Study of the thermal noise caused by inhomogeneously distributed loss

The normal modal expansion is the most frequently used method to estimate the thermal noise of interferometric gravitational wave detectors. However, the method does not agree with new estimation methods, direct approaches, when the loss is distributed inhomogeneously. We have checked the modal expansion and direct approaches experimentally using a mechanical oscillator, such as a mirror. The experiments showed that the modal expansion is invalid. On the other hand, the measured spectra are consistent with the direct approaches. We calculated the thermal noise of a real mirror with inhomogeneous loss using the direct approaches. This calculation showed that the thermal motions caused by loss in the reflective coating and at coil-magnet actuators are comparable with the sensitivity goals of future gravitational wave detector projects. In addition, according to our calculation, a mechanical loss may cause much larger or much smaller thermal motion than is expected in modal expansion, depending on the loss distribution. The thermal fluctuation caused by coating loss is about three times larger than the estimation of the modal expansion, The thermal motion of the coil-magnet actuators is 15 times smaller. This implies that, in order to discuss the research strategy for the thermal noise, in addition to the loss quantity represented by Q-values, one should identify the distribution of all the major loss origins and use direct approaches instead of depending on the conventional modal expansion method.