tokens: excited normal modes, since we only need the normal-mode amplitudes. We then obtainwhere S p ( ω ) is the spectral density of effective pressure fluctuations acting on the Moon’s surface isotropically owing to a steady flux of meteoroids, which also depends on the formation of ejecta, elasticity properties of the impact, and the transfer efficiency of impact energy to the seismic field (typically a small fraction of the kinetic energy of a meteoroid; Lognonné et al. 2009 ). The last equation has the on-resonance formThe term depends on the Moon’s internal structure and is of the order of 0.2/ M for lower-order quadrupole modes, where M = 7.3 × 10 22 kg is the mass of the Moon, so that we can approximate the last equation asThe spectral density of pressure fluctuations is related to pressure rms by below 1 Hz (Theodorsen et al. 2017 ), where τ is the average duration of meteoroid impacts henceforth assumed to be τ = 0.1 s neglecting complications like the formation of ejecta. The effective pressure 〈 p 〉 produced by meteoroids with flux F and momentum mv is given bywhere α is the efficiency of momentum transfer to the seismic field. For our order-of-magnitude estimate, we go with the approximation , where we use F 0 = 10 −5 m −2 s −1 for the flux and m 0 v 0 = 10 −3 kg m s −1 for the average meteoroid momentum (Grün et al. 2011 ), and α = 0.01, which seems to be a generous overestimation of the impact-energy-to-seismic conversion efficiency (Lognonné et al. 2009 ; Quillen et al. 2019 ). Note that this expression is independent of the dynamical timescale τ of the impact since we are interested in the average force or pressure, which means that the relevant timescale Δ t of momentum transfer Δ P is given by the average time between impacts, which is contained in the meteoroid flux. It is possible that the total (undirected) momentum transfer onto the Moon is dominated by rare impacts of larger meteoroids, where rare means less frequent than once per Q n / f n , which is about once per day for the lower-order quadrupole modes. With 4 π R 2 × 1 day = 3 × 10 18 m 2 s, we estimate that impacts of meteoroids with mass greater than 1 kg occur less than once per day (Grün et al. 2011 ). These events need to be treated individually and cannot be considered part of the stationary background noise anymore. As for any other larger seismic disturbance, one needs to exclude the stretch of data containing the large impact event from GW analyses, or attempt a subtraction of the seismic signal from the seismometer data. Inserting the expression of the surface pressure from meteoroid impacts into Equation ( A6 ), we obtainConfronting this equation with the on-resonance normal-mode response to GWs, we can say that the effective strain noise in mode n from meteoroid impacts iswhere the numerical value depends weakly on the order of normal modes below about 10 mHz according to our simplified response model. The value lies well below the LGWA strain-noise target of 10
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