`m(Θ, ϕ) h`m(t)

−100 −75 −50 −25 25 50 75 100

(t −t22

peak)/M

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14

Dashed: SEOBNRv4HM Solid: NR

|h22| 2×|h21| 2×|h33| 3×|h44| 4×|h55|

q = 8, χ1 = −0.5, χ2 = 0

Θ (credit: Cotesta) (see also Mehta et al. 17, London et al. 17, Varma et al. 19, García-Quíros et al. 20, Nagar et al. 2020)

−0.75 −0.50 −0.25 0.00 0.25 0.50 0.75

χ1

0.1 0.2 0.3 0.4 0.5

|h`m(t`m

peak)|/|h22(t22 peak)|

q =8

(3, 3) (2, 1) (5, 5) (4, 3) (4, 4) (3, 2)

• Mismatch against SXS NR catalog

(1485) of multipolar spin-precessing waveforms.

• SEOBNRv4PHM: multipolar spin-

precessing waveform model with .

(2, ± 2), (2, ± 1), (3, ± 3), (4, ± 4), (5, ± 5)

binary’s inclination:

Accuracy of multipolar precessing SEOBNR model against NR

(Ossokine, AB, Marsat, Cotesta et al. 20)

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14

maxM MSNR

100 200 300 400

number of cases

` = 5 NR vs ` = 2 SEOBNRv4P ` = 5 NR vs ` = 5 SEOBNRv4PHM −0.50 −0.25 0.00 0.25 0.50 SEOBNRv4P Unfaithfulness: 5.9 × 10−2 −0.20 −0.15 −0.10 −0.05 0.00

Time (s)

−0.50 −0.25 0.00 0.25 0.50 SEOBNRv4PHM Unfaithfulness: 8.5 × 10−3

(see also Khan et al. 19; Pratten et al. 20, Akcay at el. 20) (Boyle et al. 19; Ossokine et al. 20)

NR

Θ = π/3

Assessing accuracy of waveform models against NR

(Ossokine, AB, Marsat, Cotesta et al. 20)

25 50 75 100 125 150 175 200

Total mass [M]

104 103 102 101 100

MSNR

IMRPhenomPv3HM

q = 4.0, χ1 = (0.00, 0.01, 0.80), χ2 = (0.37, 0.42, 0.57) q = 4.0, χ1 = (0.00, 0.01, 0.80), χ2 = (0.56, 0.57, 0.00)

25 50 75 100 125 150 175 200

Total mass [M]

104 103 102 101 100

MSNR

SEOBNRv4PHM

q = 6.0, χ1 = (0.06, 0.78, 0.47), χ2 = (0.08, 0.17, 0.23) q = 4.0, χ1 = (0.38, 0.39, 0.58), χ2 = (0.33, 0.73, 0.01)

IMRPhenomPv3 (Khan et al. 19)

• Mismatch against SXS NR public catalog (1344) of multipolar spin-

precessing waveforms. (Boyle et al. 19)

• Waveform models are not calibrated in the precessing sector.

Assessing accuracy of waveform models among themselves

(Ossokine, AB, Marsat, Cotesta et al. 20)

2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0

q

−0.5 0.0 0.5

χeff

2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0

q

0.00 0.25 0.50 0.75 1.00

χp

10−3 10−2 10−1

MSNR

• Waveform models differ the most for large mass ratios (> 10) and large spins (> 0.6)

and stronger precession.

• Mismatch between two multipolar spin-precessing waveforms.

IMRPhenomPv3 (Khan et al. 19) SEOBNRv4PHM (Ossokine et al. 20)

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.5 2.0 2.5 3.0

0.4 0.6 0.8

a1

1.5 2.0 2.5 3.0

θ1[rad]

50 60 70 80 90 100 110 7.5 10.0 12.5 15.0 17.5

60 80 100

m1[M]

10 15

m2[M]

Assessing accuracy of waveform models with Bayesian analysis

(Ossokine, AB, Marsat, Cotesta et al. 20) SNR = 21 SEOBNRv4PHM unfaithfulness =

4.4 %

IMRPhenomPv3HM unfaithfulness =

8.8 %

• NR is injected

Θ = π/2

M = 76M, q = 6, χ1 = (−0.06, 0.78, −0.47), χ2 = (0.08, −0.17, −0.23)

GW190814: a binary with a puzzling companion

(Abbott et al. ApJ Lett 896 (2020) 2, L44)

• Systematics due to waveform

modeling smaller than statistical errors.

• Using waveform models with higher-

modes and spin-precession constrains more tightly the secondary mass.

• Either the largest neutron star or

the smallest black hole.

• More massive BH rotated with

spin .

< 0.07

GW190412: a signal like none before

• Systematics due to waveform

modeling are not negligible when spins and higher modes are relevant.

• More massive BH rotated with

spin at CI

0.17 − 0.59 90 %

(Abbott et al. PRD 102 (2020) 4)

GW190521: a signal produced by the largest BHs so far

(Abbott et al. PRL 125 (2020) 10, ApJ Lett 900 (2020) L13) (credit: Fischer, Pfeiffer & AB; SXS Collaboration)

• Systematics due to waveform modeling are not negligible when spin

precession and higher modes are relevant.

GW190521: a signal produced by the largest BHs so far

(Abbott et al. PRL 125 (2020) 10, ApJ Lett 900 (2020) L13)

Results from interplay with scattering amplitude methods & EFT

(Levi et al. 20, Antonelli et al. 20)

• 0.03
• 0.02
• 0.01

0.00 0.30 0.35 0.40 0.45

• 0.03
• 0.02
• 0.01

0.00

(Foffa et al. 19, Blümlein et al. 20, Damour 20, Bini, Damour & Geralico 20)

• 2-body non-spinning Hamiltonian at 5PN

& 6PN partially computed using EFT or interplay between bound and unbound

• rbits, and gravitational self-force results.
• Relevant to incorporate these new results in waveform models to assess

improvement in accuracy for GW observations. (Antonelli, AB et al. 19)

new!

• 2-body Hamiltonian at 3PM (2PM) for nonspinning (spinning, precessing) BHs.

(Bini et al. 17, 18, Vines 18, Cheung et al. 19, 20, Bern et al. 19, 20, Blümlein et al. 20, Kälin et al. 20)

• 2-body spin-orbit Hamiltonian at 4.5PN

computed using EFT or interplay between bound and unbound orbits, and self-force results.

(Antonelli et al. 20)

face-on face-off edge-on

Inferring best science by including more physical effects

• How to discriminate among binary’s formation scenarios, and probe

astrophysical environment? Eccentricity and spin-precession can disclose this information.

1800 2000 2200 2400 2600

(t − R)/M

−0.3 −0.2 −0.1 0.0 0.1 0.2 0.3

(DL/M)<(h22)

e0 = 0.4, p0 = 13M, q = 4

10800 11000 11200 11400 11600 11800

(t R)/M

0.4 0.3 0.2 0.1 0.0 0.1 0.2 0.3 0.4

(DL/M)<(h22)

e0 = 0.3, p0 = 20M, q = 1

(Hinderer & Babak 17)

• Eccentric compact-object binary:

mass ratio = 7 NR simulation non-spinning EOB waveform model (Lewis et al. 16)

• Current eccentric models do not cover all physical effects (e.g., spin-precession

and harmonics) or all stages of coalescence or entire range of eccentricity.

(many PN papers on eccentricity; Bini et al. 12; East et al. 13; Huerta et al. 14-19, Hinder et al. 17; Cao & Han 17; Loutrel & Yunes 16, 17; Ireland et al. 19, Moore & Yunes 19, Chiaramello & Nagar 20, Buades et al. 20)

Waveforms for eccentric BBHs using EOBNR model

• Mismatches smaller than

for .

1.6 % 0 ≤ e0 < 0.6

• Quasi-circular templates can be

used to match eccentric templates up to .

e0 < 0.1

SEOBNREv4 waveform model

e0 = 0.59

• SEOBNREv4: waveform model with

aligned spins and eccentricity.

(Cao et al. 17, Liu et al. 19, Liu, Cao et al. in prep 20) Mf0 = 0.002

mismatch with SXS NR waveforms

• Using SEOBNRE, GW190521 is

consistent with aligned-spin binary with eccentricity at 10 Hz.

> 0.1

(Romero-Shaw et al. 20)

Toward the era of precision gravitational-wave astrophysics

• So far, inference from GW observations is dominated by statistical instead of

modeling error, but most recent GW events have started to show some differences in waveform modeling.

• We have not missed “loud” GW events. For sub-threshold events, it might be

critical to use templates in model-search pipelines with more physics.

• State-of-the-art waveform models: higher harmonics and spin precession for

quasi-circular orbits.

• Highest priorities:
• generalize waveform models to generic (eccentric) orbits
• produce NR simulations with large mass ratios (> 4) and large spins (> 0.8),

with larger number of GW cycles (> 50) to calibrate/validate waveform models

• combine PN, PM, GSF and EOB more effectively to

improve analytical solution of 2-body problem. Relevant developments employing scattering amplitude methods.

• develop more accurate waveform models for binaries

with matter

(credit: APS/Stonebraker)