Post on 22-May-2020
Paik-1
Lecture 15Gravitational Wave Experiment:
Resonant-Mass Detectors
Ho Jung Paik
University of Maryland
April 3, 2007
Physics 798G Spring 2007
Paik-2
Gravitational Waves
,0),(12
2
22 =⎟⎟
⎠
⎞⎜⎜⎝
⎛∂∂
−∇ BEtc
μνμν Tc
GG 4
π8=Field equation in General Relativity:
⇒ A wave equation, in the weak-field limit.
μνμνμνμν η hghtc
+==⎟⎟⎠
⎞⎜⎜⎝
⎛∂∂
−∇ ,012
2
22
Transverse, spin 1
EM wave: Gravitational wave:
Transverse, spin 2
Paik-3
Gravitational Wave Detection
Joseph Weber (c1960)
A gravitational wave will deposit energy into an elastic solid. (Weber, 1959)
Paik-4
Resonant-Mass Detector
⎥⎦
⎤⎢⎣
⎡⎥⎦
⎤⎢⎣
⎡=⎥
⎦
⎤⎢⎣
⎡)()(
)()(
2221
1211
ωω
ωω
Iu
ZZZZ
Vf
22m
1221
ZMZZ
ωβ ≡
• Antenna ⇒ Transducer ⇒ Amplifier
• Transducer is characterized by an impedance matrix.
Energy coupling:
f(ω) u(ω) I(ω) V(ω)ijZ
Active transducers
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡=
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
++
−−
+++
+−
−−−
++
−−
)()()(
0
0
)()()(
1
*
1
1111
*1
*
1
*
ωωω
ωωω
IuI
ZZZZZ
ZZ
Vf
V
ωωωω
β ±=≡ ±
±±
±±± pZM
ZZ,
m
11
u(ω) I±(ω ±)ijZf(ω) V±(ω ±)
V(ωp)
Passive transducers
Paik-5
Sensitivity of the Detector
• Condition to detect a GW pulse with strength h:
( ) ⎥⎦
⎤⎢⎣
⎡++≥
22
π2 S
SNB
a
aa
22S2
τβωτβω
τωω TkQ
TkDhM B
• Optimal strategy:
noise. thermal thereduce toneeded is largeA
2 , 2N
a
aBN
S
S
S
ββ
βωω
βωτ
⇒
⎟⎟⎠
⎞⎜⎜⎝
⎛+≈≈
Δ⇒≈ T
QTkE
Signal Antenna noise Amplifier noiseThermal Wideband Backaction
Paik-6
Transducer Options
0Ljω
Type Z11 Z12 Z21 Z22 β
Capacitive (passive)
Inductive (passive)
C-modulated resonator (active)
L-modulated resonator (active)
ωjCE 2
0 )(ωj
E0
ωjE0
Cjω1
2
20
ωMCE
0
20 )(
11
LjIωγΛ
+− 0IΛ 0IΛ−
02
20 )(
11
LMIωγΛ
+
CQCEp
0
2
4)(
ωωω±±
02ωQEp−
02ωωω QEp±m
CQ
0ω 2
2
4 ωMQCEp
LQIp
0
2)2/(ωω
ω Λ±m
20
QI pΛ±
ωω
m2
0QI pΛ
ωω
LMQI p
2
2)2/(ω
Λ
Problem: β = 10-6 ~ 10-5 for M ≥ 103 kg.
⇒ Narrow bandwidth and high thermal noise
LQ0ω
Paik-7
Resonant Transducer
• To get large β, a resonantmass is attached to the antenna (Paik, 1972)
⇒ Displacement gain:(M/m)1/2 ≥ 102
⇒ Energy transfer time:τ ≈ (π/ωa) (M/m)1/2
• An additional resonant mass with μ = (Mm)1/2 can be added to increase ΔωS further.
⇒ Energy transfer time:τ ≈ (π/ωa) (M/m)1/4
Paik-8
S/C Inductive Transducer
MOUNTING FLANGE
ANTENNA
TEST MASS
DC SQUID
CIRCUIT BOARD
AIR FILTER
1.0~01.0
)2/(20
02
≈
≈dm
ABωμβ
Paik-9
ALLEGRO
4-K antenna at LSU with a UM s/c inductive transducer
Paik-10
3-Mode S/C Transducer
1.0E-22
1.0E-21
1.0E-20
1.0E-19
1.0E-18
800 850 900 950 1000
Frequency (Hz)
Stra
in S
ensi
tivity
([H
z]-1/2)
LSU 2-mode
UMD 2-mode
LSU 3-mode
Current designUMD 3-mode
Sensitivity of Allegro with various transducers
Paik-11
AURIGA
Best result obtained:h < 5 x 10-21 Hz-1/2 within ~100 Hz band
100-mK antenna in Italy with a capactive transducercoupled to a dc SQUID
Paik-12
ExplorerSwitzerland
Allegro USA NiobeAustralia
Nautilus, italy
Auriga, Italy
Resonant Bar Detectors
Paik-13
Network of Resonant Bars
Allegro Explorer Auriga
Nautilus
NiobeIGEC Network
Paik-14
Rate(y –1)
Search threshold h
1.E+00
1.E+01
1.E+02
1.E+03
1E-18 1E-17 1E-16
h ~ 2 ×10-18 ~ 0.02 M⊙ converted @ 10 kpc
• Upper limit on the rate of gravitational waves bursts from the Galactic Center (1997-2000)
The area above the blue curve is excluded with a coverage > 90%
P. Astone, et al. PRD 68 (2003) 022001
IGEC Coincidence Search
• No evidence for gravity wave bursts was found.
Paik-15
Spherical Antenna
• Sphere is omni-directional. ⇒ All-sky coverage• By detecting its 5 quadrupole modes, the source
direction (θ, φ) and wave polarization (h+, h×) can be determined. (Wagoner & Paik, 1976)
• Much larger cross-section than a bar of the same resonance frequency (up to 70 x)
• 6 radial transducers on truncated icosahedralconfiguration maintains “spherical” symmetry.(Johnson & Merkowitz, 1993)
⇒ TIGA (Truncated Icosahedral Gravitational Antenna)
Paik-16
Resonant Spheres
MiniGrailThe Netherlands
SchenbergBrazil
Paik-17
Moon as a Spherical Antenna?
The Moon is very quiet seismically due to lack of plate tectonics, ocean, and atmosphere. “Strong” quakes: ~10–9 m Hz–1/2 at 0.1-1 Hz, 0.5-1.3 Richter
First attempt: (Weber, 1972)Apollo 17 Lunar Surface Gravimeter
Paik-18
Instrumenting the Moon
6 s/c horizontal seismometers integrated with cryocoolers in TIGAconfiguration (Paik & Venkateswara, 2004).
Resonant detector at its two lowest quadrupolemodes (~1, 2 mHz).
⇒ Sensitivity could be comparable to LISA, but in narrow band.
Wideband detector below its lowest quadrupolemode (< 1 mHz).
Levitation Coil
Superconducting
DiskSQUID
Sensing Coil
Sensing Coil
I0
Major challenges:1. Noise-free cryocooler
technology is not yet ready.
2. Instrument delivery to the Moon is very expensive.