QFT methods for gravitational wave astronomy fileJan Steinhoff (AEI) QFT methods for gravitational...
Transcript of QFT methods for gravitational wave astronomy fileJan Steinhoff (AEI) QFT methods for gravitational...
QFT methods for gravitational wave astronomyapplication to spin effects and dynamic tides
Jan Steinhoff
Max-Planck-Institute for Gravitational Physics (Albert-Einstein-Institute), Potsdam-Golm, Germany
Fields and Strings Seminar, Humboldt University Berlin, June 1st, 2016
Jan Steinhoff (AEI) QFT methods for gravitational wave astronomy HU Berlin, June 1st, 2016 1 / 19
Outline
1 IntroductionSpin and tidal effectsUpcoming ObservatoriesCommon view on analytic description of binariesEffective field theory for compact objects in gravity
2 Spin effectsTwo Facts on Spin in RelativityPoint Particle Action in General RelativityPost-Newtonian ApproximationSpin and GravitomagnetismResults for post-Newtonian approximation with spin (conservative)
3 Dynamical tidesNeutron starsNeutron Star Equations of StateDynamical tidesConvenient concept: response functionRelativistic effects on dynamic tides
Jan Steinhoff (AEI) QFT methods for gravitational wave astronomy HU Berlin, June 1st, 2016 2 / 19
Spin and tidal effects
Jan Steinhoff (AEI) QFT methods for gravitational wave astronomy HU Berlin, June 1st, 2016 3 / 19
pics/binarywave2
binary black holes
Spin and tidal effects
Jan Steinhoff (AEI) QFT methods for gravitational wave astronomy HU Berlin, June 1st, 2016 3 / 19
pics/binarywave2
binary black holes
GW150914 a.k.a. The Event
peak strain 10−21 at ∼ 1 Gly⇒ strain 10−7 at 1 AU
3 M radiated in a fraction of a second⇒ power > all stars in the visible universe
Spin and tidal effects
Jan Steinhoff (AEI) QFT methods for gravitational wave astronomy HU Berlin, June 1st, 2016 3 / 19
pics/binarywave2
binary black holes
pics/ligo
Spin and tidal effects
Jan Steinhoff (AEI) QFT methods for gravitational wave astronomy HU Berlin, June 1st, 2016 3 / 19
pics/binarywave2
binary black holes
pics/ligo
LIGO, www.ligo.org
black holes→ large spinstrong precession→ tests of gravitycompute spin effects!
Spin and tidal effects
Jan Steinhoff (AEI) QFT methods for gravitational wave astronomy HU Berlin, June 1st, 2016 3 / 19
pics/binarywave2
binary black holes
pics/ligo
LIGO, www.ligo.org
black holes→ large spinstrong precession→ tests of gravitycompute spin effects!
pics/neutronstar
www.astroscu.unam.mx/neutrones/
Spin and tidal effects
Jan Steinhoff (AEI) QFT methods for gravitational wave astronomy HU Berlin, June 1st, 2016 3 / 19
pics/binarywave2
binary black holes
pics/ligo
LIGO, www.ligo.org
black holes→ large spinstrong precession→ tests of gravitycompute spin effects!
pics/crust
crustneutron star model
Spin and tidal effects
Jan Steinhoff (AEI) QFT methods for gravitational wave astronomy HU Berlin, June 1st, 2016 3 / 19
pics/binarywave2
binary black holes
pics/ligo
LIGO, www.ligo.org
black holes→ large spinstrong precession→ tests of gravitycompute spin effects!
pics/crust
crustneutron star model
tidal forces↔ oscillation modes⇒ resonances & dynamic tides!
Spin and tidal effects
Jan Steinhoff (AEI) QFT methods for gravitational wave astronomy HU Berlin, June 1st, 2016 3 / 19
pics/binarywave2
binary black holes
pics/ligo
LIGO, www.ligo.org
black holes→ large spinstrong precession→ tests of gravitycompute spin effects!
pics/crust
crustneutron star model
tidal forces↔ oscillation modes⇒ resonances & dynamic tides!
pics/grb3
pics/swift
Swift/BAT
Spin and tidal effects
Jan Steinhoff (AEI) QFT methods for gravitational wave astronomy HU Berlin, June 1st, 2016 3 / 19
pics/binarywave2
binary black holes
pics/ligo
LIGO, www.ligo.org
black holes→ large spinstrong precession→ tests of gravitycompute spin effects!
pics/crust
crustneutron star model
tidal forces↔ oscillation modes⇒ resonances & dynamic tides!
pics/grb3
gamma ray burstsgravitationalwaves
→ mode spectrum
pics/swift
Swift/BAT
Spin and tidal effects
Jan Steinhoff (AEI) QFT methods for gravitational wave astronomy HU Berlin, June 1st, 2016 3 / 19
pics/binarywave2
binary black holes
pics/ligo
LIGO, www.ligo.org
black holes→ large spinstrong precession→ tests of gravitycompute spin effects!
pics/crust
crustneutron star model
tidal forces↔ oscillation modes⇒ resonances & dynamic tides!
pics/grb3
gamma ray burstsgravitationalwaves
→ mode spectrum
pics/swift
Swift/BAT
Spin and tidal effects
Jan Steinhoff (AEI) QFT methods for gravitational wave astronomy HU Berlin, June 1st, 2016 3 / 19
pics/binarywave2
binary black holes
pics/ligo
LIGO, www.ligo.org
black holes→ large spinstrong precession→ tests of gravitycompute spin effects!
pics/crust
crustneutron star model
tidal forces↔ oscillation modes⇒ resonances & dynamic tides!
pics/grb3
gamma ray burstsgravitationalwaves
→ mode spectrum
pics/spectral
pics/swift
Swift/BAT
Spin and tidal effects
Jan Steinhoff (AEI) QFT methods for gravitational wave astronomy HU Berlin, June 1st, 2016 3 / 19
pics/ligo
LIGO, www.ligo.org
black holes→ large spinstrong precession→ tests of gravitycompute spin effects!
tidal forces↔ oscillation modes⇒ resonances & dynamic tides!
pics/grb3
gamma ray burstsgravitationalwaves
→ mode spectrum
pics/spectral
pics/swift
Swift/BAT
pics/binarywave2
pics/crust
−→ spin effects
−→ dynamical tides
Upcoming and Planned Observatories
Jan Steinhoff (AEI) QFT methods for gravitational wave astronomy HU Berlin, June 1st, 2016 4 / 19
Gravitational wave detectors:
pics/et
Upcoming and Planned Observatories
Jan Steinhoff (AEI) QFT methods for gravitational wave astronomy HU Berlin, June 1st, 2016 4 / 19
Gravitational wave detectors:
pics/et
Einstein Telescope
LIGO like detectors:
Virgo (Italy)LIGO-IndiaKagra (Japan)
Upcoming and Planned Observatories
Jan Steinhoff (AEI) QFT methods for gravitational wave astronomy HU Berlin, June 1st, 2016 4 / 19
Gravitational wave detectors:
pics/et
Einstein Telescope
pics/lisa
eLISA space mission
LIGO like detectors:
Virgo (Italy)LIGO-IndiaKagra (Japan)
Upcoming and Planned Observatories
Jan Steinhoff (AEI) QFT methods for gravitational wave astronomy HU Berlin, June 1st, 2016 4 / 19
Radio astronomy:
pics/ska
Square Kilometre Array (SKA)
Gravitational wave detectors:
pics/et
Einstein Telescope
pics/lisa
eLISA space mission
LIGO like detectors:
Virgo (Italy)LIGO-IndiaKagra (Japan)
Common view on analytic description of binariesmatching of zone, see, e.g., Ireland, etal, arXiv:1512.05650
various zones:inner zone (IZ)
around compact objectsnear zone (NZ)
for the orbitfar zone (FZ)
for the waves
in between: buffer zones (BZ)for the matching
Problematic: different gaugesin different zones
Jan Steinhoff (AEI) QFT methods for gravitational wave astronomy HU Berlin, June 1st, 2016 5 / 19
pics/zones
from Ireland, etal, arXiv:1512.05650
Common view on analytic description of binariesmatching of zone, see, e.g., Ireland, etal, arXiv:1512.05650
various zones:inner zone (IZ)
around compact objectsnear zone (NZ)
for the orbitfar zone (FZ)
for the waves
in between: buffer zones (BZ)for the matching
Problematic: different gaugesin different zones
Jan Steinhoff (AEI) QFT methods for gravitational wave astronomy HU Berlin, June 1st, 2016 5 / 19
pics/zones
from Ireland, etal, arXiv:1512.05650
Common view on analytic description of binariesmatching of zone, see, e.g., Ireland, etal, arXiv:1512.05650
various zones:inner zone (IZ)
around compact objectsnear zone (NZ)
for the orbitfar zone (FZ)
for the waves
in between: buffer zones (BZ)for the matching
Problematic: different gaugesin different zones
Jan Steinhoff (AEI) QFT methods for gravitational wave astronomy HU Berlin, June 1st, 2016 5 / 19
pics/zones
from Ireland, etal, arXiv:1512.05650
Effective field theory for compact objects in gravityGoldberger, Rothstein, PRD 73 (2006) 104029; Goldberger, arXiv:hep-ph/0701129
zones → scales
separation of scales:scale µobject size rs
orbital size rvelocity v→ frequency ∼ v
r
effective action replaces buffer zonesin traditional approach
Jan Steinhoff (AEI) QFT methods for gravitational wave astronomy HU Berlin, June 1st, 2016 6 / 19
pics/GRtower
from Goldberger, arXiv:hep-ph/0701129
Effective field theory for compact objects in gravityGoldberger, Rothstein, PRD 73 (2006) 104029; Goldberger, arXiv:hep-ph/0701129
zones → scales
separation of scales:scale µobject size rs
orbital size rvelocity v→ frequency ∼ v
r
effective action replaces buffer zonesin traditional approach
Jan Steinhoff (AEI) QFT methods for gravitational wave astronomy HU Berlin, June 1st, 2016 6 / 19
pics/GRtower
from Goldberger, arXiv:hep-ph/0701129
Outline
1 IntroductionSpin and tidal effectsUpcoming ObservatoriesCommon view on analytic description of binariesEffective field theory for compact objects in gravity
2 Spin effectsTwo Facts on Spin in RelativityPoint Particle Action in General RelativityPost-Newtonian ApproximationSpin and GravitomagnetismResults for post-Newtonian approximation with spin (conservative)
3 Dynamical tidesNeutron starsNeutron Star Equations of StateDynamical tidesConvenient concept: response functionRelativistic effects on dynamic tides
Jan Steinhoff (AEI) QFT methods for gravitational wave astronomy HU Berlin, June 1st, 2016 7 / 19
Two Facts on Spin in Relativity
1. Minimal Extension
R
V
ring of radius R and mass Mspin: S = R M Vmaximal velocity: V ≤ c⇒ minimal extension:
R =S
MV≥ S
Mc
2. Center-of-mass
fast & heavy
slow & light
∆zv
spin
now moving with velocity vrelativistic mass changes inhom.frame-dependent center-of-massneed spin supplementary condition:
e.g., Sµνpν = 0
Jan Steinhoff (AEI) QFT methods for gravitational wave astronomy HU Berlin, June 1st, 2016 8 / 19
Two Facts on Spin in Relativity
1. Minimal Extension
R
V
ring of radius R and mass Mspin: S = R M Vmaximal velocity: V ≤ c⇒ minimal extension:
R =S
MV≥ S
Mc
2. Center-of-mass
fast & heavy
slow & light
∆zv
spin
now moving with velocity vrelativistic mass changes inhom.frame-dependent center-of-massneed spin supplementary condition:
e.g., Sµνpν = 0
Jan Steinhoff (AEI) QFT methods for gravitational wave astronomy HU Berlin, June 1st, 2016 8 / 19
Point Particle Action in General RelativityWestpfahl (1969); Bailey, Israel (1975); Porto (2006); Levi & Steinhoff (2014)
SPP =
∫dσ[−m
√gµνuµuν + ...
]Legendre transformation in uµ (from Nambu-Goto to Polyakov action)
SPP =
∫dσ[pµ
Dzµ
dσ− λ
2H+
12
SµνΛAµDΛAν
dσ− pµSµν
pρpρDpνdσ− χµCµ
]
constraint, interactions inM: H := pµpµ +M2 = 0 mass-shell constraint
ΛAµ : frame field on the worldline, “body-fixed” frame
Action is invariant under a “spin gauge symmetry”:spin gauge constraint: Cµ := Sµν(pν + pΛ0
µ) ∼ generator of symmetry
action invariant under a boost of ΛAµ plus transformation of Sµν
gauge related choice of center → spin supplementary condition
Jan Steinhoff (AEI) QFT methods for gravitational wave astronomy HU Berlin, June 1st, 2016 9 / 19
Point Particle Action in General RelativityWestpfahl (1969); Bailey, Israel (1975); Porto (2006); Levi & Steinhoff (2014)
SPP =
∫dσ[−m
√gµνuµuν + ...
]Legendre transformation in uµ (from Nambu-Goto to Polyakov action)
SPP =
∫dσ[pµ
Dzµ
dσ− λ
2H+
12
SµνΛAµDΛAν
dσ− pµSµν
pρpρDpνdσ− χµCµ
]
constraint, interactions inM: H := pµpµ +M2 = 0 mass-shell constraint
ΛAµ : frame field on the worldline, “body-fixed” frame
Action is invariant under a “spin gauge symmetry”:spin gauge constraint: Cµ := Sµν(pν + pΛ0
µ) ∼ generator of symmetry
action invariant under a boost of ΛAµ plus transformation of Sµν
gauge related choice of center → spin supplementary condition
Jan Steinhoff (AEI) QFT methods for gravitational wave astronomy HU Berlin, June 1st, 2016 9 / 19
Point Particle Action in General RelativityWestpfahl (1969); Bailey, Israel (1975); Porto (2006); Levi & Steinhoff (2014)
SPP =
∫dσ[−m
√gµνuµuν + ...
]Legendre transformation in uµ (from Nambu-Goto to Polyakov action)
SPP =
∫dσ[pµ
Dzµ
dσ− λ
2H+
12
SµνΛAµDΛAν
dσ− pµSµν
pρpρDpνdσ− χµCµ
]
constraint, interactions inM: H := pµpµ +M2 = 0 mass-shell constraint
ΛAµ : frame field on the worldline, “body-fixed” frame
Action is invariant under a “spin gauge symmetry”:spin gauge constraint: Cµ := Sµν(pν + pΛ0
µ) ∼ generator of symmetry
action invariant under a boost of ΛAµ plus transformation of Sµν
gauge related choice of center → spin supplementary condition
Jan Steinhoff (AEI) QFT methods for gravitational wave astronomy HU Berlin, June 1st, 2016 9 / 19
Post-Newtonian Approximation
Application: post-Newtonian approximationfor bound orbitsone expansion parameter, εPN ∼ v2
c2 ∼ GMc2r 1 (weak field & slow motion)
propagation “almost” instantaneoustime dependence of metric gµν treated perturbatively
→ Kaluza-Klein decomposition useful [Kol, Smolkin, arXiv:0712.4116]
ds2 = gµνdxµdxν ≡ e2φ(dt − Aidx i )2 − e−2φγijdx idx j
Leads to gravitomagnetic analogy:φ : gravito-electric fieldAi : gravito-magnetic fieldγij : spin-2 field
Jan Steinhoff (AEI) QFT methods for gravitational wave astronomy HU Berlin, June 1st, 2016 10 / 19
Post-Newtonian Approximation
Application: post-Newtonian approximationfor bound orbitsone expansion parameter, εPN ∼ v2
c2 ∼ GMc2r 1 (weak field & slow motion)
propagation “almost” instantaneoustime dependence of metric gµν treated perturbatively
→ Kaluza-Klein decomposition useful [Kol, Smolkin, arXiv:0712.4116]
ds2 = gµνdxµdxν ≡ e2φ(dt − Aidx i )2 − e−2φγijdx idx j
Leads to gravitomagnetic analogy:φ : gravito-electric fieldAi : gravito-magnetic fieldγij : spin-2 field
Jan Steinhoff (AEI) QFT methods for gravitational wave astronomy HU Berlin, June 1st, 2016 10 / 19
Post-Newtonian Approximation
Application: post-Newtonian approximationfor bound orbitsone expansion parameter, εPN ∼ v2
c2 ∼ GMc2r 1 (weak field & slow motion)
propagation “almost” instantaneoustime dependence of metric gµν treated perturbatively
→ Kaluza-Klein decomposition useful [Kol, Smolkin, arXiv:0712.4116]
ds2 = gµνdxµdxν ≡ e2φ(dt − Aidx i )2 − e−2φγijdx idx j
Leads to gravitomagnetic analogy:φ : gravito-electric fieldAi : gravito-magnetic fieldγij : spin-2 field
Jan Steinhoff (AEI) QFT methods for gravitational wave astronomy HU Berlin, June 1st, 2016 10 / 19
Post-Newtonian Approximation
Application: post-Newtonian approximationfor bound orbitsone expansion parameter, εPN ∼ v2
c2 ∼ GMc2r 1 (weak field & slow motion)
propagation “almost” instantaneoustime dependence of metric gµν treated perturbatively
→ Kaluza-Klein decomposition useful [Kol, Smolkin, arXiv:0712.4116]
ds2 = gµνdxµdxν ≡ e2φ(dt − Aidx i )2 − e−2φγijdx idx j
Leads to gravitomagnetic analogy:φ : gravito-electric fieldAi : gravito-magnetic fieldγij : spin-2 field
Jan Steinhoff (AEI) QFT methods for gravitational wave astronomy HU Berlin, June 1st, 2016 10 / 19
Spin and Gravitomagnetism
Jan Steinhoff (AEI) QFT methods for gravitational wave astronomy HU Berlin, June 1st, 2016 11 / 19
Interaction with gravito-magnetic field Ai ≈ −gi0:
12
SµνΛAµDΛAν
dσ
12
Sij∂iAj
S1
Ai AjS2
LS1S2 =12
Ski1 〈∂k Ai ∂`Aj〉
12
S`j2
=12
Ski1
12
S`j2 δij (−16πG)∂
∂xk1 ∂x`2
∫dk
(2π)3ei~k(~x1−~x2)
~k2
= −GSki1 S`i2
∂
∂xk1 ∂x`2
(1
r12
)
Here: r12 = |~x1 − ~x2|Ignoring factors like δ(t1 − t2)
Feynman rules see e.g. [arXiv:1501.04956]
Status: NNLO (many more diagrams, loops)
Spin and Gravitomagnetism
Jan Steinhoff (AEI) QFT methods for gravitational wave astronomy HU Berlin, June 1st, 2016 11 / 19
Interaction with gravito-magnetic field Ai ≈ −gi0:
12
SµνΛAµDΛAν
dσ
12
Sij∂iAj
S1
Ai AjS2
LS1S2 =12
Ski1 〈∂k Ai ∂`Aj〉
12
S`j2
=12
Ski1
12
S`j2 δij (−16πG)∂
∂xk1 ∂x`2
∫dk
(2π)3ei~k(~x1−~x2)
~k2
= −GSki1 S`i2
∂
∂xk1 ∂x`2
(1
r12
)
Here: r12 = |~x1 − ~x2|Ignoring factors like δ(t1 − t2)
Feynman rules see e.g. [arXiv:1501.04956]
Status: NNLO (many more diagrams, loops)
Spin and Gravitomagnetism
Jan Steinhoff (AEI) QFT methods for gravitational wave astronomy HU Berlin, June 1st, 2016 11 / 19
Interaction with gravito-magnetic field Ai ≈ −gi0:
12
SµνΛAµDΛAν
dσ
12
Sij∂iAj
S1
Ai AjS2
LS1S2 =12
Ski1 〈∂k Ai ∂`Aj〉
12
S`j2
=12
Ski1
12
S`j2 δij (−16πG)∂
∂xk1 ∂x`2
∫dk
(2π)3ei~k(~x1−~x2)
~k2
= −GSki1 S`i2
∂
∂xk1 ∂x`2
(1
r12
)
Here: r12 = |~x1 − ~x2|Ignoring factors like δ(t1 − t2)
Feynman rules see e.g. [arXiv:1501.04956]
Status: NNLO (many more diagrams, loops)
Spin and Gravitomagnetism
Jan Steinhoff (AEI) QFT methods for gravitational wave astronomy HU Berlin, June 1st, 2016 11 / 19
Interaction with gravito-magnetic field Ai ≈ −gi0:
12
SµνΛAµDΛAν
dσ
12
Sij∂iAj
S1
Ai AjS2
LS1S2 =12
Ski1 〈∂k Ai ∂`Aj〉
12
S`j2
=12
Ski1
12
S`j2 δij (−16πG)∂
∂xk1 ∂x`2
∫dk
(2π)3ei~k(~x1−~x2)
~k2
= −GSki1 S`i2
∂
∂xk1 ∂x`2
(1
r12
)
Here: r12 = |~x1 − ~x2|Ignoring factors like δ(t1 − t2)
Feynman rules see e.g. [arXiv:1501.04956]
Status: NNLO (many more diagrams, loops)
Spin and Gravitomagnetism
Jan Steinhoff (AEI) QFT methods for gravitational wave astronomy HU Berlin, June 1st, 2016 11 / 19
Interaction with gravito-magnetic field Ai ≈ −gi0:
12
SµνΛAµDΛAν
dσ
12
Sij∂iAj
S1
Ai AjS2
LS1S2 =12
Ski1 〈∂k Ai ∂`Aj〉
12
S`j2
=12
Ski1
12
S`j2 δij (−16πG)∂
∂xk1 ∂x`2
∫dk
(2π)3ei~k(~x1−~x2)
~k2
= −GSki1 S`i2
∂
∂xk1 ∂x`2
(1
r12
)
Here: r12 = |~x1 − ~x2|Ignoring factors like δ(t1 − t2)
Feynman rules see e.g. [arXiv:1501.04956]
Status: NNLO (many more diagrams, loops)
Spin and Gravitomagnetism
Jan Steinhoff (AEI) QFT methods for gravitational wave astronomy HU Berlin, June 1st, 2016 11 / 19
Interaction with gravito-magnetic field Ai ≈ −gi0:
12
SµνΛAµDΛAν
dσ
12
Sij∂iAj
S1
Ai AjS2
LS1S2 =12
Ski1 〈∂k Ai ∂`Aj〉
12
S`j2
=12
Ski1
12
S`j2 δij (−16πG)∂
∂xk1 ∂x`2
∫dk
(2π)3ei~k(~x1−~x2)
~k2
= −GSki1 S`i2
∂
∂xk1 ∂x`2
(1
r12
)
Here: r12 = |~x1 − ~x2|Ignoring factors like δ(t1 − t2)
Feynman rules see e.g. [arXiv:1501.04956]
Status: NNLO (many more diagrams, loops)
Results for post-Newtonian approximation with spinconservative part of the motion of the binary
post-Newtonian (PN) approximation: expansion around 1c → 0 (Newton)
order c0 c−1 c−2 c−3 c−4 c−5 c−6 c−7 c−8
N 1PN 2PN 3PN 4PN
non spin " " " " "
spin-orbit " " "
S21 " " "
S1S2 " " "
Spin3 "(!)
Spin4 "(!)...
. . .
" known (!) partial " derived last yearWork by many people (“just” for the spin sector): Barker, Blanchet, Bohe, Buonanno, O’Connell,Damour, D’Eath, Faye, Hartle, Hartung, Hergt, Jaranowski, Marsat, Levi, Ohashi, Owen, Perrodin,Poisson, Porter, Porto, Rothstein, Schafer, Steinhoff, Tagoshi, Thorne, Tulczyjew, Vaidya
Jan Steinhoff (AEI) QFT methods for gravitational wave astronomy HU Berlin, June 1st, 2016 12 / 19
Outline
1 IntroductionSpin and tidal effectsUpcoming ObservatoriesCommon view on analytic description of binariesEffective field theory for compact objects in gravity
2 Spin effectsTwo Facts on Spin in RelativityPoint Particle Action in General RelativityPost-Newtonian ApproximationSpin and GravitomagnetismResults for post-Newtonian approximation with spin (conservative)
3 Dynamical tidesNeutron starsNeutron Star Equations of StateDynamical tidesConvenient concept: response functionRelativistic effects on dynamic tides
Jan Steinhoff (AEI) QFT methods for gravitational wave astronomy HU Berlin, June 1st, 2016 13 / 19
A neutron star model
pics/neutronstar
Neutron star picture by D. Pagewww.astroscu.unam.mx/neutrones/
”Lab“ for various areas in physics
magnetic field, plasmacrust (solid state)superfluiditysuperconductivityunknown matter in corecondensate of quarks, hyperons,kaons, pions, . . . ?
accumulation of dark matter ?
Related objects:pulsarsmagnetarsquark stars/strange stars
Jan Steinhoff (AEI) QFT methods for gravitational wave astronomy HU Berlin, June 1st, 2016 14 / 19
A neutron star model
pics/neutronstar
Neutron star picture by D. Pagewww.astroscu.unam.mx/neutrones/
”Lab“ for various areas in physics
magnetic field, plasmacrust (solid state)superfluiditysuperconductivityunknown matter in corecondensate of quarks, hyperons,kaons, pions, . . . ?
accumulation of dark matter ?
Related objects:pulsarsmagnetarsquark stars/strange stars
Jan Steinhoff (AEI) QFT methods for gravitational wave astronomy HU Berlin, June 1st, 2016 14 / 19
A neutron star model
pics/neutronstar
Neutron star picture by D. Pagewww.astroscu.unam.mx/neutrones/
”Lab“ for various areas in physics
magnetic field, plasmacrust (solid state)superfluiditysuperconductivityunknown matter in corecondensate of quarks, hyperons,kaons, pions, . . . ?
accumulation of dark matter ?
Related objects:pulsarsmagnetarsquark stars/strange stars
Jan Steinhoff (AEI) QFT methods for gravitational wave astronomy HU Berlin, June 1st, 2016 14 / 19
Neutron Star Equations of State
pics/NSMassRad
mpifr-bonn.mpg.de
Jan Steinhoff (AEI) QFT methods for gravitational wave astronomy HU Berlin, June 1st, 2016 15 / 19
Neutron Star Equations of State
pics/NSMassRad
mpifr-bonn.mpg.de
Jan Steinhoff (AEI) QFT methods for gravitational wave astronomy HU Berlin, June 1st, 2016 15 / 19
However, a measurement of the tidal defor-mations through gravitational waves can be agood alternative to radius measurements.
Dynamical tides of neutron starsJS etal, in preparation Hinderer etal, PRL 116 (2016) 181101 (Research Highlight in Nature)
Neutron stars can oscillate→ effective harmonic oscillator action
Ltide ∼DAµν
dσDAµνdσ
− ω20AµνAµν − I0
2AµνEµν +
K4
EµνEµν + ...
(electric) tidal field Eµν = Rαµβνuαuβ
Amplitude Aµν must be SO(3) irreducuble, i.e, symmetric-tracefree:
A[µν] = 0 = Aµµ, Aµνuν = 0
Here: quadrupolar amplitude, strongly couples to gravityMore oscillators in the action→ more modes→ spectrumIn Newtonian limit: easy to compute constants ω0, I0, K , . . .
How to get these constants in relativistic case? → matching
Other important references: Flanagan, Hinderer, PRD 77 (2008) 021502Hinderer, ApJ 677 (2008) 1216 Chakrabarti, Delsate, JS, arXiv:1304.2228Alexander, MNRAS 227 (1987) 843 Bini, Damour, Faye, PRD 85 (2012) 124034
Jan Steinhoff (AEI) QFT methods for gravitational wave astronomy HU Berlin, June 1st, 2016 16 / 19
Dynamical tides of neutron starsJS etal, in preparation Hinderer etal, PRL 116 (2016) 181101 (Research Highlight in Nature)
Neutron stars can oscillate→ effective harmonic oscillator action
Ltide ∼DAµν
dσDAµνdσ
− ω20AµνAµν − I0
2AµνEµν +
K4
EµνEµν + ...
(electric) tidal field Eµν = Rαµβνuαuβ
Amplitude Aµν must be SO(3) irreducuble, i.e, symmetric-tracefree:
A[µν] = 0 = Aµµ, Aµνuν = 0
Here: quadrupolar amplitude, strongly couples to gravityMore oscillators in the action→ more modes→ spectrumIn Newtonian limit: easy to compute constants ω0, I0, K , . . .
How to get these constants in relativistic case? → matching
Other important references: Flanagan, Hinderer, PRD 77 (2008) 021502Hinderer, ApJ 677 (2008) 1216 Chakrabarti, Delsate, JS, arXiv:1304.2228Alexander, MNRAS 227 (1987) 843 Bini, Damour, Faye, PRD 85 (2012) 124034
Jan Steinhoff (AEI) QFT methods for gravitational wave astronomy HU Berlin, June 1st, 2016 16 / 19
Dynamical tides of neutron starsJS etal, in preparation Hinderer etal, PRL 116 (2016) 181101 (Research Highlight in Nature)
Neutron stars can oscillate→ effective harmonic oscillator action
Ltide ∼DAµν
dσDAµνdσ
− ω20AµνAµν − I0
2AµνEµν +
K4
EµνEµν + ...
(electric) tidal field Eµν = Rαµβνuαuβ
Amplitude Aµν must be SO(3) irreducuble, i.e, symmetric-tracefree:
A[µν] = 0 = Aµµ, Aµνuν = 0
Here: quadrupolar amplitude, strongly couples to gravityMore oscillators in the action→ more modes→ spectrumIn Newtonian limit: easy to compute constants ω0, I0, K , . . .
How to get these constants in relativistic case? → matching
Other important references: Flanagan, Hinderer, PRD 77 (2008) 021502Hinderer, ApJ 677 (2008) 1216 Chakrabarti, Delsate, JS, arXiv:1304.2228Alexander, MNRAS 227 (1987) 843 Bini, Damour, Faye, PRD 85 (2012) 124034
Jan Steinhoff (AEI) QFT methods for gravitational wave astronomy HU Berlin, June 1st, 2016 16 / 19
Dynamical tides of neutron starsJS etal, in preparation Hinderer etal, PRL 116 (2016) 181101 (Research Highlight in Nature)
Neutron stars can oscillate→ effective harmonic oscillator action
Ltide ∼DAµν
dσDAµνdσ
− ω20AµνAµν − I0
2AµνEµν +
K4
EµνEµν + ...
(electric) tidal field Eµν = Rαµβνuαuβ
Amplitude Aµν must be SO(3) irreducuble, i.e, symmetric-tracefree:
A[µν] = 0 = Aµµ, Aµνuν = 0
Here: quadrupolar amplitude, strongly couples to gravityMore oscillators in the action→ more modes→ spectrumIn Newtonian limit: easy to compute constants ω0, I0, K , . . .
How to get these constants in relativistic case? → matching
Other important references: Flanagan, Hinderer, PRD 77 (2008) 021502Hinderer, ApJ 677 (2008) 1216 Chakrabarti, Delsate, JS, arXiv:1304.2228Alexander, MNRAS 227 (1987) 843 Bini, Damour, Faye, PRD 85 (2012) 124034
Jan Steinhoff (AEI) QFT methods for gravitational wave astronomy HU Berlin, June 1st, 2016 16 / 19
Convenient concept: response functionChakrabarti, Delsate, Steinhoff, PRD 88 (2013) 084038 and arXiv:1304.2228
quadrupolar sector: ` = 2
linear responseF−→
external quadrupolar field −→ deformation −→ quadrupolar responseφ ∼ r `
∑2F1 φ ∼ r−`−1∑
2F1
0.00 0.05 0.10 0.15 0.20 0.25
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
frequency: Ω R 2 Π
resp
on
se:
F
R5
quadrupolarresponse fit:
F ≈∑
n
I2n
ω2n − ω2
ωn: mode frequencyIn: coupling constantR: radius
poles⇒ resonances!
pics/resonance
Tacoma Bridge
Jan Steinhoff (AEI) QFT methods for gravitational wave astronomy HU Berlin, June 1st, 2016 17 / 19
Convenient concept: response functionChakrabarti, Delsate, Steinhoff, PRD 88 (2013) 084038 and arXiv:1304.2228
quadrupolar sector: ` = 2
linear responseF−→
external quadrupolar field −→ deformation −→ quadrupolar responseφ ∼ r `
∑2F1 φ ∼ r−`−1∑
2F1
0.00 0.05 0.10 0.15 0.20 0.25
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
frequency: Ω R 2 Π
resp
on
se:
F
R5
quadrupolarresponse fit:
F ≈∑
n
I2n
ω2n − ω2
ωn: mode frequencyIn: coupling constantR: radius
poles⇒ resonances!
pics/resonance
Tacoma Bridge
Jan Steinhoff (AEI) QFT methods for gravitational wave astronomy HU Berlin, June 1st, 2016 17 / 19
Convenient concept: response functionChakrabarti, Delsate, Steinhoff, PRD 88 (2013) 084038 and arXiv:1304.2228
quadrupolar sector: ` = 2
linear responseF−→
external quadrupolar field −→ deformation −→ quadrupolar responseφ ∼ r `
∑2F1 φ ∼ r−`−1∑
2F1
0.00 0.05 0.10 0.15 0.20 0.25
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
frequency: Ω R 2 Π
resp
on
se:
F
R5
quadrupolarresponse fit:
F ≈∑
n
I2n
ω2n − ω2
ωn: mode frequencyIn: coupling constantR: radius
poles⇒ resonances!
pics/resonance
Tacoma Bridge
Jan Steinhoff (AEI) QFT methods for gravitational wave astronomy HU Berlin, June 1st, 2016 17 / 19
Relativistic effects on dynamic tides
All that was said hold also in Newtonian gravity . . .
What is new in the relativistic case?
values of constants ω0, I0, K , . . .is differentNewtonian: K = 0relativistic K 6= 0redshift effectframe dragging effect∼ Zeeman effect
Jan Steinhoff (AEI) QFT methods for gravitational wave astronomy HU Berlin, June 1st, 2016 18 / 19
Relativistic effects on dynamic tides
All that was said hold also in Newtonian gravity . . .
What is new in the relativistic case?
values of constants ω0, I0, K , . . .is differentNewtonian: K = 0relativistic K 6= 0redshift effectframe dragging effect∼ Zeeman effect
Jan Steinhoff (AEI) QFT methods for gravitational wave astronomy HU Berlin, June 1st, 2016 18 / 19
Relativistic effects on dynamic tides
All that was said hold also in Newtonian gravity . . .
What is new in the relativistic case?
values of constants ω0, I0, K , . . .is differentNewtonian: K = 0relativistic K 6= 0redshift effectframe dragging effect∼ Zeeman effect
Jan Steinhoff (AEI) QFT methods for gravitational wave astronomy HU Berlin, June 1st, 2016 18 / 19
Relativistic effects on dynamic tides
All that was said hold also in Newtonian gravity . . .
What is new in the relativistic case?
values of constants ω0, I0, K , . . .is differentNewtonian: K = 0relativistic K 6= 0redshift effectframe dragging effect∼ Zeeman effect
Jan Steinhoff (AEI) QFT methods for gravitational wave astronomy HU Berlin, June 1st, 2016 18 / 19
frame of the neutron star is draggedin the direction of the orbital motion
Summary
black holes→ large spins→ strong gravitomagnetic effects→ interesting/new tests of gravity
NS structure largely unknown/mysterious→ tidal effects in gravitational waves and electromagnetic
counterparts can enlighten nuclear interactions
GW astronomy exciting new and interdisciplinary field
important to use common language→ effective field theorybut need to go a bit beyond standard techniquese.g., in-in formalism, see [Galley PRL 110, 174301 (2013)]“good” level of abstraction:
DeWitt, The Global Approach to Quantum Field Theory
Jan Steinhoff (AEI) QFT methods for gravitational wave astronomy HU Berlin, June 1st, 2016 19 / 19