Thick Lunar Crust Amplifies Deci-Hertz Gravitational-Wave Signal

TL;DR

This study models the Moon's complex topography and interior to evaluate its potential as a resonant detector for deci-Hertz gravitational waves, revealing significant signal amplification in certain regions.

Contribution

First high-resolution 2D lunar GW response model combining spectral-element simulations and normal-mode theory, revealing topographical effects and signal amplification mechanisms.

Findings

Up to tenfold signal amplification in thick-crust lunar regions.

Normal-mode analysis shows mode-coupling causes energy redistribution into higher-order modes.

Resonant amplification varies spatially, guiding optimal detector site selection.

Abstract

Gravitational waves (GWs) in the $0.01\sim1$ Hz band encode unique signatures of the early universe and merging compact objects, but they are beyond the reach of existing observatories. Theoretical models suggest that the Moon could act as a resonant detector, but the unknown influence of its rugged surface and heterogeneous interior poses a challenge to the accurate modeling of its response. Here, we address this long-standing uncertainty by constructing the first high-resolution, two-dimensional model of the lunar GW response, more realistic than previous ones. We achieve this by combining high-fidelity spectral-element simulations with the analytical power of normal-mode perturbation theory, thereby resolving topographical effects down to 2 km grid spacing while maintaining the capacity to discern global free-oscillation patterns. This dual-methodology approach not only recovers the expected predominant quadrupole ($l=2$) oscillation mode, but also exposes a systematic signal amplification in thick-crust regions. This enhancement is traced by our normal-mode analysis to a mode-coupling process, in which the original quadrupolar oscillation induced by the passing GW distributes energy into a series of higher-order modes, the hybridized eigenmodes of a laterally heterogeneous Moon. In certain narrow frequency ranges, we observe up to tenfold amplification spanning into the deci-hertz band, highlighting the power of numerical simulations in resolving these structurally fine-tuned features for designing future detectors. Our work establishes the Moon as a resonant GW detector albeit its complex topographical structures, and the resulting amplification maps provide quantitative guide for the optimal landing site selection.