Download Searching for ultra-light new particles with black hole superradiance

Searching for ultra-light new
particles with black holes
Robert Lasenby, Perimeter Institute
0905.4720
1004.3558
1411.2263
1604.03958
16xx.xxxxx
…
A. Arvanitaki, S. Dimopoulos, S. Dubovsky, N. Kaloper, J. March-Russell
A. Arvanitaki, S. Dubovsky
A. Arvanitaki, M. Baryakhtar, X. Huang
A. Arvanitaki, M. Baryakhtar, S. Dimopoulos, S. Dubovsky, RL
M. Baryakhtar, RL
Outline
•
Light, weakly-coupled new particles — motivation &
constraints
•
Black hole superradiance — particle production by energy
extraction
•
Observational signatures
•
Spin-down of black holes
•
Coherent gravitational wave emission
Light, weakly-coupled new
particles
Coupling
to SM
Standard
Model
SUSY?
Grand
Unification?
Experimentally
excluded
New long
Axions?
range forces?
Mass
Light, weakly-coupled new
particles
Coupling
to SM
Standard
Model
LHC
Experimentally
excluded
Black hole
superradiance
Mass
Gravitational production of
light particles
•
New particles must couple to SM through gravity
•
Problem: astrophysically, spacetime curvature scale & km
=> effective source density very low
•
•
e.g. BH Hawking temperature, TH = 1/(8⇡GM ) ⇠ 10
Take advantage of coherence enhancement: classical
energy extraction from spinning BHs
8
K
Extracting energy and angular
momentum from black holes
•
Spinning BHs have ergosphere - region where particles can
have negative energy (as viewed from infinity)
Ergosphere
•
Event horizon
Mechanical Penrose process: throwing negative-energy
particle into horizon
Extracting energy and angular
momentum from black holes
•
Spinning BHs have ergosphere - region where particles can
have negative energy (as viewed from infinity)
Ergosphere
•
Event horizon
Mechanical Penrose process: throwing negative-energy
particle into horizon
Extracting energy and angular
momentum from black holes
•
Spinning BHs have ergosphere - region where particles can
have negative energy (as viewed from infinity)
Ergosphere
•
Event horizon
Mechanical Penrose process: throwing negative-energy
particle into horizon
Extracting energy and angular
momentum from black holes
•
Spinning BHs have ergosphere - region where particles can
have negative energy (as viewed from infinity)
Ergosphere
•
Event horizon
Mechanical Penrose process: throwing negative-energy
particle into horizon
Extracting energy and angular
momentum from black holes
•
Spinning BHs have ergosphere - region where particles can
have negative energy (as viewed from infinity)
Ergosphere
•
Event horizon
Mechanical Penrose process: throwing negative-energy
particle into horizon
Extracting energy and angular
momentum from black holes
•
Spinning BHs have ergosphere - region where particles can
have negative energy (as viewed from infinity)
Ergosphere
•
Event horizon
Wave Penrose process: transmitted wave has negative
energy, reflected wave carries extra energy away
Extracting energy and angular
momentum from black holes
•
Spinning BHs have ergosphere - region where particles can
have negative energy (as viewed from infinity)
Ergosphere
•
Event horizon
Wave Penrose process: transmitted wave has negative
energy, reflected wave carries extra energy away
Wave superradiance
•
Ingoing flux at horizon can
correspond to negative E1 flux
•
For wave with angular quantum
number m,
' ⇠ ei!t
1 2
P = '0 AH !(!
2
•
im
m⌦H )
Incoming waves can be
scattered with amplification
(max 4.4% for spin-1, 138% for
spin-2)
[Teukolsky & Press, 1974]
Wave superradiance
•
Ingoing flux at horizon can
correspond to negative E1 flux
•
For wave with angular quantum
number m,
' ⇠ ei!t
1 2
P = '0 AH !(!
2
•
im
m⌦H )
Incoming waves can be
scattered with amplification
(max 4.4% for spin-1, 138% for
spin-2)
[Teukolsky & Press, 1974]
Black hole bombs and bound
states
•
“Black hole bomb” : superradiant scattering with a mirror
[Teukolsky & Press, 1972]
•
Massive particles can form bound states around BH, enabling same
exponential amplification
Black hole bombs and bound
states
•
“Black hole bomb” : superradiant scattering with a mirror
[Teukolsky & Press, 1972]
•
Massive particles can form bound states around BH, enabling same
exponential amplification
Black hole bombs and bound
states
•
“Black hole bomb” : superradiant scattering with a mirror
[Teukolsky & Press, 1972]
•
Massive particles can form bound states around BH, enabling same
exponential amplification
Black hole bombs and bound
states
•
“Black hole bomb” : superradiant scattering with a mirror
[Teukolsky & Press, 1972]
•
Massive particles can form bound states around BH, enabling same
exponential amplification
(Pseudo)scalar bound states
•
For small mass, bound state spectrum is hydrogen-like
↵ ⌘ GM µ = rg µ
✓
!n ' µ 1
2
↵
2n2
n2
rn ⇠
⇠4
µ↵
Im(!) ⇠ '20 (a⇤ m
◆
400rg
2µr+ )
(Pseudo)scalar bound states
•
For small mass, bound state spectrum is hydrogen-like
↵ ⌘ GM µ = rg µ
✓
!n ' µ 1
2
↵
2n2
n2
rn ⇠
⇠4
µ↵
Im(!) ⇠ '20 (a⇤ m
◆
400rg
2µr+ )
(Pseudo)scalar bound states
•
For small mass, bound state spectrum is hydrogen-like
↵ ⌘ GM µ = rg µ
✓
!n ' µ 1
2
↵
2n2
n2
rn ⇠
⇠4
µ↵
Im(!) ⇠ '20 (a⇤ m
◆
400rg
2µr+ )
Superradiant growth rates
Im(!) ⇠ ↵4l+4 (a⇤ m
amplitude near horizon suppressed
2µr+ )µ
a
0.5
1.
1.5
=1
M = 10 Mü
=2
10-4
2.
a* = 0.99
=3
10-6
10-8
a* = 0.9
10-2
=4
10-10
100
10-12
102
10-14
0.5
1
1.5
ma H10-11 eVL
2
2.5
Gsr rg
Smaller alpha, larger l
Gsr -1 HyearsL
•
Superradiant growth rates
Smaller alpha, larger l
Im(!) ⇠ ↵4l+4 (a⇤ m
If ↵/l > 1/2
then angular phase -4
10
velocity faster than
horizon, so mode -2
10
is decaying
Gsr -1 HyearsL
•
•
Fastest growth
rate for
µ ⇠ 1/(GMBH )
amplitude near horizon suppressed
2µr+ )µ
a
0.5
1.
1.5
2.
M = 10 Mü
a* = 0.99
10-6
10-8
a* = 0.9
10-10
100
10-12
102
10-14
0.5
1
1.5
ma H10-11 eVL
2
2.5
Gsr rg
•
Superradiant growth rates
If ↵/l > 1/2
then angular phase -4
10
velocity faster than
horizon, so mode -2
10
is decaying
Gsr -1 HyearsL
•
•
Fastest growth
rate for
µ ⇠ 1/(GMBH )
2µr+ )µ
a
0.5
1.
1.5
2.
M = 10 Mü
a* = 0.99
10-6
10-8
a* = 0.9
10-10
100
10-12
102
10-14
0.5
1
1.5
ma H10-11 eVL
2
2.5
Gsr rg
Im(!) ⇠ ↵4l+4 (a⇤ m
amplitude near horizon suppressed
0.4
Smaller alpha, larger l
0.3
•
Superradiant growth rates
Smaller alpha, larger l
Im(!) ⇠ ↵4l+4 (a⇤ m
amplitude near horizon suppressed
2µr+ )µ
a
0.5
1.
1.5
=1
For stellar BH, efolding times in
plot ~100 sec 100 yr
-1
Gsrsr-1
HyearsL
•
M = 10 Müü
=2
-4
10-4
2.
a**= 0.99
=3
-6
10-6
-8
10-8
a** = 0.9
-2
10-2
=4
-10
10-10
1000
-12
10-12
1022
-14
10-14
0.5
1
1.5
-11 eVL
maa H10-11
2
2.5
Gsrsr rgg
•
Black hole spin-down
a*
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M�� /M☉
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Black hole spin-down
a*
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Black hole spin-down
a*
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Black hole spin-down
a*
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Exclusions from BH spin
measurements
•
Higher BH spin => innermost stable orbit at smaller radius
rISCO
•
•
GM
Accretion
disk can get closer to BH
8
Detect X-rays from accretion disk, infer disk
properties
Contra-rotrating
6
4
Co-rotrating
2
0.2
0.4
0.6
0.8
1.0
a*
Exclusions from BH spin
measurements
•
Higher BH spin => innermost stable orbit at smaller radius
•
Accretion disk can get closer to BH
•
Detect X-rays from accretion disk, infer disk properties
X-ray spin measurements
Spin measurements from different black holes:
1.0
Black Hole Spin a*
0.8
0.6
0.4
0.2
ma =10-11 eV
0.0
5
10
Black Hole Mass HMüL
15
20
X-ray spin measurements
Spin measurements from different black holes:
1.0
Black Hole Spin a*
0.8
0.6
0.4
0.2
ma =10-11 eV
0.0
5
10
Black Hole Mass HMüL
15
20
X-ray spin measurements
Spin measurements from different black holes:
1.0
Black Hole Spin a*
0.8
0.6
0.4
0.2
ma =3x10-12 eV
0.0
5
10
Black Hole Mass HMüL
15
20
Light particle exclusion limits
Large self-coupling => bosonic cloud growth cut off
Self-
coupling
-14
-16
4
2
1
1: M33 X-7
2: LMC X-1
3: GRO J1655-40
4: Cyg X-1
5: GRS 1915+105
Log@l H10-10 eVêmaL2D
Log@GeVê fa D
-12
2s exclusion
-60
-65
5
3
Q
-70
on
i
x
a
CD
-18
-20
-13
-75
-12
-11
Log@maêeVD
Mass
-10
-9
Binary black hole mergers
[Abbot et al, 2016]
•
LIGO GW150914: first
direct detection of
gravitational waves!
•
From 2.5 events so far,
infer merger rate of 9-240
/ Gpc yr
•
At design sensitivity,
70-1200 visible mergers /
year!
BBH spin measurements
[Abbot et al, 2016]
•
Spin-orbit interaction => BH
spin components parallel to
orbital axis affect inspiral
waveform
•
Spin components misaligned
with orbital axis can cause
precession, modulating inspiral
waveform
•
Intrinsic spins contribute to spin
of final BH, which is constrained
by merger and ringdown
waveform
•
GW150914: if spins are aligned,
obtain a1 < 0.2 , a2 < 0.3 (90%)
Spin-down
1.0
Black Hole Spin a!
0.8
0.6
0.4
0.2
Initial Spin
!actual"
0.0
0
20
40
60
Black Hole Mass !M!"
80
100
Spin-down
1.0
Black Hole Spin a*
0.8
0.6
0.4
0.2
0.0
0
20
40
60
Black Hole Mass HMüL
ma = 6 x 10-13 eV
HactualL
80
100
Spin-down
measured
1.0
Black Hole Spin a*
0.8
0.6
0.4
0.2
0.0
0
20
40
60
Black Hole Mass HMüL
ma = 6 x 10-13 eV
HmeasuredL
80
100
Gravitational radiation from
bound states
•
Bosonic cloud corresponds to classical scalar field oscillations =>
oscillating energy-momentum
•
Oscillating Tµ⌫ = rµ 'r⌫ '
radiation
•
gµ⌫ (. . . ) sources gravitational
1 Xp
Ni
Decomposing into levels, ' = p
2µ i
have
1 ⇣
Tij =
N1 (ri
2µ
1 )(rj
1 )e
“Annihilations”
2i!1 t
+
p
N1 N2 (ri
ie
i!i t
⇤
1 )(rj
+ h.c.
2 )e
“Transitions”
i(!2 !1 )t
+ ...
⌘
Gravitational radiation from
bound states
•
Bosonic cloud corresponds to classical scalar field oscillations =>
oscillating energy-momentum
•
Oscillating Tµ⌫ = rµ 'r⌫ '
radiation
•
gµ⌫ (. . . ) sources gravitational
1 Xp
Ni
Decomposing into levels, ' = p
2µ i
have
1 ⇣
Tij =
N1 (ri
2µ
1 )(rj
1 )e
“Annihilations”
2i!1 t
+
p
N1 N2 (ri
ie
i!i t
⇤
1 )(rj
+ h.c.
2 )e
“Transitions”
i(!2 !1 )t
+ ...
⌘
All-Sky GW search
•
From each BH with a cloud, expect GWs from annihilations at frequency
✓
! ' 2µ 1
•
Coherent, monochromatic
signals, very slow
frequency drift
Signals from different black
holes clustered just below
! = 2µ
•
•
Expected signals
determined by BH mass
and spin distribution potentially hundreds
eventually visible!
Most signals from BHs in
our galaxy
↵
2n2
◆
= 2µ (1
[0, 0.03])
100
f HHzL
1000
10000
Explorer
Voyager
aLIGO Design
aLIGO 2015
ANNIHILATIONS
104
Expected Events
•
2
X-ray spin
limits
100
1
Initial LIGO
limits
0.01
10-13
ttot = 1 year
tcoh =2 days
10-12
ma HeVL
10-11
10-10
Summary
•
Black hole superradiance is a unique probe of light, weakly-coupled bosons
•
Gravitational wave detectors can probe SR in multiple, complementary
ways:
•
•
Monochromatic GWs from cloud
•
Statistics of BH spins, measured in mergers
•
Signals possible in near future!
Observations of supermassive black holes, via telescopes and future lowerfrequency GW detectors, can constrain lower-mass bosons
•
Less clean astrophysical environment - further investigation required
Statistical evidence
Could obtain statistical evidence for structure in mass-spin
plane with 50-200 measurements
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time to merge:107 years
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•
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time to merge:1010 years
�� × ��-��
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μ� /��
�� × ��-�� �� × ��-��
GWs from newly formed BHs
•
Measure parameters of
newly-formed BH =>
prediction for SR process,
given axion mass
•
Axion cloud takes days/years
to grow
•
Typical reach ~ 30 Mpc for
annihilation GW signals
•
e.g. if GW150914 had been
< 10 Mpc away, potentially
observable signal
GWs from newly formed BHs
•
•
•
f HHzL
Measure parameters of
newly-formed BH =>
prediction for SR process,
given axion mass
100
1000
1000
Explorer
Voyager
aLIGO Design
DIRECT SEARCHES
100
aLIGO 2015
BH-BH
Expected Events
•
Axion cloud takes days/years
to grow
Typical reach ~ 30 Mpc for
annihilation GW signals
e.g. if GW150914 had been
< 10 Mpc away, potentially
observable signal
10
1
BH-NS
0.1
0.01
0.001
1 ¥ 10-13
2 ¥ 10-13
5 ¥ 10-13
1 ¥ 10-12
ma HeVL
2 ¥ 10-12
5 ¥ 10-12