Thermoelastic Noise and Homogeneous Thermal Noise in Finite Sized Gravitational-Wave Test Masses

TL;DR

This paper analyzes thermoelastic and homogeneous thermal noise in finite-sized gravitational-wave detector test masses, showing modest increases due to finite-size effects and correcting errors in existing formulas.

Contribution

It provides a detailed analysis of finite-size effects on thermoelastic noise and corrects inaccuracies in the formulas for homogeneous thermal noise in test masses.

Findings

Finite-size effects increase thermoelastic noise by less than 10%.

Corrected formulas increase homogeneous thermal noise estimates by less than 5%.

Results inform design considerations for gravitational-wave detectors.

Abstract

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 of order 10 per cent. 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 of order 5 per cent for LIGO-II-type configurations.