resonant mass gravitational wave detectors david blair university of western australia historical...
TRANSCRIPT
Resonant Mass Gravitational Wave Detectors
David BlairUniversity of Western Australia
• Historical Introduction
• Intrinsic Noise in Resonant Mass Antennas
• Transducers
• Transducer-Antenna interaction effects
• Suspension and Isolation
• Data Analysis
Sources and Materials
• These notes are about principles and not projects.
• Details of the existing resonant bar network may be found on the International Gravitational Events Collaboration web page.
• References and some of the content can be found in
• Ju, Blair and Zhou Rep Prog Phys 63,1317,2000.
• Online at www.iop.org/Journals/rp
• Draft of these notes available www.gravity.uwa.edu.au
•Sao Paulo
•Leiden
•Frascati
•Sphere developments
Existing Resonant Bar Detectors and sphere developments
Weber’s Pioneering Work• Joseph Weber Phys Rev 117, 306,1960• Mechanical Mass Quadrupole Harmonic
Oscillator: Bar, Sphere or Plate• Designs to date:
Bar
Sphere
Torsional Quadrupole Oscillator
Weber’s suggestions:
Earth: GW at 10-3 Hz.
Piezo crystals: 107 Hz
Al bars: 103 Hz
Detectable flux spec density: 10-7Jm-2s-1Hz-1
( h~ 10-22 for 10-3 s pulse)
Gravity Wave Burst Sources and Detection
223
16 hhG
cS
Energy Flux of a gravitational wave:
Short Bursts of duration g
Assume ghh /2 2
23 4
16 g
h
G
cS
J m-2 s-1
gG
h
G
cE
23 4
16
Total pulse energy density EG = S.g
J m-2 s-1
Jm-2
Flux Spectral Density
Bandwidth of short pulse: ~ 1/g
Reasonable to assume flat spectrum: F() ~ E/ g
ie: G
hcF
4)(
23 J.m-2.Hz-1
For short bursts: F() ~ 20 x 1034 h2
Gravitational wave bursts with g~10-3s were the original candidate signals for resonant mass detectors.
However stochastic backgrounds and monochromatic signals are all detectable with resonant masses.
Black Hole Sources and Short Bursts
Start with Einstein’s quadrupole formula for gravitational wave luminosity LG:
jk
jkG
dt
Dd
c
GL
2
3
3
55
where the quadrupole moment Djk is defined as: xdxxxtD jkkj
jk32
3
1
Notice: for a pair of point masses D=ML2 ,
for a spherical mass distribution D=0
for a binary star system in circular orbit D varies as sin2t
Burst Sources Continued
Notice also that represents non-spherical kinetic energy
ie the kinetic energy of non-spherically symmetric motions.
D
For binary stars (simplest non sperically symmetric source), projected length (optimal orientation) varies sinusoidally,
D~ML2sin22t,
64255
16~
LMc
GLG
32~ MLDThe numerical factor comes from the time average of the third time derivative of sin2t.
Now assume isotropic radiation
24 r
LS G
2
3
16h
G
cS
but also use
Note that KE=1/2Mv2= 1/8ML22
To order of magnitude2
22
532
r
E
c
G
c
Gh ns
andr
E
c
Gh ns
4
Maximal source: Ens=Mc2……merger of two black holes r
r
r
Mc
c
Gh s~
2
4
In general for black hole births r
rh s Here is conversion
efficiency to gravitational waves
•Weber used arguments such as the above to show that gravitational waves created by black hole events near the galactic centre could create gravitational wave bursts of amplitude as high as 10-16.
•He created large Al bar detectors able to detect such signals.
•He identified many physics issues in design of resonant mass detectors.
• His results indicated that 103 solar masses per year were being turned into gravitational waves.
•These results were in serious conflict with knowledge of star formation and supernovae in our galaxy.
•His data analysis was flawed.
•Improved readout techniques gave lower noise and null results.
Weber’s Research
Energy deposited in a resonant mass
Energy deposited in a resonant mass EG
dFEG
is the frequency dependent cross section
F is the spectral flux density
Treat F as white over the instrument bandwidth
Then dFE aG
28
c
v
c
Gmd s
Paik and Wagoner showed for fundamental quadrupole mode of bar:
x
y
zEnergy deposited in an initially stationary bar Us
Us=F(a).sin4sin22 Mc
v
c
G s 2
28
Incoming wave
Energy and Antenna Pattern for Bar
Sphere is like a set of orthogonal bars giving omnidirectional sensitivity and higher cross section
M, TA
Ta a
F
v
Z11 Z12
Z21 Z22
Se
SiG
V
Ii
Bar Transducer Amplifier Recorder
Detection Conditions
• Detectable signal Us Noise energy Un
•Transducer: 2-port device:
Current
velocity
Z
Z
Z
Z
Voltage
Force
22
12
21
11
computer
•Amplifier , gain G, has effective current noise spectral density Si and voltage noise spectral density Se
Mechanical input impedance Z11
Forward transductance Z21 (volts m-1s-1)
Reverse transductance Z12 (kg-amp-1)
Electrical output impedance Z22
X2
X1
P1P2
X1=AsinResonant
masstransducer
Vsinat ~
XG
X2=Acos
Reference oscillator
multiply
0o 90o
Bar, Transducer and Phase Space Coordinates
determines time for transducer to reach equilibrium
•X1 and X2 are symmetrical phase space coordinates
•Antenna undergoes random walk in phase space
•Rapid change of state measured by length of vector (P1,P2)
•High Q resonator varies its state slowly
Asin(at+
Bar
C
Pump Oscillator
Modulated Output
Persistent Current 1
SQUIDOutput a
Two Transducer Concepts
Parametric Direct
•Signal detected as modulation of pump frequency
•Critical requirements: low pump noise low noise amplifier at
modulation frequency
•Signal at antenna frequency
•Critical requirements: low noise SQUID amplifier low mechanical loss circuitry
Mechanical Impedance Matching
•High bandwidth requires good impedance matching between acoustic output impedance of mechanical system and transducer input impedance
•Massive resonators offer high impedance
•All electromagnetic fields offer low impedance (limited by energy density in electromagnetic fields)
•Hence mechanical impedance trasformation is essential
•Generally one can match to masses less than 1kg at ~1kHz
Mechanical model of transducer with intermediate mass resonant transformer
Resonant transformer creates two mode system
Two normal modes split byeff
a M
m
T r a n s d u c e r A s s e m b l y
B a r
B e n d in g f l a p
G lu e j o in t2 4 h r e p o x y
P u m p F r e q u e n c y : 9 .5 G H z
f / x = T u n i n g C o e f f : 3 0 0 M H z / µ m
T o a c h i e v e 9 .5 0 0 1 M H zr e q u i r e x = x 0 3 n m ( x 0 = 1 0 µ m )
Bending flap secondary resonatorMicrowave
cavity
Data Acquisition
Mixers
Phase shifters
Filter
Electronically adjustable phase shifter & attenuator
SO Filter
Phase servo
Frequency servo
W-amplifierPrimaryW-amplifier
SpareW-amplifier
Microstripantennae
Microwave interferometer
Cryogenic components
Bar
Bending flap
Transducer
RF
9.049GHz 451MHz
9.501GHz
CompositeOscillator
Microwave Readout System of NIOBÉ (upgrade)
Secondary Resonator (“mushroom”) and Transducer
Pickup Coil
DC SQUID (Amplifier. Its output is proportioanl to the motion of the mushroom)
Direct Mushroom Transducer
A superconducting persistent current is modulated by the motion of the mushroom resonator and amplified by
a DC SQUID.
Aluminium antenna
Niobium Coils
Niobium Diaphragm
Heat Switch
Heat Switch
SQUID Amplifier input coil
Pair of pick-up coils
Current supply leads
resonant superconducting diaphragm
Niobium Diaphragm Direct Transducer (Stanford)
Three Mode Niobium Transducer (LSU)
•Two secondary resonators
•Three normal modes
•Easier broadband matching
•Mechanically more complex
Three general classes of noise
Brownian Motion Noise
kT noise energy
Series Noise Back Action Noise
2
2
22
1
4
aeff
ath
M
kTx
Low loss angle compresses thermal noise into narrow bandwidth at resonance.
Decreases for high bandwidth.(small i)
Broadband Amplifier noise, pump phase noise or other additive noise contributions.
Series noise is usually reduced if transductance Z21 is high.
Always increases with bandwidth
Amplifier noise acting back on antenna.
Unavoidable since reverse transductance can never be zero.
A fluctuating force indistingushable from Brownian motion.
Noise Contributions
Total noise referred to input:
i
eeffii
effa
ian
S
Z
MS
M
ZkTU
)(2
)(2
22
21
212
Reduces as i/a because of predictability of high Q oscillator
Reduces as i/M because fluctuations take time to build up and have less effect on massive bar
Increases as M/i reduces due to increased bandwidth of noise contribution, and represents increased noise energy as referred to input
Quantum Limits
Noise equation shows any system has minimum noise level and optimum integration time set by the competing action of series noise and back action noise.
Since a linear amplifier has a minimum noise level called the standard quantum limit this translates to a standard quantum limit for a resonant mass.
Noise equation may be rewritten
where A is Noise Number: equivalent number of quanta.
The sum AB+AS cannot reduce below~1: the Standard Quantum Limit
SBTa
n AAAU
A
s
a
seff
aSQL v
kms
M
tonne
kHz
f
vMh
15.05.021
5.0
22
101
1101.1~
2
Burst strain limit~10-22 (100t sphere) corres to h()~3.10-24
Thermal Noise Limit
Thermal noise only becomes negligible for Q/T>1010 (100Hz bandwidth)
5.0
22
QvM
kTh
seff
aith
(Q=a/
5.09
2
1021 100
1.0
1010
110
B
Hz
K
T
QvM
J
kHz
fh
seffth
Thermal noise makes it difficult to exceed hSQL
Ideal Parametric Transducer
Noise temperature characterises noise energy of any system.Since photon energy is frequency dependent, noise number is more useful.Amplifier effective noise temperature must be referred to antenna frequency For example a = 2 x 700Hz pump= 2 x 9.2 GHz
Tn = 10K: Hence and Teff = 8 10-7 K
Cryogenic microwave amplifiers greatly exceed the performance of any existing SQUID and have robust performance•Oscillator noise and thermal noise degrade system noise
np
aeff TT
pump
nkTA
BPF
LOOP OSCILLATOR
Microwave Interferometer
LORF
LNA
Circulator
Phase error detector
mixer
Loop filter
Sapphire loaded cavity resonator
Qe~3107
varactor
DC Bias
W-amplifier
W-amplifier
Filtered output
+
+
Non-filtered output
Pump Oscillators for Parametric Transducer
A low noise oscillator is an essential component of a parametric transducer
A stabilised NdYAG laser provides a similar low noise optical oscillator for optical parametric transducers and for laser interferometers which are similar parametric devices.
Nb bar primary mechanical oscilator
microstrip antenas
re-entrant cavity transducer
cryogenic circulator
AM noise reduction system
low noise SLOCSC oscillator mixed with a HP 8662A synthesizer (9.5GHz)
low pass filter
output signal
room temperature low-noise amplifier
cryogenic low-noise amplifier
3dB Hybrid TEE
attenuatorphase shifter
phase tracking
quadrature channel
frequency trackingin-phase channel
carrier suppression interferometer
bending flap secondary mechanical oscillator
Coupling and Transducer Scattering Picture
a
p
+=p+a
-=p-a
?
transducer
Pump photons
Signal phonons
Output sidebands
Treat transducer as a photon scatterer
Because transducer has negligible loss use energy conservation to understand signal power flow- Manley-Rowe relations.
Note that power flow may be altered by varying asper previous slide
0
PPP
a
a
0
PPP
p
p
Formal solution but results are intuitively obvious
Upper mode Lower modeCold damping of bar modes by parametric transducer
Bar mode
frequency tuning by pump tuning
Parametric transducer damping and elastic stiffness
Electromechanical Coupling of Transducer to Antenna
signal energy in transducersignal energy in bar
•In direct transducer = (1/2CV2)/M2x2
•In parametric transducer =(p/a)(1/2CV2)/M2x2
•Total sideband energy is sum of AM and PM sideband energy, depends on pump frequency offset
Manley-Rowe Solutions
If p>>a, Pp ~ -(P++P-).
If P+/+ < P-/- ,then Pa< 0…..negative power flow…instability
If P+/+ > P-/- ,then Pa> 0…..positive power flow…cold damping
By manipulating using offset tuning can cold-damp the resonator…very convenient and no noise cost.Enhance upper sideband by operating with pump frequency below resonance.
Offset tuning to vary Q and in high Q limit
If transducer cavity has a Qe>p/a , then
b is maximised near the cavity resonance or at the sideband frequencies. Strong cold damping is achieved for p=cavity-a .
Thermal noise contributions from bar and secondary resonator
Thermal noise components for a bar Q=2 x108 (antiresonance at mid band) and secondary resonator Q=5 x 107
m2 H
z-1
Frequency Hz
bar
Secondary resonator
Low high series noise,
low back action noise
Spectral Strain
sensitivity
SNR/Hz/mK
Transducer Optimisation
This and the following curves from M Tobar
Thesis UWA 1993
Relations between Sensitivity and Bandwidth
effT
T
Q
fBandwidth
42
M
kT
v
L
f
Sh
gs
ah
g
222
)(1
Minimum detectable energy is defined by the ratio of wideband noise to narrow band noise
Express minimum detectable energy as an effective temperature
fnoisenarrowband
isewidebandnoTE 2min
Optimum spectral sensitivity depends on ratioMQ
T
Independent of readout noise
Bandwidth and minimum detectable burst depends
on transducer and amplifier
Burst detection: maximum total
bandwidth important
Search for pulsar signals (CW) in spectral minima.
More bandwidth=more sources
at same sensitivity
Stochastic background: use two detectors with coinciding spectral
minima
Improving Bar Sensitivity with Improved Transducers
High , low noise,3 mode
Two mode, low , high series noise
Optimal filter
Signal to noise ratio is optimised by a filter which has a transfer function proportional to the complex conjugate of the signal Fourier transform divided by the total noise spectral density
d
S
FjGSNR
x
)(
)()(
2
122
Fourier tfm of impulse response of displacement sensed by transducer for force input to bar
Fourier tfm of input signal force
Double sided spectral density of noise refered to the transducer displacement
Monochromatic and Stochastic Backgrounds
Both methods allow the limits to bursts to be easily exceeded.
Monochromatic (or slowly varying) : (eg Pulsar signals):Long term coherent integration or FFTVery narrow bandwidth detection outside the thermal noise bandwidth.
Stochastic Background: Cross correlate between independent detectors.
Thermal noise is independent and uncorrelated between detectors.
Excess Noise and Coincidence Analysis
Log
num
ber
of
sam
ples
Energy
Excess noiseD
etector noise
•All detectors show non-thermal noise.
•Source of excess noise is not understood
•Similar behaviour (not identical) in all detectors.
•All excess noise can be elliminated by coincidence analysis between sufficient detectors. (>4)
Measure noise performance by noise temperature.
Typically h~(few x 10-17).Tn1/2
Coincidence Statistics
rRP 1Probability of event above threshhold:
(Event rate R, resolving time r)
Prob of accidental coincidence in coincidence window c
If all antennas have same background
Hence in time ttot the number of accidental
coincidences is
Ni
iNcN RP
,1
Nc
NN RP
1 Nc
Nac RN
0 5 10 15 20
10-14
10-12
10-10
10-8
10-6
10-4
10-2
100
102
104
events/day
1 bar 1982
2 bars 1991
3 bars 1999
4 bars 1999 (not enough data)
hburst
x 1018
Improvements through coincidence analysis
Suspension Systems•General rule:Mode control. Acoustic resonance=short circuit.
• Low acoustic loss suspension: many systems.
•Low vibration coupling to cryogenics:
•Cable couplings: Taber isolators or non-contact readout
•Multistage isolation in cryogenic environment
•Room Temperature isolation stages
Dead bug
cables
Nodal point
Important tool: Finite element modelling
Suspension choices
Intermediate MassLiquid Helium
Niobium Bar
Microwave Electronics
Transducer
Conning Tower Ti alloy suspesion rod Lead/Rubber vibration isolation Non-contacting radiative heat shunt Bellows to decouple the dewar from the antenna suspension Antenna suspension supports Experimental tank suspension tube
Experimental tank
Liquid nitrogen shield30 K shield
Cryogenic cantilever suspension
Interface for electrical leads, vacuum lines and cryogenic liquids
Niobe: 1.5 tonne Niobium Antenna with Parametric Transducer
vibration isolation
•Nodal suspension
• Integrated secondary and tertiary resonators for reasonable bandwidth
•non-superconducting for efficient cooldown
•mass up to 100 tonnes
Sphere
Current limits set by bars
Bursts: 7 x 10-2 solar masses converted to gravity waves at galactic centre (IGEC)
Spectral strain sensitivity: h(f)= 6 x 10-23/Rt Hz (Nautilus)
Pulsar signals in narrow band (95 days): h~ 3 x 10-24
(Explorer)
Stochastic background: h~10-22
(Nautilus-Explorer)
Summary
Bars are well understood
Major sensitivity improvements underway
SQUIDs for direct transducers now making progress (see Frossati’s talk)
All significant astrophysical limits have been set by bars.
At high frequency bars achieve spectral sensitivity in narrow bands that is likely to exceed interferometer sensitivity for the forseeable future.