Suspensions thermal noise in the LIGO gravitational wave detector

We present a calculation of the maximum sensitivity achievable by the LIGO gravitational wave detector in construction, due to limiting thermal noise of its suspensions. We present a method to calculate thermal noise that allows the prediction of the suspension thermal noise in all of its six degrees of freedom, from the energy dissipation due to the elasticity of the suspension wires. We show how this approach encompasses and explains previous ways to approximate the thermal noise limit in gravitational wave detectors. We show how this approach can be extended to more complicated suspensions to be used in future LIGO detectors.