Upper-limit on the Advanced Virgo output mode cleaner cavity length noise

The Advanced Virgo detector uses two monolithic optical cavities at its output port to suppress higher order modes and radio frequency sidebands from the carrier light used for gravitational wave detection. These two cavities in series form the output mode cleaner. We present a measured upper limit on the length noise of these cavities that is consistent with the thermo-refractive noise prediction of $8 \times 10^{-16}\,\textrm{m/Hz}^{1/2}$ at 15 Hz. The cavity length is controlled using Peltier cells and piezo-electric actuators to maintain resonance on the incoming light. A length lock precision of $3.5 \times 10^{-13}\,\textrm{m}$ is achieved. These two results are combined to demonstrate that the broadband length noise of the output mode cleaner in the 10-60 Hz band is at least a factor 10 below other expected noise sources in the Advanced Virgo detector design configuration.