KIW3 Terrestrial Detector for Low Frequency GW Based on Full Tensor Measurement Hyung Mok Lee Department of Physics and Astronomy, Seoul National University The Third KAGRA International Workshop May 21-22, 2017 Taipei
KIW3 http://rhcole.com/apps/GWplotter by Moore, Cole & Berry } 2 Gravitational Waves in Wide Spectral Range There is a gap here (0.1 - 10 Hz)
3 BH masses grew over time Measurement by SNU group: are we witnessing the growth of the BH? Small M seed (10M � �� is acceptable if BH accreted at Eddington limit, but larger M seed is more plausible Jun et al. 2015
KIW3 4 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 Harms et al. 2013
5 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.
KIW3 6 Gravity Gradiometer as a GW Detector d 2 x i • Geodesic deviation equation: dt 2 = − R i 0 j 0 x j • In weak field limit ∂ 2 φ R i 0 j 0 ≈ ∂ x i ∂ x j • Strain Amplitude ∂ 2 h ij R i 0 j 0 = − 1 ≈ 1 2 ω 2 h ij ∂ t 2 2
7 KIW3 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)
8 KIW3 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
9 KIW3 Superconducting Tensor Gravity Gradiometer (Univ. of Maryland) Test masses are magnetically suspend (f DM ~ 0.01 Hz). 100x higher sensitivity Six test masses mounted a cube Test masses are levitated by a current induced form a tensor gradiometer. along a tube.
10 KIW3 Superconducting tensor GW Detector (Paik et al. 2016, CQG, 33, 075003) • Superconducting Omni-directional Gravitational Radiation Observatory (SOGRO) h ii ( t ) = 1 L [ x + ii ( t ) − x − ii ( t )] h ij ( t ) = 1 L { [ x + ij ( t ) − x − ij ( t )] − [ x − ji ( t ) − x + ji ( t )] } • By detecting all six components of Riemann tensor, the source direction and the polarization can be determined
KIW3 11 Requirements and Philosophy ∂ 2 φ h ij ∼ 1 ω 2 ∂ x i ∂ x j • 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
KIW3 12 Basic Design of SOGRO
KIW3 Achievable detector noise ⎧ 2 2 ⎫ 1 / 2 ω − ω D ⎛ ⎞ 8 k T 1 ⎪ ⎪ ω ⎪ ⎪ B D ⎜ ⎟ ! S ( f ) 1 k T , k T n , 5 channels combined = + + = ω ⎨ ⎬ h B N B N p 2 4 2 ⎜ ⎟ Q ω ML ω D p β ⎪ ⎪ ⎝ ⎠ ⎪ ⎪ ⎩ ⎭ 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 / He 3 -He 4 dilution refrigerator Platform temp T pl 1.5 K 1.5 K Large-scale cryogenics Platform Q factor Q pl 10 6 10 7 Square Al tube construction DM frequency f D 0.01 Hz 0.01 Hz Magnetic levitation (horizontal only) DM quality factor 10 7 10 8 Surface polished pure Nb Pump frequency f p 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 S h 1/2 ( f ) 1 × 10 − 20 Hz − 1/2 3 × 10 − 21 Hz − 1/2 Computed at 1 Hz ▪ aSOGRO requires Q D ~ 10 8 for test masses and Q pl ~ 10 7 for the platform. ▪ aSOGRO requires improvement by a factor of 2 over best SQUIDs achieved so far.
KIW3 Various noise contributions ▪ At present, the greatest challenge appears to be platform design and construction.
Seismic noise KIW3 15 ▪ 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 Seismic noise of underground sites
KIW3 16 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. GW could be distinguished In GW frame,with the wave traveling along the 3rd axis, from near-field Newtonian gravity. h + ( ω ) + h 0 NG, 11 ( ω ) h ⇥ ( ω ) + h 0 NG, 12 ( ω ) h 0 NG, 13 ( ω ) h 0 ( ω ) = h ⇥ ( ω ) + h 0 − h + ( ω ) + h 0 h 0 NG, 12 ( ω ) NG, 22 ( ω ) NG, 23 ( ω ) h 0 h 0 h 0 NG, 13 ( ω ) NG, 23 ( ω ) NG, 33 ( ω ) Due to Rayleigh By combining tensor components, we get Waves ✓ ω 13 ( ω ) + csc 2 θ 2 π G ρ 0 ◆ X γ R h + ( ω ) = h 0 11 ( ω ) − 2 cot θ h 0 exp ξ ( ω ) z ω c R c R i ✓ ω ◆ + csc 2 θ 4 π G δρ i ( ω ) sin 2 ϑ i exp X z sin ϑ i Due to Infrasound waves ω 2 c IS i Similar expression can be found for h x ( ω ).
KIW3 Mitigation of NN NN due to Rayleigh waves removed by NN due to infrasound removed by using using h ’ 13 , h ’ 23 , h ’ 33 , a z (CM), plus 7 h ’ 13 , h ’ 23 , h ’ 33 and 15 mikes of SNR = 10 4 , 1 seismometers with SNR = 10 3 at the at the detector, 7 each at radius 600 m and radius of 5 km. 1 km. ▪ 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. Harms & Paik, PRD 92, 022001 (2015) 17
Summary KIW3 18 ▪ 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. Maximum distances to detect IMBH- IMBH binary merger (SOGRO 2) Paik et al. 2016, 30m and 100 baseline
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