Constraining the gravitational-wave energy density of the Universe in the range 0.1 Hz to 1 Hz using the Apollo Seismic Array

In this paper, we describe an analysis of Apollo-era lunar seismic data that places an upper limit on an isotropic stochastic gravitational-wave background integrated over a year in the frequency range 0.1–1 Hz. We find that because the Moon’s ambient noise background is much quieter than that of the Earth, significant improvements over an Earth-based analysis were made. We find an upper limit of ${\mathrm{\Omega }}_{\mathrm{GW}}<1.2\times {10}^5$, which is 3 orders of magnitude smaller than a similar analysis of a global network of broadband seismometers on Earth and the best limits in this band to date. We also discuss the benefits of a potential Earth-Moon correlation search and compute the time-dependent overlap reduction function required for such an analysis. For this search, we find an upper limit an order of magnitude larger than the Moon-Moon search.

Figure 1

Currently valid upper limits on GW energy density. These limits were set by correlating data from torsion-bar antennas [4], Doppler-tracking measurements of the Cassini spacecraft [9], monitoring Earth’s free-surface response with seismometers [2], measuring the normal modes of the Earth [10], and correlating data from the first-generation, large-scale GW detectors at LIGO [11].

Figure 2

On the left are the P- and S-wave velocities and density structure for the whole-Moon model displayed for the near-surface layers (0–50 km) [21]. On the right is the dispersion curve calculated using Geopsy’s gplivemodel for this layered model.

Figure 3

Spectral variation of combined lunar seismic spectra. The dash-dotted lines in gray represent the global new low- and high-noise models [31].

Figure 4

Point estimate and error bars for the three seismometer pairs, as well as for the combination of the three pairs.

Figure 5

Geometry of the Earth-Moon correlation derivation. The sum of $\overrightarrow{v_1}$ and $\overrightarrow{v_2}$ corresponds to the Earth seismometer, while the sum of $\overrightarrow{v_3}$ and $\overrightarrow{v_4}$ corresponds to the Moon seismometer.

Figure 6

Overlap reduction function between example Earth and Moon seismometers as a function of time at 0.1 Hz. This is computed for the S12 lunar station and Albuquerque, New Mexico, USA (ANMO) seismic stations at the beginning of 1976. It displays a daily variation due to the rotation of the Earth, as well as a monthly cycle, due to the libration of the Moon.

Figure 7

Overlap reduction function between two seismometers on the Moon separated by 0.4 rad.