Terrestrial Detector for Low Frequency GW Based on Full ...

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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http://rhcole.com/apps/GWplotter


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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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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• 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


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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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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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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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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Basic Design of SOGRO

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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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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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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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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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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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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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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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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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Terrestrial Detector for Low Frequency GW Based on Full ...

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