terrestrial detector for low frequency gw based on full
TRANSCRIPT
Hyung Mok Lee Department of Physics and Astronomy, Seoul National University
Collaborators: H. Paik, Vol Moody, Cornelius Griggs, Ettore Majorana, Jan Harms, C. Kim, A. Nielsen
KCK Meeting, Dec. 14, 2015 Beijing
Terrestrial Detector for Low Frequency GW Based on Full Tensor
Measurement
2015 KCK, Dec. 14-16, Beijing HMLee
Gravitational Waves in Wide Spectral Range
http://rhcole.com/apps/GWplotter by Moore, Cole & Berry
}
There is a gap here (0.1 - 10 Hz)
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2015 KCK, Dec. 14-16, Beijing HMLee
Terrestrial Detector Concepts for Low Frequencies
• Astrophyiscal requirement for detectors at ~ 0.1 Hz: should be better than 10-20 Hz-1/2 (Harms et al. 2013)
• Following Detector Concepts have been considered 1. Atom-laser interferometer 2. Torsional bar with laser interferometer (TOBA)
3. Michelson interferometer
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2015 KCK, Dec. 14-16, Beijing HMLee
Gravity Gradiometer as a GW Detecror
•Geodesic deviation equation:
• In weak field limit
• Strain Amplitude
d
2x
i
dt
2= �R
i0j0x
j
Ri0j0 ⇡ @
2�
@x
i@x
j
Ri0j0 = �1
2
@2hij
@t2⇡ 1
2!2hij
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2015 KCK, Dec. 14-16, Beijing HMLee
• Truncated icosahedral gravitational wave antenna (Johnson & Merkowitz 1993)
• Omni-directional
• Measure direction and polarization
• Spherical Resonant Detectors
• MiniGRAIL (Leiden)
• Schenberg (Sao Paulo)
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Full Tensor Detectors
2015 KCK, Dec. 14-16, Beijing HMLee
Tunable Free Mass GW Detector (Wagoner et al. 1979)• The relative motion of two masses induces driving emf of
resonant L-C circuit • The relative momentum is determined by the current in the
circuits • Can be tuned over a wide frequency range
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2015 KCK, Dec. 14-16, Beijing HMLee
Superconducting Tensor Gravity Gradiometer (Univ. of Maryland)
Test masses are magnetically suspend (fDM ~ 0.01 Hz). 100x higher sensitivity
Six test masses mounted a cube form a tensor gradiometer.
Test masses are levitated by a current induced along a tube.
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2015 KCK, Dec. 14-16, Beijing HMLee
Superconducting tensor GW Detector
• Superconducting Omni-directional Gravitational Radiation Observatory (SOGRO)
• By detecting all six components of Riemann tensor, the source direction and the polarization can be determined
hii(t) =1
L
[x+ii(t)� x�ii(t)]
hij(t) =1
L
{[x+ij(t)� x�ij(t)]� [x�ji(t)� x+ji(t)]}
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2015 KCK, Dec. 14-16, Beijing HMLee
Requirements and Philosophy
• Extremely low detector noise is required • Low temperature, high Q and quantum limited detector
• Test mass suspension frequency should be lowered to below the signal bandwidth (0.1 - 10 Hz) • Almost free test masses by magnetic levitation
• Seismic noise is more difficult to isolate at low frequencies • High CM rejection in a superconducting differential
accelerometer • Newtonian noise increases sharply below 10 Hz
• Tensor detector which can discriminate against the near-field gravity
hij ⇠1
!
2
@
2�
@x
i@x
j
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2015 KCK, Dec. 14-16, Beijing HMLee
Basic Design of SOGRO
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2015 KCK, Dec. 14-16, Beijing HMLee
Suspension• Go underground to reduce seismic and gravity gradient
noise
• Nodal support in order to suppress the odd harmonics
• 25m pendulum gives fp=0.1 Hz for two horizontal modes and fr <0.001 Hz for three angular modes
• passive isolation for high frequencies
• Triangulate with thin wall tubes to make the platform rigid
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2015 KCK, Dec. 14-16, Beijing HMLee
Magnetic Levitation• Field required to levitate 5 ton mass:
• The biggest challenges: • To obtain symmetry, vertical DM resonance frequencies
must also reduced to 0.01 Hz. • Employ “push-pull levitation”
B2
2µ0A = Mg, B =
✓2µ0Mg
A
◆1/2
⇡ 0.16T
(Moody, Chan and Paik, JAP, 1986)
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2015 KCK, Dec. 14-16, Beijing HMLee
Tuned Capacity-Bridge Transducer
•Capacitor bridge coupled to a near quantum-limited SQUID thru S/C transformer.
•LC resonance increases energy coupling β by Qp .
•Oscillator noise is rejected by the bridge balance. • Maintain precise
balance by feedback.
EN (f) =kBT!D
QD+
|!2 � !2D|
!p
✓1 +
1
�2
◆1/2
kBTN
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2015 KCK, Dec. 14-16, Beijing HMLee
Achievable detector noiseFor CW signal impedance matched bridge transducer
Parameter SOGRO 1 SOGRO 2 Method Employed (SOGRO 1 / 2)Each mass M 5 ton 5 ton Nb square tubeSeparation L 30 m 100 m Over “rigid” mounting platformAntenna temp T 1.5 K 0.1 K Superfluid He / dilution refrigeratorDM frequency fD 0.01 Hz 0.01 Hz Magnetic levitation w/ negative springDM quality factor QD 108 109 Surface polished pure NbSignal frequency f 0.1-10 Hz 0.1-10 Hz Detector noise computed at 1 HzPump frequency fp 50 kHz 50 kHz Tuned capacitor bridge transducerAmplifier noise no. n 200 10 Near-quantum-limited SQUIDDetector noise S 1/2(f )
h 2×10�20 Hz�1/2 2×10�21 Hz�1/2 Two phase development
Sh(!) =8
ML2!4
(kB!D
QD+
|!2 � !2D|
!p
✓1 +
1
�2
◆1/2
kBTN
), kBTN = n!p
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2015 KCK, Dec. 14-16, Beijing HMLee
Seismic noise
Seismic noise of underground sites
▪ 20-m pendulum with nodal support ⇒ Passive isolation for f > 0.1 Hz. ▪ 110 dB reduction by combining passive
and active isolation with CM rejection of the detector.
Seismic background
Active isolation
Axis alignment and scale factor match
Error compensation
Paik 14
SOGRO 1 sensitivity
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Major challenges: ▪ Large-scale cryogenics. ▪ Mitigation of Newtonian noise. 13
Sensitivity goals of SOGRO
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2015 KCK, Dec. 14-16, Beijing HMLee
Newtonian gravity noise (NN)▪ Seismic and atmospheric density modulations cause
Newtonian gravity gradient noise. ▪ GWs are transverse and do not have longitudinal
components whereas the Newtonian gradient does.In GW frame,with the wave traveling along the 3rd axis,
GW could be distinguished from near-field Newtonian
gravity.
h0(!) =
0
@h+(!) + h0
NG,11(!) h⇥(!) + h0NG,12(!) h0
NG,13(!)h⇥(!) + h0
NG,12(!) �h+(!) + h0NG,22(!) h0
NG,23(!)h0NG,13(!) h0
NG,23(!) h0NG,33(!)
1
A
By combining tensor components, we get
Similar expression can be found for hx(ω).
h+(!) = h011(!)� 2 cot ✓h0
13(!) + csc
2 ✓2⇡G⇢0
!
�RcR
exp
✓!
cRz
◆X
i
⇠(!)
+ csc
2 ✓4⇡G
!2
X
i
�⇢i(!) sin2 #i exp
✓!
cISz sin#i
◆
Due to Rayleigh Waves
Due to Infrasound waves
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2015 KCK, Dec. 14-16, Beijing HMLee
Removal of Newtonian noise
Tensor + 8 microphones 100 m ( 100m, SNR 105)
Harms and Paik, PRD (2015)
Tensor + ver CM (0 noise)
Ω
Meets sensitivity goal of SOGRO 1.
Tensor + ver CM (SNR 106
+7 seisemometers (5km, SNR 103)
Tensor + 15 microphones(0, 0.6, 1 km, SNR 104)
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2015 KCK, Dec. 14-16, Beijing HMLee
Summary
Maximum distances to detect IMBH- IMBH binary merger (SOGRO 2)
▪ SOGRO would fill in the missing signal band between eLISA and aLIGO/Virgo/KAGRA, 0.1 – 10 Hz.
▪ SOGRO is a tensor detector with all-sky coverage and with the ability to locate the source and determine wave polarization.
▪ SOGRO, a full-tensor detector, has an advantage in rejecting NN. ▪ Technical details have to be further studied.
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