Subtraction of temperature induced phase noise in the LISA frequency band

Temperature fluctuations are expected to be one of the limiting factors for gravitational-wave detectors in the very-low-frequency range. Here we report the characterization of this noise source in the LISA Pathfinder optical bench and propose a method to remove its contribution from the data. Our results show that temperature fluctuations are indeed limiting our measurement below one millihertz, and that their subtraction leads to a factor 5.6 (15 dB) reduction in the noise level at the lower end of the LISA measurement band (10^-4 Hz), which increases to 20.2 (26 dB) at even lower frequencies, i.e., 1.5×10^-5 Hz. The method presented here can be applied to the subtraction of other noise sources in gravitational-wave detectors in the general situation where multiple sensors are used to characterize the noise source.