Atmospheric Newtonian noise modeling for third-generation gravitational wave detectors

The sensitivity and the frequency bandwidth of third-generation gravitational-wave detectors are such that the Newtonian noise (NN) signals produced by atmospheric turbulence could become relevant. We build models for atmospheric NN that take into account finite correlation times and inhomogeneity along the vertical direction, and are therefore accurate enough to represent a reliable reference tool for evaluating this kind of noise. We compute the NN spectral density from our models and compare it with the expected sensitivity curve of the Einstein Telescope (ET) with the xylophone design. The noise signal decays exponentially for small values of the frequency and the detector's depth, followed by a power law for large values of the parameters. We find that, when the detector is built at the Earth's surface, the NN contribution in the low-frequency band is above the ET sensitivity curve for strong wind. Building the detector underground is sufficient to push the noise signal under the ET sensitivity curve, but the decrement is close to marginal for strong wind. In light of the slow decay with depth of the NN, building the detector underground could be only partially effective as passive noise mitigation.