Thermoelastic noise and homogeneous thermal noise in finite sized gravitational-wave test masses

An analysis is given of thermoelastic noise (thermal noise due to thermoelastic dissipation) in finite sized test masses of laser interferometer gravitational-wave detectors. Finite-size effects increase the thermoelastic noise by a modest amount. for example, for the sapphire test masses tentatively planned for LIGO-II and plausible beam-spot radii, the increase is less than or similar to 10 percent. As a side issue, errors are pointed out in the currently used formulas for conventional, homogeneous thermal noise (noise associated with dissipation which is homogeneous and described by an imaginary part of the Young's modulus) in finite sized test masses. Correction of these errors increases the homogeneous thermal noise by less than or similar to5 percent for LIGO-II-type configurations.