ar X iv : g r - qc / 0 10 20 45 v 1 1 1 Fe b 20 01 Angular

In interferometric gravitational wave detectors such as LIGO, the mirrors are suspended on fine wires. In designs for advanced detectors, the pendulums where the mirrors hang have multiple stages with both horizontal and vertical soft spring constants. The pendulum frequencies (around or below 1 Hz) are much lower than the frequency with optimal sensitivity for gravitational waves (around 100 Hz). The suspended configuration, which is necessary for many reasons (free masses, seismic isolation and immunity to thermal noise), has the disadvantage of allowing large pendular motions that need to be controlled to keep the detectors in a linear regime. Much attention has been paid to the horizontal motion of the masses, since they are directly observed by the interferometer and thus limit the sensitivity to gravitational waves. However, the angular motion of the mirrors can also be an important source of sensitivity degradation, especially in long baseline optical cavities. Requirements for the acceptable amount of angular noise come in two flavors: (i) How much before we cannot lock easily the interferometer? (ii) How much can be tolerated while in operation? For the LIGO detectors now in construction, answers are (i) 0.5 mrad rms and (ii)10 rad rms, and contributions less than 5% of shot noise . For advanced interferometers, the requirements may be up to 10 times tighter, which is very difficult to achieve: this highlights the need for their accurate estimation. The identified sources of angular noise are straight seismic excitation (depends on pendulum mechanics); seismic excitation through mechanical cross-coupling; electronic excitation due to sensing/control noise; electronic excitation through actuators. cross couplings; and the always unavoidable thermal noise. Seismic noise produces angular noise through straightforward pendulum dynamics. In LIGO these calculations predict motions smaller than the required tolerance. However, due to mechanical asymmetries, it is likely that a larger angular motion is produced by cross couplings of other degrees of freedom. This problem will be compounded in multiple pendulums, and needs to be carefully studied. We have an experimental program in Penn State to such effect . The control of the masses done to damp the pendular motions is usually applied as several forces on different points of the mirror that add up to the required forces and torques derived in a feedback mechanism from sensors at the same points where the actuation is done. The sensed signals can be decomposed in the natu-