Gas cooling of test masses for future gravitational-wave observatories

Recent observations made with Advanced LIGO and Advanced Virgo have initiated the era of gravitational-wave astronomy. The number of events detected by these "2nd Generation" (2G) ground-based observatories is partially limited by noise arising from temperature-induced position fluctuations of the test mass mirror surfaces used for probing space time dynamics. The design of next-generation gravitational-wave observatories addresses this limitation by using cryogenically cooled test masses; current approaches for continuously removing heat (resulting from absorbed laser light) rely on heat extraction via black-body radiation or conduction through suspension fibers. As a complementing approach, we investigate cooling via helium gas impinging on the test mass in free molecular flow. We present analytical models for cooling power and related displacement noise, validated by comparison to numerical simulations. Applying this theoretical framework with regard to the conceptual design of the Einstein Telescope (ET), we find a cooling power of 10 mW at 18 K for a gas pressure that increases the ET design strain noise goal by at most a factor of $\sim 3$ in a 8 Hz wide frequency band centered at 7 Hz. A cooling power of 100 mW at 18 K corresponds to a gas pressure that increases the ET design strain noise goal by at most a factor of $\sim 11$ in a 26 Hz wide frequency band centered at 7 Hz.