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We present an analysis of Brownian force noise from residual gas damping ofreference test masses as a fundamental sensitivity limit in small forceexperiments. The resulting acceleration noise increases significantly when thedistance of the test mass to the surrounding experimental apparatus is smallerthan the dimension of the test mass itself. For the Advanced LIGOinterferometric gravitational wave observatory, where the relevant test mass isa suspended 340 mm diameter cylindrical end mirror, the force noise power isincreased by roughly a factor 40 by the presence of a similarly shaped reactionmass at a nominal separation of 5 mm. The force noise, of order 20 fN\rthz\ for$2 \times 10^{-6}$ Pa of residual H$_2$ gas, rivals quantum opticalfluctuations as the dominant noise source between 10 and 30 Hz. We present herea numerical and analytical analysis for the gas damping force noise forAdvanced LIGO, backed up by experimental evidence from several recentmeasurements. Finally, we discuss the impact of residual gas damping on thegravitational wave sensitivity and possible mitigation strategies.

Brownian force noise from molecular collisions and the sensitivity of advanced gravitational wave observatories