Gravitational-Wave Observatory (LIGO) provides evidence that ...

If I've read the article right, the temperature is an effective one for a particular mode within the interferometer. If my memory serves me correctly there is the 'equipartition' theorem in thermodynamics which states that energy is distributed, in equilibrium, equally between all independent degrees of freedom for a system. So yes, if you have say a large group of interacting particles - like the mirror's crystal lattice - without internal degrees of movement of the particles ( like rotations ) then that leaves you with the 3 spatial directions of motion. As you get kT/2 for each dimension that is thus 3kT/2 overall for 'ordinary' kinetic energy. Or put another way temperature is a measure of the average kinetic energy of the molecules.

It seems they have divided the motion of the mirror atoms into two components : that which is about the centre of mass of the mirror, and that which is the motion of the centre of mass. One can legitimately do this as it comes down to simple vector decomposition of each atom's velocity vector. You could interpret the motion about centre of mass as 'ordinary' temperature. The motion of centre of mass ( measured via changes in separation of the mirrors ) is allotted an equivalent temperature - the microKelvins quoted. I guess the point is that we don't have equilibrium in that the interferometer actuators can drain energy from the mode defined as differential mirror motion especially. So you assign what energy that is left in that mode as equal to kT/2, solve for T - getting those microKelvins.

This trick can be used to define a 'spin temperature', say, in magnetic materials. There you define some mode related to spin alignments in some external magnetic field. Find the energy attributable to that interaction, regardless of whatever else might be going on in the substance, set that equal to kT/2 etc. An interesting issue would be to what extent does kinetic motion alter the spin alignments, and hence how is the total energy of the system ( all forms ) distributed amongst the modes. Are we in equilibrium? Have we waited long enough compared to some characteristic 'relaxation' time and so on.

Cheers, Mike.

Whatever the results of LIGO, VIRGO, etc. I would like to point out the difference between the astronomers' and astrophysicists' method, that of observing the Universe at all wavelengths, and the experimental physicists', that of making matter colliding with other matter at always rising energies (and costs) as the CERN history shows. A great experimental physicist like Edoardo Amaldi has switched his interests from particle accelerators to gravitational waves detectors in the latter part of his life, Another great Italian physicist, Enrico Fermi, once convinced his Italian colleagues not to build another cyclotron in Pisa but the first Italian designed computer, which Olivetti later named Elea. He understood that the future of physics lied not in accelerators but in computers.
Tullio