Constraining the stochastic gravitational wave background using the future lunar seismometers

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 reevaluate 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 Ω_GW^{Chang' e}<2.4 ×10² and Ω_GW^LGWA<2.0 ×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 Hz ) by various types of experiments.