Modeling lunar response to gravitational waves using normal-mode approach and tidal forcing

TL;DR

This paper investigates the potential of using the Moon as a gravitational wave detector by modeling its elastic response to GWs through a normal-mode approach, considering regolith effects and frequency dependencies.

Contribution

It provides an analytical framework for GW interaction with lunar elastic structures and explores how regolith variations influence detection capabilities.

Findings

Detection is challenging in the 0.1-1 Hz frequency range without detailed regolith data.

The interaction depends strongly on lunar regolith structure.

Future lunar GW detectors require geophysical constraints for effective operation.

Abstract

In the light of the recent advances in lunar space missions a great interest into using Moon as a future environment for gravitational waves (GWs) detectors has been initiated. Moon offers a unique environment for such detectors due to constrained noise sources, since unlike Earth it does not have ocean and atmosphere. In this paper, we further explore the idea of using Moon as a giant resonator of GWs, a proposal that was first introduced by Weber in 1969. This idea is relaying on the theory how GWs interact with free masses and finally elastic solids, such as is a planet to some approximation. We start by carefully setting up General Relativity (physics) and elastic theory (geophysics) background to be able to derive analytically the coupling between GWs and elastic solids through associated equations of motion. Once the analytical solution is derived, we explore the parameter space this interaction depends on. This eventually provides us with the transfer function, which defines the frequency band of the interest. We show how this interaction robustly depends on the regolith structure by altering the initial lunar model and exploring different regolith models. Our results show that detection might be troublesome in the high frequency regime between 0.1 and 1 Hz, without beforehand constraining the regolith structure with geophysical methods. Finally, we discuss what are the implications of detecting these signals with the future GW detectors build on the Moon.