LIGO Publication Abstract
Thermal Noise in the Initial LIGO Interferometers
Gillespie, A.D.
PhD Thesis, Caltech (1995)

Gravitational wave detectors capable of detecting broadband gravitational wave bursts with a strain amplitude sensitivity near 10E-21 at frequencies around 100 Hz are currently under construction by the LIGO (Laser Interferometer Gravitational-wave Observatory) and VIRGO groups. One challenge facing these groups is how to detect the motion of the center of an inertial mass to a precision of 10E-18 m when the mass consists of atoms each of which individually moves much more than that due to thermal energy. The uncertainty in the interferometer's measurement due to these thermal motions is called thermal noise. This thesis describes the thermal noise of the initial LIGO detectors. The thermal noise was analyzed by modelling the normal modes of the test mass suspension system as harmonic oscillators with dissipation and applying the fluctuation dissipation theorem. The dissipation of all modes which contribute significant thermal noise to the interferometer was measured and from these measurements the total thermal noise was estimated. The frequency dependence of the dissipation of the pendulum mode was characterized from measurements of the violin modes. A steel music wire suspension system was found to meet the goals of the initial LIGO detectors. A mathematical technique was developed which relates the energy in each vibrational mode to the motion of the mirror surface measured by the interferometer. Modes with acoustic wavelengths greater than the laser beam spot size can contribute significant thermal noise to the interferometer measurements. The dissipation of the test masses of LIGO's 40-m interferometer at Caltech was investigated, and a technique for suspending and controlling the test masses which lowered the dissipation and met the thermal noise goals of the initial LIGO detector was developed. New test masses were installed in the 40-m interferometer resulting in improved noise performance. The implications of thermal noise to detecting gravitational waves from inspiralling compact binaries was investigated. An optimal pendulum length for detecting these signals was found. It was shown that the narrow band thermally excited violin resonances could be efficiently filtered from the broadband gravitational wave signal.


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