From Ringdown to Tests of General Relativity For

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Credits to: Buonanno, Ossokine 1 FOR WHOM THE BLACK HOLE TOLLS: FROM RINGDOWN TO TESTS OF GENERAL RELATIVITY

Gregorio Carullo 104° Congresso Nazionale Società Italiana di Fisica OUTLINE OF THE PRESENTATION

▸ Introduction

▸ Quasi-normal modes of a black hole

▸ GW150914: the day we saw a black hole ringing

▸ Recent developments

▸ Tests of General Relativity with second-generation detectors

▸ Conclusions

Gregorio Carullo BINARY BLACK HOLES COALESCENCES

▸ Coalescences of binary black holes emit gravitational waves detectable on earth

Gregorio Carullo GW170814: A Three-Detector Observation of Gravitational Waves from a Binary Black Hole Coalescence, LVC collaboration, PRL 119, 141101 (2017) BINARY BLACK HOLES COALESCENCES

▸ Coalescences of binary black holes emit gravitational waves detectable on earth

▸ Three main phases of the coalescence:

Gregorio Carullo Observation of Gravitational Waves from a Binary Black Hole Merger, LVC collaboration, PRL 116, 061102 (2016) BINARY BLACK HOLES COALESCENCES

▸ Coalescences of binary black holes emit gravitational waves detectable on earth

▸ Three main phases of the coalescence:

▸ Inspiral: Post-Newtonian theory

Gregorio Carullo Observation of Gravitational Waves from a Binary Black Hole Merger, LVC collaboration, PRL 116, 061102 (2016) BINARY BLACK HOLES COALESCENCES

▸ Coalescences of binary black holes emit gravitational waves detectable on earth

▸ Three main phases of the coalescence:

▸ Inspiral: Post-Newtonian theory

▸ Plunge-merger: numerical simulations

Gregorio Carullo Observation of Gravitational Waves from a Binary Black Hole Merger, LVC collaboration, PRL 116, 061102 (2016) BINARY BLACK HOLES COALESCENCES

▸ Coalescences of binary black holes emit gravitational waves detectable on earth

▸ Three main phases of the coalescence:

▸ Inspiral: Post-Newtonian theory

▸ Plunge-merger: numerical simulations

▸ Ringdown: perturbation theory and numerical simulations

Gregorio Carullo Observation of Gravitational Waves from a Binary Black Hole Merger, LVC collaboration, PRL 116, 061102 (2016) WHAT IS RINGDOWN?

▸ Space-time is a geometrical dynamical entity

Gregorio Carullo WHAT IS RINGDOWN?

▸ Space-time is a geometrical dynamical entity

▸ Space-time itself can undergo oscillations even when no matter is present

Gregorio Carullo WHAT IS RINGDOWN?

▸ Space-time is a geometrical dynamical entity

▸ Space-time itself can undergo oscillations even when no matter is present

▸ The ringdown phase corresponds to the emission of the normal modes of the remnant black hole, damped by the presence of an horizon Vishveshwara, Nature 227, 936 (1970)

Gregorio Carullo WHAT IS RINGDOWN?

▸ Space-time is a geometrical dynamical entity

▸ Space-time itself can undergo oscillations even when no matter is present

▸ The ringdown phase corresponds to the emission of the normal modes of the remnant black hole, damped by the presence of an horizon

▸ Intrinsically dissipative system, unlike external damping of normal modes in classical systems

Gregorio Carullo WHAT IS RINGDOWN?

▸ Space-time is a geometrical dynamical entity

▸ Space-time itself can undergo oscillations even when no matter is present

▸ The ringdown phase corresponds to the emission of the normal modes of the remnant black hole, damped by the presence of an horizon

▸ Intrinsically dissipative system, unlike external damping of normal modes in classical systems

▸ Analytical solution of the linearized Einstein equations on a Black Hole background Regge, Wheeler, Phys. Rev. 108, 1063 (1957)

Zerilli, Phys. Rev. Lett. 24, 737 (1970)

Gregorio Carullo RINGDOWN: QUASI-NORMAL MODES SOLUTIONS

▸ In terms of gravitational wave multipoles:

Gregorio Carullo Nollert, Characteristic Oscillations of Black Holes and Neutron Stars (CQG, 2000)

RINGDOWN: QUASI-NORMAL MODES SOLUTIONS

▸ In terms of gravitational wave multipoles:

▸ Frequencies and damping times spectrum predicted by perturbation theory, ﬁxed only by mass and spin of the black hole

Gregorio Carullo Nollert, Characteristic Oscillations of Black Holes and Neutron Stars (CQG, 2000)

RINGDOWN: QUASI-NORMAL MODES SOLUTIONS

▸ In terms of gravitational wave multipoles:

▸ Frequencies and damping times spectrum predicted by perturbation theory, ﬁxed only by mass and spin of the black hole

▸ Amplitudes and relative phases predicted by numerical relativity

Gregorio Carullo Nollert, Characteristic Oscillations of Black Holes and Neutron Stars (CQG, 2000)

RINGDOWN: QUASI-NORMAL MODES SOLUTIONS

▸ In terms of gravitational wave multipoles:

▸ Frequencies and damping times spectrum predicted by perturbation theory, ﬁxed only by mass and spin of the black hole

▸ Amplitudes and relative phases predicted by numerical relativity

▸ Notion of linear regime (hence beginning of ringdown) ambiguous

Gregorio Carullo Nollert, Characteristic Oscillations of Black Holes and Neutron Stars (CQG, 2000)

MOTIVATIONS OF THE ANALYSIS

▸ Ringdown will be much louder in the near future

Gregorio Carullo Observation of Gravitational Waves from a Binary Black Hole Merger, LVC collaboration, PRL 116, 061102 (2016) MOTIVATIONS OF THE ANALYSIS

▸ Ringdown will be much louder in the near future

▸ Standard LIGO-Virgo analyses infer the initial physical parameters of the binary

Gregorio Carullo Observation of Gravitational Waves from a Binary Black Hole Merger, LVC collaboration, PRL 116, 061102 (2016) MOTIVATIONS OF THE ANALYSIS

▸ Ringdown will be much louder in the near future

▸ Standard LIGO-Virgo analyses infer the initial physical parameters of the binary

▸ Final parameters are then ﬁxed from the predictions of GR given the initial sampled parameters (masses and spins)

Gregorio Carullo Observation of Gravitational Waves from a Binary Black Hole Merger, LVC collaboration, PRL 116, 061102 (2016) MOTIVATIONS OF THE ANALYSIS

▸ Ringdown will be much louder in the near future

▸ Standard LIGO-Virgo analyses infer the initial physical parameters of the binary

▸ Final parameters are then ﬁxed from the predictions of GR given the initial sampled parameters (masses and spins)

▸ We aim at an independent sampling of the parameters of the ﬁnal black hole, enabling a consistency test of GR predictions

Gregorio Carullo Observation of Gravitational Waves from a Binary Black Hole Merger, LVC collaboration, PRL 116, 061102 (2016) GW150914: THE DAY WE SAW A BLACK HOLE RINGING

▸ First and only ringdown observation: GW150914

▸ Different start times yields different results

▸ Results completely consistent with General Relativity if start time is large enough

▸ Unmodelled analysis, not exploited all the available theoretical information ▸

Gregorio Carullo Tests of General Relativity with GW150914, LVC collaboration, Phys. Rev. Lett. 116, 221101 (2016) GW150914: THE DAY WE SAW A BLACK HOLE RINGING

▸ First and only ringdown observation: GW150914

▸ Different start times yields different results

▸ Results completely consistent with General Relativity if start time is large enough

▸ Unmodelled analysis, not exploited all the available theoretical information ▸

Gregorio Carullo Tests of General Relativity with GW150914, LVC collaboration, Phys. Rev. Lett. 116, 221101 (2016) GW150914: THE DAY WE SAW A BLACK HOLE RINGING

▸ First and only ringdown observation: GW150914

▸ Different start times yields different results

▸ Results completely consistent with General Relativity if start time is large enough

▸ Unmodelled analysis, not exploited all the available theoretical information ▸

Gregorio Carullo Tests of General Relativity with GW150914, LVC collaboration, Phys. Rev. Lett. 116, 221101 (2016) GW150914: THE DAY WE SAW A BLACK HOLE RINGING

▸ First and only ringdown observation: GW150914

▸ Different start times yields different results

▸ Results completely consistent with General Relativity if start time is large enough

▸ Unmodelled analysis, not exploited all the available theoretical information ▸

Gregorio Carullo Tests of General Relativity with GW150914, LVC collaboration, Phys. Rev. Lett. 116, 221101 (2016) GW150914 REVISITED

▸ Use Kerr model to provide a measurement of ﬁnal mass and ﬁnal spin from ringdown only

Gregorio Carullo Carullo, Del Pozzo, Veitch (In preparation) GW150914 REVISITED

▸ Use an unmodelled template to compute the evidence that ringdown contains a given GR frequency

Gregorio Carullo Carullo, Del Pozzo, Veitch (In preparation) GW150914 REVISITED

▸ Use an unmodelled template to compute the evidence that ringdown contains a given GR frequency

▸ BH spectroscopy is already here!

▸ Dreyer et al., CQG (2004) Berti, Cardoso, Will, PRD (2006)

Gregorio Carullo Carullo, Del Pozzo, Veitch (In preparation) RECENT DEVELOPMENTS

▸ Numerically calibrated theoretical model London et al., PRD 2014

▸ Dynamically adaptive method to isolate the linear regime

▸ New statistic keeping into account both statistical and systematic uncertainties

▸ Indipendent numerical techniques conﬁrm our results (Bhagwat et al. PRD 2018)

Gregorio Carullo RECENT DEVELOPMENTS

SNR ▸ Numerically calibrated theoretical 24.7 24.6 24.0 22.2 19.9 17.2 16.1 15.6 15.3 13.8 12.0 )

model 80 M London et al., PRD 2014 ( 70 f

M 60

▸ Dynamically adaptive method to 0.8 f

isolate the linear regime a 0.6 Simulated value 1.0

▸ New statistic keeping into account ]  [ both statistical and systematic B 0.5 10 11 12 13 14 15 16 17 18 19 20 uncertainties (t t )/M start peak ▸ Indipendent numerical techniques conﬁrm our results Carullo et al., Phys. Rev. D 98, 104020 (2018) (Bhagwat et al. PRD 2018)

Gregorio Carullo RECENT DEVELOPMENTS

SNR ▸ Numerically calibrated theoretical 24.7 24.6 24.0 22.2 19.9 17.2 16.1 15.6 15.3 13.8 12.0 )

model 80 M London et al., PRD 2014 ( 70 f

M 60

▸ Dynamically adaptive method to 0.8 f

isolate the linear regime a 0.6 Simulated value 1.0

Gregorio Carullo RECENT DEVELOPMENTS

SNR ▸ Numerically calibrated theoretical 24.7 24.6 24.0 22.2 19.9 17.2 16.1 15.6 15.3 13.8 12.0 )

model 80 M London et al., PRD 2014 ( 70 f

M 60

▸ Dynamically adaptive method to 0.8 f

isolate the linear regime a 0.6 Simulated value 1.0

▸ New statistic keeping into account ]  [ both statistical and systematic B 0.5 10 11 12 13 14 15 16 17 18 19 20 uncertainties (t t )/M start peak ▸ Independent numerical techniques conﬁrm our results Carullo et al., Phys. Rev. D 98, 104020 (2018) Bhagwat et al. PRD 2018

Gregorio Carullo PARAMETRIZED DEVIATIONS FROM GR: RESULTS

▸ Meidam et al. (2014):

▸ Detector: Einstein Telescope

▸ Accuracy: 6% (5 events) Gossan, Veitch, Sathyaprakash PRD 85, 124056 (2012)

Gregorio Carullo PARAMETRIZED DEVIATIONS FROM GR: RESULTS

▸ Meidam et al. (2014):

▸ Detector: Einstein Telescope

▸ Accuracy: 6% (5 events)

0.15 ▸ Carullo et al. (2018): 0.10 0.05 ▸ Detector: LIGO-Virgo network 220

ˆ 0.00 ! (design) 0.05 0.10 ▸ Accuracy: 1.5% (5 events) 0.15 Agrees with Brito, Buonanno, Raymond 1 2 3 4 5 6 probability density Nevents Phys. Rev. D 98, 084038 (2018)

Gregorio Carullo CONCLUSIONS

▸ Determined the effective start time of the ringdown

Gregorio Carullo CONCLUSIONS

▸ Determined the effective start time of the ringdown

▸ Developed a pipeline able to perform an independent measure of the ﬁnal regime of a binary black hole coalescence with current network of interferometers

Gregorio Carullo CONCLUSIONS

▸ Determined the effective start time of the ringdown

▸ Developed a pipeline able to perform an independent measure of the ﬁnal regime of a binary black hole coalescence with current network of interferometers

▸ Performed agnostic mode identiﬁcation

Gregorio Carullo CONCLUSIONS

▸ Determined the effective start time of the ringdown

▸ Developed a pipeline able to perform an independent measure of the ﬁnal regime of a binary black hole coalescence with current network of interferometers

▸ Performed agnostic mode identiﬁcation

▸ Measure deviations from GR predictions already with the LIGO-Virgo network

Gregorio Carullo CONCLUSIONS

▸ Determined the effective start time of the ringdown

▸ Developed a pipeline able to perform an independent measure of the ﬁnal regime of a binary black hole coalescence with current network of interferometers

▸ Performed agnostic mode identiﬁcation

▸ Measure deviations from GR predictions already with the LIGO-Virgo network

▸ From multiple observations, constrain deviations from GR with a precision of 1.5%, already from a small (~5) number of sources