SlideShare a Scribd company logo
Gravitational Collider Physics
Daniel Baumann
Based on work with
H.S. Chia R. Porto J. Stout G. Tomaselli G. Bertone
DB, Chia and Porto
Probing Ultralight Bosons with Binary Black Holes
arXiv:1804.03208 PRD [Editor’s Suggestion]
DB, Chia, Porto and Stout
Gravitational Collider Physics
arXiv:1912.04932
DB, Bertone, Stout and Tomaselli
Ionization of Gravitational Atoms
arXiv:2112.14777
DB, Bertone, Stout and Tomaselli
Sharp Signals of Boson Clouds in Black Hole Binary Inspirals
arXiv:22xx.xxxxx (PRL accepted) [Editor’s Suggestion]
DB, Chia, Stout and ter Haar
The Spectra of Gravitational Atoms
arXiv:1908.10370
Can it also become a new tool for fundamental physics?
The detection of GWs marked the beginning of a new era of multi-messenger
astronomy:
particle collider
Standard
Model
Neutrinos
1020
1010
1
10 10
10 20
Energy [eV]
New physics is often associated with high energies (short distances):
We expect this to have small effects on long-wavelength GW signals.
cosmological
collider
New physics may also occur at low energies, if it is weakly coupled:
particle collider
Standard
Model
Neutrinos
1020
1010
1
10 10
10 20
Energy [eV]
EM
Strong
Weak
Gravity
Coupling
gravitational
collider
This may be probed by GW signals from binary black hole mergers.
cosmological
collider
superradiance
Ultralight bosons can form bound states around rotating black holes:
This resembles the hydrogen atom and is therefore often called a
gravitational atom.
Zel’dovich ’72
Starobinsky ’73
Arvanitaki et al ‘09
superradiance
A companion will perturb the cloud with a slowly increasing frequency.
DB, Chia, Porto, and Stout ’19
DB, Chia, Porto, and Stout ’19
This interaction is enhanced at certain resonance frequencies.
DB, Chia, Porto, and Stout ’19
The backreaction of the cloud’s dynamics on the orbit leaves distinct
imprints in the gravitational waves emitted by the binary.
Outline
1) Gravitational Atoms
2) Evolution in Binaries
3) Gravitational Wave Signals
GRAVITATIONAL
ATOMS
I.
A scalar field around a rotating black hole is described by the KG equation:
g↵
r↵r µ2
= 0
We will focus on fields whose Compton wavelength is larger than the BH:
Ultralight Bosons around Black Holes
1 km 1010
km
10 10
eV 10 20
eV
Such light fields see the far-field limit of the geometry:
Ultralight Bosons around Black Holes
µ2
ds2
=
✓
1
2↵
r
◆
dt2
+
✓
1 +
2↵
r
◆
dr2 4↵2
ã sin2
✓
r
dt d + r2
d⌦2
where ↵ ⌘ rg/ c is the gravitational fine-structure constant.
spin
i
d
dt
=
✓
1
2µ
r2 ↵
r
+ V
◆
The KG equation then reduces to a Schrödinger equation:
with = (t, x)eiµt
Coulomb
potential
fine structure
corrections
V
0 2 6 12
αr
|ψ
n!m
(r)|
2
|10m!
|21m!
|32m!
|43m!
Bound States
The energy eigenstates are the same as those of the hydrogen atom:
with “quantum numbers”:
principal orbital azimuthal
m
`
n
r/r0
0 5 10
µαr
|ψ
k;!m
(r)|
2
|0; 11!
|1; 11!
|2; 11!
|3; 11!
|211!
Unbound States
There are also unbound continuum states:
r/r0
with “quantum numbers”:
energy orbital azimuthal
m
`
E
Bound State Spectrum
En`m = µ
✓
1
↵2
2n2
+ fn`↵4
+ hn`m↵5
+ · · ·
◆
The bound state spectrum is the same as for the hydrogen atom:
! = 0
|211!
|311!
! = 1
|322!
! = 2
n = 1
n = 2
n = 3
` = 0
|211i
|311i
` = 1
|322i
` = 2
n = 1
n = 2
n = 3
Growing and Decaying Modes
Unlike in the hydrogen atom, the states are only quasi-stationary:
!n`m = En`m + i n`m
decaying
growing
ΩH
ω < mΩH
Superradiant Scattering
The growing modes are populated by superradiance:
Outgoing wave
Incoming wave
/ exp(im i!t)
This is the wave analog of the Penrose process.
Penrose ’71
Zel’dovich ’72
Starobinsky ’73
Black Hole Bomb
A reflecting mirror around the BH creates a black hole bomb:
Press and Teukolsky ‘72
For a massive field, the mirror is provided by the angular momentum barrier:
This creates an exponential amplification of small fluctuations.
Superradiant Instability
Growth Rates
1013
1011
109
107
105
103
10
0.02 0.05 0.1 0.15 0.2 0.25
α
|211!
|322!
|321!
The different bound states grow at different rates: n`m / ↵4`+5
Detweiler ‘80
Initial State of the Cloud
adiance
The fastest growing mode is the state
We take this as the initial state of the cloud.
1
211 = 103
yrs
✓
M
60M
◆ ✓
0.04
↵
◆9
|211i:
T211 = 1010
yrs
✓
M
60M
◆ ✓
0.04
↵
◆15
Lifetime of the Cloud
adiance
In isolation, the gravitational atom is very long lived:
We would like to understand what happens to the atom when it is part of a
binary system.
EVOLUTION IN
BINARIES
II.
The binary companion can induce transitions between bound states
(“Rabi oscillations”) and excite unbound states (“photoelectric effect”):
DB, Chia and Porto 2018
DB, Chia, Porto and Stout 2019
DB, Bertone, Stout and Tomaselli 2021
We will first study the transitions between bound states:
Ω = ∆E
∆E
DB, Chia and Porto 2018
DB, Chia, Porto and Stout 2019
Gravitational Perturbation
ϕ∗
M∗
R∗
In a binary, the cloud gets perturbed at a slowly increasing frequency:
i
d
dt
=
✓
1
2µ
r2 ↵
r
+ V + V⇤(R⇤(t), '⇤(t))
◆
This perturbation induces level mixing:
ha|V⇤(t)|bi = ⌘ab(t)e i(ma mb)'⇤(t)
⌦i =
Ei
mi
⇠ 0.01 Hz
✓
60M
M
◆ ⇣ ↵
0.04
⌘3
Resonant Transitions
At specific frequencies, the perturbation is resonantly enhanced:
⌦1
⌦2
⌦3
Selection Rules
! = 0
|211!
∆E
|311!
|31 −1!
! = 1
|322!
! = 2
n = 1
n = 2
n = 3
For a scalar atom, the level mixings typically involve only two states.
Only certain transitions are allowed by selection rules:
Ω = ∆E
ϕ∗(t)
ηeiϕ∗(t) ηe−iϕ∗(t)
∆E
Two-State System
A simple two-state system is therefore a good model for the dynamics:
H =
1
2 E ⌘ei'⇤(t)
⌘e i'⇤(t) 1
2 E
!
HD =
(⌦(t) E)/2 ⌘
⌘ (⌦(t) E)/2
!
Two-State System
Rotating along with the companion, isolates the slow motion:
E
Near the resonance, we can write ⌦(t) = ⌦res + t
determines nature of transition
HD(t) =
t
2
✓
1 0
0 1
◆
+ ⌘
✓
0 1
1 0
◆
Landau ’32
Zener ’32
E
Two-State System
Landau-Zener Transition
Landau ’32
Zener ’32
The analogous problem in QM was solved by Landau and Zener.
The evolution depends on the size of the parameter :
z ⌘ ⌘2
/
40 20 0 20 40
0
0.5
1
z = 102
p
t
|c
a
(t)|
2
40 20 0 20 40
0
0.5
1
z = 10 2
p
t
|c0|2
|c1|2
• For slow transitions, the initial state gets fully converted.
• For fast transitions, some of the initial state can survive.
Multi-State Transitions
Clouds of spinning particles involve multi-state transitions:
50 0 50 100 150
0
0.5
1
p
t
|c
a
(t)|
2
|c1|2
|c2|2
|c3|2
50 0 50
p
t
• The final state is generically a superposition of states.
• There can be neutrino-like oscillations between the states.
Backreaction on the Orbit
The transitions force the cloud’s energy and angular momentum to change:
tbefore tres tafter
Sc(t)
Sc(t)
tres
These changes must be balanced by changes in the orbital dynamics.
Backreaction on the Orbit
Conservation of angular momentum requires
d
dt
⇣
L + Sc
⌘
= TGW ⇡ 0
cloud
orbit
The dynamics of the cloud affects the orbital motion!
DB, Chia, Porto, and Stout ’20
1 0.5 0 0.5 1 1.5 2
0
0.5
1
1.5
2
t/⌦r
⌦/⌦
r
1 0.5 0 0.5 1
t/⌦r
Floating Orbits
The binary floats when it absorbs angular momentum from the cloud:
The binary emits transient, nearly monochromatic GWs.
DB, Chia, Porto, and Stout ’20
1 0.5 0 0.5 1 1.5 2
0
0.5
1
1.5
2
t/⌦r
⌦/⌦
r
1 0.5 0 0.5 1
t/⌦r
Sinking Orbits
The binary sinks when it releases angular momentum to the cloud:
This leads to a dephasing in the GW signal.
DB, Chia, Porto, and Stout ’20
Multiple Transitions
The sequence of transitions is a fingerprint of the atomic spectra:
⌦1
⌦2
⌦3
t
⌦(t)
⌦1
⌦2
⌦3
Multiple Transitions
The evolution can be described by a series of scattering events:
⌦1
⌦2
⌦3
⌦(t) = ⌦1 ⌦(t) = ⌦2 ⌦(t) = ⌦3
t
| i S1| i S2S1| i S3S2S1| i
DB, Chia, Porto, and Stout ’20
Final State of the Cloud
Qc(t) =
X
a
|ca(t)|2
Qc,a +
X
a6=b
|ca(t)cb(t)| Qab cos( Eab t)
scalar cloud vector cloud
The S-matrix formalism predicts the final state of the cloud:
|f i =
N
Y
n=1
Sn | i i
The shape and time dependence of this state depends on the internal
structure of the cloud:
E
Gravitational Collider Physics
• Mass: Position of the resonance
• Spin: Angular dependence
• Mass: Position of the resonances
• Spin: Structure of the final state
As in ordinary particle colliders, the signals depend on the mass and spin of
the particles:
10 -3
10 -2
10 -1
1 2
fres (Hz)
10 -1
1
10
102
103
104
M
§
/M
1
0
-
6
1
0
-
4
1
0
-
2
1
1
0
2
1%
10%
100%
M = 60MØ
0.01 0.05 0.1 0.2 0.3
Æ
10 -8
10 -6
10 -4
10 -2
1
102
104
¢t
tot
(yrs)
Gravitational Wave Signatures
• The resonances naturally occur in the LISA band:
• The dephasing of the signals can be significant:
III. SIGNATURES OF
IONIZATION
What happens when the orbital frequency becomes large enough to
excite transitions to unbound states?
Ω = Eb
E
Eb
DB, Bertone, Stout and Tomaselli 2021
Fermi’s Golden Rule
The transition rate (per unit energy) is given by Fermi’s Golden Rule:
Ω = Eb
ϕ∗(t)
−Eb
E
η!m(E)eiϕ∗(t)
η!m(E)e−iϕ∗(t)
Eb
d `m = dE ⌘`m(E; t)
2
E Eb ⌥ (m mb)⌦(t)
level mixing: hE; `m|V⇤(t)|nb`bmbi
2
Pion(t) =
Mc(t)
µ
X
`,m
(m mb) ⌦(t) ⌘`m E
(m)
⇤ ; t
2
⇥ E
(m)
⇤
Ionization Power
Ω = Eb
ϕ∗(t)
−Eb
E
η!m(E)eiϕ∗(t)
η!m(E)e−iϕ∗(t)
Eb
Summing over all bound states gives the total ionization power:
E
(m)
⇤ ⌘ Eb ± (m mb) ⌦(t)
Ionization Power
• The orbital energy lost due to ionization can be very large.
| (R )|2
300 200 100 0
0
100
200
R /M
P
ion
/P
GW
Evaluating this numerically, we find
• It has sharp features are specific separations:
R
(g)
⇤ =
M
↵2

4g2
✓
1 +
M⇤
M
◆
n4
b
1/3
, g = 1, 2, · · ·
0 200 400 600 800
10
200
400
+
t [yrs]
R
∗
/M
Backreaction on the Orbit
Ionization can significantly shorten the merger time:
Frequency Evolution
We get sharp features in the frequency evolution of the GW signals:
−20 −15 −10 −5 0
t − tmerg
(f
/
)
−8/3
f(2)
f(3)
f(4)
These discontinuities are distinctive signatures of the boson clouds.
CONCLUSIONS
AND OUTLOOK
• Precise waveform modeling is needed to apply this to GW searches.
• We studied the dynamics of boson clouds in black hole binaries.
• The backreaction on the orbit produces distinct GW signatures.
Thank you for your attention!

More Related Content

What's hot

Cosmology
CosmologyCosmology
Cosmology
DanielBaumann11
 
On the Origin of Structure in the Universe
On the Origin of Structure in the UniverseOn the Origin of Structure in the Universe
On the Origin of Structure in the Universe
DanielBaumann11
 
Letting Go of Spacetime
Letting Go of SpacetimeLetting Go of Spacetime
Letting Go of Spacetime
Sean Carroll
 
Many Worlds, the Born Rule, and Self-Locating Uncertainty
Many Worlds, the Born Rule, and Self-Locating UncertaintyMany Worlds, the Born Rule, and Self-Locating Uncertainty
Many Worlds, the Born Rule, and Self-Locating Uncertainty
Sean Carroll
 
What We (Don't) Know About the Beginning of the Universe
What We (Don't) Know About the Beginning of the UniverseWhat We (Don't) Know About the Beginning of the Universe
What We (Don't) Know About the Beginning of the Universe
Sean Carroll
 
Quantum entaglement
Quantum entaglementQuantum entaglement
Quantum entaglement
Sreepadmanabh M
 
EPR paradox
EPR paradoxEPR paradox
EPR paradox
surat murthy
 
Quantum Field Theory and the Limits of Knowledge
Quantum Field Theory and the Limits of KnowledgeQuantum Field Theory and the Limits of Knowledge
Quantum Field Theory and the Limits of Knowledge
Sean Carroll
 
Quantum Entanglement - Cryptography and Communication
Quantum Entanglement - Cryptography and CommunicationQuantum Entanglement - Cryptography and Communication
Quantum Entanglement - Cryptography and Communication
Yi-Hsueh Tsai
 
Bethe salpeter equation
Bethe salpeter equationBethe salpeter equation
Bethe salpeter equation
Claudio Attaccalite
 
Quantum teleportation
Quantum  teleportationQuantum  teleportation
Quantum teleportation
Sidharth Mohapatra
 
Density functional theory (DFT) and the concepts of the augmented-plane-wave ...
Density functional theory (DFT) and the concepts of the augmented-plane-wave ...Density functional theory (DFT) and the concepts of the augmented-plane-wave ...
Density functional theory (DFT) and the concepts of the augmented-plane-wave ...
ABDERRAHMANE REGGAD
 
Quick and Dirty Introduction to Mott Insulators
Quick and Dirty Introduction to Mott InsulatorsQuick and Dirty Introduction to Mott Insulators
Quick and Dirty Introduction to Mott Insulators
ABDERRAHMANE REGGAD
 
Quantum Entanglement
Quantum EntanglementQuantum Entanglement
Quantum Entanglement
Alexis Diaz
 
Role of excitonic effects in nonlinear optical properties of 2D materials
Role of excitonic effects in nonlinear optical properties of 2D materialsRole of excitonic effects in nonlinear optical properties of 2D materials
Role of excitonic effects in nonlinear optical properties of 2D materials
Claudio Attaccalite
 
Lf 2020 langevin
Lf 2020 langevinLf 2020 langevin
Lf 2020 langevin
luc faucheux
 
Quantum Entanglement
Quantum EntanglementQuantum Entanglement
Quantum Entanglement
pixiejen
 
Quantum entanglement
Quantum entanglementQuantum entanglement
Quantum entanglement
AKM666
 
Quantum tunneling composite
Quantum tunneling compositeQuantum tunneling composite
Quantum tunneling composite
Arefin Haque Tahsin
 
Schrodinger cat (Copenhagen & Many-worlds interpretation + phase-damping)
Schrodinger cat (Copenhagen & Many-worlds interpretation + phase-damping)Schrodinger cat (Copenhagen & Many-worlds interpretation + phase-damping)
Schrodinger cat (Copenhagen & Many-worlds interpretation + phase-damping)
Gabriel O'Brien
 

What's hot (20)

Cosmology
CosmologyCosmology
Cosmology
 
On the Origin of Structure in the Universe
On the Origin of Structure in the UniverseOn the Origin of Structure in the Universe
On the Origin of Structure in the Universe
 
Letting Go of Spacetime
Letting Go of SpacetimeLetting Go of Spacetime
Letting Go of Spacetime
 
Many Worlds, the Born Rule, and Self-Locating Uncertainty
Many Worlds, the Born Rule, and Self-Locating UncertaintyMany Worlds, the Born Rule, and Self-Locating Uncertainty
Many Worlds, the Born Rule, and Self-Locating Uncertainty
 
What We (Don't) Know About the Beginning of the Universe
What We (Don't) Know About the Beginning of the UniverseWhat We (Don't) Know About the Beginning of the Universe
What We (Don't) Know About the Beginning of the Universe
 
Quantum entaglement
Quantum entaglementQuantum entaglement
Quantum entaglement
 
EPR paradox
EPR paradoxEPR paradox
EPR paradox
 
Quantum Field Theory and the Limits of Knowledge
Quantum Field Theory and the Limits of KnowledgeQuantum Field Theory and the Limits of Knowledge
Quantum Field Theory and the Limits of Knowledge
 
Quantum Entanglement - Cryptography and Communication
Quantum Entanglement - Cryptography and CommunicationQuantum Entanglement - Cryptography and Communication
Quantum Entanglement - Cryptography and Communication
 
Bethe salpeter equation
Bethe salpeter equationBethe salpeter equation
Bethe salpeter equation
 
Quantum teleportation
Quantum  teleportationQuantum  teleportation
Quantum teleportation
 
Density functional theory (DFT) and the concepts of the augmented-plane-wave ...
Density functional theory (DFT) and the concepts of the augmented-plane-wave ...Density functional theory (DFT) and the concepts of the augmented-plane-wave ...
Density functional theory (DFT) and the concepts of the augmented-plane-wave ...
 
Quick and Dirty Introduction to Mott Insulators
Quick and Dirty Introduction to Mott InsulatorsQuick and Dirty Introduction to Mott Insulators
Quick and Dirty Introduction to Mott Insulators
 
Quantum Entanglement
Quantum EntanglementQuantum Entanglement
Quantum Entanglement
 
Role of excitonic effects in nonlinear optical properties of 2D materials
Role of excitonic effects in nonlinear optical properties of 2D materialsRole of excitonic effects in nonlinear optical properties of 2D materials
Role of excitonic effects in nonlinear optical properties of 2D materials
 
Lf 2020 langevin
Lf 2020 langevinLf 2020 langevin
Lf 2020 langevin
 
Quantum Entanglement
Quantum EntanglementQuantum Entanglement
Quantum Entanglement
 
Quantum entanglement
Quantum entanglementQuantum entanglement
Quantum entanglement
 
Quantum tunneling composite
Quantum tunneling compositeQuantum tunneling composite
Quantum tunneling composite
 
Schrodinger cat (Copenhagen & Many-worlds interpretation + phase-damping)
Schrodinger cat (Copenhagen & Many-worlds interpretation + phase-damping)Schrodinger cat (Copenhagen & Many-worlds interpretation + phase-damping)
Schrodinger cat (Copenhagen & Many-worlds interpretation + phase-damping)
 

Similar to Gravitational Collider Physics

Nanomagnetism columbia 2013
Nanomagnetism columbia 2013Nanomagnetism columbia 2013
Nanomagnetism columbia 2013
oriolespinal
 
"Squeezed States in Bose-Einstein Condensate"
"Squeezed States in Bose-Einstein Condensate""Squeezed States in Bose-Einstein Condensate"
"Squeezed States in Bose-Einstein Condensate"
Chad Orzel
 
Introduction to the phenomenology of HiTc superconductors.
Introduction to  the phenomenology of HiTc superconductors.Introduction to  the phenomenology of HiTc superconductors.
Introduction to the phenomenology of HiTc superconductors.
ABDERRAHMANE REGGAD
 
ECE692_3_1008.pptdfdfdfdfdfdfdffdfdfdfddf
ECE692_3_1008.pptdfdfdfdfdfdfdffdfdfdfddfECE692_3_1008.pptdfdfdfdfdfdfdffdfdfdfddf
ECE692_3_1008.pptdfdfdfdfdfdfdffdfdfdfddf
hushamss2271
 
Theoretical picture: magnetic impurities, Zener model, mean-field theory
Theoretical picture: magnetic impurities, Zener model, mean-field theoryTheoretical picture: magnetic impurities, Zener model, mean-field theory
Theoretical picture: magnetic impurities, Zener model, mean-field theory
ABDERRAHMANE REGGAD
 
Sergey Sibiryakov "Galactic rotation curves vs. ultra-light dark matter: Impl...
Sergey Sibiryakov "Galactic rotation curves vs. ultra-light dark matter: Impl...Sergey Sibiryakov "Galactic rotation curves vs. ultra-light dark matter: Impl...
Sergey Sibiryakov "Galactic rotation curves vs. ultra-light dark matter: Impl...
SEENET-MTP
 
Lecture15_Hall_effect.pdf
Lecture15_Hall_effect.pdfLecture15_Hall_effect.pdf
Lecture15_Hall_effect.pdf
MofasserMallick1
 
Topological flat bands without magic angles in massive twisted bilayer graphe...
Topological flat bands without magic angles in massive twisted bilayer graphe...Topological flat bands without magic angles in massive twisted bilayer graphe...
Topological flat bands without magic angles in massive twisted bilayer graphe...
JAVVAJI SRIVANI
 
Quantum Nanomagetism (USA, 2011)
Quantum Nanomagetism (USA, 2011)Quantum Nanomagetism (USA, 2011)
Quantum Nanomagetism (USA, 2011)
oriolespinal
 
Lecture 7 pseudogap
Lecture 7 pseudogapLecture 7 pseudogap
Lecture 7 pseudogap
AllenHermann
 
Crystal structure analysis
Crystal structure analysisCrystal structure analysis
Crystal structure analysis
zoelfalia
 
Manhpowerpoint
ManhpowerpointManhpowerpoint
Manhpowerpoint
Tiền Mạnh
 
Mcrowave and Radar engineering
Mcrowave and Radar engineeringMcrowave and Radar engineering
Mcrowave and Radar engineering
Priyanka Anni
 
Workshop problems solving
Workshop problems solvingWorkshop problems solving
Workshop problems solving
Prof. Dr. Ahmed Ennaoui
 
.wave deformation
.wave deformation.wave deformation
.wave deformation
kochadaiyaan
 
Flow Induced vibration fundamentals present
Flow Induced vibration fundamentals presentFlow Induced vibration fundamentals present
Flow Induced vibration fundamentals present
JaimeCruz978742
 
4 radio wave propagation over the earth
4 radio wave propagation over the earth4 radio wave propagation over the earth
4 radio wave propagation over the earth
Solo Hermelin
 
Chapter 4a interference
Chapter 4a interferenceChapter 4a interference
Chapter 4a interference
Gabriel O'Brien
 
Quantum information probes
Quantum information probes Quantum information probes
Quantum information probes
SM588
 
Lecture 3_thermal property drude model.pdf.pdf
Lecture 3_thermal property drude model.pdf.pdfLecture 3_thermal property drude model.pdf.pdf
Lecture 3_thermal property drude model.pdf.pdf
AwnishTripathi4
 

Similar to Gravitational Collider Physics (20)

Nanomagnetism columbia 2013
Nanomagnetism columbia 2013Nanomagnetism columbia 2013
Nanomagnetism columbia 2013
 
"Squeezed States in Bose-Einstein Condensate"
"Squeezed States in Bose-Einstein Condensate""Squeezed States in Bose-Einstein Condensate"
"Squeezed States in Bose-Einstein Condensate"
 
Introduction to the phenomenology of HiTc superconductors.
Introduction to  the phenomenology of HiTc superconductors.Introduction to  the phenomenology of HiTc superconductors.
Introduction to the phenomenology of HiTc superconductors.
 
ECE692_3_1008.pptdfdfdfdfdfdfdffdfdfdfddf
ECE692_3_1008.pptdfdfdfdfdfdfdffdfdfdfddfECE692_3_1008.pptdfdfdfdfdfdfdffdfdfdfddf
ECE692_3_1008.pptdfdfdfdfdfdfdffdfdfdfddf
 
Theoretical picture: magnetic impurities, Zener model, mean-field theory
Theoretical picture: magnetic impurities, Zener model, mean-field theoryTheoretical picture: magnetic impurities, Zener model, mean-field theory
Theoretical picture: magnetic impurities, Zener model, mean-field theory
 
Sergey Sibiryakov "Galactic rotation curves vs. ultra-light dark matter: Impl...
Sergey Sibiryakov "Galactic rotation curves vs. ultra-light dark matter: Impl...Sergey Sibiryakov "Galactic rotation curves vs. ultra-light dark matter: Impl...
Sergey Sibiryakov "Galactic rotation curves vs. ultra-light dark matter: Impl...
 
Lecture15_Hall_effect.pdf
Lecture15_Hall_effect.pdfLecture15_Hall_effect.pdf
Lecture15_Hall_effect.pdf
 
Topological flat bands without magic angles in massive twisted bilayer graphe...
Topological flat bands without magic angles in massive twisted bilayer graphe...Topological flat bands without magic angles in massive twisted bilayer graphe...
Topological flat bands without magic angles in massive twisted bilayer graphe...
 
Quantum Nanomagetism (USA, 2011)
Quantum Nanomagetism (USA, 2011)Quantum Nanomagetism (USA, 2011)
Quantum Nanomagetism (USA, 2011)
 
Lecture 7 pseudogap
Lecture 7 pseudogapLecture 7 pseudogap
Lecture 7 pseudogap
 
Crystal structure analysis
Crystal structure analysisCrystal structure analysis
Crystal structure analysis
 
Manhpowerpoint
ManhpowerpointManhpowerpoint
Manhpowerpoint
 
Mcrowave and Radar engineering
Mcrowave and Radar engineeringMcrowave and Radar engineering
Mcrowave and Radar engineering
 
Workshop problems solving
Workshop problems solvingWorkshop problems solving
Workshop problems solving
 
.wave deformation
.wave deformation.wave deformation
.wave deformation
 
Flow Induced vibration fundamentals present
Flow Induced vibration fundamentals presentFlow Induced vibration fundamentals present
Flow Induced vibration fundamentals present
 
4 radio wave propagation over the earth
4 radio wave propagation over the earth4 radio wave propagation over the earth
4 radio wave propagation over the earth
 
Chapter 4a interference
Chapter 4a interferenceChapter 4a interference
Chapter 4a interference
 
Quantum information probes
Quantum information probes Quantum information probes
Quantum information probes
 
Lecture 3_thermal property drude model.pdf.pdf
Lecture 3_thermal property drude model.pdf.pdfLecture 3_thermal property drude model.pdf.pdf
Lecture 3_thermal property drude model.pdf.pdf
 

More from DanielBaumann11

Timeless Cosmology: Towards a Geometric Origin of Cosmological Correlations
Timeless Cosmology: Towards a Geometric Origin of Cosmological CorrelationsTimeless Cosmology: Towards a Geometric Origin of Cosmological Correlations
Timeless Cosmology: Towards a Geometric Origin of Cosmological Correlations
DanielBaumann11
 
Our Universe: From the Big Bang to the Multiverse
Our Universe: From the Big Bang to the MultiverseOur Universe: From the Big Bang to the Multiverse
Our Universe: From the Big Bang to the Multiverse
DanielBaumann11
 
The Big Bang and the Origin of Structure
The Big Bang and the Origin of StructureThe Big Bang and the Origin of Structure
The Big Bang and the Origin of Structure
DanielBaumann11
 
Lessons from the Past
Lessons from the PastLessons from the Past
Lessons from the Past
DanielBaumann11
 
Bootstrapping Cosmological Correlations
Bootstrapping Cosmological CorrelationsBootstrapping Cosmological Correlations
Bootstrapping Cosmological Correlations
DanielBaumann11
 
Cosmology and String Theory
Cosmology and String TheoryCosmology and String Theory
Cosmology and String Theory
DanielBaumann11
 

More from DanielBaumann11 (6)

Timeless Cosmology: Towards a Geometric Origin of Cosmological Correlations
Timeless Cosmology: Towards a Geometric Origin of Cosmological CorrelationsTimeless Cosmology: Towards a Geometric Origin of Cosmological Correlations
Timeless Cosmology: Towards a Geometric Origin of Cosmological Correlations
 
Our Universe: From the Big Bang to the Multiverse
Our Universe: From the Big Bang to the MultiverseOur Universe: From the Big Bang to the Multiverse
Our Universe: From the Big Bang to the Multiverse
 
The Big Bang and the Origin of Structure
The Big Bang and the Origin of StructureThe Big Bang and the Origin of Structure
The Big Bang and the Origin of Structure
 
Lessons from the Past
Lessons from the PastLessons from the Past
Lessons from the Past
 
Bootstrapping Cosmological Correlations
Bootstrapping Cosmological CorrelationsBootstrapping Cosmological Correlations
Bootstrapping Cosmological Correlations
 
Cosmology and String Theory
Cosmology and String TheoryCosmology and String Theory
Cosmology and String Theory
 

Recently uploaded

mô tả các thí nghiệm về đánh giá tác động dòng khí hóa sau đốt
mô tả các thí nghiệm về đánh giá tác động dòng khí hóa sau đốtmô tả các thí nghiệm về đánh giá tác động dòng khí hóa sau đốt
mô tả các thí nghiệm về đánh giá tác động dòng khí hóa sau đốt
HongcNguyn6
 
Leaf Initiation, Growth and Differentiation.pdf
Leaf Initiation, Growth and Differentiation.pdfLeaf Initiation, Growth and Differentiation.pdf
Leaf Initiation, Growth and Differentiation.pdf
Renu Jangid
 
Topic: SICKLE CELL DISEASE IN CHILDREN-3.pdf
Topic: SICKLE CELL DISEASE IN CHILDREN-3.pdfTopic: SICKLE CELL DISEASE IN CHILDREN-3.pdf
Topic: SICKLE CELL DISEASE IN CHILDREN-3.pdf
TinyAnderson
 
8.Isolation of pure cultures and preservation of cultures.pdf
8.Isolation of pure cultures and preservation of cultures.pdf8.Isolation of pure cultures and preservation of cultures.pdf
8.Isolation of pure cultures and preservation of cultures.pdf
by6843629
 
Nucleic Acid-its structural and functional complexity.
Nucleic Acid-its structural and functional complexity.Nucleic Acid-its structural and functional complexity.
Nucleic Acid-its structural and functional complexity.
Nistarini College, Purulia (W.B) India
 
Travis Hills' Endeavors in Minnesota: Fostering Environmental and Economic Pr...
Travis Hills' Endeavors in Minnesota: Fostering Environmental and Economic Pr...Travis Hills' Endeavors in Minnesota: Fostering Environmental and Economic Pr...
Travis Hills' Endeavors in Minnesota: Fostering Environmental and Economic Pr...
Travis Hills MN
 
ESR spectroscopy in liquid food and beverages.pptx
ESR spectroscopy in liquid food and beverages.pptxESR spectroscopy in liquid food and beverages.pptx
ESR spectroscopy in liquid food and beverages.pptx
PRIYANKA PATEL
 
Phenomics assisted breeding in crop improvement
Phenomics assisted breeding in crop improvementPhenomics assisted breeding in crop improvement
Phenomics assisted breeding in crop improvement
IshaGoswami9
 
The debris of the ‘last major merger’ is dynamically young
The debris of the ‘last major merger’ is dynamically youngThe debris of the ‘last major merger’ is dynamically young
The debris of the ‘last major merger’ is dynamically young
Sérgio Sacani
 
Unveiling the Energy Potential of Marshmallow Deposits.pdf
Unveiling the Energy Potential of Marshmallow Deposits.pdfUnveiling the Energy Potential of Marshmallow Deposits.pdf
Unveiling the Energy Potential of Marshmallow Deposits.pdf
Erdal Coalmaker
 
NuGOweek 2024 Ghent programme overview flyer
NuGOweek 2024 Ghent programme overview flyerNuGOweek 2024 Ghent programme overview flyer
NuGOweek 2024 Ghent programme overview flyer
pablovgd
 
Comparing Evolved Extractive Text Summary Scores of Bidirectional Encoder Rep...
Comparing Evolved Extractive Text Summary Scores of Bidirectional Encoder Rep...Comparing Evolved Extractive Text Summary Scores of Bidirectional Encoder Rep...
Comparing Evolved Extractive Text Summary Scores of Bidirectional Encoder Rep...
University of Maribor
 
Shallowest Oil Discovery of Turkiye.pptx
Shallowest Oil Discovery of Turkiye.pptxShallowest Oil Discovery of Turkiye.pptx
Shallowest Oil Discovery of Turkiye.pptx
Gokturk Mehmet Dilci
 
The binding of cosmological structures by massless topological defects
The binding of cosmological structures by massless topological defectsThe binding of cosmological structures by massless topological defects
The binding of cosmological structures by massless topological defects
Sérgio Sacani
 
DMARDs Pharmacolgy Pharm D 5th Semester.pdf
DMARDs Pharmacolgy Pharm D 5th Semester.pdfDMARDs Pharmacolgy Pharm D 5th Semester.pdf
DMARDs Pharmacolgy Pharm D 5th Semester.pdf
fafyfskhan251kmf
 
What is greenhouse gasses and how many gasses are there to affect the Earth.
What is greenhouse gasses and how many gasses are there to affect the Earth.What is greenhouse gasses and how many gasses are there to affect the Earth.
What is greenhouse gasses and how many gasses are there to affect the Earth.
moosaasad1975
 
Medical Orthopedic PowerPoint Templates.pptx
Medical Orthopedic PowerPoint Templates.pptxMedical Orthopedic PowerPoint Templates.pptx
Medical Orthopedic PowerPoint Templates.pptx
terusbelajar5
 
Nucleophilic Addition of carbonyl compounds.pptx
Nucleophilic Addition of carbonyl  compounds.pptxNucleophilic Addition of carbonyl  compounds.pptx
Nucleophilic Addition of carbonyl compounds.pptx
SSR02
 
Eukaryotic Transcription Presentation.pptx
Eukaryotic Transcription Presentation.pptxEukaryotic Transcription Presentation.pptx
Eukaryotic Transcription Presentation.pptx
RitabrataSarkar3
 
Remote Sensing and Computational, Evolutionary, Supercomputing, and Intellige...
Remote Sensing and Computational, Evolutionary, Supercomputing, and Intellige...Remote Sensing and Computational, Evolutionary, Supercomputing, and Intellige...
Remote Sensing and Computational, Evolutionary, Supercomputing, and Intellige...
University of Maribor
 

Recently uploaded (20)

mô tả các thí nghiệm về đánh giá tác động dòng khí hóa sau đốt
mô tả các thí nghiệm về đánh giá tác động dòng khí hóa sau đốtmô tả các thí nghiệm về đánh giá tác động dòng khí hóa sau đốt
mô tả các thí nghiệm về đánh giá tác động dòng khí hóa sau đốt
 
Leaf Initiation, Growth and Differentiation.pdf
Leaf Initiation, Growth and Differentiation.pdfLeaf Initiation, Growth and Differentiation.pdf
Leaf Initiation, Growth and Differentiation.pdf
 
Topic: SICKLE CELL DISEASE IN CHILDREN-3.pdf
Topic: SICKLE CELL DISEASE IN CHILDREN-3.pdfTopic: SICKLE CELL DISEASE IN CHILDREN-3.pdf
Topic: SICKLE CELL DISEASE IN CHILDREN-3.pdf
 
8.Isolation of pure cultures and preservation of cultures.pdf
8.Isolation of pure cultures and preservation of cultures.pdf8.Isolation of pure cultures and preservation of cultures.pdf
8.Isolation of pure cultures and preservation of cultures.pdf
 
Nucleic Acid-its structural and functional complexity.
Nucleic Acid-its structural and functional complexity.Nucleic Acid-its structural and functional complexity.
Nucleic Acid-its structural and functional complexity.
 
Travis Hills' Endeavors in Minnesota: Fostering Environmental and Economic Pr...
Travis Hills' Endeavors in Minnesota: Fostering Environmental and Economic Pr...Travis Hills' Endeavors in Minnesota: Fostering Environmental and Economic Pr...
Travis Hills' Endeavors in Minnesota: Fostering Environmental and Economic Pr...
 
ESR spectroscopy in liquid food and beverages.pptx
ESR spectroscopy in liquid food and beverages.pptxESR spectroscopy in liquid food and beverages.pptx
ESR spectroscopy in liquid food and beverages.pptx
 
Phenomics assisted breeding in crop improvement
Phenomics assisted breeding in crop improvementPhenomics assisted breeding in crop improvement
Phenomics assisted breeding in crop improvement
 
The debris of the ‘last major merger’ is dynamically young
The debris of the ‘last major merger’ is dynamically youngThe debris of the ‘last major merger’ is dynamically young
The debris of the ‘last major merger’ is dynamically young
 
Unveiling the Energy Potential of Marshmallow Deposits.pdf
Unveiling the Energy Potential of Marshmallow Deposits.pdfUnveiling the Energy Potential of Marshmallow Deposits.pdf
Unveiling the Energy Potential of Marshmallow Deposits.pdf
 
NuGOweek 2024 Ghent programme overview flyer
NuGOweek 2024 Ghent programme overview flyerNuGOweek 2024 Ghent programme overview flyer
NuGOweek 2024 Ghent programme overview flyer
 
Comparing Evolved Extractive Text Summary Scores of Bidirectional Encoder Rep...
Comparing Evolved Extractive Text Summary Scores of Bidirectional Encoder Rep...Comparing Evolved Extractive Text Summary Scores of Bidirectional Encoder Rep...
Comparing Evolved Extractive Text Summary Scores of Bidirectional Encoder Rep...
 
Shallowest Oil Discovery of Turkiye.pptx
Shallowest Oil Discovery of Turkiye.pptxShallowest Oil Discovery of Turkiye.pptx
Shallowest Oil Discovery of Turkiye.pptx
 
The binding of cosmological structures by massless topological defects
The binding of cosmological structures by massless topological defectsThe binding of cosmological structures by massless topological defects
The binding of cosmological structures by massless topological defects
 
DMARDs Pharmacolgy Pharm D 5th Semester.pdf
DMARDs Pharmacolgy Pharm D 5th Semester.pdfDMARDs Pharmacolgy Pharm D 5th Semester.pdf
DMARDs Pharmacolgy Pharm D 5th Semester.pdf
 
What is greenhouse gasses and how many gasses are there to affect the Earth.
What is greenhouse gasses and how many gasses are there to affect the Earth.What is greenhouse gasses and how many gasses are there to affect the Earth.
What is greenhouse gasses and how many gasses are there to affect the Earth.
 
Medical Orthopedic PowerPoint Templates.pptx
Medical Orthopedic PowerPoint Templates.pptxMedical Orthopedic PowerPoint Templates.pptx
Medical Orthopedic PowerPoint Templates.pptx
 
Nucleophilic Addition of carbonyl compounds.pptx
Nucleophilic Addition of carbonyl  compounds.pptxNucleophilic Addition of carbonyl  compounds.pptx
Nucleophilic Addition of carbonyl compounds.pptx
 
Eukaryotic Transcription Presentation.pptx
Eukaryotic Transcription Presentation.pptxEukaryotic Transcription Presentation.pptx
Eukaryotic Transcription Presentation.pptx
 
Remote Sensing and Computational, Evolutionary, Supercomputing, and Intellige...
Remote Sensing and Computational, Evolutionary, Supercomputing, and Intellige...Remote Sensing and Computational, Evolutionary, Supercomputing, and Intellige...
Remote Sensing and Computational, Evolutionary, Supercomputing, and Intellige...
 

Gravitational Collider Physics

  • 2. Based on work with H.S. Chia R. Porto J. Stout G. Tomaselli G. Bertone DB, Chia and Porto Probing Ultralight Bosons with Binary Black Holes arXiv:1804.03208 PRD [Editor’s Suggestion] DB, Chia, Porto and Stout Gravitational Collider Physics arXiv:1912.04932 DB, Bertone, Stout and Tomaselli Ionization of Gravitational Atoms arXiv:2112.14777 DB, Bertone, Stout and Tomaselli Sharp Signals of Boson Clouds in Black Hole Binary Inspirals arXiv:22xx.xxxxx (PRL accepted) [Editor’s Suggestion] DB, Chia, Stout and ter Haar The Spectra of Gravitational Atoms arXiv:1908.10370
  • 3. Can it also become a new tool for fundamental physics? The detection of GWs marked the beginning of a new era of multi-messenger astronomy:
  • 4. particle collider Standard Model Neutrinos 1020 1010 1 10 10 10 20 Energy [eV] New physics is often associated with high energies (short distances): We expect this to have small effects on long-wavelength GW signals. cosmological collider
  • 5. New physics may also occur at low energies, if it is weakly coupled: particle collider Standard Model Neutrinos 1020 1010 1 10 10 10 20 Energy [eV] EM Strong Weak Gravity Coupling gravitational collider This may be probed by GW signals from binary black hole mergers. cosmological collider
  • 6. superradiance Ultralight bosons can form bound states around rotating black holes: This resembles the hydrogen atom and is therefore often called a gravitational atom. Zel’dovich ’72 Starobinsky ’73 Arvanitaki et al ‘09 superradiance
  • 7. A companion will perturb the cloud with a slowly increasing frequency. DB, Chia, Porto, and Stout ’19
  • 8. DB, Chia, Porto, and Stout ’19 This interaction is enhanced at certain resonance frequencies.
  • 9. DB, Chia, Porto, and Stout ’19 The backreaction of the cloud’s dynamics on the orbit leaves distinct imprints in the gravitational waves emitted by the binary.
  • 10. Outline 1) Gravitational Atoms 2) Evolution in Binaries 3) Gravitational Wave Signals
  • 12. A scalar field around a rotating black hole is described by the KG equation: g↵ r↵r µ2 = 0 We will focus on fields whose Compton wavelength is larger than the BH: Ultralight Bosons around Black Holes 1 km 1010 km 10 10 eV 10 20 eV
  • 13. Such light fields see the far-field limit of the geometry: Ultralight Bosons around Black Holes µ2 ds2 = ✓ 1 2↵ r ◆ dt2 + ✓ 1 + 2↵ r ◆ dr2 4↵2 ã sin2 ✓ r dt d + r2 d⌦2 where ↵ ⌘ rg/ c is the gravitational fine-structure constant. spin i d dt = ✓ 1 2µ r2 ↵ r + V ◆ The KG equation then reduces to a Schrödinger equation: with = (t, x)eiµt Coulomb potential fine structure corrections V
  • 14. 0 2 6 12 αr |ψ n!m (r)| 2 |10m! |21m! |32m! |43m! Bound States The energy eigenstates are the same as those of the hydrogen atom: with “quantum numbers”: principal orbital azimuthal m ` n r/r0
  • 15. 0 5 10 µαr |ψ k;!m (r)| 2 |0; 11! |1; 11! |2; 11! |3; 11! |211! Unbound States There are also unbound continuum states: r/r0 with “quantum numbers”: energy orbital azimuthal m ` E
  • 16. Bound State Spectrum En`m = µ ✓ 1 ↵2 2n2 + fn`↵4 + hn`m↵5 + · · · ◆ The bound state spectrum is the same as for the hydrogen atom: ! = 0 |211! |311! ! = 1 |322! ! = 2 n = 1 n = 2 n = 3
  • 17. ` = 0 |211i |311i ` = 1 |322i ` = 2 n = 1 n = 2 n = 3 Growing and Decaying Modes Unlike in the hydrogen atom, the states are only quasi-stationary: !n`m = En`m + i n`m decaying growing
  • 18. ΩH ω < mΩH Superradiant Scattering The growing modes are populated by superradiance: Outgoing wave Incoming wave / exp(im i!t) This is the wave analog of the Penrose process. Penrose ’71 Zel’dovich ’72 Starobinsky ’73
  • 19. Black Hole Bomb A reflecting mirror around the BH creates a black hole bomb: Press and Teukolsky ‘72
  • 20. For a massive field, the mirror is provided by the angular momentum barrier: This creates an exponential amplification of small fluctuations. Superradiant Instability
  • 21. Growth Rates 1013 1011 109 107 105 103 10 0.02 0.05 0.1 0.15 0.2 0.25 α |211! |322! |321! The different bound states grow at different rates: n`m / ↵4`+5 Detweiler ‘80
  • 22. Initial State of the Cloud adiance The fastest growing mode is the state We take this as the initial state of the cloud. 1 211 = 103 yrs ✓ M 60M ◆ ✓ 0.04 ↵ ◆9 |211i:
  • 23. T211 = 1010 yrs ✓ M 60M ◆ ✓ 0.04 ↵ ◆15 Lifetime of the Cloud adiance In isolation, the gravitational atom is very long lived: We would like to understand what happens to the atom when it is part of a binary system.
  • 25. The binary companion can induce transitions between bound states (“Rabi oscillations”) and excite unbound states (“photoelectric effect”): DB, Chia and Porto 2018 DB, Chia, Porto and Stout 2019 DB, Bertone, Stout and Tomaselli 2021
  • 26. We will first study the transitions between bound states: Ω = ∆E ∆E DB, Chia and Porto 2018 DB, Chia, Porto and Stout 2019
  • 27. Gravitational Perturbation ϕ∗ M∗ R∗ In a binary, the cloud gets perturbed at a slowly increasing frequency: i d dt = ✓ 1 2µ r2 ↵ r + V + V⇤(R⇤(t), '⇤(t)) ◆ This perturbation induces level mixing: ha|V⇤(t)|bi = ⌘ab(t)e i(ma mb)'⇤(t)
  • 28. ⌦i = Ei mi ⇠ 0.01 Hz ✓ 60M M ◆ ⇣ ↵ 0.04 ⌘3 Resonant Transitions At specific frequencies, the perturbation is resonantly enhanced: ⌦1 ⌦2 ⌦3
  • 29. Selection Rules ! = 0 |211! ∆E |311! |31 −1! ! = 1 |322! ! = 2 n = 1 n = 2 n = 3 For a scalar atom, the level mixings typically involve only two states. Only certain transitions are allowed by selection rules:
  • 30. Ω = ∆E ϕ∗(t) ηeiϕ∗(t) ηe−iϕ∗(t) ∆E Two-State System A simple two-state system is therefore a good model for the dynamics: H = 1 2 E ⌘ei'⇤(t) ⌘e i'⇤(t) 1 2 E !
  • 31. HD = (⌦(t) E)/2 ⌘ ⌘ (⌦(t) E)/2 ! Two-State System Rotating along with the companion, isolates the slow motion: E
  • 32. Near the resonance, we can write ⌦(t) = ⌦res + t determines nature of transition HD(t) = t 2 ✓ 1 0 0 1 ◆ + ⌘ ✓ 0 1 1 0 ◆ Landau ’32 Zener ’32 E Two-State System
  • 33. Landau-Zener Transition Landau ’32 Zener ’32 The analogous problem in QM was solved by Landau and Zener. The evolution depends on the size of the parameter : z ⌘ ⌘2 / 40 20 0 20 40 0 0.5 1 z = 102 p t |c a (t)| 2 40 20 0 20 40 0 0.5 1 z = 10 2 p t |c0|2 |c1|2 • For slow transitions, the initial state gets fully converted. • For fast transitions, some of the initial state can survive.
  • 34. Multi-State Transitions Clouds of spinning particles involve multi-state transitions: 50 0 50 100 150 0 0.5 1 p t |c a (t)| 2 |c1|2 |c2|2 |c3|2 50 0 50 p t • The final state is generically a superposition of states. • There can be neutrino-like oscillations between the states.
  • 35. Backreaction on the Orbit The transitions force the cloud’s energy and angular momentum to change: tbefore tres tafter Sc(t) Sc(t) tres These changes must be balanced by changes in the orbital dynamics.
  • 36. Backreaction on the Orbit Conservation of angular momentum requires d dt ⇣ L + Sc ⌘ = TGW ⇡ 0 cloud orbit The dynamics of the cloud affects the orbital motion! DB, Chia, Porto, and Stout ’20
  • 37. 1 0.5 0 0.5 1 1.5 2 0 0.5 1 1.5 2 t/⌦r ⌦/⌦ r 1 0.5 0 0.5 1 t/⌦r Floating Orbits The binary floats when it absorbs angular momentum from the cloud: The binary emits transient, nearly monochromatic GWs. DB, Chia, Porto, and Stout ’20
  • 38. 1 0.5 0 0.5 1 1.5 2 0 0.5 1 1.5 2 t/⌦r ⌦/⌦ r 1 0.5 0 0.5 1 t/⌦r Sinking Orbits The binary sinks when it releases angular momentum to the cloud: This leads to a dephasing in the GW signal. DB, Chia, Porto, and Stout ’20
  • 39. Multiple Transitions The sequence of transitions is a fingerprint of the atomic spectra: ⌦1 ⌦2 ⌦3 t ⌦(t) ⌦1 ⌦2 ⌦3
  • 40. Multiple Transitions The evolution can be described by a series of scattering events: ⌦1 ⌦2 ⌦3 ⌦(t) = ⌦1 ⌦(t) = ⌦2 ⌦(t) = ⌦3 t | i S1| i S2S1| i S3S2S1| i DB, Chia, Porto, and Stout ’20
  • 41. Final State of the Cloud Qc(t) = X a |ca(t)|2 Qc,a + X a6=b |ca(t)cb(t)| Qab cos( Eab t) scalar cloud vector cloud The S-matrix formalism predicts the final state of the cloud: |f i = N Y n=1 Sn | i i The shape and time dependence of this state depends on the internal structure of the cloud:
  • 42. E Gravitational Collider Physics • Mass: Position of the resonance • Spin: Angular dependence • Mass: Position of the resonances • Spin: Structure of the final state As in ordinary particle colliders, the signals depend on the mass and spin of the particles:
  • 43. 10 -3 10 -2 10 -1 1 2 fres (Hz) 10 -1 1 10 102 103 104 M § /M 1 0 - 6 1 0 - 4 1 0 - 2 1 1 0 2 1% 10% 100% M = 60MØ 0.01 0.05 0.1 0.2 0.3 Æ 10 -8 10 -6 10 -4 10 -2 1 102 104 ¢t tot (yrs) Gravitational Wave Signatures • The resonances naturally occur in the LISA band: • The dephasing of the signals can be significant:
  • 45. What happens when the orbital frequency becomes large enough to excite transitions to unbound states? Ω = Eb E Eb DB, Bertone, Stout and Tomaselli 2021
  • 46. Fermi’s Golden Rule The transition rate (per unit energy) is given by Fermi’s Golden Rule: Ω = Eb ϕ∗(t) −Eb E η!m(E)eiϕ∗(t) η!m(E)e−iϕ∗(t) Eb d `m = dE ⌘`m(E; t) 2 E Eb ⌥ (m mb)⌦(t) level mixing: hE; `m|V⇤(t)|nb`bmbi 2
  • 47. Pion(t) = Mc(t) µ X `,m (m mb) ⌦(t) ⌘`m E (m) ⇤ ; t 2 ⇥ E (m) ⇤ Ionization Power Ω = Eb ϕ∗(t) −Eb E η!m(E)eiϕ∗(t) η!m(E)e−iϕ∗(t) Eb Summing over all bound states gives the total ionization power: E (m) ⇤ ⌘ Eb ± (m mb) ⌦(t)
  • 48. Ionization Power • The orbital energy lost due to ionization can be very large. | (R )|2 300 200 100 0 0 100 200 R /M P ion /P GW Evaluating this numerically, we find • It has sharp features are specific separations: R (g) ⇤ = M ↵2  4g2 ✓ 1 + M⇤ M ◆ n4 b 1/3 , g = 1, 2, · · ·
  • 49. 0 200 400 600 800 10 200 400 + t [yrs] R ∗ /M Backreaction on the Orbit Ionization can significantly shorten the merger time:
  • 50. Frequency Evolution We get sharp features in the frequency evolution of the GW signals: −20 −15 −10 −5 0 t − tmerg (f / ) −8/3 f(2) f(3) f(4) These discontinuities are distinctive signatures of the boson clouds.
  • 52. • Precise waveform modeling is needed to apply this to GW searches. • We studied the dynamics of boson clouds in black hole binaries. • The backreaction on the orbit produces distinct GW signatures.
  • 53. Thank you for your attention!