# How thermal noise is avoided in LIGO?

I think I have understood properly the principle of LIGO, however the sensitivity is around $10^{-18}~\rm m$ of accuracy of distortion. That looks pretty small... just starting with simpler phenomena, for example, thermal expansion. In order to avoid thermal expansion, the temperature needs to be control within a variation of $10^{-10}~\rm K$ or $10^{-11}~\rm K$ along the tubes.

I guess that the tubes do not need to be exactly $4~\rm{km}$ equal as the lasers can be synchronized although the distance is not exactly 4km within the range of $\left[10^{-18}~\rm m\right]$

How is the thermal noise avoided currently in LIGO, related to suspension and not complete vacuum?

It is already demonstrated that the frequency cut-off is low, but, how is that achieved? Which materials and isolation supported it?

• You can read it in all detail in the technical design report and other documents relating to the instrument: dcc.ligo.org/cgi-bin/DocDB/ListTopics. The effective length of the interferometer arms is 1600km, by the way, not 4km, so I am not sure your estimate about the temperature control is correct. Having said that, the instrument doesn't need DC stability and the noise increases very quickly below its intended operating frequency range. Feb 13, 2016 at 10:51
• I used their web ligo.caltech.edu/page/ligos-ifo , anyhow for a difference of factor 2 or 3 my argument is not challenged... Feb 13, 2016 at 10:56
• The length of the tubes is not the relevant factor. The light in these interferometer arms goes forth and back 400 times to make the effective size of the instrument much larger than its physical size. That's also explained on the same page, by the way. They key to the stability of the instrument is, as I said, that it only works at fairly high frequencies, where all terrestrial noise sources can be controlled. Future space based gravitational wave observatories will not suffer from that limitation. Feb 13, 2016 at 10:59
• Possible duplicate of How does LIGO remove the effects of environmental noise?
– Danu
Feb 16, 2016 at 17:09
• Definitely not a duplicate -- thermal expansion and seismic vibrations are unrelated.
– user10851
Feb 18, 2016 at 1:06

It also has a lower frequency cut-off of 10Hz, so any perturbation that is slower than 10Hz won't affect the measurements. In particular temperatures changes will happen on a timescale of hours so if they change the length of the tube that doesn't matter. When LIGO measures the $10^{-18}$ m change in the tube length it doesn't matter if that length is a bit longer at midday than at midnight.