Testing the nature of dark compact objects with gravitational waves - - PowerPoint PPT Presentation

Elisa Maggio Sapienza University of Rome https://web.uniroma1.it/gmunu

Testing the nature of dark compact objects with gravitational waves

Advances and Challenges in Computational Relativity

Sep 14-18, 2020

Gravitational waves from binary mergers

Elisa Maggio Testing dark compact objects with GWs @ICERM 2020 1/21

Up to date 15 gravitational wave events from the coalescence of compact binaries have been detected.

Abbott+, PRL 116, 061102 (2016)

The signal has 3 stages:

• Inspiral
• Merger
• Ringdown

Gravitational waves from binary mergers

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Abbott+, PRL 116, 061102 (2016)

What is the nature of the compact remnant? The signal has 3 stages:

• Inspiral
• Merger
• Ringdown

Up to date 15 gravitational wave events from the coalescence of compact binaries have been detected.

Elisa Maggio Testing dark compact objects with GWs @ICERM 2020

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Ringdown stage

The ringdown stage is dominated by the quasi-normal modes of the remnant which describe the response of the compact object to a perturbation.

ω = ωR + iωI

The signal can be modeled as a sum of exponentially damped sinusoids:

fGW|ringdown = ωR 2π

τdamping = − 1 ωI

Elisa Maggio Testing dark compact objects with GWs @ICERM 2020

Buonanno, CQG 19, 1267-1278 (2002)

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Ringdown detections

The least-damped quasi-normal mode has been observed in the ringdown of the events GW150914 and GW190521. Both detections are compatible with Kerr black hole remnants.

Abbott+, PRL 116, 221101 (2016)

GW150914

Abbott+, ApJL 900, L13 (2020)

GW190521

However, the characterization of the remnant is still an open problem.

Elisa Maggio Testing dark compact objects with GWs @ICERM 2020

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Test of the BH paradigm

Kerr black holes are uniquely determined by 2 parameters:

• Mass
• Angular momentum

Carter, PRL 26, 331 (1971); Robinson, PRL 34, 905 (1975)

A test of the no-hair theorem requires the identification of at least two QNM frequencies in the ringdown.

Dreyer+, CQG 21, 787 (2004)

Elisa Maggio Testing dark compact objects with GWs @ICERM 2020

Louder GW events and improvements of the detector sensitivity will allow to test the BH hypothesis.

Berti, Cardoso, Will, PRD 73, 064030 (2006)

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Questions

I. Are there alternative models to black holes?

• II. Are they astrophysically viable?
• III. What is the gravitational wave signal that they produce?
• IV. Is their gravitational wave signal detectable?

Elisa Maggio Testing dark compact objects with GWs @ICERM 2020

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• I. Alternatives to black holes

Elisa Maggio Testing dark compact objects with GWs @ICERM 2020

There is a zoo of theoretical compact objects without horizon which:

• can overcome paradoxes of BHs:
• can form in the presence of dark matter fields
• are not excluded by GW and electromagnetic observations
• quantify the “BH-ness” of a source

Curvature singularity Hawking information loss

Mazur, Mottola, PNAS 101, 9545-9550 (2004) Mathur, Fortsch. Phys. 53, 793-827 (2005) Liebling, Palenzuela, LRR 20, 5 (2017); Brito+, Phys. Lett. B 752, 291-295 (2016) Abbott+, ApJ 896: L44 (2020); Abbott+, PRL 125, 101102 (2020); Calderón Bustillo+, arXiv: 2009.05376 (2020); EHT, ApJ 875, L5 (2019)

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Dark compact object

We analyze a generic model which deviates from a black hole for its:

• Compactness

since the radius of the object is located at

• “Darkness”

which is related to the reflectivity of the object Black hole gravastar wormhole nonlocal star boson star

r0 = r+(1 + ✏)

Ultracompact

• bjects

Compact

• bjects

✏

R(ω)

Cardoso, Pani, LRR 22:4 (2019)

10−40

0.5

|R(ω)|2

1

tight fuzzball diffuse fuzzball

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• II. Are dark compact objects astrophysically viable?

Spinning compact objects with an ergoregion but without an event horizon might be unstable due to the ergoregion instability.

Event horizon Ergoregion

Brito, Cardoso, Pani, Lect. Notes Phys. (2020) Penrose, Riv. Nuovo Cim. 1, 252-276 (1969)

If confirmed, the ergoregion instability could provide a strong theoretical argument in favor of the black hole paradigm.

Friedman, Commun. Math. Phys. 63, 243-255 (1978); Comins+, Proc. R. Soc. Lond. A 364: 211-226 (1978); Yoshida, Eriguchi, MNRAS 282, 580-586 (1996)

Infinite redshift surface

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Quasi-normal mode spectrum

+ 2 boundary conditions eigenvalue problem for the QNMs

• At infinity: outgoing waves
• At : perfectly reflecting surface

for an ultracompact object

Detweiler, Proc. R. Soc. Lond. A 352 (1977)

r0

d2ψ dz2 + V (z, ω)ψ = 0

A gravitational perturbation is governed by

|R(ω)|2 = 1

ωI < 0

ωI > 0

stable remnant unstable remnant if if

Dark compact

• bject

Black hole

Cardoso, Pani, LRR (2019) 22:4

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Ergoregion instability

Critical spin stable unstable

Dark compact objects with a perfectly reflecting surface are unstable above a critical value of the spin due to the ergoregion instability.

0.0 0.2 0.4 0.6 0.8 1.0 10-10 10-8 10-6 10-4

a/M |M I|

EM, Pani, Ferrari, PRD 96, 104047 (2017); EM, Cardoso, Dolan, Pani, PRD 99, 064007 (2019)

Axial,

0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0

a/M M R ✏ = 10−10

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Astrophysical impact of the instability

A putative dark compact object remnant with the same spin as GW150914 and GW190521 would be unstable.

• 5
• 10
• 15
• 20
• 25
• 30
• 35
• 40

0.2 0.4 0.6 0.8 1.0

Log10() acrit/M

• The timescale of instability is:

τinstability ∼ 50 ✓ M 10M ◆ s

EM, Cardoso, Dolan, Pani, PRD 99, 064007 (2019)

A stochastic GW background from spin loss is expected. A negative search in O1 already imposes stringent constraints on dark compact objects.

Barausse+, CQG 35, 20 (2018); Fan, Chen, PRD 98, 044020 (2018)

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How to quench the ergoregion instability

Partial absorption at the surface makes dark compact objects stable. The minimum absorption rate to quench the instability is the maximum amplification factor of superradiance of black holes.

Spin Absorption 0.7 0.9 any 0.3% 6% ~60%

Cardoso, Pani, LRR 22:4 (2019) Vilenkin, Phys. Lett. B 78, 301-303 (1978) EM, Cardoso, Dolan, Pani, PRD 99, 064007 (2019) Oshita, Wang, Afshordi, JCAP 04, 016 (2020)

Elisa Maggio Testing dark compact objects with GWs @ICERM 2020

Membrane paradigm A static observer outside the horizon can replace the interior of a perturbed BH by a perturbed fictitious membrane located at the horizon. The membrane is a viscous fluid with shear viscosity and bulk viscosity which are related to the reflectivity of the BH.

η

We generalize the membrane paradigm to any dark compact object with a Schwarzschild exterior.

Damour, PRD 18, 10 (1978); Price, Thorne, PRD 33, 4 (1986) EM, Buoninfante, Mazumdar, Pani, arXiv:2006.14628 (2020), PRD in press

ζ

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• III. What is the gravitational wave signal?

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Quasi-normal modes of dark compact objects

η = ηBH

• The isospectrality of axial and polar modes in BHs is broken and the

QNMs form a doublet.

• The measurement accuracy of the QNM of GW150914 agrees with

modified scenarios.

Axial Polar =BH

10-4 0.001 0.010 0.100 1 1.0 1.5 2.0 2.5

• I/IBH

Axial Polar =BH

10-4 0.001 0.010 0.100 1 0.6 0.7 0.8 0.9 1.0 1.1

• R/RBH

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Ringdown of dark compact objects

Ultracompact objects ( ):

BH

=10-8, =0.1BH =10-8, =0.5BH

50 100 150 200

• 0.6
• 0.4
• 0.2

0.0 0.2 0.4 t/M [r=10M,t]

BH

=0.1, =BH =0.4, =BH =0.49, =BH

10 20 30 40 50 60 70

• 0.6
• 0.4
• 0.2

0.0 0.2 0.4 0.6 t/M [r=10M,t]

Compact objects ( ):

• Modified prompt ringdown
• No echoes

✏ ⌧ 1

✏ & 0.01

• Echoes

due to excitation of photon sphere

• Same prompt ringdown

due to trapped modes

⌧echo/M ∼ | log ✏|

EM, Buoninfante, Mazumdar, Pani, arXiv:2006.14628 (2020), PRD in press

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Template for echoes

Parameters: The signal emitted by a dark compact object at infinity can be written in terms

• f the signal emitted by a black hole
• Standard BH ringdown:
• +2 parameters:

M, χ, A+,×, φ+,×, t0

Mark+, PRD 96, 084002 (2017); Testa, Pani, PRD 98, 044018 (2018)

Transfer function

˜ Z∞

DCO(ω) = ˜

Z∞

BH(ω) + K ˜

ZH

BH(ω)

16/21 Elisa Maggio Testing dark compact objects with GWs @ICERM 2020

Template for echoes

Parameters: The signal emitted by a dark compact object at infinity can be written in terms

• f the signal emitted by a black hole
• Standard BH ringdown:
• +2 parameters:

M, χ, A+,×, φ+,×, t0

Mark+, PRD 96, 084002 (2017); Testa, Pani, PRD 98, 044018 (2018)

Transfer function

˜ Z∞

DCO(ω) = ˜

Z∞

BH(ω) + K ˜

ZH

BH(ω)

EM, Testa, Bhagwat, Pani, PRD 100, 064056 (2019)

Analytical low-frequency template

Numerical Analytical

0.01 0.02 0.05 0.10 0.20 103 101 10-1 10-3

M Im( Z

BH/Z

+

BH) Numerical Analytical

0.01 0.02 0.05 0.10 0.20 1 10 100 1000

M | Z

BH/Z

+

BH|

χ = 0.7

Plus polarization Cross polarization

https://www.darkgra.org/gw-echo-catalogue.html

Ringdown+echo waveforms

17/21 Elisa Maggio Testing dark compact objects with GWs @ICERM 2020

EM, Testa, Bhagwat, Pani, PRD 100, 064056 (2019)

Plus polarization Cross polarization

Ringdown+echo waveforms

17/21 Elisa Maggio Testing dark compact objects with GWs @ICERM 2020

• The mixing of the

polarizations occurs for a spinning object

• r a complex .

EM, Testa, Bhagwat, Pani, PRD 100, 064056 (2019) https://www.darkgra.org/gw-echo-catalogue.html

Plus polarization Cross polarization

Ringdown+echo waveforms

17/21 Elisa Maggio Testing dark compact objects with GWs @ICERM 2020

• The phase in

modifies the echo pattern.

• The mixing of the

polarizations occurs for a spinning object

• r a complex .

EM, Testa, Bhagwat, Pani, PRD 100, 064056 (2019) https://www.darkgra.org/gw-echo-catalogue.html

• IV. Are GW echoes detectable?

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• A tentative evidence for echoes in LIGO/Virgo data has been reported

Abedi+, PRD 96, 082004 (2017); Conklin, Holdom, PRD 98, 044021 (2018); Abedi, Afshordi, JCAP 11, 010 (2019)

• Independent searches argued that the statistical significance of echoes

is low and consistent with noise

Westerweck+, PRD 97, 124037 (2018); Nielsen+, PRD 99, 104012 (2019); Uchikata+, PRD 100, 062006 (2019); Lo+, PRD 99, 084052 (2019); Tsang+, PRD 101, 064012 (2020) Abedi, Afshordi, Oshita, Wang, Universe 6 no. 3, 43 (2020)

• Reviews

Cardoso, Pani, Living Reviews in Relativity 22:4 (2019)

Constraints on dark compact objects

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• Current measurement accuracies impose that the compactness of the

remnant cannot be smaller than 99% that of a BH.

• LISA will be able to probe values of the reflectivity close to the BH one.

EM, Testa, Bhagwat, Pani, PRD 100, 064056 (2019) EM, Buoninfante, Mazumdar, Pani, arXiv:2006.14628 (2020), PRD in press

(I-IBH)/IBH%

• 50

50 100 150

Resolvability of the doublet

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Log10[res] 1 2 3 4 5

The resolution of the doublet is more challenging than the detection of the deviations from the BH quasi-normal mode.

EM, Buoninfante, Mazumdar, Pani, arXiv:2006.14628 (2020), PRD in press

We use the Rayleigh resolvability criterion: max[σf1, σf2] < |f1 − f2|

max[σQ1, σQ2] < |Q1 − Q2|

where the uncertainties are computed with a Fisher analysis.

Conclusions and open challenges

21/21 Elisa Maggio Testing dark compact objects with GWs @ICERM 2020

• We can understand the nature of compact objects and look for new physics

at the horizon scale through gravitational waves.

• Dark compact objects are not excluded by current GW measurements.
• LISA will allow to perform unprecedented tests of the BH paradigm.
• Simulations of the formation of dark compact objects need to be developed.
• Physically motivated boundary conditions are needed.
• Accurate echo templates are crucial for matched-filter searches.