Advanced LIGO’s ability to detect apparent violations of ......Advanced LIGO’s ability to detect...

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

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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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SpEC q=1

BAM FAU BAM HHB S00

BAM HHB S25 BAM HHB S50


LazEv Lean c

MayaKranc e0 MayaKranc e02

t/M t/M

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CCATIE r0 CCATIE r2

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CCATIE s6 Hahndol kick

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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

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• 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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LazEv Lean c

MayaKranc e0 MayaKranc e02

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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

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m1, m2, �1 =j1

(m1)2, �2 =

j2(m2)2

, �1 / k2r51, �2 / k2r

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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




In a CBC event:

� ⌘ j

m2 1

�1 1 and �2 1

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� ⌘ 23k2r

5 = 0




In a CBC event:

� ⌘ j

m2 1

BBH

�1 1 and �2 1

NS-BH

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� ⌘ 23k2r

5 = 0




In a CBC event: In a CBC event:

� ⌘ j

m2 1

BBH

�1 1 and �2 1

NS-BH

�1 = 0 �2 = 0and

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� ⌘ 23k2r

5 = 0





� ⌘ j

m2 1

BBH

�1 1 and �2 1

NS-BH

�1 = 0 �2 = 0and

BBH

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� ⌘ 23k2r

5 = 0





� ⌘ j

m2 1

�1 = 0 �2 = 0andNot a Kerr BH in PN formalism!

Exotic object? Not Kerr?Not GR? Waveform inaccuracy?

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�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

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0 < ⌘ 14

�1 �s, �a 1

Measured Parameters


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

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0 < ⌘ 14

�1 �s, �a 1


Measured Parameters


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

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0 < ⌘ 14

�1 �s, �a 1


Measured Parameters


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

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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)

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prior knowledge ofparameter space

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0 < ⌘ 14

improved by?




accuracy ofPN waveform

h = A(f ; ~✓)ei (f ;~✓)

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0 < ⌘ 14

improved by?

vary from 0-2.5 PN, with and without spin in amp.




accuracy ofPN waveform

h = A(f ; ~✓)ei (f ;~✓)

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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

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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

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Additional improvement in spin measurability seen when spin corrections are included in the amplitude: degeneracy breaking between spin and chirp mass


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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


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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


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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


no no no

noyes, starting at

1.0 pN in amplitude

N/A

Summary of Results

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space

including higher


spinning BBH

spinning NS-BH

tidal BBH




no no no

noyes, starting at

1.0 pN in amplitude

N/A

Summary of Results

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}


space

including higher


spinning BBH

spinning NS-BH

tidal BBH




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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Advanced LIGO’s ability to detect apparent violations of ......Advanced LIGO’s ability to detect...

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