The recent LIGO announcement Observation of Gravitational Waves from a Binary Black Hole Merger has some technical details about LIGO. For example,
- LIGO is a modified Michelson interferometer. The test masses are 40 kg fused silica mirrors that form a resonant optical cavity. The power of the laser beam in the cavity is 100 kW. This implies the mirrors need to be cooled.
- Air molecules bouncing off the mirrors would change the length of the cavity. Light scattering off air molecules would change the frequency of the light. For these reasons, the entire 4 km cavities are in high vacuum.
- Vibrations would change the length of the cavity. For this reason, the mirrors are mounted on a quadruple pendulum system, which is mounted on an active seismic isolation platform. The pendulums are made of fused silica fibers.
This story from phys.org says that the mirrors are cooled to 1 $\mu$K. So they must need really good cooling.
So how do you cool a mirror hanging from fibers in high vacuum to 1$\mu$K when it is illuminated by a 100 kW laser?
The public LIGO Document Control Center makes LIGO design documents available, including some cool conceptual design documents. For example, How to build a Gravitational-wave Detector. This document discusses the properties of Si at temperatures down to 5 K as it relates to LIGO detectors. It may be there, but I didn't find anything that answered my question.