Noise requirements of the cryogenic shielding for next generation cryocooled gravitational wave observatories: Newtonian noise

We explore the vibration isolation requirements imposed by Newtonian noise on the cryogenic shielding for next-generation gravitational-wave observatories relying on radiative cooling. Two sources of Newtonian noise from the shield arrays are analyzed: the tidal coupling from the motion of a shield segment to its nearby test mass's displacement, and the effect of density fluctuations due to heterogeneous boiling of cryogenic liquids in the vicinity of the test masses. It was determined that the outer shields require no additional vibration isolation from ground motion to mitigate the Newtonian noise coupling to levels compatible with the LIGO Voyager design. Additionally, it was determined that the use of boiling nitrogen as the heat sink for the cryogenic arrays is unlikely to create enough Newtonian noise to compromise the detector performance for either Voyager or Cosmic Explorer phase 2. However, the inherent periodicity of the nucleation cycle might acoustically excite structural modes of the cryogenic array which could contaminate the signals from the interferometer through other means. This last effect could be circumvented by using a single-phase coolant to absorb the heat from the cryogenic shields.