Real measurements of real black holes - Beyond CenterAnatomy of the waveform What a detector like LIGO measures is a weighted sum of the two fundamental GW polarizations: Scott A

Real measurements of real black holes

What do and what can we learn about black holes and strong gravity when we measure

their gravitational waves?

Image: Steve Drasco, CalPoly

Beyond Center @ ASU, Feb 17 - 18, 2019Scott A. Hughes, MIT

Black holes pre September 2015If I were giving this talk 3.5 years ago, I would point

to astronomical evidence for objects that are

Scott A. Hughes, MIT Beyond Center @ ASU, Feb 17 - 18, 2019

Compact Massive

Dark

Objects which possess necessary conditions to be black holes …

Example: Center of our galaxy. Long known to be a

crowded, dense region …




Compact Massive

Dark


Point-like structure apparent as we zoom in to smaller and

smaller length scales…




Compact Massive

Dark


Stars observed to orbit a dark object; orbits

yield mass estimate of about 3.5 x 106 Msun.

Black holes post 2015Situation changed in 0.2 seconds on the

morning of 14 September 2015


LIGO measurements precisely match model of last several orbits of two black holes that merge and then

settle down into a single black hole remnant… Consistency with GR predictions of near-horizon

spacetime needed to explain data.

Note: Event Horizon Telescope results coming very soon

Using millimeter wavelength observations with a

synthesized aperture of about 104 kilometers can achieve

angular resolution necessary to observe emission near the event horizon of black hole in

our galactic center.


Graphics provided by Dimitrios Psaltis, University of Arizona

Note: Event Horizon Telescope results coming very soon

Using millimeter wavelength observations with a

synthesized aperture of about 104 kilometers can achieve

angular resolution necessary to observe emission near the event horizon of black hole in

our galactic center.


Animation: Avery Broderick, Perimeter Institute and the

University of Waterloo

Anatomy of the waveformWhat a detector like LIGO measures is a weighted

sum of the two fundamental GW polarizations:


h = h+(cos �)F+(�, �,�) + h�(cos �)F�(�, �,�)

Two polarizations generated by the binary, depend on binary’s inclination to the line of sight

Antenna response functions, depend on binary’s position on

sky, orientation at that position.

Anatomy of the waveformWhat a detector like LIGO measures is a weighted

sum of the two fundamental GW polarizations:


Waveform example: Binary system with members widely separated. Leading order form is

h = h+(cos �)F+(�, �,�) + h�(cos �)F�(�, �,�)

h+ =ADM5/3f2/3(1 + cos2 ◆) cos(2�)

<latexit sha1_base64="RHkcbBk0i/XIe92UMfWjQT1qJj4=">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</latexit>

h⇥ =ADM5/3f2/3 cos ◆ sin(2�)

<latexit sha1_base64="+sZ5p6stzkgNROKC+vkz8Gmr4Ys=">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</latexit>

M =(m1m2)3/5

(m1 + m2)1/5

Key point: Waveform phase is measured MUCH more accurately than amplitude.

Anatomy of the waveformGW phase tracks the binary’s orbital phase (modulo a factor of two for the loudest quadrupole mode).


M =(m1m2)3/5

(m1 + m2)1/5

df

dt=

96�8/3

5

�GMc3

�5/3

f11/3

Leading solution: how frequency changes due to backreaction of GW emission

With corrections to take into account effect of eccentricity, this yields the inspiral that was

measured by Hulse and Taylor.

Anatomy of the waveformGW phase tracks the binary’s orbital phase (modulo a factor of two for the loudest quadrupole mode).


Going beyond the leading solution incorporates additional physics about the nature of the binary’s

members into the inspiral law:df

dt=

96�8/3

5

�GMc3

�5/3

f11/3

�1�

�743336

+114

µ

M

�(�Mf)2/3 + [4� � �(t)](�Mf)

+�

3410318144

+136612016

µ

M+

5918

µ2

M2+ �(t)

�(�Mf)4/3

�

Higher order solution introduces dependence on reduced mass µ; parameters β and σ depend

on members’ spins S1 and S2.

Scott A. Hughes, MIT

Example 1: Two non-spinning

black holes.

GWs with spin vs GWs withoutInfluence of the spin terms in the phase leaves

a strong imprint on the waveform.

Beyond Center @ ASU, Feb 17 - 18, 2019


Example 2: Two rapidly spinning

black holes.

GWs with spin vs GWs withoutInfluence of the spin terms in the phase leaves

a strong imprint on the waveform.


Anatomy of the waveformWhen the final state is a black hole, we expect that the final waves will be quasi-normal modes of that

hole: Damped sinusoids whose properties are determined by the hole’s mass and spin.


hring =�

lm

Alme�t/�lm sin(2�flmt + �)

Longest lived modes have l = m = 2:

f22 �c3

2�GM

�1� 0.63(1� a)3/10

�

Q22 � �f22�22 � 2(1� a)�9/20


Listening to a black hole ringExample of a signal dominated by the ringing of

a black hole.

Final black hole has spin a = 0.8 …

yields Q ≈ 4



Listening to a black hole ringExample of a signal dominated by the ringing of

a black hole.Note: Ringdown has not yet been unambiguously detected. Best fit waves

include ringdown, but as a separate entity ringdown

is consistent with data, but not detected at high

significance.


Critical point to bear in mind: GW emission “coarse grains” its source


We only get information about features of the source on length scales comparable to or larger

the GW wavelength, or that vary on timescales corresponding to source’s gravitational dynamics.

How will this evolve?Current detectors are being improved; new

detectors are in preparation:


Current sensitivityNext run (O3) takes advantage of lessons

learned from previous runs, plus techniques to improve

high-frequency noise.

How will this evolve?Current detectors are being improved; new

detectors are in preparation:


On time scale of years, input laser power will be increased to ~200 Watts, pushing noise floor down.

X

LIGO-India

KAGRA


Planned network: mid 2020s


Go to space to escape low-frequency noise: sensitive in band ~3×10-5 Hz < f < 1 Hz

A target-rich frequency band

Space-based detectors: LISA


2.5 million km interferometer antenna in space. ESA mission for 2034, NASA participation.


Low frequency antenna sensitive to massive objects: Opens window onto events with million solar mass black holes in distant galaxies.

Space-based detectors: LISA


2.5 million km interferometer antenna in space. ESA mission for 2034, NASA participation.

As detector noise is reduced, we will measure the last wave

cycles more and more clearly.


Improved merger and ringdown signal strengths …

These cycles arise from processes nearest to the horizon — but there is substantial variability

due to “prosaic” physics, such as misalignment of the orbital plane

with black hole spin axis.From Hughes et al, arXiv:1901.05900

As detector noise is reduced, we will measure the last wave

cycles more and more clearly.


Improved merger and ringdown signal strengths …

These cycles arise from processes nearest to the horizon — but there is substantial variability

due to “prosaic” physics, such as misalignment of the orbital plane

with black hole spin axis.From Hughes et al, arXiv:1901.05900

With broader detector band, and if nature provides sources with large mass ratios, systems will spiral

through band slowly … improves mass and spin measurements, chance to find additional structure.


… longer inspirals, enabling much higher precision measurements

Graphic courtesy of Marc Freitag

Champions: Extreme mass ratio inspirals. Typically a stellar mass black hole (10 — 30 Msun) scattered onto near horizon orbit of black

hole in galaxy center.

With broader detector band, and if nature provides sources with large mass ratios, systems will spiral

through band slowly … improves mass and spin measurements, chance to find additional structure.


… longer inspirals, enabling much higher precision measurements

Graphic courtesy of Marc Freitag

For big black holes in mass range ~105 Msun up to ~107 Msun, the gravitational waves generated by these

inspirals are right in the “sweet spot” for LISA.

The physics view of an “EMRI”Thens of thousands of slowly evolving orbits are

executed in the near-horizon region of large black hole … GWs that they generate are sensitive to the nature of the near-horizon black hole spacetime.If we can coherently track these GWs, can use them to measure spacetime properties; expect measurement

errors to scale as 1/Norb and 1/(signal to noise).


Probe of BH spacetimeThanks to large mass ratio, EMRIs function as nearly

a test particle probe of black hole spacetimes.Measurement analogous to geodesy: Measurements of

orbit precisely map gravitational potential; enforce field equation

GRACE gravity model

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infer mass distribution.

�g = �GM

r+

1X

l=2

lX

m=�l

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a test particle probe of black hole spacetimes.

GRACE gravity model

Bothrodesy: Mapping the multipoles that govern a black hole spacetime.

Kerr expectation: Axisymmetry (no non-zero m modes)

Mass and current moments set by hole’s mass and spin:

Ml + iSl = M(ia)l







Ml + iSl = M(ia)l

Barack & Cutler PRD 69, 082005 (2004) Babak et al PRD 95, 103012 (2017)

Mass, spin, mass ratio: δM/M, δa, δη ~ 10-5 — 10-3

Orbit geometry: δe ~ 10-5 — 10-3

δ(spin direction) ~ a few deg2 δ(sky position) ≲ 10 deg2

Distance to binary: δD/D ~ 0.03 — 0.1







Ml + iSl = M(ia)l

Distance to binary: δD/D ~ 0.03 — 0.1

Higher multipoles: δ(mass quadrupole) ~ 10-3

[degrades by ~3 each increase in l]Ryan PRD 56, 1845 (1997); Barack & Cutler PRD 75, 042003 (2007)

Babak et al PRD 95, 103012 (2017)

Mass, spin, mass ratio: δM/M, δa, δη ~ 10-5 — 10-3

Orbit geometry: δe ~ 10-5 — 10-3

δ(spin direction) ~ a few deg2 δ(sky position) ≲ 10 deg2


Probe of horizon physicsInspiraling body spends many orbits near horizon;

how it interacts substantially impacts inspiral:


Horizon term strongly depends on black hole spin:

✓dE

dt

◆orb

= �✓dE

dt

◆1�

✓dE

dt

◆H

<latexit sha1_base64="j9R/Tr5b8JqrfTQHXgePo/v4ie8=">AAACV3ichVFdS8MwFE07P+b8mvroS3AM5oOjFUFfBFGEPU5wU1jrSNN0C0vTktwKpfRPii/7K75oNvegTvRA4HDOvTe5J0EquAbHmVp2ZWV1bb26Udvc2t7Zre/t93WSKcp6NBGJegyIZoJL1gMOgj2mipE4EOwhmNzM/IdnpjRP5D3kKfNjMpI84pSAkYZ16QkWQcuLFKFFeFsWIZSe4qMxHD8VnopxooISX+KTP+o8LiPI8Qn+b1anHNYbTtuZAy8Td0EaaIHusP7ihQnNYiaBCqL1wHVS8AuigFPBypqXaZYSOiEjNjBUkphpv5jnUuKmUUIcJcocCXiufu0oSKx1HpsFmzGBsf7pzcTfvEEG0YVfcJlmwCT9vCjKBIYEz0LGIVeMgsgNIVRx81ZMx8TEAuYraiYE9+fKy6R/2nYNvztrXF0v4qiiQ3SEWshF5+gKdVAX9RBFr+jNqlgr1tR6t9fs6mepbS16DtA32Hsf7t21lQ==</latexit><latexit sha1_base64="j9R/Tr5b8JqrfTQHXgePo/v4ie8=">AAACV3ichVFdS8MwFE07P+b8mvroS3AM5oOjFUFfBFGEPU5wU1jrSNN0C0vTktwKpfRPii/7K75oNvegTvRA4HDOvTe5J0EquAbHmVp2ZWV1bb26Udvc2t7Zre/t93WSKcp6NBGJegyIZoJL1gMOgj2mipE4EOwhmNzM/IdnpjRP5D3kKfNjMpI84pSAkYZ16QkWQcuLFKFFeFsWIZSe4qMxHD8VnopxooISX+KTP+o8LiPI8Qn+b1anHNYbTtuZAy8Td0EaaIHusP7ihQnNYiaBCqL1wHVS8AuigFPBypqXaZYSOiEjNjBUkphpv5jnUuKmUUIcJcocCXiufu0oSKx1HpsFmzGBsf7pzcTfvEEG0YVfcJlmwCT9vCjKBIYEz0LGIVeMgsgNIVRx81ZMx8TEAuYraiYE9+fKy6R/2nYNvztrXF0v4qiiQ3SEWshF5+gKdVAX9RBFr+jNqlgr1tR6t9fs6mepbS16DtA32Hsf7t21lQ==</latexit><latexit sha1_base64="j9R/Tr5b8JqrfTQHXgePo/v4ie8=">AAACV3ichVFdS8MwFE07P+b8mvroS3AM5oOjFUFfBFGEPU5wU1jrSNN0C0vTktwKpfRPii/7K75oNvegTvRA4HDOvTe5J0EquAbHmVp2ZWV1bb26Udvc2t7Zre/t93WSKcp6NBGJegyIZoJL1gMOgj2mipE4EOwhmNzM/IdnpjRP5D3kKfNjMpI84pSAkYZ16QkWQcuLFKFFeFsWIZSe4qMxHD8VnopxooISX+KTP+o8LiPI8Qn+b1anHNYbTtuZAy8Td0EaaIHusP7ihQnNYiaBCqL1wHVS8AuigFPBypqXaZYSOiEjNjBUkphpv5jnUuKmUUIcJcocCXiufu0oSKx1HpsFmzGBsf7pzcTfvEEG0YVfcJlmwCT9vCjKBIYEz0LGIVeMgsgNIVRx81ZMx8TEAuYraiYE9+fKy6R/2nYNvztrXF0v4qiiQ3SEWshF5+gKdVAX9RBFr+jNqlgr1tR6t9fs6mepbS16DtA32Hsf7t21lQ==</latexit><latexit sha1_base64="j9R/Tr5b8JqrfTQHXgePo/v4ie8=">AAACV3ichVFdS8MwFE07P+b8mvroS3AM5oOjFUFfBFGEPU5wU1jrSNN0C0vTktwKpfRPii/7K75oNvegTvRA4HDOvTe5J0EquAbHmVp2ZWV1bb26Udvc2t7Zre/t93WSKcp6NBGJegyIZoJL1gMOgj2mipE4EOwhmNzM/IdnpjRP5D3kKfNjMpI84pSAkYZ16QkWQcuLFKFFeFsWIZSe4qMxHD8VnopxooISX+KTP+o8LiPI8Qn+b1anHNYbTtuZAy8Td0EaaIHusP7ihQnNYiaBCqL1wHVS8AuigFPBypqXaZYSOiEjNjBUkphpv5jnUuKmUUIcJcocCXiufu0oSKx1HpsFmzGBsf7pzcTfvEEG0YVfcJlmwCT9vCjKBIYEz0LGIVeMgsgNIVRx81ZMx8TEAuYraiYE9+fKy6R/2nYNvztrXF0v4qiiQ3SEWshF5+gKdVAX9RBFr+jNqlgr1tR6t9fs6mepbS16DtA32Hsf7t21lQ==</latexit>

If black hole spins rapidly, absorption can significantly

prolong inspiral.

[From Hughes, PRD 64, 064004 (2001).]

Executes ~104 additional orbits vs model that does not include absorption.

a = 0.998M





✓dE

dt

◆orb

= �✓dE

dt

◆1�

✓dE

dt

◆H


a = 0.3594M

For slower spin, effect can be negligible, can switch sign.

Can we use this to test the physics of horizon

absorption?

[From Hughes, PRD 64, 064004 (2001).]





✓dE

dt

◆orb

= �✓dE

dt

◆1�

✓dE

dt

◆H


In classical GR, there is a duality between “radiation absorbed by the horizon” and

“geometry of tidally distorted black hole”: This effect is due to classical horizon structure

being distorted by orbiting body’s tide.Hawking and Hartle, Commun. Math Phys. 27, 283 (1972); Hartle, Phys. Rev. D 8, 1010 (1973); Hartle, Phys. Rev. D 9, 2749 (1974).

Example of horizon distortion

Scott A. Hughes, MIT Faculty lunch, 2 April 2015

O’Sullivan and Hughes, Phys. Rev. D 90, 124039 (2014); O’Sullivan and Hughes, Phys. Rev. D 94, 044057 (2016).

Scott A. Hughes, MIT Faculty lunch, 2 April 2015

O’Sullivan and Hughes, Phys. Rev. D 90, 124039 (2014); O’Sullivan and Hughes, Phys. Rev. D 94, 044057 (2016).

Example of horizon distortion

CAUTIONARY NOTE: Subtle effects can be strongly correlated with more

prosaic bits of source physicsIn present GW data, strong

correlations between some parameters.


This animation: Successive steps in a Markov Chain Monte Carlo exploration of the posterior distribution for fitting

different model parameters to the data.

Simulation finds best fit in a 15-D parameter space

(2 masses, 6 spin components, 1 distance, 2 sky position angles, 2 orbit orientation angles, 1 initial time, 1 initial phase.)

CAUTIONARY NOTE: Subtle effects can be strongly correlated with more

prosaic bits of source physicsIn present GW data, strong

correlations between some parameters.


This animation: Successive steps in a Markov Chain Monte Carlo exploration of the posterior distribution for fitting

different model parameters to the data.

Simulation finds best fit in a 15-D parameter space

(2 masses, 6 spin components, 1 distance, 2 sky position angles, 2 orbit orientation angles, 1 initial time, 1 initial phase.)

Examples of issuesSmall body spin: Smaller body is not a featureless

point mass! Its spin (and other properties) couple to spacetime; it precesses, feels additional “forces.”

(Linearizing in the spin tensor, which is of order µ2 if the small object is itself a black hole.)

DS↵�

d⌧= 0

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F↵S = �1

2R↵

⌫��u⌫S��

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Examples of issuesSmall body spin: Smaller body is not a featureless

point mass! Its spin (and other properties) couple to spacetime; it precesses, feels additional “forces.”

Spin-curvature coupling “force” is comparable

to other effects we want to measure.

[From Ruangsri, Vigeland, and Hughes, PRD 94, 044008 (2016).]


Examples of issues

Yang & Casals examined what happens if a 107 Msun black hole

is 0.1 parsecs from an EMRI.

3rd body breaks axisymmetry!Perturbation of 3rd is

particularly strong due to resonances between r and φ motions … causes precession

of EMRI’s orbital plane.

[From Yang and Casals, PRD 96, 083015 (2017).]


Other bodies: A third body near an EMRI will distort its spacetime … exerting an influence that can change the properties of orbits and inspirals.

Examples of issuesOther bodies: A third body near an EMRI will distort

its spacetime … exerting an influence that can change the properties of orbits and inspirals.

Tide from a 107 Msun body at 0.1 parsecs is identical

to tide from a 10 Msun body at 0.001 parsecs …

0.001 parsecs = 1 light day.

Our galactic center has several stars of this mass which come within a light day of Sgr A*.


ConclusionWe are now gathering data from processes

that originate in the spacetimes near black hole event horizons.


Can we use these data to advance our understanding of the fundamental nature of gravity? It will depend on in detail on how gravity beyond classical GR manifests itself.

Important to understand what these measurements actually measure in order

to assess what they teach us, and to formulate such a program.

Documents

Real measurements of real black holes - Beyond CenterAnatomy of the waveform What a detector like LIGO measures is a weighted sum of the two fundamental GW polarizations: Scott A