Terrestrial Detector for Low Frequency GW Based on Full Tensor - - PowerPoint PPT Presentation

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Hyung Mok Lee

Department of Physics and Astronomy, Seoul National University

The Third KAGRA International Workshop May 21-22, 2017 Taipei

Terrestrial Detector for Low Frequency GW Based on Full Tensor Measurement

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Gravitational Waves in Wide Spectral Range

http://rhcole.com/apps/GWplotter by Moore, Cole & Berry

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There is a gap here (0.1 - 10 Hz)

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BH masses grew over time

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Jun et al. 2015

Measurement by SNU group: are we witnessing the growth of the BH?

Small Mseed (10Mis acceptable if BH accreted at Eddington limit, but larger Mseed is more plausible

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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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Harms et al. 2013

IMBH merger secnarios

• Mergers between two star clusters harboring IMBH

( Amaro-Seone P and Freitag M 2006)

• Collisional run-away formation of two BHs in young

dense star clusters (Fregeau J M et al 2006)

• Capturing of a free-flying IMBH by a compact young

cluster in ultra-compact galaxies (Amaro-Seone P et al 2014)

• Low (or mid) frequency detector would be useful.

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Gravity Gradiometer as a GW Detector

• Geodesic deviation equation:
• In weak field limit
• Strain Amplitude

d2xi dt2 = −Ri

0j0xj

Ri0j0 ≈ ∂2φ ∂xi∂xj Ri0j0 = −1 2 ∂2hij ∂t2 ≈ 1 2ω2hij

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Full Tensor Detectors

• 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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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 (Paik et al. 2016, CQG, 33, 075003)

• 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 ω2 ∂2φ ∂xi∂xj

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Basic Design of SOGRO

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Achievable detector noise

combined channels 5 , , 1 1 8 ) (

2 / 1 2 2 2 4 2 p N B N B p D D D B h

n T k T k Q T k ML f S ω β ω ω ω ω ω ! = ⎪ ⎪ ⎭ ⎪ ⎪ ⎬ ⎫ ⎪ ⎪ ⎩ ⎪ ⎪ ⎨ ⎧ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + − + =

Parameter SOGRO aSOGRO Method employed (/aSOGRO) Each test mass M 5 ton 5 ton Nb shell Arm-length L 50 m 50 m Over “rigid” platform Antenna temp T 1.5 K 0.1 K Liquid He / He3-He4 dilution refrigerator Platform temp Tpl 1.5 K 1.5 K Large-scale cryogenics Platform Q factor Qpl 106 107 Square Al tube construction DM frequency fD 0.01 Hz 0.01 Hz Magnetic levitation (horizontal only) DM quality factor 107 108 Surface polished pure Nb Pump frequency fp 50 kHz 50 kHz Tuned capacitor bridge transducer Amplifier noise no. n 20 5 Two-stage dc SQUID cooled to 0.1 K Detector noise Sh1/2(f ) 1 × 10−20 Hz−1/2 3 × 10−21 Hz−1/2 Computed at 1 Hz

▪ aSOGRO requires QD ~ 108 for test masses and Qpl ~ 107 for the platform. ▪ aSOGRO requires improvement by a factor of 2 over best SQUIDs achieved so far.

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Various noise contributions

▪ At present, the greatest challenge appears to be platform design and construction.

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Seismic noise

Seismic noise of underground sites

▪ 20-m pendulum with nodal support ⇒ Passive isolation for f > 0.1 Hz. ▪ Reduction by combining passive and active isolation with CM rejection of the detector can reduce seismic noise below detector noise

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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(ω) =   h+(ω) + h0

NG,11(ω)

h⇥(ω) + h0

NG,12(ω)

h0

NG,13(ω)

h⇥(ω) + h0

NG,12(ω)

−h+(ω) + h0

NG,22(ω)

h0

NG,23(ω)

h0

NG,13(ω)

h0

NG,23(ω)

h0

NG,33(ω)

 

By combining tensor components, we get Similar expression can be found for hx(ω).

h+(ω) = h0

11(ω) − 2 cot θh0 13(ω) + csc2 θ2πGρ0

ω γR cR exp ✓ ω cR z ◆ X

i

ξ(ω) + csc2 θ4πG ω2 X

i

δρi(ω) sin2 ϑi exp ✓ ω cIS z sin ϑi ◆

Due to Rayleigh Waves Due to Infrasound waves

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Mitigation of NN

NN due to Rayleigh waves removed by using h’13, h’23, h’33, az (CM), plus 7 seismometers with SNR = 103 at the radius of 5 km. NN due to infrasound removed by using h’13, h’23, h’33 and 15 mikes of SNR = 104, 1 at the detector, 7 each at radius 600 m and 1 km.

Harms & Paik, PRD 92, 022001 (2015)

▪ First remove Rayleigh NN by using seismometers only, then remove infrasound NN by using microphones and cleaned-up SOGRO outputs. ▪ SOGRO can remove NN from infrasound for all incident angles.

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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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Paik et al. 2016, 30m and 100 baseline