Constraining the stochastic gravitational wave background using the future lunar seismometers

TL;DR

This paper assesses the potential of lunar seismometers, especially future projects like Chang'e and LGWA, to detect or constrain the stochastic gravitational wave background with improved sensitivity over previous methods.

Contribution

It updates the lunar response model, derives new pattern functions, and calculates overlap reduction functions for lunar seismometer networks, evaluating their capability to constrain the SGWB.

Findings

Chang'e could constrain _{ ext{GW}} to < 2.4 imes 10^{2}

LGWA could constrain _{ ext{GW}} to < 2.0 imes 10^{-10}

Results surpass previous mid-frequency band constraints on the SGWB.

Abstract

Motivated by the old idea of using the moon as a resonant gravitational-wave (GW) detector, as well as the recent updates in modeling the lunar response to GWs, we re-evaluate the feasibility of using a network of lunar seismometers to constrain the stochastic GW background (SGWB). In particular, using the updated model of the lunar response, we derive the pattern functions for the two polarizations of GW. With these pattern functions, we further calculate the overlap reduction functions for a network of lunar seismometers, where we have relaxed the conventional assumption that lunar seismometers are perfectly leveled to measure only the vertical acceleration. We apply our calculation to two future lunar projects, namely, Chang'e and the Lunar Gravitational-Wave Antenna (LGWA). We find that the two projects could constrain the SGWB to a level of $\Omega_{\text{GW}}^{\text{Chang'e}} < 2.4 \times 10^{2}$ and $\Omega_{\text{GW}}^{\text{LGWA}} < 2.0 \times 10^{-10}$, respectively, which corresponds to a signal-to-noise ratio of SNR $=3$. These results are better than the constraints placed previously on the SGWB in the mid-frequency band (around $10^{-3}- 10~\text{Hz}$) by various types of experiments.