Advanced LIGO’s ability to detect apparent violations of cosmic censorship and the no-hair theorem through CBC detectionsMadeline Wade1, Jolien D.E. Creighton1, Evan Ochsner1, and Alex B. Nielsen2
1University of Wisconsin - Milwaukee2Max-Planck-Institute for Gravitational Physics
23rd Midwest Relativity Meeting, UWM, July 26, 2013
arXiv:1306.3901DOI: 10.1103/PhysRevD.88.083002LIGO-G1300522
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• Gravitational waves (GWs) from CBC events
• Possible tests of GR from a CBC GW detection involving a black hole (BH)
• Cosmic censorship conjecture
• No-hair theorem
• Results for improving tests of GR through parameter measurability
Outline
2
Compact Binary Coalescence (CBC)
• Stellar mass black hole and/or neutron star CBC events are among some of the most promising sources for ground-based interferometers, such as aLIGO
Results from the first NINJA project 8
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-2000 -1000 0
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SpEC q=1
BAM FAU BAM HHB S00
BAM HHB S25 BAM HHB S50
BAM HHB S75 BAM HHB S85
LazEv Lean c
MayaKranc e0 MayaKranc e02
t/M t/M
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CCATIE r0 CCATIE r2
CCATIE r4 CCATIE r6
CCATIE s6 Hahndol kick
Hahndol non Lean 2
PU CP PU T52W
UIUC cp UIUC punc
t/M t/M
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BAM FAU BAM HHB S00 BAM HHB S25 BAM HHB S50 BAM HHB S75 BAM HHB S85
CCATIE r0 CCATIE r2 CCATIE r4 CCATIE r6 CCATIE s6 Hahndol kick
Hahndol non LazEv Lean 2 Lean c MayaKranc e0 MayaKranc e02
PU CP PU T52W SpEC q=1 UIUC cp UIUC punc
t/M t/M t/M t/M t/M t/M
Figure 1. Summary of all submitted numerical waveforms:r/M Re(h22) The x-axis shows time in units of M and the y-axis showsthe real part of the (!, m) = (2, 2) component of the dimensionless wave strainrh = rh+ ! irh!. The top panels show the complete waveforms: the top-leftpanel includes waveforms that last more than about 700M , and the top-rightpanel includes waveforms shorter than about 700M . The bottom panel shows anenlargement of the merger phase for all waveforms.
strain
time
inspiral merger ringdown
3
• Inspiral is well-modeled with post-Newtonian (PN) waveforms
• PN waveforms depend on source parameters:
Compact Binary Coalescence (CBC)Results from the first NINJA project 8
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-2000 -1000 0
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-2000 -1000 0
SpEC q=1
BAM FAU BAM HHB S00
BAM HHB S25 BAM HHB S50
BAM HHB S75 BAM HHB S85
LazEv Lean c
MayaKranc e0 MayaKranc e02
t/M t/M
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CCATIE r0 CCATIE r2
CCATIE r4 CCATIE r6
CCATIE s6 Hahndol kick
Hahndol non Lean 2
PU CP PU T52W
UIUC cp UIUC punc
t/M t/M
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0
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0
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0
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BAM FAU BAM HHB S00 BAM HHB S25 BAM HHB S50 BAM HHB S75 BAM HHB S85
CCATIE r0 CCATIE r2 CCATIE r4 CCATIE r6 CCATIE s6 Hahndol kick
Hahndol non LazEv Lean 2 Lean c MayaKranc e0 MayaKranc e02
PU CP PU T52W SpEC q=1 UIUC cp UIUC punc
t/M t/M t/M t/M t/M t/M
Figure 1. Summary of all submitted numerical waveforms:r/M Re(h22) The x-axis shows time in units of M and the y-axis showsthe real part of the (!, m) = (2, 2) component of the dimensionless wave strainrh = rh+ ! irh!. The top panels show the complete waveforms: the top-leftpanel includes waveforms that last more than about 700M , and the top-rightpanel includes waveforms shorter than about 700M . The bottom panel shows anenlargement of the merger phase for all waveforms.
strain
time
4
m1, m2, �1 =j1
(m1)2, �2 =
j2(m2)2
, �1 / k2r51, �2 / k2r
52
Tests of General Relativity with Black Holes
Cosmic Censorship No-Hair Theorem
For a Kerr BH: For a non-spinning Kerr BH:
� ⌘ j
m2 1
5
� ⌘ 23k2r
5 = 0
Tests of General Relativity with Black Holes
Cosmic Censorship No-Hair Theorem
For a Kerr BH: For a non-spinning Kerr BH:
In a CBC event:
� ⌘ j
m2 1
�1 1 and �2 1
6
� ⌘ 23k2r
5 = 0
Tests of General Relativity with Black Holes
Cosmic Censorship No-Hair Theorem
For a Kerr BH: For a non-spinning Kerr BH:
In a CBC event:
� ⌘ j
m2 1
BBH
�1 1 and �2 1
NS-BH
7
� ⌘ 23k2r
5 = 0
Tests of General Relativity with Black Holes
Cosmic Censorship No-Hair Theorem
For a Kerr BH: For a non-spinning Kerr BH:
In a CBC event: In a CBC event:
� ⌘ j
m2 1
BBH
�1 1 and �2 1
NS-BH
�1 = 0 �2 = 0and
8
� ⌘ 23k2r
5 = 0
Tests of General Relativity with Black Holes
Cosmic Censorship No-Hair Theorem
For a Kerr BH: For a non-spinning Kerr BH:
In a CBC event: In a CBC event:
� ⌘ j
m2 1
BBH
�1 1 and �2 1
NS-BH
�1 = 0 �2 = 0and
BBH
9
� ⌘ 23k2r
5 = 0
Tests of General Relativity with Black Holes
Cosmic Censorship No-Hair Theorem
For a Kerr BH: For a non-spinning Kerr BH:
In a CBC event: In a CBC event:
� ⌘ j
m2 1
�1 = 0 �2 = 0andNot a Kerr BH in PN formalism!
Exotic object? Not Kerr?Not GR? Waveform inaccuracy?
10
�1 1 and �2 1
� ⌘ 23k2r
5 = 0
Relevant Parameters and Parameter Space Bounds
Measured Parameters
Parameter Space Bounds
Mass
Spin
Tidal
⌘ =m1m2
(m1 + m2)2
M = (m1 + m2)⌘3/5
�s =12(�1 + �2)
�a =12(�1 � �2)
⇤̃ =�̃(�1, �2)
(m1 + m2)5�BH = 0! ⇤̃BBH = 0
11
0 < ⌘ 14
�1 �s, �a 1
Measured Parameters
Parameter Space Bounds
Mass
Spin
Tidal
Relevant Parameters and Parameter Space Bounds
⌘ =m1m2
(m1 + m2)2
M = (m1 + m2)⌘3/5
�s =12(�1 + �2)
�a =12(�1 � �2)
⇤̃ =�̃(�1, �2)
(m1 + m2)5�BH = 0! ⇤̃BBH = 0
physical bound
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0 < ⌘ 14
�1 �s, �a 1
Relevant Parameters and Parameter Space Bounds
Measured Parameters
Parameter Space Bounds
Mass
Spin
Tidal
⌘ =m1m2
(m1 + m2)2
M = (m1 + m2)⌘3/5
�s =12(�1 + �2)
�a =12(�1 � �2)
⇤̃ =�̃(�1, �2)
(m1 + m2)5�BH = 0! ⇤̃BBH = 0
physical bound
cosmic censorship
13
0 < ⌘ 14
�1 �s, �a 1
Relevant Parameters and Parameter Space Bounds
Measured Parameters
Parameter Space Bounds
Mass
Spin
Tidal
⌘ =m1m2
(m1 + m2)2
M = (m1 + m2)⌘3/5
�s =12(�1 + �2)
�a =12(�1 � �2)
⇤̃ =�̃(�1, �2)
(m1 + m2)5�BH = 0! ⇤̃BBH = 0
physical bound
cosmic censorship
no-hairtheorem
14
0 < ⌘ 14
�1 �s, �a 1
Improving aLIGO’s Ability to Test Cosmic Censorship and the No-Hair Theorem
Limiting Factor: Measurement uncertaintyof spin (cosmic censorship) and tides (no hair theorem)
15
Improving aLIGO’s Ability to Test Cosmic Censorship and the No-Hair Theorem
Limiting Factor: Measurement uncertaintyof spin (cosmic censorship) and tides (no hair theorem)
prior knowledge ofparameter space
16
0 < ⌘ 14
improved by?
Improving aLIGO’s Ability to Test Cosmic Censorship and the No-Hair Theorem
Limiting Factor: Measurement uncertaintyof spin (cosmic censorship) and tides (no hair theorem)
prior knowledge ofparameter space
accuracy ofPN waveform
h = A(f ; ~✓)ei (f ;~✓)
17
0 < ⌘ 14
improved by?
vary from 0-2.5 PN, with and without spin in amp.
Improving aLIGO’s Ability to Test Cosmic Censorship and the No-Hair Theorem
Limiting Factor: Measurement uncertaintyof spin (cosmic censorship) and tides (no hair theorem)
prior knowledge ofparameter space
accuracy ofPN waveform
h = A(f ; ~✓)ei (f ;~✓)
18
0 < ⌘ 14
improved by?
Improving Measurability of Spin for a Near-Equal Mass, Non-Precessing BBH system (10, 11) Msun
Blue: minimal detectable violation at 1-sigma for an SNR of 10
Physical prior on symmetric mass ratio important for near-equal mass BBH systems when using Newtonian amplitude waveform
19
Improving Measurability of Spin for a Near-Equal Mass, Non-Precessing BBH system (10, 11) Msun
Non-spinning amplitude corrections important for near-equal mass BBH system: degeneracy breaking between spin and symmetric mass ratio
Blue: minimal detectable violation at 1-sigma for an SNR of 10Red: 1-sigma error ellipse for fiducial spins at SNR of 10
20
Improving Measurability of Spin for a Near-Equal Mass, Non-Precessing BBH system (10, 11) Msun
Additional improvement in spin measurability seen when spin corrections are included in the amplitude: degeneracy breaking between spin and chirp mass
Blue: minimal detectable violation at 1-sigma for an SNR of 10Red: 1-sigma error ellipse for fiducial spins at SNR of 10
21
No Improvement in Measurability of Spin for a Non-Precessing NS-BH system (1.4, 10) Msun
No effect from physical prior on symmetric mass ratio or amplitude corrections, with or without spin
Blue: minimal detectable violation at 1-sigma for an SNR of 10Red: 1-sigma error ellipse for fiducial spins at SNR of 10
22
Improvement in Measurability of Tides for a Near-Equal Mass BBH system (10, 11) Msun
Amplitude corrections improve the measurability of the tidal deformability: degeneracy decreases between chirp mass and tides, and symmetric mass
ratio and tides
Blue: minimal detectable violation at 1-sigma for an SNR of 10Red: 1-sigma error ellipse for fiducial spins at SNR of 10
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restricting parameter
space
including higher
harmonicsincluding spin in amplitude
spinning BBH
spinning NS-BH
tidal BBH
yes, only at 0.0 pN in amplitude
yes, starting at 0.5 pN in amplitude
yes, starting at 1.0 pN in amplitude
no no no
noyes, starting at
1.0 pN in amplitude
N/A
Summary of Results
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restricting parameter
space
including higher
harmonicsincluding spin in amplitude
spinning BBH
spinning NS-BH
tidal BBH
yes, only at 0.0 pN in amplitude
yes, starting at 0.5 pN in amplitude
yes, starting at 1.0 pN in amplitude
no no no
noyes, starting at
1.0 pN in amplitude
N/A
Summary of Results
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}
restricting parameter
space
including higher
harmonicsincluding spin in amplitude
spinning BBH
spinning NS-BH
tidal BBH
yes, only at 0.0 pN in amplitude
yes, starting at 0.5 pN in amplitude
yes, starting at 1.0 pN in amplitude
no no no
noyes, starting at
1.0 pN in amplitude
N/A
Summary of Results
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}
Conclusions
• Consider physical parameter space bounds (already done in LIGO’s Bayesian parameter estimation framework)
• Use more accurate approximations to the amplitude of the waveform, since this can break parameter degeneracies
• These effects are most important for near-equal mass systems
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