How are LIGO mirrors cooled?

Question

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.

Answer 1

The mirrors in Advanced LIGO are not cooled. Future detectors may utilize cryogenic temperatures to reduce thermal noise, but we aren't there yet.

Answer 2

In light of this new article:

The mirrors themselves are near room temperature. The bulk translational motion of the object is "cooled" to far below what it would normally have if resting quiescently in thermal equilibrium. But how?

0. The mirrors are in high vacuum and absorb very little light. They aren't metal, they are dielectric mirrors specialized to reflect the laser frequency. Only 1 out of 3.3 million photons are absorbed vs about 20% loss for household mirrors. This prevents air-current noise and vastly reduces mirror heating.

1. The mirrors are mounted with special fused quartz fibers that have very little damping: if plucked like a guitar string, it would take hundreds of millions of oscillations before the "violin mode" loses 50% of it's amplitude. In everyday experiences, such as a pendulum in a clock, damping removes energy from systems. But for a pendulum that is moving even less than thermal equilibrium dictates damping adds energy to it. (The vibration isolation system also handles non-thermal sources such as road traffic).

2. Motions in the mirrors are actively counteracted. This is done with electrostatic actuation among other tools. Like the air conditioning in your home, this must consume energy and export waste heat (the low-damping environment is analogous to the insulation in your walls). However, it only cools the bulk mechanical motions and vibrations rather than "temperature" as would be sensed by a human hand or a thermometer. This makes it much easier to achieve ~80 nano-Kelvin effective temperatures.

3. Filters remove the noise at certain resonance peaks, for the purposes of detecting the waves.

4. For the purposes of this paper, which is about macroscopic quantum effects rather than merging black holes, they added an electrostatic "stiffening" feedback force so that the mirror oscillates at ~920Hz. This increased the energy between the quantum states making it easier to achieve the low quantum numbers. Although putting a 10kg vibrating reduced mass at quantum numbers of ~10 is very impressive, I am not sure if the stiffness would be useful for gravitational wave detection.

5. Future mirrors may be cryogenically cooled, which would further reduce the influx of unwanted thermal energy into the low-frequency modes and so reduce the lowest effective temperature that the "air-conditioners" can reach.