real measurements of real black holes - beyond centeranatomy of the waveform what a detector like...
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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 …
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 …
Point-like structure apparent as we zoom in to smaller and
smaller length scales…
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 …
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
Scott A. Hughes, MIT Beyond Center @ ASU, Feb 17 - 18, 2019
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.
Scott A. Hughes, MIT Beyond Center @ ASU, Feb 17 - 18, 2019
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.
Scott A. Hughes, MIT Beyond Center @ ASU, Feb 17 - 18, 2019
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:
Scott A. Hughes, MIT Beyond Center @ ASU, Feb 17 - 18, 2019
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:
Scott A. Hughes, MIT Beyond Center @ ASU, Feb 17 - 18, 2019
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=">AAACMXicbZDLSgMxFIYz9VbrrerSTbAILYU60yq6Eepl0Y1QwV6g05ZMmmlDM5MhyQhlmFdy45uImy4UcetLmF4W2nog5OP/zyE5vxMwKpVpjo3Eyura+kZyM7W1vbO7l94/qEseCkxqmDMumg6ShFGf1BRVjDQDQZDnMNJwhrcTv/FEhKTcf1SjgLQ91PepSzFSWuqmK4NuHl5B2xUIRzZGDF7H0V0MZ3wfd6Lz01LsdqKivrIWzEMbc9kp2pQrlJtwtmhXBzTXTWfMgjktuAzWHDJgXtVu+tXucRx6xFeYISlblhmodoSEopiROGWHkgQID1GftDT6yCOyHU03juGJVnrQ5UIfX8Gp+nsiQp6UI8/RnR5SA7noTcT/vFao3Mt2RP0gVMTHs4fckEHF4SQ+2KOCYMVGGhAWVP8V4gHS4SkdckqHYC2uvAz1YsEqFcyHs0z5Zh5HEhyBY5AFFrgAZVABVVADGDyDN/AOPowXY2x8Gl+z1oQxnzkEf8r4/gEYjacb</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).
Scott A. Hughes, MIT Beyond Center @ ASU, Feb 17 - 18, 2019
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).
Scott A. Hughes, MIT Beyond Center @ ASU, Feb 17 - 18, 2019
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
Scott A. Hughes, MIT
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.
Beyond Center @ ASU, Feb 17 - 18, 2019
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.
Scott A. Hughes, MIT Beyond Center @ ASU, Feb 17 - 18, 2019
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
Scott A. Hughes, MIT
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
Beyond Center @ ASU, Feb 17 - 18, 2019
Scott A. Hughes, MIT
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.
Beyond Center @ ASU, Feb 17 - 18, 2019
Critical point to bear in mind: GW emission “coarse grains” its source
Scott A. Hughes, MIT Beyond Center @ ASU, Feb 17 - 18, 2019
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:
Scott A. Hughes, MIT Beyond Center @ ASU, Feb 17 - 18, 2019
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:
Scott A. Hughes, MIT Beyond Center @ ASU, Feb 17 - 18, 2019
On time scale of years, input laser power will be increased to ~200 Watts, pushing noise floor down.
X
LIGO-India
KAGRA
Scott A. Hughes, MIT
Planned network: mid 2020s
Beyond Center @ ASU, Feb 17 - 18, 2019
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
Scott A. Hughes, MIT
2.5 million km interferometer antenna in space. ESA mission for 2034, NASA participation.
Beyond Center @ ASU, Feb 17 - 18, 2019
Low frequency antenna sensitive to massive objects: Opens window onto events with million solar mass black holes in distant galaxies.
Space-based detectors: LISA
Scott A. Hughes, MIT Beyond Center @ ASU, Feb 17 - 18, 2019
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.
Beyond Center @ ASU, Feb 17 - 18, 2019Scott A. Hughes, MIT
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.
Beyond Center @ ASU, Feb 17 - 18, 2019Scott A. Hughes, MIT
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.
Beyond Center @ ASU, Feb 17 - 18, 2019Scott A. Hughes, MIT
… 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.
Beyond Center @ ASU, Feb 17 - 18, 2019Scott A. Hughes, MIT
… 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).
Scott A. Hughes, MIT Beyond Center @ ASU, Feb 17 - 18, 2019
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
MlmYlm(✓,�)<latexit sha1_base64="yLCwjdvJtdfr7pogmmnKuq9hbq4=">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</latexit><latexit sha1_base64="yLCwjdvJtdfr7pogmmnKuq9hbq4=">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</latexit><latexit sha1_base64="yLCwjdvJtdfr7pogmmnKuq9hbq4=">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</latexit><latexit sha1_base64="yLCwjdvJtdfr7pogmmnKuq9hbq4=">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</latexit>
Scott A. Hughes, MIT Beyond Center @ ASU, Feb 17 - 18, 2019
Probe of BH spacetimeThanks to large mass ratio, EMRIs function as nearly
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
Scott A. Hughes, MIT Beyond Center @ ASU, Feb 17 - 18, 2019
Probe of BH spacetimeThanks to large mass ratio, EMRIs function as nearly
a test particle probe of black hole spacetimes.
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
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
Scott A. Hughes, MIT Beyond Center @ ASU, Feb 17 - 18, 2019
Probe of BH spacetimeThanks to large mass ratio, EMRIs function as nearly
a test particle probe of black hole spacetimes.
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
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
Scott A. Hughes, MIT Beyond Center @ ASU, Feb 17 - 18, 2019
Probe of horizon physicsInspiraling body spends many orbits near horizon;
how it interacts substantially impacts inspiral:
Scott A. Hughes, MIT Beyond Center @ ASU, Feb 17 - 18, 2019
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
Probe of horizon physicsInspiraling body spends many orbits near horizon;
how it interacts substantially impacts inspiral:
Scott A. Hughes, MIT Beyond Center @ ASU, Feb 17 - 18, 2019
Horizon term strongly depends on black hole spin:
✓dE
dt
◆orb
= �✓dE
dt
◆1�
✓dE
dt
◆H
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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).]
Probe of horizon physicsInspiraling body spends many orbits near horizon;
how it interacts substantially impacts inspiral:
Scott A. Hughes, MIT Beyond Center @ ASU, Feb 17 - 18, 2019
Horizon term strongly depends on black hole spin:
✓dE
dt
◆orb
= �✓dE
dt
◆1�
✓dE
dt
◆H
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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.
Scott A. Hughes, MIT Beyond Center @ ASU, Feb 17 - 18, 2019
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.
Scott A. Hughes, MIT Beyond Center @ ASU, Feb 17 - 18, 2019
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
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Scott A. Hughes, MIT Beyond Center @ ASU, Feb 17 - 18, 2019
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).]
Scott A. Hughes, MIT Beyond Center @ ASU, Feb 17 - 18, 2019
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).]
Scott A. Hughes, MIT Beyond Center @ ASU, Feb 17 - 18, 2019
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*.
Scott A. Hughes, MIT Beyond Center @ ASU, Feb 17 - 18, 2019
ConclusionWe are now gathering data from processes
that originate in the spacetimes near black hole event horizons.
Scott A. Hughes, MIT Beyond Center @ ASU, Feb 17 - 18, 2019
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.