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Lecture 15Gravitational Wave Experiment:

Resonant-Mass Detectors

Ho Jung Paik

University of Maryland

April 3, 2007

Physics 798G Spring 2007

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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

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Gravitational Wave Detection

Joseph Weber (c1960)

A gravitational wave will deposit energy into an elastic solid. (Weber, 1959)

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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

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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

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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

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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

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S/C Inductive Transducer

MOUNTING FLANGE

ANTENNA

TEST MASS

DC SQUID

CIRCUIT BOARD

AIR FILTER

1.0~01.0

)2/(20

02

≈

≈dm

ABωμβ

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ALLEGRO

4-K antenna at LSU with a UM s/c inductive transducer

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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

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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

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ExplorerSwitzerland

Allegro USA NiobeAustralia

Nautilus, italy

Auriga, Italy

Resonant Bar Detectors

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Network of Resonant Bars

Allegro Explorer Auriga

Nautilus

NiobeIGEC Network

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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.

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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)

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Resonant Spheres

MiniGrailThe Netherlands

SchenbergBrazil

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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

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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.