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Numerical black hole mergers beyond general relativity Leo C. Stein - - PowerPoint PPT Presentation

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Numerical black hole mergers beyond general relativity Leo C. Stein (Theoretical astrophysics @ Caltech) 2018 2 23 YKIS2018a Preface Me, Kent Yagi, Nico Yunes Takahiro Tanaka Many other colleagues, Maria (Masha) Okounkova SXS

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Numerical black hole mergers beyond general relativity

Leo C. Stein (Theoretical astrophysics @ Caltech) 2018 · 2 · 23 — YKIS2018a

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Preface

Me, Kent Yagi, Nico Yunes Takahiro Tanaka Maria (Masha) Okounkova Many other colleagues, SXS collaboration, taxpayers

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Numerical black hole mergers beyond general relativity

Leo C. Stein (Theoretical astrophysics @ Caltech) 2018 · 2 · 23 — YKIS2018a

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Goal: Use gravitational waves for precision tests of general relativity (and beyond) in the dynamical, non-linear, strong field

Leo C. Stein (Caltech) Numerical BH mergers beyond GR 1

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Goal: Use gravitational waves for precision tests of general relativity (and beyond) in the dynamical, non-linear, strong field

  • General relativity must be incomplete
  • LIGO: New opportunity to test GR in strong-field
  • Present tests’ shortcomings
  • Almost no theory-specific tests
  • Theory-independent tests need more guidance
  • Challenge: Find spacetime solutions in theories beyond GR
  • Our contribution: First binary black hole mergers in

dynamical Chern-Simons gravity

  • General method appropriate for many deformations of GR
  • Still lots of work to do, stay tuned or get involved!

Leo C. Stein (Caltech) Numerical BH mergers beyond GR 1

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Knowns and unknowns

Gravitational waves are here to stay. Get as much science out as possible

  • Binary black hole populations
  • Mass function, spins,

clusters/fields, progenitors,

  • evolution. . .
  • Testing general relativity
  • Neutron stars
  • GRB relation, central engine,

r-process elements. . .

  • Dense nuclear equation of

state?

Leo C. Stein (Caltech) Numerical BH mergers beyond GR 2

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Why test GR?

General relativity successful but incomplete Gab = 8π ˆ Tab

  • Can’t have mix of quantum/classical
  • GR not renormalizable
  • GR+QM=new physics (e.g. BH information paradox)

Leo C. Stein (Caltech) Numerical BH mergers beyond GR 3

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Why test GR?

General relativity successful but incomplete Gab = 8π ˆ Tab

  • Can’t have mix of quantum/classical
  • GR not renormalizable
  • GR+QM=new physics (e.g. BH information paradox)

Approach #1: Theory

  • Look for good UV completion =

⇒ strings, loops, . . .

  • Need to explore strong-field
  • Deeper understanding of breakdown, quantum regime of GR

Leo C. Stein (Caltech) Numerical BH mergers beyond GR 4

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Why test GR?

General relativity successful but incomplete Gab = 8π ˆ Tab

  • Can’t have mix of quantum/classical
  • GR not renormalizable
  • GR+QM=new physics (e.g. BH information paradox)

Approach #2: Empiricism Ultimate test of theory: ask nature

  • So far, only precision tests are weak-field
  • Lots of theories ≈ GR
  • Need to explore strong-field
  • Strong curvature • non-linear • dynamical

Leo C. Stein (Caltech) Numerical BH mergers beyond GR 5

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[Baker, Psaltis, Skordis (2015)]

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  • 54

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Curvature, ξ (cm

  • 2)

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  • 12 10
  • 10 10
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Potential, ε

BBN Lambda Last scattering

WD MS

PSRs

NS

Clusters Galaxies

MW M87 S stars R M SS BH

SMBH P(k)| z=0 Accn. scale Satellite CMB peaks

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Big picture

  • Before aLIGO: precision tests of GR in weak field
  • Weak field: distant binary of black holes or neutron stars

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Big picture

  • Before aLIGO: precision tests of GR in weak field
  • Weak field: distant binary of black holes or neutron stars
  • Now: first direct measurements of dynamical, strong field regime
  • Future: precision tests of GR in the strong field
  • Changing nuclear EOS is degenerate with changing gravity
  • Need black hole binary merger for precision

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Big picture

  • Before aLIGO: precision tests of GR in weak field
  • Weak field: distant binary of black holes or neutron stars
  • Now: first direct measurements of dynamical, strong field regime
  • Future: precision tests of GR in the strong field
  • Changing nuclear EOS is degenerate with changing gravity
  • Need black hole binary merger for precision

Question: How to perform precision tests of GR in strong field?

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How to perform precision tests

  • Two approaches: theory-specific and theory-agnostic
  • Agnostic: parameterize, e.g. PPN, PPE

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Parameterized post-Einstein framework

  • Insert power-law corrections to amplitude and phase (u3 ≡ πMf)

˜ h(f) = ˜ hGR(f) × (1 + αua) × exp[iβub]

  • Parameters: (α, a, β, b)
  • Inspired by post-Newtonian calculations in beyond-GR theories

Leo C. Stein (Caltech) Numerical BH mergers beyond GR 10

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How to perform precision tests

  • Two approaches: theory-specific and theory-agnostic
  • Agnostic: parameterize, e.g. PPN, PPE
  • Want more powerful parameterization
  • Don’t know how to parameterize in strong-field!
  • Need guidance from specific theories

Leo C. Stein (Caltech) Numerical BH mergers beyond GR 11

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How to perform precision tests

  • Two approaches: theory-specific and theory-agnostic
  • Agnostic: parameterize, e.g. PPN, PPE
  • Want more powerful parameterization
  • Don’t know how to parameterize in strong-field!
  • Need guidance from specific theories

Problem: Only simulated BBH mergers in GR!*

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The problem

From Lehner+Pretorius 2014: Don’t know if other theories have good initial value problem

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Numerical relativity

  • Nonlinear, quasilinear, 2nd order

hyperbolic PDE, 10 functions, 3+1 coordinates

  • Attempts from ’60s until 2005.

Merging BHs for 13 years

  • Want to evolve.

How do you know if good IBVP?

  • Both under- and over-constrained.
  • gauge
  • constraints (not all data free; need

constraint damping)

  • Avoid singularities: punctures or excision

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Numerical relativity

  • Nonlinear, quasilinear, 2nd order

hyperbolic PDE, 10 functions, 3+1 coordinates

  • Attempts from ’60s until 2005.

Merging BHs for 13 years

  • Want to evolve.

How do you know if good IBVP?

  • Both under- and over-constrained.
  • gauge
  • constraints (not all data free; need

constraint damping)

  • Avoid singularities: punctures or excision

Every other gravity theory will have at least these difficulties

Leo C. Stein (Caltech) Numerical BH mergers beyond GR 13

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Some other theories

“Scalar-tensor”: G⋆

µν = 2

  • ∂µϕ∂νϕ − 1

2g⋆

µν∂σϕ∂σϕ

  • − 1

2g⋆

µνV (ϕ) + 8πT ⋆ µν

✷g⋆ϕ = −4πα(ϕ)T ⋆ + 1 4 dV dϕ BBH in S-T:

  • Massless scalar =

⇒ ϕ → 0, agrees with GR

  • Only differ if funny boundary or initial conditions

Hirschmann+ paper on Einstein-Maxwell-dilaton

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Some other theories

  • Higher derivative EOMs
  • Ostrogradski instability. H unbounded below
  • Some theories try to avoid, e.g. Horndeski
  • Massive gravity theories. B-D ghost, cured by dRGT.
  • Problems even with second-derivative EOMs:

If not quasi-linear, may have (∂tφ)2 ≃ Source, but . . .

  • Papallo and Reall papers on Lovelock, Horndeski, EdGB

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A solution

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A solution

  • Treat every theory as an effective field theory (EFT)
  • Particle and condensed matter physicists always do this.
  • Sorta do this for GR. Valid below some scale
  • Theory only needs to be approximate, approximately well-posed

General relativity Special relativity post-Newtonian G→0 v/c→0 Standard Model QED Maxwell h→0

  • Example: weak force below EWSB scale (lose unitarity above)

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A solution

  • Treat every theory as an effective field theory (EFT)
  • Particle and condensed matter physicists always do this.
  • Sorta do this for GR. Valid below some scale
  • Theory only needs to be approximate, approximately well-posed

General relativity Special relativity post-Newtonian G→0 v/c→0 Standard Model QED Maxwell h→0

  • Example: weak force below EWSB scale (lose unitarity above)

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A solution

General relativity Special relativity post-Newtonian G→0 v/c→0 Standard Model QED Maxwell h→0

  • Same should happen in gravity EFT:

lose predictivity (bad initial value problem) above some scale

  • Theory valid below cutoff Λ ≫ E. Must recover GR for Λ → ∞.
  • Assume weak coupling, use perturbation theory

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A solution

General relativity Special relativity post-Newtonian G→0 v/c→0 Standard Model QED Maxwell h→0

  • Same should happen in gravity EFT:

lose predictivity (bad initial value problem) above some scale

  • Theory valid below cutoff Λ ≫ E. Must recover GR for Λ → ∞.
  • Assume weak coupling, use perturbation theory

Example: Dynamical Chern-Simons gravity

Leo C. Stein (Caltech) Numerical BH mergers beyond GR 18

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What is dynamical Chern-Simons gravity?

  • Chern-Simons = GR + axion + interaction

S =

  • d4x√−g
  • R − 1

2(∂ϑ)2 + ε ϑ ∗RR

  • ϑ = ε ∗RR ,

Gab + ε Cab[∂ϑ∂3g] = Tab

  • Anomaly cancellation, low-E string theory, LQG. . .

(see Nico’s review Phys. Rept. 480 (2009) 1-55)

  • Lowest-order EFT with parity-odd ϑ, shift symmetry (long range)
  • Phenomenology unique from other R2

(e.g. Einstein-dilaton-Gauss-Bonnet)

  • Gravity version of QCD axion, sourced by rotation

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Black holes in dCS

  • a = 0 (Schwarzschild) is exact solution with ϑ = 0
  • Rotating BHs have dipole+ scalar hair

LCS, PRD 90, 044061 (2014) [arXiv:1407.2350]

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Black holes in dCS

  • a = 0 (Schwarzschild) is exact solution with ϑ = 0
  • Rotating BHs have dipole+ scalar hair

LCS, PRD 90, 044061 (2014) [arXiv:1407.2350] Extremal: QCG 33, 235013 (2016) [arXiv:1512.05453] Coming soon, NHEK (with Baoyi Chen)

  • Post-Newtonian of BBH inspiral in

PRD 85 064022 (2012) [arXiv:1110.5950]

  • See also review

CQG 32 243001 (2015) [arXiv:1501.07274]

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Back to problem and solution

  • DCS had principal part ∂3g coming from Cab tensor.

Probably not well-posed, Delsate/Hilditch/Witek PRD 91, 024027.

  • Theory is GR + ε × deformation. Expand everything in ε
  • Derivation
  • At every order in ε, principal part is Princ[Gab]

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Back to problem and solution

  • DCS had principal part ∂3g coming from Cab tensor.

Probably not well-posed, Delsate/Hilditch/Witek PRD 91, 024027.

  • Theory is GR + ε × deformation. Expand everything in ε
  • Derivation
  • At every order in ε, principal part is Princ[Gab]

Background dynamics are well-posed = ⇒ perturbations well-posed

Leo C. Stein (Caltech) Numerical BH mergers beyond GR 21

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−6 6 ×10−2 (GM)Re[RΨ(2,2)

4

] −2 2 ×10−3 (ℓ/GM)−2Re[Rϑ(1)

(1,0)]

Numerical Post-Newtonian −6 6 ×10−4 (ℓ/GM)−2Re[Rϑ(1)

(2,1)]

−6 −5 −4 −3 −2 −1 1 (t∗ − tPeak)/GM ×102 −1 1 ×10−3 (ℓ/GM)−2Re[Rϑ(1)

(3,2)]

Mode amplitude

From Okounkova, LCS+, PRD 96, 044020 (2017) [arXiv:1705.07924]

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−3 −2 −1 (t∗ − tPeak)/GM ×103 10−16 10−12 10−8 10−4 ˙ E × (GM)2 0.3ˆ z 0.3ˆ z 0.1ˆ z 0.0ˆ z ˙ E(0) NR (ℓ/GM)−4 ˙ E(ϑ,2) NR (ℓ/GM)−4 ˙ E(ϑ,2) PN From Okounkova, LCS+, PRD 96, 044020 (2017) [arXiv:1705.07924]

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Instantaneous regime of validity −2 −1 (t − tMerger)/GM ×103 100 101 |ℓ/GM|

Perturbation theory invalid Perturbation theory valid

0.3ˆ z 0.1ˆ z 0.0ˆ z

From Okounkova, LCS+, PRD 96, 044020 (2017) [arXiv:1705.07924]

Leo C. Stein (Caltech) Numerical BH mergers beyond GR 23

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Secular regime of validity — dephasing

LIGO most sensitive to phase

  • Expand phase in ε around time t0

φ = φ(0) + ε2∆φ + O(ε3) , ∆φ(t) = ∆φ(t0) + (t − t0)d∆φ dt

  • t=t0

+ 1 2(t − t0)2 d2∆φ dt2

  • t=t0 + O(t − t0)3
  • Pretend orbits quasicircular, adiabatic =

⇒ E = E(ω(t))

  • Use chain rule, relate d∆ω/dt to energy, flux

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Secular regime of validity — dephasing

10−7 10−5 10−3 10−1 101 (ℓ/GM)−4∆φ 0.3ˆ z 0.1ˆ z 0.0ˆ z −2.0 −1.5 −1.0 −0.5 0.0 0.5 1.0 (t∗ − t0)/GM ×102 −3 3 (GM)Re[RΨ(2,2)

4

] ×10−2 χ1,2 = 0.3ˆ z

From Okounkova, LCS+, PRD 96, 044020 (2017) [arXiv:1705.07924]

Leo C. Stein (Caltech) Numerical BH mergers beyond GR 25

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Bounds

∆φgw = 2∆φ σφ Spin M bound M ≈ 60M⊙ 0.3

  • ℓ

GM

  • 0.13

σφ

0.1

1/4 ℓ 11 km σφ

0.1

1/4 0.1

  • ℓ

GM

  • 0.2

σφ

0.1

1/4 ℓ 18 km σφ

0.1

1/4 0.0

  • ℓ

GM

  • 1.4

σφ

0.1

1/4 ✗ — 7 orders of magnitude improvement over Solar System

Leo C. Stein (Caltech) Numerical BH mergers beyond GR 26

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Future work

Lots of work to do!

  • Work in progress on O(ε2)
  • Run lots of simulations
  • Waveform modeling: build surrogates!

> > > import NRSur7dq2

  • Study degeneracy
  • Bayesian model selection with existing LIGO/Virgo detections
  • Turn the crank: explore more theories
  • Guide theory-agnostic parameterizations

Leo C. Stein (Caltech) Numerical BH mergers beyond GR 27

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  • First binary black hole mergers in dCS
  • Inspiral: qualitative agreement with analytics
  • Merger: discovered new phenomenology, dipole burst
  • Estimated ∆φ, bound on ℓ O(10) km
  • For better bounds:
  • Higher SNR
  • Longer waveform/lower mass
  • Higher BH spins
  • Working on O(ε2)

For details, see Okounkova, LCS+, PRD 96, 044020 (2017) [arXiv:1705.07924]

Leo C. Stein (Caltech) Numerical BH mergers beyond GR 28

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Goal: Use gravitational waves for precision tests of general relativity (and beyond) in the dynamical, non-linear, strong field

  • General relativity must be incomplete
  • LIGO: New opportunity to test GR in strong-field
  • Present tests’ shortcomings
  • Almost no theory-specific tests
  • Theory-independent tests need more guidance
  • Challenge: Find spacetime solutions in theories beyond GR
  • Our contribution: First binary black hole mergers in

dynamical Chern-Simons gravity

  • General method appropriate for many deformations of GR
  • Still lots of work to do, stay tuned or get involved!

Leo C. Stein (Caltech) Numerical BH mergers beyond GR 29

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Other slides

Leo C. Stein (Caltech) Numerical BH mergers beyond GR 30

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Distant compact binaries

  • Post-Newtonian:

bodies are ∼ point particles

  • Motion of distant bodies boils

down to multipoles

  • Different theories, different

moments (“hairs”)

  • Brans-Dicke: NS , BH ✗
  • EDGB:

NS ✗, BH

  • DCS: dipoles
  • . . .
  • BH proof by Sotiriou, Zhou
  • NS proof by Yagi, LCS, Yunes

PRD 93, 024010 (2016) [arXiv:1510.02152]

Leo C. Stein (Caltech) Numerical BH mergers beyond GR 31

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Distant compact binaries

x y t t=0 t=T n Cr,T Identify

  • Post-Newtonian:

bodies are ∼ point particles

  • Motion of distant bodies boils

down to multipoles

  • Different theories, different

moments (“hairs”)

  • Brans-Dicke: NS , BH ✗
  • EDGB:

NS ✗, BH

  • DCS: dipoles
  • . . .
  • BH proof by Sotiriou, Zhou
  • NS proof by Yagi, LCS, Yunes

PRD 93, 024010 (2016) [arXiv:1510.02152]

Leo C. Stein (Caltech) Numerical BH mergers beyond GR 31

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Distant compact binaries

Parameterize over multipole moments: LCS, Yagi PRD 89, 044026 (2014) [arXiv:1310.6743]

  • Sun's

surface Earth's surface LAGEOS J0737 3039 Mercury precession LLR NS merger BH merger SMBH merger NS Ω timing EDGB dCS

1012 1010 108 106 104 0.01 1 1012 109 106 0.001 1 100 102 104 106 108 1010 Gmr compactness ΞGmr312 km1 inv. curvature radius km

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Next issues

Gravitational waves at O(ε2):

  • Two sets of gauges, constraints
  • Find stable gauge
  • Linearization of damped harmonic
  • But may experience secular drift (hint: Kerr PT

)

  • Regime of validity of perturbation scheme
  • ε2h(2)
  • ≪
  • g(0)
  • Renormalization? See e.g. Galley and Rothstein [1609.08268]

Leo C. Stein (Caltech) Numerical BH mergers beyond GR 33

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Only 10 numbers in parametrized post-Newtonian [Slide from Wex]

Norbert Wex / 2016-Jul-19 / Caltech

PPN formalism for metric theories of gravity

8

g00 = −1 + 2U − 2βU 2 − 2ξΦW + (2γ + 2 + α3 + ζ1 − 2ξ)Φ1 + 2(3γ − 2β + 1 + ζ2 + ξ)Φ2 +2(1 + ζ3)Φ3 + 2(3γ + 3ζ4 − 2ξ)Φ4 − (ζ1 − 2ξ)A − (α1 − α2 − α3)w2U − α2wiwjUij +(2α3 − α1)wiVi + O(3), g0i = −1 2(4γ + 3 + α1 − α2 + ζ1 − 2ξ)Vi − 1 2(1 + α2 − ζ1 + 2ξ)Wi − 1 2(α1 − 2α2)wiU −α2wjUij + O(5/2), gij = (1 + 2γU)δij + O(2).

U = Z ρ0 |x − x0| d3x0, Uij = Z ρ0(x − x0)i(x − x0)j |x − x0|3 d3x0, ΦW = Z ρ0ρ00(x − x0) |x − x0|3 · x0 − x00 |x − x00| − x − x00 |x0 − x00|

  • d3x0 d3x00,

A = Z ρ0[v0 · (x − x0)]2 |x − x0|3 d3x0, Z Φ1 = Z ρ0v02 |x − x0| d3x0, Φ2 = Z ρ0U 0 |x − x0| d3x0, Φ3 = Z ρ0Π0 |x − x0| d3x0, Φ4 = Z p0 |x − x0| d3x0, Z Z | − | Vi = Z ρ0v0

i

|x − x0| d3x0, Wi = Z ρ0[v0 · (x − x0)](x − x0)i |x − x0|3 d3x0.

Metric'poten+als:' Metric:'

(Newtonian"potenPal)

w:"moPon"w.r.t."preferred"reference"frame

WMAP/NASA

["Will"1993,"Will&2014,&Living&Reviews&in&Rela9vity&] Leo C. Stein (Caltech) Numerical BH mergers beyond GR 34

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LIGO’s tests

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LIGO’s tests

Two tests I like:

  • Any deviation from GR must be below 4% of signal power
  • Test of dispersion relation

Leo C. Stein (Caltech) Numerical BH mergers beyond GR 36