Thermal noises calculations: Gaussian vs Mesa beams Juri Agresti α,β and Riccardo DeSalvo α α LIGO Laboratory, California Institute of Technology, Pasadena, California 91125, USA. β University of Pisa, “Enrico Fermi” Physics Department, Pisa 56127, Italy. Introduction Gravitational Wave (GW) detectors monitor the possible presence of a GW by carefully measuring, by interferometric means, the distance between the surfaces of suspended and seismic attenuated mirrors. An error is introduced by the fact that a perfect detection of a GW would require the measurement of a test mass centre of mass, while only the test mass surface position is measurable. The incessant fluctuating redistribution of thermal energy inside the mirrors produces a fluctuating change of test mass’s shape and a change of the position of its reflecting surface, which is undistinguishable from a GW induced motion of the test mass’s centre of mass. Mirror thermal noise is expected to be the limiting factor of the sensitivity of the next generation of GW detector interferometers [4] in the frequency range between ∼50Hz and ∼200Hz. Thermal noise takes origin from the dissipation mechanisms that redistribute energy inside the mirror structure. There are various types of internal mirror thermal noise, each one associated with a specific dissipation mechanism. The relative importance of one with respect to the other is determined by the mechanical and thermodynamical properties of the test mass materials. Of course we are dealing here only with thermal noise of mirrors in complete thermo-dynamical equilibrium, disregarding any effect that may come from macroscopic thermal differences and heat flows. Brownian thermal noise [7] is due to intrinsic losses in the material and is associated with all forms of dissipation that are describable by an imaginary part of the Young’s modulus. Thermo-elastic noise [9] is created by the stochastic flow of heat within each test mass, producing fluctuations of temperature; due to the thermal expansion coefficient, the test-mass material expands in the hot spots and contract in the cold spots, creating fluctuating bumps and valleys on the mirror faces. It has been pointed out [11] that it is critically important how the losses are distributed inside the test masses. Losses far from the beam spot contribute less to the total thermal noise, whereas losses near the spot, for example in the dielectric coating directly reflecting the beam, contribute more. Coating thermal noise [12] due to internal losses is expected to be the dominant contribution to the thermal noise for mirrors with a SiO 2 /Ta 2 O 5 coating on a fused silica substrate, whereas the thermo-elastic noise of the substrate is the dominant contribution for sapphire mirrors at room temperature. The local surface fluctuations produced by thermal noise are averaged by the intensity distribution of the laser beam spot over the mirror surface. Reading the entire mirror surface with uniform sensitivity would minimize the thermal noise. 1 LIGO-T050269-00-R