Spherical Gravitational Wave Antenna. Krishna Venkateswara Experimental Gravitation and Astrophysics April 5 th, 2007

Transcription

1 Spherical Gravitational Wave Antenna Krishna Venkateswara Experimental Gravitation and Astrophysics April 5 th, 007 1

2 Content Introduction Spherical antenna Dual sphere detector Using the Moon as an antenna References

3 Introduction Gravitational waves GW appear as vacuum solutions to the linearized Einstein equations in the weak field limit g = η h µν µν µν h = z h t z µν h t c c To calculate order of magnitude for h, h G Q ns G E kin 4 4 c r c r 3

4 h 10 and h for r~hubble distance for r~virgo cluster For a 3 m bar, this is a displacement of l = hl= meters!! 4

5 GW Polarizations h h 5

6 Spherical Antenna A sphere has 5 degenerate quadrupole modes. Full-sky coverage with uniform cross section. Can determine both source direction θ, φ and wave polarization h, h. Much larger cross-section than a comparable bar antenna. Due to overdetermination, non-gw disturbances can be vetoed. Wagoner & Paik, 1976 Mario Schenberg, Brazilian GW detector 6

7 Equation of motion for elastic sphere is ρ t s = λ µ s µ s F where s is the displacement field of the sphere. s The general solution for the spheroidal modes have the form p nlm r, θ, φ = A nl ry lm θ, φ nˆ - B nl ri nˆ L Y lm θ, φ 7

8 Truncated Icosahedral Gravitational wave Antenna TIGA Mount 6 radial transducers on facecenters of a truncated icosahedron Johnson & Merkowitz, Spherically symmetric detection of the sphere. Signal extracted from simple combination of outputs of 6 transducers. 8

9 Mini-Grail 68 cm spherical detector made of CuAl 6% alloy with a mass of 1400 Kg, a resonance frequency of.9 khz and a bandwidth around 30 Hz. Peak strain sensitivity of about 1.5 x 10-0 Hz -1/. Sources could be nonaxisymmetric instabilities in rotating single and binary neutron stars, small black-hole or neutron-star mergers MiniGRAIL, Leiden University, Netherlands 9

10 Dual sphere detector! " # 10

11 Dual sphere configuration *%%,% -. *% % /" $ %& ' %! 11

12 1 = j ba FF j l nl nl nl nl nl ba th uu S P a A M l Q kt L a A M l S nl ] [ n n π π = c FL P F h c S c l ba FF π ν ζ π $ ] [, ] [, ~ h u u S S S S solid hollow shot uu ba th solid uu ba th hollow uu hh = Hz m P F c FL S c shot uu = π

13 Sensitivity at Standard Quantum Limit SQL Features R = 0.95 m, and a = 0.57 m Cross section proportional to v s 5 Molybdenum = kg/m 3 and v s = 6. km/s Q ~ 0 million at T 4 K Input light power of 7 W, Q/T 10 8 K -1 13

14 '% 01! %! " # 01 :! ; 8 < 9 14

15 Moon as a Spherical Detector Due to lack of plate tectonics, the Moon is extremely quiet seismically. The energy release per year is 10 8 times lower than the Earth. Strong quakes: ~10 9 m Hz 1/ at Hz, on Richter! With the absence of ocean waves and winds, the seismic noise level between moonquakes may be extremely low. But how low? The Moon does not have atmosphere or water. The Moon is thermally quiet except at sunrise and sunset. A more stable thermal environment could be achieved by burying the instrument under the Moon dust. 15

16 A superconducting disk is levitated magnetically. Almost free horizontally. Horizontal displacement is sensed in two directions with a superconducting circuit. Intrinsic displacement noise: S x 4 m Q Sensing Coil 0 f = k T E f 1 0 βη0 4 B A I 0 Superconducting Disk Levitation Coil Sensing Coil 0 Q SQUID With m = 100 kg, f 0 = 0.3 Hz, T = K, Q = 10 7, βη = 0.5, E A f = J Hz Hz / f, S x 1/ f m Hz -1/, f = 0.3 Hz 10 6 times more sensitive than the lunar seismometers 16

17 Resonant spherical detector Moon s quadrupole modes to 10 Hz are monitored. Directionality of various configurations: Triangle at great circle Tetrahedral configuration Icosahedral configuration 6 horizontal motion sensors in truncated icosahedral configuration Full-sky coverage with uniform cross section. Detection of the source direction and wave polarization. Discrimination against seismic and other disturbances. 17

18 Wideband spherical detector Wideband detection against the rigid Moon < Hz. Directionality of various configurations: Triangle at great circle Tetrahedral configuration Icosahedral configuration 6 horizontal motion sensors in truncated icosahedral configuration Full-sky coverage with uniform cross section. Detection of the source direction and wave polarization. Discrimination against seismic and other disturbances. 18

19 Thank you! 19

20 References 1. Johnson W W and Merkowitz S M 1993 Phys. Rev. Lett Lobo J A 1995 Phys. Rev. D Gottardi L 007 Phys. Rev. D 75, Paik, HJ and Venkateswara K 006 Moon as a Gravitational Wave Detector 6. Cerdonio M et al 001 Phys. Rev. Lett Antonio Ortega Ruiz J 1997 Thesis Spherical Gravitational Wave Detectors, University of Barcelona 0