# The Lunar Gravitational-wave Antenna: Mission Studies and Science Case

Parameswaran Ajith, Pau Amaro Seoane, Manuel Arca Sedda, Riccardo Arcodia, Francesca Badaracco, Enis Belgacem, Stefano Benetti, Alexey Bobrick, Alessandro Bonforte, Elisa Bortolas, et al.

► To cite this version:

Parameswaran Ajith, Pau Amaro Seoane, Manuel Arca Sedda, Riccardo Arcodia, Francesca Badaracco, et al. The Lunar Gravitational-wave Antenna: Mission Studies and Science Case. Journal of Cosmology and Astroparticle Physics, 2025, 01, pp.108. 10.1088/1475-7516/2025/01/108 hal-04600021

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# The Lunar Gravitational-wave Antenna: mission studies and science case

To cite this article: Parameswaran Ajith *et al* JCAP01(2025)108

View the [article online](#) for updates and enhancements.

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# The Lunar Gravitational-wave Antenna: mission studies and science case

**Jan Harms et al.**

Full author list at the end of the paper

E-mail: jan.harms@gssi.it

**ABSTRACT:** The Lunar Gravitational-wave Antenna (LGWA) is a proposed array of next-generation inertial sensors to monitor the response of the Moon to gravitational waves (GWs). Given the size of the Moon and the expected noise produced by the lunar seismic background, the LGWA would be able to observe GWs from about 1 mHz to 1 Hz. This would make the LGWA the missing link between space-borne detectors like LISA with peak sensitivities around a few millihertz and proposed future terrestrial detectors like Einstein Telescope or Cosmic Explorer. In this article, we provide a first comprehensive analysis of the LGWA science case including its multi-messenger aspects and lunar science with LGWA data. We also describe the scientific analyses of the Moon required to plan the LGWA mission.

**KEYWORDS:** gravitational wave detectors, gravitational waves / sources

ARXIV ePRINT: 2404.09181

<figure><img src="image_3.png" /></figure>
# Contents

<table><tr><td>1</td><td>Introduction</td><td>2</td></tr><tr><td>1.1</td><td>Science traceability matrices</td><td>4</td></tr><tr><td>2</td><td>The Lunar Gravitational-wave Antenna</td><td>8</td></tr><tr><td>2.1</td><td>Mission concept</td><td>9</td></tr><tr><td>2.2</td><td>Observational capabilities</td><td>17</td></tr><tr><td>2.3</td><td>Studies of the lunar surface environment and of the deployment site</td><td>29</td></tr><tr><td>2.4</td><td>Soundcheck and other relevant lunar missions</td><td>43</td></tr><tr><td>3</td><td>Science objectives</td><td>46</td></tr><tr><td>3.1</td><td>Lunar science</td><td>46</td></tr><tr><td>3.2</td><td>Gravitational-wave science</td><td>56</td></tr><tr><td>3.3</td><td>Multi-messenger observations</td><td>84</td></tr><tr><td></td><td>Author List</td><td>163</td></tr></table>

# List of abbreviations

<table><tr><td>AGN</td><td>Active galactic nuclei</td></tr><tr><td>BH</td><td>Black hole</td></tr><tr><td>BBH</td><td>Binary black hole</td></tr><tr><td>BNS</td><td>Binary neutron star</td></tr><tr><td>CBC</td><td>Compact binary coalescence</td></tr><tr><td>CCSN</td><td>Core-collapse supernova</td></tr><tr><td>CGWB</td><td>Cosmological gravitational-wave background</td></tr><tr><td>DE</td><td>Dark Energy</td></tr><tr><td>DM</td><td>Dark Matter</td></tr><tr><td>DWD</td><td>Double white dwarf</td></tr><tr><td>EM</td><td>Electromagnetic</td></tr><tr><td>EMRI</td><td>Extreme mass ratio inspiral</td></tr><tr><td>EoS</td><td>Equation of State</td></tr><tr><td>GR</td><td>General Relativity</td></tr><tr><td>GW</td><td>Gravitational wave</td></tr><tr><td>IMBH</td><td>Intermediate mass black hole</td></tr><tr><td>IMRI</td><td>Intermediate mass ratio inspiral</td></tr><tr><td>LIGS</td><td>Lunar inertial gravitational-wave sensor</td></tr><tr><td>NS</td><td>Neutron star</td></tr><tr><td>NSWD</td><td>Neutron star — white dwarf</td></tr><tr><td>PBHs</td><td>Primordial black hole</td></tr></table>
<table><tr><td>PNS</td><td>Proto-neutron star</td></tr><tr><td>ppE</td><td>Parametrized post-Einsteinian</td></tr><tr><td>PPISN</td><td>Pulsational pair-instability supernova</td></tr><tr><td>PSR</td><td>Permanently shadowed region</td></tr><tr><td>QNM</td><td>Quasi normal mode</td></tr><tr><td>QPE</td><td>Quasi-periodic eruptions</td></tr><tr><td>RMS</td><td>Root mean square</td></tr><tr><td>SBN</td><td>Seismic background noise</td></tr><tr><td>SGWB</td><td>Stochastic gravitational wave background</td></tr><tr><td>SMBH</td><td>Supermassive black hole</td></tr><tr><td>SN</td><td>Supernova</td></tr><tr><td>SNR</td><td>Signal-to-noise ratio</td></tr><tr><td>TDE</td><td>Tidal disruption event</td></tr><tr><td>WD</td><td>White dwarf</td></tr></table>

# 1 Introduction

The first generation of GW detectors Virgo and LIGO have opened a new observational window to the Universe [1, 2]. Additionally, the Pulsar Timing Array collaborations have recently reported the first signs of a possible GW background in their data [3–5]. Expanding the current observational window can be accomplished with two technological approaches: (1) by developing new instruments with better sensitivity within existing observation bands, as for example the proposed Einstein Telescope [6] and Cosmic Explorer [7], and (2) by opening new frequency bands for GW observations. The LISA mission was recently adopted by ESA and is scheduled for launch in 2035 [8]. New probes of the cosmic-microwave background aimed at revealing imprints of GWs on its polarization pattern are in the planning [9]. Despite this well-developed roadmap for GW science, it is important to realize that the exploration of our Universe through GWs is still in its infancy. In addition to the immense impact expected on astrophysics and cosmology, this field holds a high probability for unexpected and fundamental discoveries.

The Lunar Gravitational-wave Antenna (LGWA) is a proposed first-generation lunar GW detector [10]. The LGWA utilizes the Moon as a planetary-scale antenna for space-time fluctuations. The mission concept is to deploy an array of inertial sensors on the surface of the Moon to measure the Moon’s vibrations caused by GWs. The LGWA is enabled by the unique geophysical conditions on the Moon: namely, its extreme seismic silence, the cryotemperature environment inside its PSRs, and its tidal lock with respect to Earth. The Moon may indeed be the only suitable planetary body in the whole solar system for LGWA.

The LGWA will serve as the missing link in the decihertz band, filling the gap between the sensitivity range of the LISA detector, which peaks at a few millihertz, and terrestrial detectors that may become sensitive down to a few hertz in the future. Unique and breakthrough contributions to GW science by LGWA are expected, which would also enable a new class of multi-messenger astronomy. In the following, we list some highlights of its science case:
* **Studying astrophysical explosions.** Only LGWA can observe astrophysical events that involve WDs like tidal disruption events and SNe Ia. Only LGWA can provide early warnings weeks to months before the mergers of solar-mass compact binaries that include NSs together with excellent sky localizations.

* **Exploring black-hole populations and their role for structure formation in our Universe.** Only LGWA can observe lighter IMBH binaries in the early Universe and understand their role in the formation of today's SMBHs.

* **Hubble constant measurement.** Only LGWA can detect GW signals from DWDs beyond our galaxy and nearby dwarf galaxies. Only DWDs produce strong enough signals and are so ubiquitous in the local Universe that a large enough number can be detected with identified host galaxies to measure the Hubble constant accurately with the help of GW observations.

* **Enabling the next level of high-precision waveform measurements.** Especially LGWA's unique role as a partner for multiband observations of GW sources enables a new level of precision in waveform measurements and searches for signs of a new fundamental physics.

* **Imaging the lunar interior and shedding light on the formation history of the Moon.** LGWA might be the first mission to be able to observe lunar normal modes complementing seismic body waves, which give direct insight into the Moon's deep internal structure and hold information about its formation history.

* **Revealing the Moon's meteoritic hum.** LGWA's inertial sensors will be more than two orders of magnitude more sensitive than any other lunar seismometer planned for geophysical studies, which enables the observation of the weakest ever resolvable lunar seismic events and of the incessant meteoritic hum.

Through multiband observations, LGWA emerges as a formidable partner of future laser-interferometric detectors both on Earth and in space. Moreover, LGWA marks the first step of a long-lasting utilization of the Moon for lunar GW detection [11].

The SciSpacE white papers of the European Space Agency (ESA) on planetary science, astrophysics, and fundamental physics,<fnref n="1" /> the Decadal Survey in Astrophysics,<fnref n="2" /> in Biological and Physical Sciences Research in Space,<fnref n="3" /> and in Planetary Science and Astrobiology<fnref n="4" /> all recognize the importance of GW detection and lunar science. The LGWA pathfinder mission *Soundcheck* was selected by ESA in 2023 into the Reserve Pool of Science Activities for the Moon.

The purpose of this paper is to provide a description of the LGWA science case and an outline of the scientific studies needed for mission planning. Instead, we do not enter into the details of the payload design and technological requirements, and of the possible

<footnote n="1">¹ESA SciSpacE white papers.</footnote>

<footnote n="2">²Astro Decadal 2020 report.</footnote>

<footnote n="3">³BPS Decadal 2023 report.</footnote>

<footnote n="4">⁴Planetary Decadal 2023 report.</footnote>
deployment scenarios, which will be provided with a dedicated document. There are also important limitations to the analyses presented in this paper. First and foremost, except for selected cases, there are no accurate simulations available yet to estimate the sky-localization capabilities of LGWA alone or as part of a network with LISA-type detectors or terrestrial detectors. This problem has analytical as well as numerical-precision aspects that must be solved. Furthermore, we lack accurate waveform models of some signals where matter effects are important, and population models are generally less developed compared to most models used in science-case studies of terrestrial detectors and LISA.

# 1.1 Science traceability matrices

## 1.1.1 Gravitational-wave science and multi-messenger astronomy

<table><thead><tr><th>Science goals</th><th>Science questions</th><th>Observational requirements</th><th>Instrument requirements</th><th>Top-level mission requirements</th></tr></thead><tbody><tr><td rowspan="3">Understanding the origin and evolution of massive black holes</td><td>What were the seeds of today's SMBHs?</td><td>Observe BBHs beyond redshift z = 10</td><td>Sensitivity better than 10<sup>-20</sup> Hz<sup>-1/2</sup> at 0.1 Hz</td><td>3 yr mission lifetime</td></tr><tr><td>What is the merger rate of MBHs as function of z and what is the distribution of physical and orbital parameters regulating MBHs in pairs?</td><td>Observe binary MBH and IMBH mergers over a wide range of redshifts.</td><td>Sensitivity better than 10<sup>-18</sup> Hz<sup>-1/2</sup> at 0.01 Hz</td><td>5 yr mission lifetime</td></tr><tr><td>What physics governs the correlations between the mass of a galaxy's central MBH and the velocity dispersion σ?</td><td>Observe binary MBH and IMBH mergers over a wide range of redshifts and combine GW and EM observations</td><td>Sensitivity better than 10<sup>-18</sup> Hz<sup>-1/2</sup> at 0.01 Hz</td><td>5 yr mission lifetime</td></tr></tbody></table>
<table><thead><tr><th>Science goals</th><th>Science questions</th><th>Observational requirements</th><th>Instrument requirements</th><th>Top-level mission requirements</th></tr></thead><tbody><tr><td rowspan="5">Understanding astrophysical explosions and their progenitors</td><td>What processes govern the final years of the lifetime of DWD and NSWD binaries?</td><td>Observe short-period (&lt; 100 s) binaries containing WDs.</td><td>Sensitivity better than 10<sup>-20</sup> Hz<sup>-1/2</sup> at 0.1 Hz</td><td>3 yr mission lifetime</td></tr><tr><td>What processes drive the low-frequency GW signals of CCSN explosions?</td><td>GW memory signal detection coincident with an optical CCSN</td><td>Sensitivity better than 10<sup>-21</sup> Hz<sup>-1/2</sup> around 0.3 Hz</td><td>10 yr mission lifetime</td></tr><tr><td>What are the jet-launching conditions in gamma-ray bursts?</td><td>Observation of a GW memory signal coincident with a gamma-ray burst</td><td>Sensitivity better than 10<sup>-22</sup> Hz<sup>-1/2</sup> around 0.3 Hz</td><td>10 yr mission lifetime (remains improbable detection)</td></tr><tr><td>What are the progenitors of SN type Ia?</td><td>Observe the last years of the life of a few DWDs</td><td>Sensitivity better than 10<sup>-21</sup> Hz<sup>-1/2</sup> around 0.3 Hz</td><td>10 yr mission lifetime (remaining an improbable detection)</td></tr><tr><td>How often do tidal disruptions of WDs near BH horizons occur?</td><td>Observe the (unmodeled) GW transient produced by a WD tidal disruption in the dHz band.</td><td>Sensitivity better than a few times 10<sup>-22</sup> Hz<sup>-1/2</sup> around 0.3 Hz</td><td>10 yr mission lifetime</td></tr></tbody></table>
<table><thead><tr><th>Science goals</th><th>Science questions</th><th>Observational requirements</th><th>Instrument requirements</th><th>Top-level mission requirements</th></tr></thead><tbody><tr><td rowspan="2">Observations of rare stellar mergers or transients</td><td>What is the asymmetry of the helium flash event?</td><td>Observation of a Galactic helium flash event</td><td>TBD</td><td>10 yr mission lifetime</td></tr><tr><td>What is the rate and mass distribution of stellar core mergers?</td><td>Observations coincident with luminous red nova events</td><td>TBD</td><td>10 yr mission lifetime</td></tr><tr><td rowspan="4">Cosmology with dHz GW signals</td><td>Are there systematic errors in the EM estimations of the Hubble parameter?</td><td>Detection of GWs from identified host galaxies with known redshift</td><td>Sensitivity better than 10<sup>-21</sup> Hz<sup>-1/2</sup> around 0.3 Hz</td><td>10 yr mission lifetime</td></tr><tr><td>Are there dark-matter particles around BBHs?</td><td>High-precision BBH waveform measurements possibly as a multiband observation.</td><td>TBD</td><td>3 yr mission lifetime</td></tr><tr><td>What processes create a CGWB in the dHz band?</td><td>Detection of a stochastic GW background via correlation measurements (or setting important upper limits on the CGWB).</td><td>Sensitivity better than a few times 10<sup>-22</sup> Hz<sup>-1/2</sup> around 0.3 Hz</td><td>10 yr mission lifetime; presence of a second dHz detector</td></tr><tr><td>Is there a primordial population of BHs?</td><td>Detection of BBHs out to and beyond z = 30.</td><td>Sensitivity better than 2 &times; 10<sup>-21</sup> Hz<sup>-1/2</sup> between 0.1 Hz and 0.5 Hz</td><td>3 yr mission lifetime</td></tr></tbody></table>
1.1.2 Lunar science

<table><thead><tr><th>Science goals</th><th>Science questions</th><th>Observational requirements</th><th>Instrument requirements</th><th>Top-level mission requirements</th></tr></thead><tbody><tr><td rowspan="3">Understanding of the internal structure of the Moon</td><td>What are the resonance frequencies and Q-values of the lunar normal modes?</td><td>Observe ringdown of normal modes produced by moonquakes.</td><td>Sensitivity better than 0.1 µm/Hz<sup>1/2</sup> at 1 mHz and better than 0.1 nm/Hz<sup>1/2</sup> at 0.1 Hz</td><td>1 yr mission lifetime</td></tr><tr><td>What is the level of fracturing in the megaregolith?</td><td>Observe the effect of seismic scattering on the wavefield generated by moonquakes and GW signals.</td><td>Sensitivity better than 0.1 nm/Hz<sup>1/2</sup> at 0.1 Hz and better than 0.1 pm/Hz<sup>1/2</sup> at 1 Hz</td><td>1 yr mission lifetime</td></tr><tr><td>What are the rheological and thermal properties and composition of the Moon's core?</td><td>Discriminate and model P- and S-waves travelling through the Moon's core and interacting with its boundary.</td><td>Sensitivity better than 1 pm/Hz<sup>1/2</sup> from 0.1 Hz to 1 Hz</td><td>1 yr mission lifetime; possibly as part of a lunar seismic network</td></tr></tbody></table>
<table><thead><tr><th>Science goals</th><th>Science questions</th><th>Observational requirements</th><th>Instrument requirements</th><th>Top-level mission requirements</th></tr></thead><tbody><tr><td rowspan="2">Understanding the nature of lunar seismicity</td><td>What is the origin of moonquakes (e.g., tectonic, thermal or tidal) and how to determine their locations (latitude, longitude, and depth)?</td><td>Perform array analysis of at least a few 100 moonquake waveforms.</td><td>Sensitivity better than 0.1 nm/Hz<sup>1/2</sup> at 0.1 Hz and better than 0.1 pm/Hz<sup>1/2</sup> at 1 Hz</td><td>3 yr mission lifetime; possibly as part of a lunar seismic network</td></tr><tr><td>Is the Moon a competitive platform for GW detection beyond LGWA?</td><td>Determine the seismic noise level in PSRs and its daily and seasonal variation.</td><td>Sensitivity better than 1 pm/Hz<sup>1/2</sup> at 0.1 Hz and better than 1 fm/Hz<sup>1/2</sup> at 1 Hz</td><td>1 yr mission lifetime</td></tr><tr><td>Observing geological processes through their seismic signatures</td><td>How to characterize the Moon's surface and crustal structure from tectonic and meteoroid impact events? How does it change in time?</td><td>Ambient noise and event coda imaging and interferometry through auto-correlations and cross-correlations.</td><td>Continuous recordings in the frequency range 0.1–5 Hz</td><td>&gt; 1 yr mission</td></tr><tr><td>Understanding the Moon's formation history and evolution</td><td>What can the deep internal structure of the Moon tell us about its formation history?</td><td>Observe the lowest-frequency normal modes.</td><td>Sensitivity better than 0.1 µm/Hz<sup>1/2</sup> at 1 mHz and better than 3 nm/Hz<sup>1/2</sup> at 10 mHz</td><td>1 yr mission lifetime</td></tr></tbody></table>

## 2 The Lunar Gravitational-wave Antenna

The planning of a lunar GW detector is a complex task, which needs to consider many environmental factors and address operational challenges. This section provides an overview of the scientific studies that need to be carried out in preparation of the LGWA. Most of the
information required for the scientific preparation of the mission will come from LGWA's pathfinder mission Soundcheck, which is a geophysical station to be deployed inside a PSR equipped with accelerometers, a thermometer and a magnetometer. However, a wealth of scientific lunar data is already available from past lunar missions, whose analysis from the perspective of lunar GW detection still needs to be completed. New important data will also be collected with upcoming lunar missions that will explore the lunar polar regions and include geophysical payloads.

The LGWA mission concept is summarized in section 2.1. The LGWA sensitivity model is used in section 2.2 to highlight some of LGWA's observational capabilities. While these first sections mostly serve as an introduction to the white paper, they also point out some open problems like the development of a calibration procedure for LGWA or the accurate modeling of waveforms given the complex motion of a lunar GW detector. In section 2.3, we provide an overview of the geophysical variables and site characteristics that need to be studied to be able to plan the LGWA mission. We then conclude this part with an overview of planned lunar missions that will provide information about the Moon relevant to LGWA and its pathfinder mission Soundcheck 2.4.

## 2.1 Mission concept

The LGWA was originally proposed in 2020 in response to a call for ideas by the European Space Agency for lunar science payloads to measure vibrations of the Moon caused by GWs [12]. The mission concept was refined in the following year [10]. The targeted observation band is 1 mHz to 1 Hz, where the lower bound is given by the frequency of the lowest order quadrupole normal mode of the Moon. Above about 1 Hz, the lunar GW response is expected to be so weak that instrumental and SBN start to dominate the LGWA signal [13, 14]. The SBN is unknown, i.e., it is so weak that it was not possible to observe it with the Apollo seismometers, but it is predicted to be several orders of magnitude quieter in the 0.1 Hz–1 Hz band than on Earth [15].

The LGWA is proposed as an array of four stations deployed in a PSR at one of the lunar poles. The PSRs are formed by craters and are defined as regions where sunlight can never directly hit the ground. Only sunlight reflected from Earth or scattered from upper parts of the crater walls can still reach the ground. The PSRs are possible only because the Moon's rotation axis is almost perpendicular to the vector pointing from the Moon towards the Sun. Some PSRs have surface temperatures continuously below 40 K, and are thermally very stable [16]. These temperature conditions together with the extremely low SBN enable lunar GW detection at frequencies well below what most people think is possible on Earth with the proposed Einstein Telescope or Cosmic Explorer [6, 7].

Each LGWA station will be equipped with two horizontal LIGS measuring surface displacements along two orthogonal directions. The horizontal measurement is preferred in terms of achievable instrument noise and current models predict stronger GW response in horizontal direction. A disadvantage is that one must deal with noise produced by ground tilt.

A more detailed payload description is given in section 2.1.1. Four stations are required for effective SBN reduction (see section 2.1.3). An important advantage of LGWA over space detectors like LISA is that there is no known hard limit to its mission lifetime. At
the poles, the rate of meteoroid impacts is smaller compared to the equatorial regions [17], and power sources like a radioisotope thermoelectric generator can operate for decades.<fnref n="5" /> Such long mission lifetimes, besides increasing the chances to detect rare GW signals, would enable future developments of the lunar GW detector network. For example, deploying stations at both poles makes it possible to carry out very sensitive searches for primordial GW backgrounds [18]. By burying stations or deploying them in lava tubes, other regions on the lunar surface might become suitable for GW detection, which makes it possible to carry out interesting additional tests of general relativity [19].

### 2.1.1 Payload description

*Main contributors:* Joris van Heijningen, Oliver Gerberding, Shreevathsa Chalathadka Subrahmanya, Morgane Zeoli

The LGWA seismic stations each have a platform with a leveling system on which the two horizontal LIGS stand. An onboard cryocooler to achieve liquid helium temperatures allows for the use of superconducting elements. Current plans for the payload for LGWA are shown in figure 1. The aim is to achieve a displacement sensitivity of $10^{-12} \text{ m}/\sqrt{\text{Hz}}$ at 0.1 Hz and $10^{-15} \text{ m}/\sqrt{\text{Hz}}$ at 1 Hz surpassing commercial state-of-the-art by about 3 orders of magnitude. Such sensitivities can be demonstrated on Earth only with the help of specialized vibration-isolation facilities to emulate the low-noise conditions on the Moon as well as possible.

The LGWA payload aims to achieve its sensitivity by high quality mechanics, cryocooling, superconducting actuation and interferometric or superconducting sensing. LGWA will employ niobium or silicon as proof mass and suspension material, thereby reaching mechanical quality factors of $10^4$ and $10^6$, respectively. Together with additional cooling using a sorption cooler [21], this leads to a thermal noise limited sensitivity below 0.3 Hz. The sorption coolers also bring the inertial sensor temperature down below the critical temperature of niobium, a superconductor traditionally used for sensing [22]. Similar coil technologies can also be used for ultra low-noise actuation of the inertial sensor proof mass, which can be used to keep the suspended proof mass in operating range.

As detailed in [20], the LGWA payload currently has two baseline designs: a niobium Watt's linkage with interferometric readout and a silicon Watt's linkage with superconducting readout. Figure 1 presented the latter option. The development of a 1-kg niobium and superconducting actuators is ongoing; the rest of this concept has been developed and used before [23]. The hybrid fabrication of a silicon Watt's linkage [24] and also the superconducting sensing has only been conceptualized. The second concept therefore requires more R&D, at the benefit of an expected 10-fold sensitivity increase in inertial displacement sensitivity directly translating to a 10-fold sensitivity to GWs. A more sensitive laser-interferometric readout with sub-fm/$\sqrt{\text{Hz}}$ sensitivity is being investigated as well, but requires an ultra-stable laser frequency reference, see [20].

The seismic stations are constructed and shielded such that effects due to varying temperatures in the local terrain are minimized. A leveling system will be needed for initial compensation of the ground slope, and later to maintain the horizontal alignment of the LIGS

<footnote n="5">⁵Radioisotope thermoelectric generator concept.</footnote>
<figure><img src="image_4.png" /><figcaption>**Figure 1.** Conceptual overview of an LGWA seismic station on a tilted surface on the lunar regolith. The roughness and tilt of the lunar surface are exaggerated for illustrative purposes. Several subsystems vital to successful operation are depicted and further detailed in the text. Subsystems are not shown to scale. Adapted from [20], with the permission of AIP Publishing.</figcaption></figure>

platform accurate to within 10 µrad to prevent the proof mass and components attached to it from touching the sensor frame. Regular or maybe even continuous adjustment of the alignment might be needed due to time-varying ground tilts (see section 2.3.4).

### 2.1.2 Main instrument-noise contributions

*Main contributors:* Joris van Heijningen, Shreevathsa Chalathadka Subrahmanya, Morgane Zeoli

The general LGWA sensitivity curves are obtained by dividing the inertial sensor displacement sensitivity curve by the lunar response to a passing GW. The latter is discussed further in section 2.1.4. The sensitivity curves of the 2 concepts — LGWA niobium interferometric and LGWA silicon superconducting — are presented in figure 2.

At low frequency, say below 0.5 Hz, thermal noise is dominant for both LGWA concepts and depends on the temperature T, the mechanical resonance frequency $\omega_0$ and mechanical quality factor Q as [25, 26]

$$x_{\text{th}}^2 = \frac{4k_{\text{B}}T}{m\omega[(\omega_0^2 - \omega^2)^2 + (\omega_0^2/Q)^2]} \frac{\omega_0^2}{Q} \quad (2.1)$$

where $k_B$ denotes the Boltzmann constant and $\omega$ the angular frequency. The quantity $\omega_0^2/Q$ is constant for structurally damped mechanical oscillators [27] and is relatively low
for high-quality materials. We model for a resonance frequency of 0.25 Hz, a Q of $10^4$ for niobium and $10^6$ for silicon.

At higher frequencies, the readout noise is dominant. The readout for two studied LGWA concepts are interferometric and superconductive. For the interferometric readout, the shot noise limit can be calculated as amplitude spectral density

$$i_{\text{sn}} = \sqrt{2eI_{\text{PD}}} = \sqrt{2e\rho P_{\text{PD}}}, \qquad (2.2)$$

where e denotes the elementary charge, ρ the responsivity in A/W of the photodiodes and $I_{\text{PD}}$ and $P_{\text{PD}}$ the photocurrent and power on the photodiode, respectively. For solid state lasers the relative intensity noise (RIN) spectrum can be roughly expressed as

$$i_{\text{RIN}} = i_{\text{sn}} \sqrt{\frac{\omega_c}{\omega} + 1}, \qquad (2.3)$$

where $\omega_c$ represents the corner frequency above which the light source intensity fluctuations converge to shot noise limit. Thanks to the differential configuration of the interferometer, $\omega_c$ can be pushed to low frequency. The effective value of $\omega_c$ can be determined experimentally. Laser frequency noise can also impact the total noise budget since a frequency noise $\nu_L$ (in Hz/√Hz) translates into a readout displacement noise

$$x_f = \frac{\nu_L}{\nu_0} \Delta L_0, \qquad (2.4)$$

where $\nu_L$ represents the laser-frequency noise, $\nu_0 = c/\lambda$ the central laser frequency and $\Delta L_0$ the static arm length difference.

A sub-fm/√Hz sensitivity can also be achieved with a superconductive readout. Referred to ground displacement, this readout noise can be calculated as follows [28]

$$x_{\text{squid}}^2 = \frac{2E_{\text{A}}(1 + f_{\text{c}}/f)}{m\omega_0\eta\beta}, \qquad (2.5)$$

where m is the suspended proof mass, $\eta\beta$ denotes the coupling efficiency from mechanical motion to the readout and $E_{\text{A}}$ the energy resolution. At 4.5 K, the latter is estimated to be $E_{\text{A}} = 50\,\text{h}$ [29]. The superconductive readout has a $1/\sqrt{f}$ characteristic below $f_c$.

Superconducting coil actuators can be used to exert forces on a superconducting surface by means of the Meissner effect. They channel the digitization noise $n_{\text{DAC}}$ from the digital-to-analog conversion (DAC) to an effective displacement noise of the proof mass motion as

$$x_{\text{act}} = \frac{\alpha n_{\text{DAC}}}{R_s m \omega^2}, \qquad (2.6)$$

where $\alpha$ denotes the actuator strength in N/A and $R_s$ the shunt resistance. It will depend on the lunar SBN if actuation on the proof mass of the inertial sensor is necessary.
<figure><img src="image_5.png" /><figcaption>**Figure 2.** Minimum detectable inertial displacement for the two LGWA concepts: (a) a niobium Watt's linkage with laser-interferometric readout and (b) a silicon Watt's linkage with superconductive readout. All readout noises are corrected by the mechanical transfer function of the proof mass suspension.</figcaption></figure>

### 2.1.3 Reduction of the seismic background

*Main contributors:* Jan Harms, Francesca Badaracco, Lucia Zaccarelli

The superposition of seismic waves produced by a large number of small events like meteoroid impacts (see section 2.3.5 for details) produces a continuous SBN in LGWA measurements [10, 13]. It is not yet known how strong the SBN is, but simulations indicate that it might limit LGWA sensitivity above 0.1 Hz [15]. For this reason, LGWA was proposed as an array of four stations with distances small enough so that the seismic signal observed in one LIGS can be modeled accurately using data from the other LIGSs, and large enough so that there is an observable phase delay or difference in amplitude between stations. If these conditions are fulfilled — how well might depend on frequency — then it is possible to distinguish between a GW signal, which is approximately the same at all LGWA stations, and the SBN.

Methods of array optimization have been developed for noise cancellation in terrestrial GW detectors like Virgo [30, 31]. Compared to background reduction in Virgo, the problem is different in LGWA since all LIGS available to LGWA also contain the GW signal, while the GW signal in terrestrial seismometers can be neglected. This means that standard optimization methods for background reduction need to be modified for LGWA. This will generally lead to a nonlinear optimization problem, considering properties of the GW signal as well. First studies of the efficiency of the LGWA SBN reduction are under way. The sensitivity models used in this white paper assume that the impact of the SBN is fully removed from the LGWA data.
<figure><img src="image_6.png" /><figcaption>**Figure 3.** Modeling of the lunar GW response in the decihertz band requires analytical studies and numerical simulations based on a geological and topographic model of the deployment site. Gravitational waves generate seismic waves propagating in normal direction to the surface and interfaces. Reproduced with permission from [32].</figcaption></figure>

### 2.1.4 Lunar response to GWs and calibration

*Main contributors:* Jan Harms, Oliver Gerberding

The response of an elastic halfspace to GWs was first modeled by Dyson [33] and later analyzed for a spherically symmetric body in the normal-mode formalism [34]. The equivalence of the standard Newtonian gravitational coupling in an elastic body to mass density, and the general relativistic coupling to shear-modulus gradients were shown in [35]. The Dyson model was used in [18, 36] and the normal-mode formalism was used in [10, 37] to estimate the sensitivity of GW searches using the Earth and the Moon as antennas. In 2024, three studies on the lunar GW response emerged with the aim to provide a deeper physical understanding of the lunar GW response in the Dyson field-theoretical formalism and in the normal-mode formalism [38, 39], and to extend the Dyson model to a horizontally layered half space [40].

Especially the GW response modeling in the 0.1 Hz–1 Hz band is important to LGWA, where most of its breakthrough science can be achieved. In lack of a well-founded numerical model, the lunar GW response remains an important uncertainty in LGWA sensitivity models at frequencies > 0.1 Hz. At these frequencies, topography and regional geology as shown in figure 3 are expected to play an important role. In this band, the approach for current LGWA sensitivity curves is to start with a simple Dyson model, and then to modify it so that it becomes consistent with lunar seismic observations. Most importantly, we include an amplification of the ground response. The quality factor inferred from moonquake observations (wave coda, wave envelopes) with Apollo seismometers is on the order of a few thousand [41, 42]. However, seismic scattering is an important effect on the Moon, and it is unclear today how much of the Q-factor can be exploited in GW signal analyses and how scattering effects fields locally at the LGWA site. This would ultimately be a problem of response calibration (see below), and assistance might come from multiband observations with space-borne or terrestrial GW detectors. For the LGWA sensitivity, we assume on-peak
amplification factors of a few 100 in the decihertz band with respect to a simple Dyson response model for a homogeneous half space.

**Calibration of LGWA data.** Calibration requires models of the (1) laser-interferometric/coil response to proof-mass displacement, (2) mechanical response to ground displacement, and (3) lunar GW response. The calibration of the mechanical and laser-interferometric response is well understood [43] and any errors will not be a dominating factor. Calibration procedures have also been developed for a superconducting coil + SQUID readout [44, 45], and calibration errors are expected to be minor also in this case compared to the uncertainty of the lunar GW response.

The main calibration error will come from the model of the lunar GW response, which depends on our understanding of the lunar internal structure ($f \lesssim 0.1$ Hz) and the geology and topography at the deployment site ($f \gtrsim 0.1$ Hz). The lunar GW response model will be obtained from numerical simulations including geological and topographic information. It can be refined with time by analyzing moonquakes observed with LGWA and using single-station inference methods of local subsurface structure [46–48]. We note that ground tilt produced by GWs is very small since GWs only excite quadrupolar modes of the Moon. The dominant gradients along the lunar surface of fields excited by GWs are likely connected to geological heterogeneity and topography. The tilt contribution to the horizontal displacement signal of a GW is likely negligible, but a careful analysis is required. It is impossible today to say what calibration errors can be achieved in this way. While the calibration task seems more complicated for LGWA than for terrestrial GW detectors, one advantage is that the lunar GW response does not change with time.

A highly accurate modeling of the lunar GW response might be possible with multiband observations; see section 2.2.4. For example, solar-mass or intermediate mass BBH could first be observed with LGWA and later with a network of terrestrial GW detectors. In this case, parameters of the GW signal can be inferred based on an accurate calibration of the data of the terrestrial detectors, and be used to calculate the waveform during the period when the signal was in the LGWA observation band. The calibration is then obtained as the function that relates the (known) waveform with the GW signal observed by LGWA. A practical challenge of this procedure is that the lunar GW response depends on the propagation direction of the GW due to geological and topographic inhomogeneities. Consequently, it might be that many multiband observations are required before an accurate model of the lunar GW response can be reached.

### 2.1.5 Sensitivity models of LGWA

*Main contributors:* Jan Harms

The power-spectral densities (PSDs) of the LGWA sensitivity models can be obtained from the GWFish repository.<fnref n="6" /> As mentioned earlier, we developed two models, one being more conservative, i.e., higher readout noise and lower quality factor of the proof-mass suspension

<footnote n="6">⁶GWFish git repository.</footnote>
<figure><img src="image_7.png" /><figcaption>Figure 4. Models of characteristic strain sensitivities.</figcaption></figure>

(referred to as the niobium model), and another being a more ambitious design with low readout noise and high-quality factor (referred to as silicon model).

The LGWA sensor array has a total of 8 horizontal seismic channels: each station monitors surface displacement along two orthogonal horizontal directions. The observation of GW signals is accurately modeled in GWFish taking contributions of the two GW polarizations into account, but for some of the analyses presented in this white paper, separate simulation software was used and a simplified approach is taken: the instrument-noise PSD of a single LGWA channel is divided by 4 and only one polarization is observed. The LGWA sensitivity models (LGWA-Nb and LGWA-Si) including the division of noise by a factor 2 (in amplitude) are shown in figure 4 as characteristic strain ($fS(f)$)¹/², where $S(f)$ is the instrument-noise PSD.

### 2.1.6 Outlook: LGWA upgrades

Main contributors: Jan Harms

There are possibilities to improve the LGWA LIGS network beyond its baseline configuration and increase its science reach. The three approaches are

* Improving LIGS instrument sensitivity

* Increasing the number of array stations for improved SBN reduction

* Extending the station network across the lunar surface for enhanced GW analyses, e.g., to enable correlation measurements between stations, or GW polarization measurements.

Improvements of the LIGS sensitivity are conceivable over the entire frequency band from 1 mHz to 1 Hz, i.e., no known fundamental sensitivity limitations prevent improvements beyond
the LGWA-Si model. Especially, innovative technologies like superconducting levitation
as proof-mass suspension could have an enormous impact on LGWA sensitivity below
0.1 Hz [28, 49, 50].

Improving LIGS technologies, it is increasingly likely that LGWA will become limited by SBN. This is especially true for improvements of the LIGS sensitivity in the frequency range 0.1 Hz–1 Hz. In this case, techniques to reduce the SBN must be improved as well. Adding stations to the LGWA array would provide a better analysis of the ambient seismic field and better noise reduction. Below 0.1 Hz, LGWA sensitivity is not expected to be limited by the SBN, and improvements of the LIGS sensitivity would directly lead to improvements of LGWA sensitivity to GWs.

It is hard to imagine LIGS and SBN technologies today that would make GW observations above 1 Hz with LGWA possible, since the lunar GW response is very weak at these frequencies. We believe that observations above 1 Hz must be done with long-baseline laser interferometry (see [11, 51, 52] for proposed lunar detector concepts).

The station network can be extended across the lunar surface. For example, deployment at both lunar poles would make it possible to carry out correlation measurements between stations at the two poles to search for a stochastic GW background [18]. It was also pointed out that a certain distribution of LIGS over the lunar surface would make it possible to precisely measure the polarization of a GW including polarization states not predicted by general relativity [19]. This however would require deployments outside the PSRs. In order to avoid excess noise from ground tilts due to temperature variations at stations outside PSRs, it would be necessary to bury the LIGS. It is not known how deep such a vault would have to be, but temperature stability is predicted to be very high already a few 10 cm below surface [53]. To further reduce the noise from ground tilt, a sensor could be deployed with the ability to measure ground tilts in addition to ground displacement as recently proposed by Li et al. [54]. In this case, the tilt measurement could be used to subtract the tilt-induced noise in the displacement measurement.

## 2.2 Observational capabilities

### 2.2.1 Detection horizons

*Main contributors:* Jacopo Tissino, Jan Harms, Martina Toscani, Manuel Arca Sedda, Alberto Sesana

Detection horizons are an important figure-of-merit of the observational capabilities of GW detectors. The detection horizon is the maximum distance of a source observed with a certain signal-to-noise ratio (SNR). Such a source emits GWs with the optimal polarization, e.g., for a compact binary, this means that its orbital plane is perpendicular to the line of sight to the source. For short GW signals, there is also an optimal sky location with respect to the detector orientation. However, for GW sources observed for months and years, the concept of optimal sky location must be generalized to take into account the change of the orientation of LGWA sensors due to the rotation of the Moon.

An often used alternative figure of merit similar to the detection horizon is the detection range, which, given some SNR threshold, quantifies the maximum distance at which a source
<figure><img src="image_8.png" /><figcaption>**Figure 5.** Left: LGWA horizon for equal-mass black hole binaries, compared to Einstein Telescope and LISA. The mass value is given in the source frame. Right: redshift threshold for detection (SNR 15) for an IMRI with primary mass $M_{\text{IMBH}}$ and secondary mass of $30M_{\odot}$. The central blue region corresponds to LGWA, which can be compared with the horizons of the Einstein Telescope (left region, green) and LISA (right region, red).</figcaption></figure>

can be seen after averaging over its orientation and sky-location angles. The horizon is about a factor 2.24 larger in luminosity distance than the detection range, but this is true only at smaller distances $z \ll 1$ where redshift effects on the waveform can be neglected.

**Binary black holes.** Here, we present three analyses to characterize the detection capabilities of LGWA. The first is the so-called waterfall plot shown in figure 5. The plot shows the horizon for SNR values 8, 50, 250, and 1000. The x-axis shows the total mass *M* of the observed binary in the detector frame, which is connected to the mass in the source frame by *M* = (1 + *z*)*M*<sub>src</sub> (*z* is the redshift). At 1000 *M*<sub>☉</sub>, the LGWA detection horizon is about a factor 8 larger in redshift compared to ET and LISA, which means that LGWA would complement the study of BBH populations possible with ET and LISA. Instead, the detection horizon of solar-mass BBH and BNS is comparable to the detection horizon of the LIGO detectors during their third observation run. The most distant detection was GW200308 at a redshift of *z* = 1.04 (albeit the analysis of this event might be biased by unphysical modes of the posterior) [2]. In the case of more extreme mass ratio events, the ideal detections for LGWA consist of light IMRIs, for which the primary IMBH is of order $10^{2-4}$ masses, up to redshift $z \sim 1$. The horizon distance limits for IMRIs consisting of a $30M_{\odot}$ secondary are shown in the right plot of figure 5, with comparisons to the Einstein Telescope and LISA.

**Detection of the GWTC signals.** In order to have a better idea of the detection capability of LGWA with respect to solar-mass binaries, we simulate the observation of the signals in the Gravitational-wave Transient Catalogues GWTC-1–GWTC-3 with LGWA [2, 55]. As shown in figure 6, of the 80 signals detected with Virgo and LIGO, 28 would have been seen with LGWA, and the same volume-time product for 1.4 + 1.4 $M_{\odot}$ would be achieved with LGWA within one year. These 28 detected GWTC signals are not the total number of expected solar-mass sources that LGWA would see per year since GWTC signals are
<figure><img src="image_9.png" /><figcaption>**Figure 6.** Signal to noise ratios of GWTC-3 signals simulated in LGWA. Even when assuming the same volume-time product that underlies the GWTC-3 detections (about 0.004 Gpc$^3$ yr referred to BNS [2], which corresponds to a year of LGWA observation), the total number of BNS and solar-mass BBH detected by LGWA will be higher than indicated in this plot since GWTC-3 is merely a subsample of all such systems within the detection horizon. The LGWA detection range for 1.4+1.4 M$_\odot$ BNS is about 100 Mpc, and for 30+30 M$_\odot$ BBH about 1.9 Gpc ($z = 0.4$).</figcaption></figure>

only a subset of all solar-mass binaries within the Virgo/LIGO or LGWA horizons (see also section 2.2.4). Also the exact number of detections depends on the absolute time of the simulation, and might vary from simulation to simulation under changes of absolute time, i.e., changing the orientation of the Moon.

**Binaries containing white dwarfs.** Another important horizon calculation concerns DWDs. They can either be observed as signals whose GW frequency increases very slowly never reaching the point of contact during the observation, or the signal inspirals and eventually comes to an end when the two WDs disrupt each other or merge. We calculate the horizon for $1M_\odot + 1M_\odot$ DWDs and $1M_\odot + 1.4M_\odot$ WD/NS, all observed over 10 years (3 years) corresponding to the designated LGWA (LISA) mission lifetime. The plot in figure 7 shows the horizons as a function of the GW frequency reached by the binary at the end of the observation time. Signals from DWDs and even WD/NS are not expected to reach 1 Hz as the merger should happen at lower frequencies depending on the masses of the white dwarfs; see equation (3.5). So, LGWA's maximum horizon for DWDs is around 100 Mpc. This horizon can be confronted with the LISA's DWD horizon, which only extends over the volume of the Galaxy. The reason why the LISA horizon decreases below 30 mHz even though its sensitivity keeps increasing down to a few mHz is because at such low frequencies, the 10 years inspiral time is so short that the SNR is accumulated over a very narrow
<figure><img src="image_10.png" /><figcaption>**Figure 7.** LGWA (LISA) detection horizons for DWD and WD/NS inspiral signals observed over 10 years or 3 years and with SNR threshold as indicated in the plot. The horizon is drawn as a function of the GW frequency reached by the DWD or WD/NS at the end of the observation time. The masses are $1M_{\odot} + 1M_{\odot}$ for DWDs and $1M_{\odot} + 1.4M_{\odot}$ for WD/NS.</figcaption></figure>

These signals are different in nature to the broadband spectra produced by compact binaries closer to their merger.

**Tidal disruption events.** In figure 8, we show the maximum distance at which LGWA can observe a WD-TDE as a function of the BH mass, for two fixed values of $\beta$: 1 and 5. We assume two signal-to-noise thresholds for detectability: 8 and 10, calculated in a similar way as outlined in [56]. The plot indicates that LGWA is capable of detecting these events in the satellites of the Milky Way, extending up to the Andromeda galaxy and almost reaching the Virgo cluster. This finding is indeed encouraging, despite the challenge of determining the expected rate of occurrence for these events (further details on the rates are discussed in section 3.3.3).

### 2.2.2 Localization of GW sources in space and time

*Main contributors:* Jan Harms, Jacopo Tissino, Michele Mancarella, Francesco Iacovelli

The localization of GW sources is an important aspect of GW observations. Unless one considers the multiband scenario described in section 2.2.4, LGWA is likely going to be an isolated detector whose localization capabilities are limited compared to detector networks. However, there are important exceptions. Solar-mass compact binaries consisting of white dwarfs, neutron stars and lighter black holes will be observed by LGWA for several weeks
<figure><img src="image_11.png" /><figcaption>**Figure 8.** Maximum distance $d_{max}$, at which LGWA can see a WD-TDE ($M = 0.5M_{\odot}$, $R_{*} = 0.01R_{\odot}$) as a function of the BH mass, for two fixed values of the penetration factor (tidal ratio to stellar pericenter): 1 (short-dashed curves) and 5 (long-dashed curves). We consider two possible thresholds for detection: 8 (orange curves) and 10 (green curves). For comparison, we also display the distances at which the Large Magellanic Cloud, the Andromeda Galaxy and the Virgo Cluster are located (horizontal black lines).</figcaption></figure>

to years. The modulation of the signal's amplitude and phase due to the Moon's rotation and orbital motion provide information about the source's location in the sky. We also point out that contrary to laser-interferometric detectors, LGWA carries out independent surface displacement measurements along two orthogonal horizontal directions, which also helps with the sky localization. Vice versa, being able to measure sky location accurately improves estimates of other parameters like distance and polarization. Such a scenario is specifically attractive for BNS observations, where the detection and localization of the source would become an early warning of a BNS merger in the band of terrestrial detectors, and electromagnetic observatories can prepare for the event [57, 58]. Also the disruption or merger of white dwarfs observable in the decihertz band would be accompanied by EM counterparts (see sections 3.2.1 and 3.3.2), and sky localization might be crucial for the detection of an EM signal.

However, we do not have a simulation yet that is able to estimate the sky-localization errors of generic sources for LGWA. The problem is outlined in the following, and we leave it to a future task to improve the current numerical simulations.

The calculation of sky-localization and merger-time estimation errors has non-trivial technical challenges especially for LGWA connected to the Fourier-domain phase term
<figure><img src="image_12.png" /><figcaption>**Figure 9.** Sky-localization estimates based on [60, eqs. (51), (52)] coming from the orbital motion of the Moon (around the Earth) and the Earth (around the Sun). The bands represent a range of frequencies from $f = 0.02$ Hz (worse localization) to 0.5 Hz (better localization) with the solid lines representing 0.1 Hz. The signal SNR increases with the square-root of the observation time reaching a value of 30 after one year.</figcaption></figure>

appearing in the signal at a detector: $\exp(i(\vec{k} \cdot \vec{r}(t(f)) - 2\pi ft_c))$, where $t_c$ is the merger time, $f$ the frequency of the GW, $\vec{k}$ is its wavevector, and $\vec{r}(t)$ is the position of the detector. The function $t(f)$ provides the time, at which the GW signal emits at frequency $f$, and it is used to simulate the changing detector position and orientation while the GW signal is being observed. This works only for certain types of GW signals and under certain conditions with respect to the frequency evolution of the signal and how quickly the detector is moving [59]. The principal problem is that with this phase term the likelihood (or Fisher matrix) is dependent on the choice of the origin of the coordinate system. There is a method to obtain coordinate independent parameter-estimation errors [60], but it has not been integrated in general simulation software yet.

A correction can however be applied for selected signals by expressing the detector positions with respect to a reference point that minimizes coordinate artifacts. This was done to analyze the localization of GW170817 with LGWA using the Fisher-matrix approximation [14], and it was shown that few-arcmin$^2$ sky-localization errors can be obtained. The order of magnitude of this result can also be estimated analytically under simplified assumptions, e.g., neglecting changing antenna patterns and assuming a fixed signal frequency [60, eqs. (51), (52)]. Results from the analytical expressions are shown in figure 9.

Accordingly, the signal modulation caused by the orbital motion around the Sun leads to the dominant sky-localization capabilities of LGWA compared to the contribution of the Moon's orbital motion. Sky localization improves quadratically with the SNR and signal frequency.
### 2.2.3 Estimates of spin and mass parameters

Main contributors: Jan Harms, Jacopo Tissino

Estimation of mass and spin parameters can be important for various reasons. Component masses together with the distance of compact binaries are the fundamental quantity to start a population study. Furthermore, spins can help to distinguish formation channels of compact binaries. The LGWA science case on population studies and the role of the various parameters are described in section 3.2.2. In this section, we provide information about the capability of LGWA to measure these intrinsic parameters. The method is based on the Fisher-matrix approximation. The waveforms were simulated with the approximant IMRPhenomXPHM [61], which can simulate precession and higher-order modes. The Fisher-matrix method leads to accurate error estimates whenever the SNR is high enough and there is no degeneracy of the waveform model involving the analyzed parameters. These conditions can be assessed post factum when finding that the parameter-estimation errors are small. Large parameter errors point to potential issues typically with model degeneracies, which can be cured by using prior distributions as well [62], or by switching to a full Bayesian analysis tool without assuming a Gaussian likelihood [63]. This means that the errors presented in this section for mass parameters are a good indication of what a full Bayesian analysis would obtain, while errors of the spin parameters might deviate significantly from full-Bayesian calculations when the error approaches unity. Error estimates from a full Bayesian analysis are typically significantly smaller in this case due to the help of (even uniform) prior distributions [62].

The results in figure 10 concern the estimation of the component mass $m_1$. The left plot shows the parameter-estimation error in the case of $1M_{\odot} + 1M_{\odot}$ DWDs as a function of distance and maximum frequency reached after a 10-year observation time with LGWA. The errors all lie orders of magnitude below the component mass even for large distances of the source close to the LGWA detection horizon. The right plot shows the mass errors for an equal-mass BBH with varying component masses expressed in the observer frame and over a range of redshifts. Also in this case, mass-estimation errors are orders of magnitude lower than the component masses. LGWA's ability to provide such precise mass estimates either comes from long observation times (DWDs) or high SNR (BBH).

The next result concerns spin measurements. We expect that LGWA can only provide decent spin estimates for BBHs; especially those merging within the LGWA observation band. This is confirmed by the results in figure 11. The left plot shows the estimation error for the spin amplitude $a_1 = 0.8$ ($a_2 = 0.3$) of the first black hole, and the right plot of the tilt of the spin direction $\tau_1 = \pi/3$ ($\tau_2 = -\pi/5$). As expected, the best spin estimation is achieved for BBHs with component masses around $10^5 M_{\odot}$ consistent with the maximal LGWA detection horizon at $z = 50$ and total masses around $1000 M_{\odot}$ (intrinsic mass) in the horizon plot in section 2.2.1. The spin estimates are very poor for BBHs with components masses under $600 M_{\odot}$ and above $8 \cdot 10^5 M_{\odot}$.
<figure><img src="image_13.png" /><figcaption>**Figure 10.** Plots of the estimation errors for the component mass $m_1$. Left: for a $1M_{\odot} + 1M_{\odot}$ DWD as a function of the distance to the source and the maximum frequency reached by the binary after a 10-year observation time. Right: for equal-mass BBHs expressed in the observer frame.</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>**Figure 11.** Plots of the estimation errors of spin amplitude $a_1$ (left) and spin tilt angle $\tau_1$ (right) as a function of the distance to the source and for equal-mass BBHs expressed in the observer frame. White areas in the plots mean that the parameter-estimation error exceeds the range of possible values of the parameter.</figcaption></figure>

### 2.2.4 Multiband GW observations

Main contributors: Michele Mancarella, Francesco Iacovelli, Pau Amaro Seoane, Niccolò Muttoni, Alberto Sesana

The next decade will witness a flourishing of GW experiments covering different frequency bands. Ground-based interferometers of “third generation” (3G) are under design and entering in advanced stages of planning, both in Europe with the Einstein Telescope (ET) [64–67] and in the U.S.A. with the Cosmic Explorer (CE) [7, 66, 68, 69]. They may be further complemented by observatories in the southern hemisphere [70]. These experiments are mostly sensitive in the frequency range between a few Hz and a few kHz. The Laser Interferometer Space Antenna (LISA), recently adopted by ESA and scheduled for launch
<figure><img src="image_15.png" /><figcaption>**Figure 12.** Conceptual illustration of the multi-band approach across the GW frequency spectrum. Black solid lines mark few representative GW signals of different astrophysical origin sweeping through their inspiral, merger and ringdown phases over the frequency bands probed by space-borne and ground-based detectors, colors as in legend. BBH (BNS) signals — which are not projected in the interferometers for illustrative purpose — are modelled by the IMRPhenomXHM (IMRPhenomD_NRTidalv2) waveform template. For reference, the SMBH binary has source masses $M_1 = 10^6$ M$_\odot, M_2 = 8 \times 10^5$ M$_\odot$ and $d_L = 1.7$ Gpc, while the IMBH binary has source masses $M_1 = 10^3$ M$_\odot, M_2 = 4 \times 10^2$ M$_\odot$ and $d_L = 2$ Gpc.</figcaption></figure>

in 2035, will instead target signals in the band 0.1 mHz to 0.1 Hz. The presence of multiple experiments covering such a broad range of frequencies opens the tantalising possibility of multi-band observations [71] that would have tremendous scientific impact. In this context, LGWA would provide a crucial bridge between LISA and ET/CE with several potential multi-band targets covering the intermediate frequency band around the dHz [72, 73].

A number of benefits of multi-band detections are shared between different sources and observatories. Detections and determination of the merger time in the LGWA and/or LISA bands can be used to pre-alert ground-based GW detectors and EM observatories, adjusting their time schedules or even tuning them for specific science goals [74–76]; parameter estimation can either be performed jointly, or sequentially, using results from detectors at lower frequencies as priors for data analysis at higher frequencies [77]; detections in ground-based interferometers can also be used to look back in LGWA/LISA data to find events at lower SNR [78]. An illustration of multi-band GW sources is provided in figure 12, where we show the LISA, LGWA, ET and CE sensitivity curves together with representative GW waveforms from different classes of compact objects. We discuss them in turn.

* *Stellar Origin Binary Black Holes.* These sources are the primary target of the LIGO and Virgo detectors, with a total of ~ 90 sources already observed [2]. Their multi-band potential is actively studied in the context of LISA and ground-based interferometers [71, 79–87]. For example, a binary Black Hole like GW150914 on a circular orbit, with source-frame masses of 36 and 29 solar masses [1], was emitting at ~ 0.016 Hz 5 yrs before merger, well inside the LISA band. The same system 1 day
before merger emits at ~0.26 Hz, which is around the peak sensitivity of LGWA. This
shows that Stellar-origin BBHs are natural candidates for joint detections even in all
the three bands accessible to LISA, LGWA, and ground-based detectors. A particularly
interesting possibility would be the measurement in LGWA of binary parameters
hardly accessible to ground-based detectors, such as eccentricity. Detecting signals
that cross a wide band from low to high frequencies would furthermore strengthen the
constraints on GW speed propagation [88], tests of GR [89–92] and the whole set of
source parameters [71]. In particular, the accurate sky localization can lead to the
unique possibility of a pre-alert of telescopes for the detection of potential counterparts,
which are possible in some astrophysical environments; knowledge of the eccentricity
can be combined with spin measurements by ground-based detectors to constrain BBH
formation channels; precise knowledge of the inspiral part of the signal will enable
unprecedented accuracy in constraining the merger physics.

It is possible to use the constraints provided by the LVK collaboration on the population
of stellar-origin BBHs to obtain preliminary estimates of the joint detection rates. We
consider a population calibrated on the latest LVK results [93], where the source-frame
mass distribution is described by the “PowerLaw+Peak” (PLP) model [94], the spin
distribution by the “Default” spin model of [94], and the evolution of the merger
rate with redshift by a Madau-Dickinson profile [95]. We refer to appendix A of [96]
for the specific numerical values adopted. The value of the local rate is taken to be
the central value inferred from the GWTC-3 catalog, i.e. $R_0 = 17 \text{ Gpc}^{-3} \text{yr}^{-1}$. With
these assumptions, we expect ~6600 sources per year up to redshift ~1, which is
approximately the LGWA horizon at $100 M_{\odot}$.<fnref n="7" /> We simulate 10 years of observations
of LGWA, and associate to each source a time to coalescence extracted from a flat
distribution in the interval $[10^{-5}, 10]$ yrs. The time to coalescence $\tau$ and the chirp mass
$M_c$ of the system determine the initial frequency of each GW source according to the
GR prediction, $f_{\text{in}} = 134 \times (1.21 M_{\odot}/M_c)^{5/8} \times (1\text{s}/\tau)^{3/8}$ Hz. We compute the SNR
of each source assuming a maximum observing time of 10 yrs in ET in its triangular
configuration, LGWA and LISA. We use the public package `gwfish` [97]. With a single
realization of the population according to the above prescriptions, we obtain ~960
sources observed by both ET and LGWA with SNR > 8, among which one source is
observed also by LISA. These numbers are subject to the uncertainty on the population
model, but they show that joint detections of LGWA and ground-based facilities should
be expected in large numbers. The SNRs in LGWA span from the minimum of 8 to a
maximum of ~20, while those in ET are always > 100, with the best events reaching
SNR ~$O(10^3)$. As for joint detections with LISA, a few of them are possible, even if
not guaranteed. A detection in three separate observatories would however represent
an extraordinary science achievement. This result is in line with the findings in [84].

* *Binary Neutron Stars.* A multiband detection of these systems would be a unique possibility opened by LGWA, since those are not accessible to LISA. For example, a Binary Neutron Star system with source-frame chirp mass $M_c = 1.188 M_\odot$, correspond-

<footnote n="7">⁷We remind that the maximum BBH mass in the PLP mass distribution is $m_{\text{max}} = 87 M_{\odot}$.</footnote>
ing to the value measured for GW170817 [98] was emitting at ~0.05Hz, at the edge of the LISA band, more than 45 yrs before the merger. This timescale is clearly too long for the possibility of a joint detection. On the contrary, such a source emits at ~0.27Hz, around the peak sensitivity of LGWA, 6 months before merger, being a perfect candidate for joint observations of LGWA and ground-based detectors, which can observe BNS systems at high rates [96]. Considering 10 years as a limit timescale for the possibility of a joint detection, a GW170817-like source could be observed from a starting frequency of ~0.09Hz. We estimate the joint detection rate in LGWA and ET using the same procedure as for stellar-origin BBHs. For BNS systems, the uncertainty on the population model is much larger; in particular, the value of the local merger rate inferred from the GWTC-3 catalog, assuming a flat mass distribution, is $R_0 = 105_{-83}^{+190}$ Gpc$^{-3}$yr$^{-1}$. Using the central value of 105 Gpc$^{-3}$yr$^{-1}$, a flat mass distribution between [1.1, 2.5] M$_{\odot}$, and values for the Madau-Dickinson profile obtained as described in appendix A of [96], we obtain ~36 sources per year within redshift $z \sim 0.1$, which corresponds to the LGWA horizon at ~few M$_{\odot}$. Over a period of 10 yrs, we obtain 5 joint detections between LGWA and ET with SNR > 8. Given the large uncertainty on the local merger rate, we also compare with the results obtained using the upper and lower rates values of 295 Gpc$^{-3}$yr$^{-1}$ and 22 Gpc$^{-3}$yr$^{-1}$, which give 24 and 1 joint LGWA-ET detections respectively. We conclude that a joint detection is a possibility that should be expected in LGWA. The particularly long time spent by BNS systems in the LGWA band would enable their precise localization prior to merger. Combined with the early detection by ground-based 3G detectors, the sky patch to scan for EM signals would further shrink making use of the long baseline between Earth and Moon. There are prediction of radio and X-ray counterparts produced well before the merger of two neutron stars [99]. Early warnings from LGWA would make it possible to prepare for the observation of these faints signals. Also, long-duration multi-band studies using LGWA and ground-based GW detectors [73, 100] can improve the estimation of parameters, in particular the tidal deformability [72]. This will lead to better constraints, ruling out many more theoretical EOS models [100].

* *Intermediate Mass Black Holes.* While the rates of these systems are still largely uncertain, their potential is high since they could accumulate a high enough SNR in LISA, LGWA and ET during the inspiral, merger and ringdown. A combined measurement could then allow a joint analysis, possibly breaking degeneracies among waveform parameters that are best constrained in different phases of the evolution. A system such as the one in figure 12 emits at ~0.002 Hz 5 years before the merger, and at ~0.27 Hz around 10 minutes before the merger. This makes imaginable an early warning by LISA to both LGWA and ground-based detectors, with the subsequent detection in all the three bands.

* *Supermassive Black Holes.* These systems represent a target for joint LISA-LGWA detections. In particular, there is ample overlap in the mass and redshift range of the two observatories between $10^3 - 10^6$ M$_{\odot}$ up to redshift ~10. For example, ref. [101] finds between ≈25 and ≈75 events per year depending on the seed model. Most or all of them
will be detected also by LGWA, which can in particular accumulate enough late inspiral-merger-ringdown SNR allowing a better localization of the sources, especially at high redshift. This is of paramount importance since a combined LISA-LGWA analysis might help pinpointing the source parameters with higher accuracy, in particular the source distance. In fact, although LISA can see MBHBs at $z > 20$, for faint sources the distance estimate is rather poor and determining the actual high redshift nature of the source might be challenging [102, 103]. Moreover, LGWA will be sensitive to the merger and ringdown part of the signal, which for systems of $M < 10^4$ at $z > 5$ is not accessible to LISA.

For some of the systems discussed above, it is important to mention the role of eccentricity. This can be a signature of formation channels [104], though its detection might be challenging. Indeed, eccentricity dampens the characteristic amplitude of each harmonic compared to a circular one. Figure 13 shows the signal of two GW150914-like sources with different initial eccentricities. Eventually, about an hour before the merger, the signal becomes indistinguishable from the circular case. On the other hand, increasing the eccentricity shifts the peak of the relative power of the GW harmonics towards higher frequencies. Therefore, more eccentric orbits will emit their maximum power at frequencies close to the sweet spot of the LGWA. More precisely, when the eccentricity $e = 0$, all the GW power is radiated by the $n = 2$ harmonic, so that GWs have a single frequency of $2/P$, where $P = 2\pi[G(M_1 + M_2)/a^3]^{-1/2}$ is the orbital period. On the other hand, at $e \simeq 1$, the $n = 2.16(1 - e)^{-3/2}$ harmonic becomes dominant [105], so most of the GW power is radiated at the peak frequency of $f_{\text{peak}} = 2.16(1 - e)^{-3/2}P^{-1}$.

A useful figure-of-merit to assess multi-band capabilities of LGWA is the detection horizon. In Figures 14 and 15 we show the joint detection horizons for LGWA-ET and LGWA-LISA respectively, for binary systems between $10^{-7} M_{\odot}$. In general, the horizon is dominated by the least sensitive detector. For stellar-origin BBHs ($\sim 5 - 100 M_{\odot}$), the LISA sensitivity will be the limiting factor for LISA+LGWA+ET multi-band sources, limiting the potential targets to $z \lesssim 0.3$. On the contrary, a joint LGWA+ET detection would enlarge the observable window to $z \lesssim 1$. Furthermore, as already pointed out, those sources would be “golden events” in ET with SNR $\ge O(100)$. As mentioned earlier, a detection in ET could also be used for an *a-posteriori* targeted search in LGWA data, allowing to further reduce the SNR threshold and increasing the horizon. Similarly, at the opposite edge of the mass range considered here, stellar-origin BBHs could be observed in both LISA and LGWA up to redshifts $> 1$ with very high SNR $\sim O(10^3)$ in LISA. Finally, we note that an interesting “sweet spot” exists for IMBHs around $10^3 M_{\odot}$ where both LISA and ET can reach horizons of $z \sim 7-8$ while LGWA is at its peak, $z \sim 40$. As a consequence the multi-band horizon is quite large even for a LISA+LGWA+ET detection. The highest potential for observing high-redshift sources is for systems between $[2 - 5] \times 10^3 M_{\odot}$ where the joint LISA-LGWA horizon exceeds redshift 30.

Finally, we stress that a crucial aspect of the multi-band science case is the time overlap between different experiments. A particularly strong point in favour of multi-band perspectives for LGWA is the absence of a strong time limit for the mission duration. The overlap with the LISA mission can be limited by the time schedule of the latter (even if an extension up to a maximum of 10 yrs may be possible), while the schedule of 3G ground-based detectors is still much more flexible.
<figure><img src="image_16.png" /></figure>

**Figure 13.** Characteristic amplitude $h_c$ of the first four harmonics (indicated with numbers) emitted by a binary of two black holes with masses $M_1 = M_2 = 30 M_\odot$ and at a luminosity distance of $D = 0.5$ Gpc. The amplitude and the orbital evolution correspond to the quadrupole approximation. We display a binary starting at a semi-major axis of $a_0 = 10^{-7}$ pc and with initially two different eccentricities: (i) $e_0 = 0.99$ (left panel), and (ii) $e_0 = 0.05$ (right panel). Along the harmonics we mark several particular moments with dots, where the labels show the time before the coalescence of the binary and the corresponding orbital eccentricities. Additionally to the LGWA, we depict the noise curves for LISA and LIGO.

## 2.3 Studies of the lunar surface environment and of the deployment site

This section summarized the studies of the Moon's surface and subsurface required to prepare and model LGWA deployment scenarios. Theoretical and numerical modeling of what we expect from the Moon will help in minimizing approximation in instrument design and in selecting most appropriate deployment scenarios for the sensors. In detail, we require modeling of the geology (section 2.3.1), the surface temperature field (section 2.3.2), the ground tilt (section 2.3.4), background seismic noise (section 2.1.3) and magnetic fluctuations (section 2.3.6).

### 2.3.1 Geologic models

*Main contributors:* Alessandro Frigeri, Angela Stallone

The geology at any site of a planetary body is the result of its unique evolution. Over time, a sequence of geological processes, deposits or erodes materials, revealing the environmental conditions of specific periods. A geological model serves as a comprehensive framework for conceptualizing the subsurface geological structures and processes representing our current state of knowledge of the subsurface of a solid planetary body.

Figure 16 shows the geological map for the Moon's southern polar region. Initially compiled after the Apollo program by Wilhelms et al. [106], it has recently been updated by Fortezzo et al. [107]. The map's fundamental components are surface portions classified
<figure><img src="image_17.png" /><figcaption>**Figure 14.** Multiband horizon for a network of Einstein Telescope and LGWA (with the Silicon sensitivity curve). As discussed in section 2.2.1, this is showing the maximum distance and redshift for which an optimally-oriented source can be detected with a given signal to noise ratio (SNR). In the grey shaded areas, the source has at least an SNR of 8 in both detectors, allowing for multi-band parameter estimation. The optimal sky position is computed for every mass. The SNRs in the shaded region are referred to the whole network, including the contribution from both detectors. The masses reported on the horizontal axis are in the source frame, i.e. as they would be measured by an observer in the same reference as the binary.</figcaption></figure>

<figure><img src="image_18.png" /><figcaption>**Figure 15.** Multiband horizon for a network of LISA and LGWA, computed as in figure 14.</figcaption></figure>
by similar morphological and/or compositional characteristics, referred as geological units represented by different colors. Besides the map, the lateral and vertical geometric relationship of the geological units enables ordering the units in space and in time of emplacement.

The geological map is the foundation for constructing any geological model, providing both geometric and physical parameters for creating a related geophysical model. The latter is used as input for numerical modeling techniques to simulate or predict physical processes occurring on Earth or any other planetary body. In the context of LGWA, our aim is to develop geophysical models that can simulate seismic background response across different deployment scenarios. This begins with one-dimensional modeling [108] and progresses towards multi-dimensional and multi-resolution models (See section 2.3.5).

As our understanding evolves with new instrumental data, the geologic map and model must be continuously updated to incorporate existing and new insights about the Moon's subsurface. This implies that modeling is an iterative process, where geological evidence and geophysical modeling dynamically interplay with each other.

## 2.3.2 Solar illumination and surface temperature

Main contributors: Philipp Gläser

Due to the small angle of 1.5° between the ecliptic plane and the lunar equatorial plane, extreme illumination conditions occur near the polar regions of the Moon. Here we find both, extensive, almost continuous illumination right next to PSRs. PSRs are found on the floors of near-polar craters and represent the darkest and coldest places on the lunar surface. Extensively illuminated regions are typically found on elevated topography such as ridges and crater rims. The PSRs are ideal deployment sites for LGWA, and in fact, it is currently believed that deployment inside a PSR is necessary since temperature changes and gradients elsewhere on the lunar surface are strong and would cause excess noise in LGWA data (see section 2.3.4). Study of surface temperature data and surface temperature modeling are necessary to identify suitable LGWA deployment site candidates.

Illumination conditions are calculated based on a high-resolution digital terrain model (DTM) derived from Lunar Orbiter Laser Altimeter (LOLA) data. Here, the LOLA DTM can be synthetically illuminated and it provides illumination conditions for any chosen time period and location [109, 110]. Based on the resulting illumination maps, PSRs and extensively illuminated spots can be identified (compare blue and red areas in figure 17). Further, illumination maps can be calculated for observers at various heights above the ground, i.e. to model illumination at elevated solar panels. It was found that there is a significant increase in illumination in the first ≈ 10 m above ground. The illumination at the surface and 2 m above ground of one of the PSRs is shown in figure 17a+b.

Illumination maps also serve as an input for a thermal model to derive (sub-)surface temperature estimates for the uppermost 2 m of regolith [111]. In order to derive meaningful temperature values inside PSRs it is crucial to consider internal heating as well as multiple scattered sunlight and thermal radiation from the surrounding terrain as these are the only energy sources. For LGWA a landing site that offers low temperatures with little to no variations would be beneficial. On the contrary, to generate power using solar panels a
<figure><img src="image_19.png" /><figcaption>**Figure 16.** Top: global-scale geological map of the Moon's southern polar region, displaying how the geological units are spatially distributed [106, 107]. The map shows a stereographic projection spanning from 55 degrees of latitude south to the South Pole. The graphical scale is referred to the lunar South Pole. Colors indicate the areal extent of different geologic units. Bottom: the vertical and lateral geometric relationship of the units gives the information to read the map in the third dimension of space and the relative timing of the emplacement of the units. The correlation of map units is not fully represented in the map and units in the map have been updated for a global stratigraphy.</figcaption></figure>
<figure><img src="image_20.png" /></figure>

**Figure 17.** Accumulated illumination at the lunar south pole calculated over a twenty-year period and one-hour intervals. Illumination is color-coded where dark blue refers to PSRs and dark red refers to extensively illuminated spots. **a:** accumulated illumination at the lunar surface. **b:** accumulated illumination for an observer at two meters above the ground. Reprinted from [109], Copyright (2018), with permission from Elsevier.

location offering extensive illumination is needed. In an initial survey we searched for small
craters that offer PSRs on their crater floors and significant illumination for a solar panel
which would be mounted on a beam at several meters above ground. A potential candidate
landing site was found in a small crater located between Shackleton and de Gerlache craters
for which these constraints were met, see figure 18.

Since the thermal characteristics of a PSR are crucial to the performance of LGWA, it is
important to carry out a systematic analysis of all PSRs at both lunar poles. Other aspects
might be considered in these analyses such as the vertical distance to sunlight with the idea
to realize a solar-energy powered experiment inside the PSR.

**2.3.3 Regolith composition**

Main contributors: Francesco Mazzarini, Goro Komatsu

On the lunar surface, regolith forms the boundary between the Moon's interiors and the
space environment, preserving key information about the geological evolution of the satellite
but also and also providing some important clues for the history of the inner Solar System
impact flux, the solar wind, and galactic cosmic rays [112]. Lunar regolith is a fine-grained
layer of fragmental debris overlying the coherent substrate consisting largely of the upper
heavily reworked dust layer, fragmented rocks, impact ejecta, breccia lenses, glass fragments,
and agglutinates [113, 114]. The regolith has been estimated to be 5 m to 20 m thick globally,
with a shear velocity of less than 100 m/s [115, 116].
<figure><img src="image_21.png" /><figcaption>**Figure 18.** A PSR with significant illumination on a solar panel mounted on a beam at 15 m above ground. **a:** the small crater showing the location of the possible landing site (black x). A sketch of a solar panel mounted directly and 15 m above the landing site is shown in blue. **b:** the five panels from top to bottom show the direct illumination at the surface, radiation coming from the surrounding terrain, radiation coming from Earth, surface temperature, and the direct illumination at 15 m above ground (solar panel). Note that the radiation coming from terrain and Earth is divided into thermal radiation (red profile) and scattered sunlight (blue profile). Panels 1–3, 5 show radiation in W/m² over time and panel 4 shows temperature in K over time.</figcaption></figure>

Regolith in the Moon forms by high-energy physical weathering processes (e.g., [117]) such as: i) micrometeorite comminution, ii) agglutination (quenched impact glass and welded particles up to 25–30 vol% of the regolith), and iii) crater impacts ([114] and references therein). In general, the continuous impacts of large and small asteroids led to the formation of the lunar regolith [114, 118]. The impact on the pristine bedrock surface generates breccia lens within the crater and a blanketing by ejecta around the crater (figure 19).

The initial formation of the regolith starts with impact bombardment onto the pristine crust, a stochastic process deforming pulverizing, and melting the pristine crust (the protolith). Recent studies suggest the occurrence of H₂O and other volatile species linked to magma ([117] and references therein).

The strength of bedrock significantly affects the crater size and hence the volume of regolith produced especially for sub-decimeter impactors. The regolith volume produced by an individual impact crater is quantitatively characterized as a function of crater diameter and pre-impact regolith thickness [114].
<figure><img src="image_22.png" /></figure>

**Figure 19.** Conceptual model of the regolith formation by impact modified after [114]. Yellow thin lines are the fractured bedrock at the impact site; BL: breccia lens; CS: coherent substrate (bedrock); EB: Ejecta blanket. D is the rim to rim crater diameter; Dt is the transient crater diameter measured with respect to the pre-impact surface. Reproduced with permission from [114].

For the lunar maria, the surface structure can be modelled as a fine-grained regolith layer atop the underlying coherent bedrock (figure 19). Depending on the ratio of crater rim-to-rim diameter (D) to pre-impact regolith thickness (T) different morphologies may form ([114] and references therein). The thickness of lava flows in lunar maria are poorly constrained, although observation within pit craters suggested that the bedrock of the regolith consists of several flows up to 10–14 m thick [119].

Being the impact the most likely forming process, the composition of the impacted surface will determine the composition of the regolith. The old anorthositic crust formed by fractional crystallizations of the pristine Lunar Magma Ocean [120, 121]. After the formation of an early anorthositic crust (the present-day highlands) the partial melting of the mantle produced a secondary crust (basalts) within impact craters. Large impact basins floored by flood basalts formed the lunar maria and oceanus, which are mostly located at equatorial and mid latitude regions [120]. In the south pole of the Moon are present both pristine crust as well as basalts filling craters [122].

The basalts in the maria and the anorthosites in the highland are low-silica magmatic effusive and intrusive rocks, respectively. The main compositional difference between them is their mineralogical composition [123]. Basalts contains MgO, FeO, TiO₂-rich mafic minerals (olivine, pyroxene, ilmenite). Anorthosites are composed of mostly plagioclase feldspar (90–100%), with a minimal mafic component (0–10%).

The lunar surface mineralogy-petrology can thus be simplified, and it has been characterized by four main mineral phases: plagioclase, pyroxenes, olivine, and ilmenite, with other oxides as accessory minerals. Beneath Mare Imbrium (mare basalts), hundreds of meters beneath the surface, SAR processed radar recordings highlighted the occurrence of well-defined layering formed by levels having the dielectric constant (ε = 3.3) typical of that lunar regolith [124].

The presence of a sequence of regolith, lava and ejecta layers to a depth of 360 m has been confirmed also for the Von Karman crater on the far side of the Moon in the South-Pole Aitken basin crater by using dual-channel lunar penetrating radar (LPR), suggesting that
<figure><img src="image_23.png" /></figure>

**Figure 20.** Highly idealized cross-section through the internal structure of the megaregolith and the upper lunar crust (modified after [123]). The depth scale is highly uncertain because regional variations are expected depending on the degree to which basin-sized impacts have influenced a region. Reprinted from [123], Copyright (2012), with permission from Elsevier.

the site underwent remodelling for multiple impacts [122]. Similar multiple regolith layers are interpreted to exist also from Chang'e-3 Yutu rover data [125].

At satellite scale, seismic evidence suggests that the cumulative ejecta thickness on the lunar highlands is possibly tens of kilometres thick [123]. The average depth of mechanically disturbed crust by impacts is not well known, conservative estimates indicate a thickness of the ejecta blankets of at least 2–3 km (megaregolith), a structural disturbance to depths of more than 10 km, and fracturing of the in situ crust down to about 25 km possibly reaching 60–80 km depth [126]. (figure 20). In the upper 1–2 km of the lunar maria, multiple layers of thick lava with regolith on top have been identified [127].

The knowledge of the regolith and the *mega regolith* is critical for creating models of wave propagation, simulating the thermal and mechanical ground response to LGWA sensors. The exact measurements of the overall regolith thickness is challenging because no direct measurements have been done below few meters. Also the lateral variation of thickness and layering strongly depends to the local geological evolution which shaped the shallow lunar crust.

The thickness and composition of the regolith is one important piece of the puzzle to plan and optimize the deployment scenario for LGWA.

### 2.3.4 Ground tilt response

*Main contributors:* Marco Olivieri, Daniele Melini, Jan Harms, Giorgio Spada

Ground deformation at the LGWA deployment site is a determinant factor for the LGWA platform stability and for its long term operation. This would require and accurate leveling in the deployment phase, but also later on during the science observations. Ground stabilization
could be a long term process consequence of the rheology of the lunar regolith and of thermal
and loading effects. In this perspective, the understanding of the regolith properties in PSRs
GREW
y the landing point. The platform of each LGWA station needs to be leveled with an
accuracy of a few tens of microradians to ensure the LIGS functionality at its best (see 2.1.1).

In this section we first describe the possible drivers of the tilt angle defined as the
variations of the angle between the normal to the surface and the local plumb line. Then,
we focus on the tidally-induced tilt providing a theoretical description and estimates of its
effects in lunar polar regions. As mentioned above, the platform leveling could require post
deployment corrections that could be occasional or even continuous, depending on the time
variations of the tilt and with the objective of minimizing the data quality degradation during
the operation of LGWA. The key factors are:

*   **Topography:** only a certain amount of ground slope can be tolerated, since it determines how much actuation range the platform leveling system must have [129]. Indeed, deploying the platform in a steep region could result in a significant fraction of the actuation range being used for initial leveling, shrinking the possibility of further adjustments in response to e.g. soil compaction or tidal effects.

*   **Thermal effects:** PSRs provide a thermally stable environment in which temperature is continuously below 100 K and, in some PSRs, even continuously below 40 K. However, even the small residual temperature changes inside a PSR might cause enough thermally induced ground tilt to perturb the GW measurement. These effects must be estimated carefully as part of an evaluation of the possible PSR deployment sites.

*   **Tidal effects:** the Moon is continuously deformed in response to time-varying gravitational attraction due to the Earth and, to a lesser extent, the Sun. The corresponding cyclic ground tilt can be estimated in order to assess its impact on LGWA operation. If the amplitude of the tidally-induced tilt is greater than the leveling tolerance for LGWA operation, periodic adjustment cycles can be scheduled to keep the platform within its operational tilt limits.

*   **Soil properties:** as mentioned above, soil at PSRs is expected to be stable. However, the platform itself will disrupt the local properties of the underlying regolith in reason of its weight, temperature and heat production. This will imply an accommodation time but it could also include fluctuations that reflect in a certain amount of induced seismic noise. Analyses of this effect are important to decide whether a mechanism is required to mount the stations to the ground.

Modeling planetary tides is a classical problem in geodynamics, since observations of
tidal deformation has provided the first indirect probe of the Earth interior before the advent
of global seismology [130, 131]. Tidal deformation of the Moon has been widely studied in
the early 1960s in view of possible inferences on the large-scale internal structure on the basis
of the geophysical scientific observations planned within the Apollo program [132, 133] and
because of the relevance of tidal deformation in estimating the lunar orbital evolution [134].
Today, accurate models of the tidal potential are available on the basis of ground-based or space-borne selenodetic observations [135], and they are essential for the analysis of spacecraft tracking data.

The largest contribution to solid lunar tides are due to gravitational attraction of the Earth, with the contribution from the Sun being at least one order of magnitude smaller. Tides raised by the Earth are controlled by the eccentricity and inclination of the lunar orbit, which result in both the amplitude and position of the tidal bulge oscillating monthly by ~±5°. Fourier analysis of the tidal potential [135] shows the largest components around the monthly period, with significant contributions also from the bimonthly, trimonthly, yearly and biyearly frequencies. Amplitudes of tidal harmonics vary with position on the Moon surface, with deformation being at the ~0.1 m level, peak tilt (relative to the local plumb line) at the ~5 × 10⁻⁶ rad level, and peak disturbance to the gravitational acceleration at the ~0.5 mGal level.

Viscoelastic relaxation processes in the Moon interior affect the tidal response by introducing a frequency dependence of the tidal processes and a lag between each tidal harmonic and the corresponding response, which is directly related to dissipation of tidal energy into the Moon mantle [see, e.g., 135]. While the frequency dependent effects are generally small compared to the elastic response, precise observation of the amplitudes and phase lags at different tidal frequencies would provide an indirect probe into the rheology and the structure of the Moon interior [136, 137].

Deformation of the lunar ground due to temperature changes can introduce excess noise in horizontal displacement measurements. Even in permanently shadowed crater floors, thermo-elastic stresses from the crater rims are present and will lead to long period motion and tilting of the ground. The amplitude of these changes is fundamentally unknown. Mars InSight found a tilt of 10⁻⁶ rad and a horizontal acceleration of 5 · 10⁻⁹ m/s² during a partial Phobos eclipse, which reduced the surface temperature in 1 m distance by 2 K over 10s [138]. Scaling this to the lunar PSR environment with 200 K temperature changes in 100-meter distance will produce horizontal signals of > 50 pm/s² at long periods. However, this is expected to be a function of the subsurface rigidity.

### 2.3.5 Seismic background noise

*Main contributors:* Matteo Di Giovanni, Jan Harms, Hrvoje Tkalcic, Marco Olivieri, Lucia Zaccarelli

The SBN might limit the sensitivity of LGWA at frequencies above 0.1 Hz [13], and this is a central part of the studies in preparation of the LGWA technical design and of the mission planning. The SBN is also one of the main targets of investigation with the LGWA pathfinder mission Soundcheck (more details in section 2.4). Most of our current knowledge of the lunar SBN comes from the Apollo missions as described in the following.

Using the data collected by the Apollo Lunar Surface Experiments Package (ALSEP) between 1969 and 1977 mainly from 4 long-lasting seismic stations, an experimental upper limit to SBN was set at about 10⁻¹⁰ m Hz⁻¹/² between 0.1 Hz and 1 Hz, corresponding to the instrument noise of the Apollo seismometers [36, 139]. A modeled estimate of the SBN was
set at about $2 \times 10^{-14}$ m Hz$^{-1/2}$ at 1 Hz [15], which is a full 6 orders of magnitude weaker in amplitude than the terrestrial SBN (depending on frequency). According to ALSEP, there are four distinct categories of natural seismic sources that contribute to the overall SBN: deep moonquakes, shallow moonquakes, thermal moonquakes and meteoroid impacts [140].

With more than 7000 events recorded [140, 141], deep moonquakes (DMQ) are the most abundant among all seismic events and occur at depths about halfway between the surface and the center of the Moon, with most of the energy below 1 Hz and an equivalent body-wave magnitude typically less than 3. Their occurrence was found to be strictly correlated with the tides raised by the Earth and the Sun [140]. Deep moonquakes were also found to be highly clustered, occurring repeatedly within 300 separate source regions, or nests, 100 of which have been precisely identified [141, 142], each nest having dimensions of 2 km or less [142, 143]. As a consequence of occurring repeatedly at nearly the same place, DMQ have almost identical waveforms for a given source region and at a given station [140, 142]. In practice, this means that the separation of the moonquakes sources is smaller than the typical wavelength at which the waveforms are observed. These nests follow a distribution that supports depths in the 700–1200 km range and are unevenly distributed in the nearside with only a few of them in the farside [42, 140–142]. The most active nest, identified as $A_1$, counts more than 400 recorded events in the years 1969–1977 [143, 144].

The lack of nests on the far side is still a matter of debate whether it is due to an actual absence of seismic activity on the antipodal region, due to the seismic waves propagation mechanism in the interior of the Moon or due to the failure to identify them [142]. Nevertheless, little progress has been made since then. With time, only 30 nests have been attributed to the far side, but none of them far enough into the far side to gather relevant information about the Moon's interior. This suggests that the area near the antipode could well be aseismic, or the structure of the deeper interior of the Moon is such that no seismic waves will propagate straight through it to get recorded on the near side [142].

To date, the exact origin of DMQ remains unclear, and the presence of fluids [145] or partial melts [141] in the Moon's interior has been hypothesized. Recently [146], it has also been argued that tidal stress not only triggers the deep moonquake activity but also acts as a dominant source of excitation, with calculated tidal stresses that are strongest in the 600–1200 km depth range, which overlaps with the range of estimated deep moonquake hypocentral depths [42, 147].

The most frequent contribution to the overall SBN, along with deep moonquakes, are the signals generated by the impacts of meteoroids on the surface of the Moon [140, 144, 148]. Between 1969 and 1977, the ALSEP recorded about 1700 impacts. Contrary to moonquakes, which can be observed only on seismic traces, meteoroid impacts have also been detected indirectly using Earth-based observations [149], allowing for more precise studies about their rate and spatial distribution to assess the risks associated with working on the surface on the Moon and to interplanetary journeys. If recorded by orbital cameras, the impact locations can serve as Ground Truth locations for calibrating seismic studies of moonquakes and lunar interiors.

Using Apollo 14 short period seismic data, [150] released a mass-dependent meteoroid flux estimate between $1.1 \times 10^{-4} \text{ hr}^{-1} \text{ km}^{-2}$ and $1.1 \times 10^{-7} \text{ 1/(hr km}^2)$. Ref. [151] completed
the picture using long-period seismic data issuing a rate between $1 \times 10^{-7}$ 1/(hr km$^2$) and $1.1 \times 10^{-9}$ 1/(hr km$^2$). These figures were also dependent on the estimation of the distance at which the events occurred as inferred from the seismograms and were accompanied by the huge uncertainties in the seismic efficiency of the impacts. In 2014, NASA's Meteoroid Environment Office (MEO), after seven years of Earth-based impact flash observations and the validation of 129 events, released the first estimate of the impact rate which was found to be $7.00 \times 10^{-8}$ 1/(hr km$^2$) [152]. Between 2018 and 2020 [153], Near Earth Orbit Lunar Impacts and Optical Transients (NELIOTA) detected 79 events with a rate of $2.05 \times 10^{-7}$ 1/(hr km$^2$) for sporadic events and $3.9 \times 10^{-7}$ 1/(hr km$^2$) for events during meteor showers. The combined rate was found to be $2.3 \times 10^{-7}$ 1/(hr km$^2$). Measured kinetic energies of impacts span between $10^6$ J and $10^9$ J, corresponding to a mass range from $1 \times 10^{-4}$ kg to 8 kg [152, 153]. Nevertheless, estimations of the mass and energy of an impactor are subject to a certain degree of uncertainty caused by the assumptions on its velocity and on the efficiency with which impact energy is converted into luminous energy [152, 153]. Among the other significant results from these new impact observations, there is evidence of a difference between 10%–20% in the impact rate measured for equatorial and polar regions. Presently, it is not clear whether this depends on the actual distribution of meteoroids in space or on the difficulty of detecting light flashes in the polar regions [153].

Concerning the morphology of the seismic signals generated by impacts, seismograms recorded by ALSEP show two distinct parts, high-frequency, and low-frequency components [150]. This work suggested that the high-frequency part could be associated with body wave energy while the low-frequency part contains mostly surface wave energy.

The third category of seismic events recorded on the Moon are shallow moonquakes [140, 144] which are rare (only 28 recorded in the ALSEP data) and larger than DMQs, with equivalent body wave magnitude between 3.6 and 5.8. Overall the estimated depth lies between 0 km and 220 km [144]. Shallow moonquake spectra include high-frequency content of up to 8 Hz, while DMQs contain less seismic energy above 1 Hz. Energy for the shallow moonquakes continues up to about 8 Hz and then rolls off. No correlation between shallow moonquakes and the tides has been observed. Important for the modeling of the lunar GW response is that moonquake observations point to very low attenuation corresponding to Q-factors of a few 1000 (see section 2.1.4).

The fourth class of seismic events is thermally triggered. Ref. [154] showed that the majority of the many thousands of seismic events recorded on the short-period seismometers were small local moonquakes triggered by diurnal temperature changes. More recently, [155] found and categorized 50,000 events recorded by the Lunar Seismic Profiling Experiment at Apollo 17. The events occurred periodically, with a sharp double peak at sunrise and a broad single peak at sunset. The origin of these events might be stress release in the ground, by the lander or payload. It is essential to the functioning of LGWA to avoid the SBN of thermal events, which is why deployment in a PSR with strongly reduced thermal gradients and fluctuations is expected.

It is also critical for the planning of LGWA to continue past efforts on the numerical modeling and simulation of the SBN [15]. Simulations of the lunar seismic field in a 3-D mesh are under preparation. They consider the shallow structure, the regolith layer, and
<figure><img src="image_24.png" /><figcaption>**Figure 21.** Sketch of the plasma and magnetic environment around the lunar orbit.</figcaption></figure>

the topography of potential LGWA deployment sites. This will give information about the expected noise level at the deployment site but also about the noise correlation between different nodes of the array, similar to what was done for the Einstein Telescope [156]. New advances in seismic inter-source correlation are also promising tools for imaging the deep lunar interior and confirming the existence of its deep layers. Through the reciprocity principle, the moonquakes are turned into virtual receivers, while the locations of the seismometers become virtual events [157, 158]. Seismic correlations are a key property for the design of the LGWA LIGS array in terms of its diameter and shape, and to predict by how much the impact of the SBN on the GW measurement can be mitigated by optimal filtering of the data (see section 2.1.3).

### 2.3.6 Magnetic fluctuations on the lunar surface

*Main contributors:* Yoshifumi Futaana

The electromagnetic field on the lunar surface is one of the key environmental factors that can be important for LGWA [10]. Magnetic actuators will be used to control the position of the LGWA proof mass (see section 2.1.1), which introduces a susceptibility to environmental magnetic fields as well. Technological solutions such as magnetic shielding are possible to reduce the magnetic susceptibility of the proof mass, but it is first of all important to assess how much magnetic noise is to be expected in LGWA measurements without mitigation.

Because of the lack of the intrinsic, dynamo magnetic dipole field and extremely low electric conductivity, the Moon is, to the first order, *transparent* in terms of the electromagnetic field and its fluctuations. It means that the electromagnetic fields and waves propagate through the body, and thus, the electromagnetic and plasma environment on the lunar surface is expected to be similar to the near-moon space.

The Moon experiences several domains (different plasma and electromagnetic environments) as it goes around the Earth [159]. The principal domains are shown in figure 21. The Moon is in the solar wind for > 60% of the time. The solar wind is a supersonic plasma flow from the Sun, mainly composed of protons and alpha particles. While the electromagnetic
environment is relatively stable in the solar wind, the intrinsically unstable nature of plasma
excites various electromagnetic waves. Particularly because the proton cyclotron frequency
at 1 AU is approximately $\omega_g = \sqrt{eB/m} \sim 0.1$ Hz (where e and m are the charge and mass
of a proton and B is the magnetic field strength), the deci-Hertz frequency waves (ultralow
frequency (ULF) waves) are common near the Moon [160]. Wave activity is manifested in the
foreshock region [161], where the reflected solar wind protons by the terrestrial bow shock
co-exist with the solar wind plasma. These protons can reach the Moon, producing the ULF
wave in the near-Moon environment [162], typically when the Moon is located on the dawn
side of the Earth (the lunar phase around 18 to 23 days).

Sometimes, severe solar storms impact the Earth and the Moon, when significant temporal
disturbances are present in the Moon's environment. The disturbance may last several days.
In the magnetosheath (the downstream of the bow shock), a disturbed electromagnetic
environment is also present.

A specific feature in terms of the lunar surface magnetic field is magnetic anomaly [163].
It is a remnant magnetic field of crustal origin distributed patchily but globally. Each anomaly
has a spatial scale of 100 to 1000 km, with a strength of 100s of nano-Tesla (about 1% of the
Earth's dipole field). Despite its small scales (spatially and strength), the crustal magnetic
field can stand off the solar wind, preventing the solar wind protons from accessing the lunar
surface below the magnetic field ([164]; [165]). This structure is called mini-magnetosphere,
and is one of the main scientific topics for the lunar plasma environment ([166]).

The interaction between the crustal magnetic field and the solar wind produces a wealth of
electromagnetic disturbances. In particular, when the crustal field is located at the terminator
region (applied to the polar regions). A manifestation of the magnetic field has been reported
since the Apollo era (sometimes called limb compression) [167]. Recent numerical simulations
reproduced the limb compression signature when the mini-magnetosphere reflects the solar
wind protons back into space ([168]).

The reflected solar wind protons generate electromagnetic wave activities, relevant for
deci-Hertz wave activities due to the resonance with proton cyclotron motion. For example, the
reflected ions excite the whistler waves near the crustal magnetic field [169]. A global proton
reflection from the lunar surface also excites such wave activities [170]. In addition, [171, 172]
reports the magnetic wave activity around 1 Hz when the magnetic field is connected to
the wake of the Moon.

Almost all the observations are based on orbiters. While the Apollo surface payloads
had magnetometers on the lunar surface, there are only a few publications on the fluctuation
of the magnetic field on the lunar surface. Recently, an effort to recover the record of the
Apollo magnetometer data has been ongoing, and [173] reported ion cyclotron waves (with
frequency 0.04-0.17 Hz) detected by an Apollo surface magnetometer when the Moon is
inside the terrestrial magnetotail.

At the PSRs near the lunar poles, the local solar wind flows nearly tangential to the
surface and interacts with large-scale topographic features such as mountains and deep large
craters. On the leeward side of large obstructions, plasma voids are formed in the solar
wind because of the absorption of plasma on the upstream surface of these obstacles. A
surface potential is established on these leeward surfaces in order to balance the currents
<figure><img src="image_25.png" /><figcaption>**Figure 22.** Conceptual overview of a Soundcheck seismic station on a tilted surface on the lunar regolith. The sketch can be compared with the LGWA payload concept shown in figure 1.</figcaption></figure>

from the electron and ion populations. There are leeward regions where solar wind ions cannot access the surface, leaving an electron-rich plasma previously identified as an “electron cloud.” A balancing current is required at the surface, and lofted negatively charged dust was proposed as a compensating current source [174]. This charging mechanism was discussed in the context of safety of lunar operation at PSRs and might create a unique electromagnetic environment at the LGWA deployment site.

In summary, very few experiments to characterize the electromagnetic environment on the lunar surface have been conducted. Our knowledge of the electromagnetic environment is based on the measurements by orbiters (typically with altitudes of 10s to 1000s of km) or in the equatorial regions by Apollo magnetometers, e.g., [175]. The measurements near the south pole are highly required to characterize the electromagnetic fields and their fluctuations near the permanently shadowed region.

## 2.4 Soundcheck and other relevant lunar missions

*Main contributors:* Jan Harms, Matteo Di Giovanni, Alessandro Frigeri, Joris van Heijningen

**Soundcheck.** As shown in the previous sections, the planning of the LGWA mission requires detailed understanding of the lunar geophysical environment inside a PSR, which is not available today. A pathfinder mission is required, which was proposed to ESA in 2022 under the name *Soundcheck*. In addition to carrying out measurements of seismic surface displacement, magnetic fluctuations and temperature, the Soundcheck mission will also be a technology demonstration. An overview of the Soundcheck payload is shown in figure 22. Soundcheck is expected to reach sub-pm/Hz¹/² inertial sensitivity above 0.1 Hz and probe the SBN with unprecedented precision.
<figure><img src="image_26.png" /><figcaption>**Figure 23.** Minimum detectable inertial displacement for the Soundcheck using a 3 kg niobium Watt's linkage with an interferometric readout. More details in the text.</figcaption></figure>

The Soundcheck technology validation focuses on deployment, inertial sensor mechanics and readout, thermal management and platform leveling. The PSRs are as of now unexplored and a deployment strategy in the dark has to be developed. A Watt's linkage inertial sensor for a space application, including a release mechanism, is under development. All parts for (interferometric) position readout and electronics are heritage to be combined into the specific Soundcheck readout. Ambient cryogenic inertial sensing with room temperature laser and battery pack requires an R&D effort as well. Lastly, platform leveling has heritage in space application [176], but not yet in a cryogenic environment.

For Soundcheck a relatively simple approach without force feedback on the proof mass is employed. As the SBN is unknown it is challenging to design an optimal feedback loop and we therefore use multi-fringe readout with sub-pm/√Hz sensitivity. There are several options, such as homodyne quadrature interferometry [e.g. 177] and deep frequency modulation interferometry [e.g. 178]. While both are theoretically similar in performance [179], the homodyne quadrature interferometric readout is less computationally demanding and therefore preferred for Soundcheck given its more stringent power budget.

**Other Lunar missions.** Almost all of our understanding of the lunar seismic field and its sources comes from the Apollo Lunar Surface Experiments Package (ALSEP) starting with Apollo 11's PSEP [180]. In 2022, seismic data from the ALSEP have been re-organized and archived on the Incorporated Research Institutions for Seismology (IRIS) servers for easy access through the FDSN protocol [181] at the following DOI:10.7914/SN/XA_1969. The catalog of the seismic events recorded by the ALSEP, updated with new detections occurred during recent reviews of the data, can be found in the electronic supplement of [144].

Concerning Earth-based observations, there are currently two active collaborations, namely MEO [152] at NASA and NELIOTA [153] at ESA, that are monitoring meteoroid impact rates on the Moon. The main goal of these research groups is to understand the
spatial distribution of meteoroids near the Earth-Moon system. This can lead not only to a better understanding about the properties of the solar system, but also to predict the small-meteoroid flux that deteriorates space equipment, predict when the next large meteoroid will impact Earth itself and assess the risks for interplanetary journeys. The information about impact rates can also provide useful data about SBN. In March 2023, NELIOTA has also made publicly available an open source software for observatories to detect meteoroid impact flashes on the Moon.

In 2022, ESA approved the Lunar Meteoroid Impact Observer (LUMIO) mission [182]. The goal of LUMIO is to monitor meteoroid impacts by use of the same technique of Earth-based observatories, but on a 12U CubeSat structure on a halo orbit at the Earth-Moon L2 point. This is expected to guarantee a higher detection efficiency and reduce the false-alarm rate let alone providing data for the farside, thus complementing Earth-based observations. LUMIO is a consortium of European research institutes led by the Politecnico di Milano (Italy) and, as of mid 2023, is building its working groups.

Of great interest for LGWA is also the Farside Seismic Suite (FSS) [183], scheduled to land in 2025 on the far side, near the south pole in the Schrödinger basin. The FSS will deploy a vertical Very Broad Band (VBB) seismometer already developed for the Mars InSight mission and a short-period seismometer [129]. Being the first seismic station on the far side of the Moon, FSS will improve our understanding of the lunar interior, the processes that shaped the lunar crust and the current micrometeoroid impact rate. The sensitivity of the FSS VBB sensor will exceed the sensitivity of the Apollo seismometers by an order of magnitude up to 1 Hz and therefore provide important new information about the lunar SBN [11].

The concept of a Lunar Geophysical Network (LGN) was also proposed [184]. The LGN is aimed at advancing our knowledge about lunar and planetary science with the deployment of geophysical stations at four locations to enable long-term geophysical measurement with a complete instrument suite providing seismic, geodetic, heat flow, and electromagnetic observations. The details will continue to be optimized throughout the formulation of this mission that has been proposed for launch in 2030.

Important for LGWA are also missions to explore the PSRs such as NASA's Volatiles Investigating Polar Exploration Rover (VIPER). It is a robotic mission designed to explore the South Pole of the Moon in search of ice and other potential resources. The goal of the VIPER mission is to characterize the distribution and physical state of lunar polar water and other volatiles in lunar cold traps and regolith to understand their origin. VIPER is equipped with a number of instruments to help it achieve its goals, including a drill that can penetrate up to 1 m into the lunar regolith, a mass spectrometer that can identify and measure the abundance of various elements and compounds in the regolith, a radar system that can detect the presence of ice beneath the surface, and cameras that can provide high-resolution images of the lunar terrain. VIPER is scheduled to launch in late 2024 and land at the South Pole of the Moon in early 2025. It will then spend 100 days exploring the lunar surface, collecting data and returning it to Earth. The data collected by VIPER will be used to inform NASA's plans for future human missions to the Moon, including the establishment of a permanent lunar base.
# 3 Science objectives

## 3.1 Lunar science

The Moon being the test mass of the LGWA experiment, its elastic properties and the presence of a continuous lunar seismic background are fundamental to the LGWA performance. As explained in section 2.3, these properties of the Moon must be understood very accurately to extract the information from GW signals. As a consequence, LGWA enables studies of the nature and distribution of seismic sources (section 3.1.1), the Moon's internal structure (section 3.1.2), formation history (section 3.1.3), and geological processes (section 3.1.4).

### 3.1.1 Seismic sources

Main contributors: Taichi Kawamura, Hrvoje Tkalčić, Jan Harms, Sabrina Menina

The LGWA will be a unique contribution to a lunar seismic network for the study of moonquakes (see section 2.4 for other proposed lunar seismic stations). Together with its pathfinder mission Soundcheck, LGWA is still the only seismic experiment proposed for deployment inside a PSR, which is expected to enhance the quality of horizontal displacement data; see section 2.3.4. Its eight horizontal channels of the four-station array will enable advanced background reduction methods also for moonquake observations (see section 2.1.3). The superior sensitivity of its accelerometer — sub-picometer precision above 0.1 Hz (see figure 2) — will make it possible to observe weakest lunar seismic events. In the following, we outline our current understanding of lunar seismic sources and a possible role of LGWA for lunar seismology together with other future lunar seismic experiments.

Apollo seismic observation revealed that the Moon is still seismically active today. After about seven years of seismic observation on the Moon, more than 13000 lunar seismic events (known as moonquakes) were identified and cataloged [185]. The catalog has been constantly updated with state-of-the-art methods applied to the data [144, 186], and even today, new events are discovered from the data [e.g. 187]. The Moon has different types of seismic sources, including the endogenic ones. This opened a new question of where and how these seismic events are excited. This is one of the key open questions in lunar seismology and was listed as one of the science goals by Artemis Science Definition Team [188].

When mapping the global scale events distribution for the Moon, the seismicity on the lunar farside is less constrained. Both, the Apollo seismic network and most of the detected moonquake sources, were located on the lunar nearside [140, 142]. A minimal number of earthquakes on the lunar farside were identified, and it remains uncertain whether this is a result of the Apollo seismic network's limited coverage or if the farside is genuinely aseismic. Given the limited sensitivity of the Apollo seismometers, it is very likely that the network did not have, for the farside, the same detection capability as for the nearside, especially for small magnitude events that dominate the catalogue [e.g. 189]. On the other hand, global observation carried out after Apollo revealed that there is a clear dichotomy on the Moon, and there are significant differences in terms of internal structure between the lunar nearside and the farside [e.g. 190, 191]. These may result in variations of the seismicity rate and spatial distribution, and to elucidate this open question, new observation at different location
<figure><img src="image_27.png" /></figure>

**Figure 24.** From the left to the right: Deep moonquake, Shallow moonquake and Meteoroid impact lunar seismograms in compressed time scale at the Apollo 16 station. LPX, LPY, and LPZ are the three orthogonal components of a long-period instrument (two horizontal and one vertical), while SPZ is the short-period vertical component (from [140] John Wiley & Sons. Copyright (1982) by the American Geophysical Union).

from Apollo will be essential. The dichotomy on the Moon is one of the key question to understand the evolution of the Moon. Seismicity will inform us about the depth of the dichotomy, which serves as an important constraint on the crust/mantle formation.

**Moonquakes.** The different types of moonquakes are generally classified with their source depth and mechanism (see figure 24). The first type is deep moonquakes, which are most frequently observed seismic event on the Moon, and more than 7000 events were reported [144, 185, 186]. Deep moonquake sources are typically located at about 900 km depth (about midway between the lunar center and the surface) and are known to occur at fixed source regions called nests [140]. More than 100 nests have been identified and the notable feature is that their waveforms are almost identical for the same set of nest and a station. Thus, deep moonquakes are classified using the cross/auto correlation technique, which also helps us improve signal to noise ratio by stacking. Another interesting feature of deep moonquakes is that their occurrences are correlated with the Earth-Moon tides [140, 141, 186] resulting from the observation of a monthly periodicity of the occurrence. These events are relatively small events with magnitude of 1-2. There is a longstanding debate whether the tidal stresses are fully responsible of the occurrence of deep moonquakes or they are merely triggered as releases of the accumulated tectonic stresses [146, 147, 192, 193]. The challenge in the
discussion is that we have little constraints on the source parameters. Unlike on Earth, obtaining parameters as the source mechanism is challenging on the Moon. This is due to the intense scattering that masks the direct waves from the hypocenter that are necessary for gathering information of the seismic source itself [126]. Generally speaking, going to longer period will result in less scattering but this is not possible for the ALSEP dataset given the limited band width of Apollo seismometers. In addition to this, the small magnitude of deep moonquakes also makes the analyses difficult.

The second type of moonquakes is shallow moonquakes, which were rarely observed, with only about 30 events identified during the Apollo observation time. Though they are small in number, they are the most energetic events detected and thus have an important impact on the seismic moment release of the Moon as well as for seismic risk assessment for future lunar explorations. The seismic sources of shallow moonquakes are estimated to be at a depth of around 60 km and shallower than 200 km [126, 140]. Both studies approached the depth determination by modeling the amplitude variation with distance and coherently concluded that the hypocenter needs to be placed at depth while it is unlikely to be at the Moon's surface. Hence the name of shallow moonquake was given to this type. The source mechanism of shallow moonquakes is not very well understood. Unlike deep moonquakes, no clear correlation with tides nor periodicity were found and the occurrence seems to be almost random [194]. Watters et al. [195] points out that there is some tendency for shallow moonquakes to occur when the Moon is far from the Earth but this could not explain all the shallow moonquake occurrences. Watters et al. [195] also points out that some shallow moonquake sources are close to newly found lobate scarps and thus attributing the thrust fault to be responsible for the excitation of shallow moonquakes. However, this does not apply to the whole shallow moonquakes catalogue. This suggests multiple origins for shallow moonquakes with some shallow moonquakes excited by shallow thrust faults visible on the surface, and others, deeper, originating from blind faults not emerging at surface. In both cases, as for deep moonquakes, the main open issue is the source mechanism of shallow events which remains poorly constrained. Better understanding the source and nature of shallow moonquakes will shed new light on the dynamics of the Moon and its tectonics, and it will also be informative to evaluate the seismic risk of the Moon.

The third type is meteorite impacts. The Moon is an airless body and is constantly bombarded by meteorites impact with wide range of size from micrometeorites, microscopic dust particles, to kg sized impactors falling on the surface which also generates impact flashes observable even from the Earth. Monitoring such impact events will give us information on current impact rate of the Earth-Moon system. Similar observation would also be possible on Earth but small impactors are likely missed while filtered by the atmosphere. This broad range of observations complements the study the impact rate for the Earth-Moon system with a further dataset. Impact rate assessment is also interesting to better understand the environmental risk for lunar based activities since even small impactors can create significant risks for future human activities on the Moon. At the same time, it is also important to understand how the impact rate evolved with time and its spatial distribution. Le Feuvre and Wiczorek [196] showed that the impact rate is not uniform on the lunar surface and depends on the latitude and longitude due to relative velocity between the impactor and the
revolving Moon. Kawamura et al. [189] confirmed this hypothesis from seismically detected impacts and pointed out that the larger heterogeneity for the smaller impacts implies that their sources are comets, whereas the sources of large impactors originate from asteroids. Information on the source will be informative to better predict the impact environment and the risk on the Moon both in terms of temporal and spatial variations. Moreover, as pointed out in section 2.3.5, impacts are expected to be the prevalent source of background seismic noise for the Moon. So, rate and spatial distribution are key aspects for the prediction and assessment of the expected background noise and its variability over time.

These three main types of moonquakes are all related to key questions in lunar and planetary science. However, the Apollo seismic data has not been sufficient to answer these questions and new observations made in new locations and with state-of-the-art, high performance instruments will be mandatory.

**Detection of exotic particles.** Among the large number of exogenic events, mostly produced by meteoroid impacts, a few detectable events might be associated with fundamental particles. The interaction of particles with the Moon can be similar to impacts, e.g., in the case of ultra-high-energy cosmic rays or the hypothesised Strange Quark Nuggets (SQNs) [197, 198]. The ability of some particles to penetrate the ground makes it possible to distinguish them from meteoroid impacts. Other forms of matter, like the hypothesised Ultralight Boson Dark Matter particles (UDMPs), would have a lasting interaction with the Moon. UDMPs are predicted to lie in a mass range between $10^{-22}$ eV and 0.1 eV. They would generate a monochromatic force acting on the Moon leading to vibrations that could be observed by an inertial sensor [199, 200]. Finally, the seismic signal of a small primordial black hole with mass of $10^{15}$ g traversing the Moon was studied [201], and primordial black holes of mass > $10^{19}$ g would form impact craters with a distinct morphology [202]. While all these scenarios are intriguing, it should be emphasized that interactions with the Moon would be very rare and even the existence of any of these particles is speculative.

### 3.1.2 Lunar internal structure

*Main contributors:* Angela Stallone, Lucia Zaccarelli, Hrvoje Tkalčić

Within the Apollo missions, ALSEP (Apollo Lunar Surface Experiments Package, [203]) data provided the first direct information on the Moon's internal structure. In particular, we have gained insights on the approximate thickness of its crust, mantle and core, as well as their elastic properties.

Similar to Earth's PREM (Preliminary Earth Reference Model, [204]), the one-dimensional model characterizing Earth's average properties in terms of seismic velocities, density, and attenuation as a function of depth, seismic data analysis resulted in a lunar equivalent model known as VPREMOON (Very Preliminary Reference Moon model) [108]. This model has been recently updated through a thorough review of seismic data and events [42, 144].

In VPREMOON, the mantle and crust velocity structure are defined to match geodetic (lunar mass, polar moment of inertia, Love numbers) and seismological data (direct and secondary P- and S-wave arrival times). The crustal thickness was also determined to align with the results from receiver function analyses, which provide a more direct indication of the
<figure><img src="image_28.png" /><figcaption>**Figure 25.** P-wave velocity (left), S-wave velocity (center), and density (right) profiles from the Moon's surface to the core (identified in red in the middle panel) for several seismic velocity models. Data used for generating these plots are from [42]. Reproduced from [10]. © The Author(s). Published by IOP Publishing Ltd. CC BY 4.0.</figcaption></figure>

mantle-crust boundary below the station [205, 206]. VPREMOON integrates knowledge from prior research and physical constraints into a comprehensive framework, serving as the primary reference model for the Moon's interior. The crustal model — P-, S-velocity and density profiles up to a depth of 30 km — is extracted from the seismic model determined by [207]. The lunar 'Moho' discontinuity (the crust-mantle interface) is set at a depth of 40 km [208] to fit geodetic observations. This, in turn, imposes a constraint on the density contrast between crust and mantle, resulting in about ~0.55. In maintaining a homogeneous lunar mantle mineralogy to match the absence of significant P- and S-velocity variations and using a model of the internal temperature field, the mantle density profile can be constructed [209].

The average reference model of the Moon describes physical properties, including core radius and density. A core radius of 380 ± 40 km and an average core mass density of 5200 ± 1000 kg/m³ were found. This considerable uncertainty arises from limited constraints on the S-wave velocity profile at the base of the mantle and inaccuracies in deep moonquake location data.

Several velocity models for the Moon, derived from the inversion of P- and S-wave arrival times, are available in the literature. They are depicted in figure 25, which also features the VPREMOON model by [108], represented in cyan. These models are overall consistent up to a depth of ~1200 km. At larger depths, uncertainties become too high and additional data (e.g. geodetic and electromagnetic sounding data), as well as a priori information, are included to constrain the velocity profiles. Variations in the inverted profiles primarily result from differences in the inversion technique and model parameterization. Beyond depths of 1200 km, differences primarily stem from the type of complementary information used. Over the course of different Apollo missions, more than 13,000 seismic events were recorded, although only a subset of them — those with the best signal to noise ratio and clear P and S identification — were used to infer the lunar internal structure.
In addition to seismic waves, also normal modes of the Moon can provide information about its internal characteristics. These free oscillations refer to a standing wave that form when a dynamic system, as for the case of planetary bodies, is excited. These oscillations manifest as long-period signals capturing a body response to an excitation. Each normal mode is characterized by a distinct vibrational pattern and a unique frequency. Then, the specific set of normal modes for any planetary body is determined by its size, composition, density distribution, and material properties. Consequently, studying normal modes can provide valuable information on its one-dimensional layered structure along with its physical properties. While normal modes are generally excited by earthquakes on Earth, on the Moon, their primary source are moonquakes, along with contributions from thermal stress and tidal forces. Since normal modes are insensitive to the specific excitation source, they serve as an ideal tool for investigating the Moon's interior. This is particularly advantageous because the precise timing and locations of all meteoroid impacts are not accurately known. Ref. [210] inverted lunar normal modes recorded by the Apollo instruments to gain new insights into the Moon's interior. However, Gagnepain-Beyneix et al. [207] raised doubts, demonstrating that the normal modes utilized by [210] fell below the instrument noise. The high signal-to-noise ratio of the GW detectors and the advanced noise-cancellation techniques pursued for LGWA will enable noise-free normal-mode observations, providing a new valuable source of information for the Moon's interior. Similar advancements have already been demonstrated for Mars (see [211]).

Similar to Earth, the main source of data to probe the Moon's interior is seismic data. However, the Apollo seismic dataset had limitations due to a narrow observation band, and stations being located only on the Moon's near side. These limitations limit our capability to gain a comprehensive understanding of the Moon's internal structure.

There is currently a renewed interest in lunar exploration within the scientific community, evident in the extensive list of planned lunar missions. Several of these missions include the deployment of seismographs on the lunar surface as part of their objectives, with LGWA and its pathfinder mission Soundcheck being two of them. This development promises to deliver new seismic data of exceptional quality and broader frequency coverage in the coming years. As a result, we are on the cusp of a new era in the exploration of the Moon's interior, with the potential for significant discoveries and insights into its inner structure.

One could argue that the number of seismographs will still be too small, thus limiting the sampling of the Moon's layers and making inferences more challenging than for the Earth. A recent paper by [158], however, demonstrates the feasibility of utilizing even a single seismograph for probing planetary interiors through global-scale moonquake coda cross-correlations between seismic events. This methodology has already proven successful in the study of Mars interior [157], and we propose to apply global-scale waveform cross-correlations to lunar seismic data as well, taking advantage of the forthcoming high-quality seismic data. Particularly, the lunar events' codas are expected to be significant due to the Moon's smaller size and relatively small attenuation compared to Earth. Moreover, the two horizontal components of ground displacements will allow the application of other techniques aimed at the Moon interior's exploration like receiver functions or seismic noise interferometry [212]. In particular, the latter has been already applied to the higher frequency
ALSEP data [139], making it possible to describe the very shallow layers, but lowering the frequencies will provide an image of the Moon's deeper structure.

### 3.1.3 Moon's formation history

Main contributors: Alessandra Mastrobuono Battisti, Matteo Di Giovanni

The Moon's internal structure and its formation history are closely interconnected. The presence of a distinct core suggests that the Moon was formed in a hot, violent event, such as a giant impact. The composition of the mantle and crust aligns with the concept that the Moon was once a molten body that cooled and differentiated. Insights into the mechanism that formed the Moon can be inferred from considerations such as the amount of differentiation, iron content, and the relative size of the core compared to the other layers. The analysis of the characteristics of seismic waves can provide information on the energy released during the formation process and refine the timeline of events that shaped the Moon.

Our understanding of the Moon's internal structure has been greatly enhanced by data collected from the Apollo missions, which returned samples of rocks and soil from the lunar surface. These data, along with seismic observations and studies of the Moon's gravitational field, have provided insights on the Moon's composition and the arrangement of its different layers.

In this context, LGWA might be the first lunar mission to observe distinct lunar normal modes excited by moonquakes, which would provide important data on the deep lunar internal structure. At the same time, site effects on seismic signals provide information about the Moon's shallow structure. The study of the lunar interior with LGWA is outlined in section 3.1.2.

This is important because the Earth-Moon system is unique in several ways, including the Moon's size relative to Earth, its small core, and the high angular momentum of the system. Different theories for the Moon's origin, including capture, fission, co-accretion, and a giant impact have been explored so far [213-215].

The giant impact theory, first proposed in the mid-1970s [213, 214], is currently the prominent one, due to its ability to explain several key features, as shown by [216, 217] and [218]. In this scenario, the Moon forms as the result of a relatively low-velocity, oblique impact between the proto-Earth and a planetary embryo of mass similar to Mars, called Theia, occurring during the latest stages of the formation of the Earth, approximately 4.5 billion years ago [219, 220]. Simulations indicate that, following the impact, a significant portion (≥ 60%) of the material that forms the Moon originates from the impactor mantle. Therefore, the composition of the Moon is expected to mirror that of Theia, which, in principle, should differ from Earth, as observed with other planets in the solar system. However, analysis of lunar samples returned from the Apollo missions revealed an exceptional degree of isotopic similarity between the Earth and the Moon.

The oxygen isotope composition, a proxy for overall Moon composition, shows a difference $\Delta^{17}O = 12\pm3$ ppm [221] compared to Earth. This difference might be even smaller ($1\pm5$ ppm), as recently found by [222] analysing different rock samples. In contrast, Mars has a much larger isotopic difference, $\Delta^{17}O = 321 \pm 13$ ppm [223]. The isotopic composition of the lunar
<figure><img src="image_29.png" /><figcaption>**Figure 26.** A cartoon picture representing the giant impact scenario (top panel), the multiple impacts scenario (middle panel) and the “synestia” model (bottom panel). Image credits are provided on the sketches. Published in Let's Talk Science [226]. Reproduced with permission from [226].</figcaption></figure>

and terrestrial mantles is indistinguishable also in terms of other isotopic ratios, including $^{50}$Ti/$^{47}$Ti [224], and $^{182}$W/$^{184}$W [225]. This unexpected similarity gave rise to what is referred to as the “isotopic crisis”, challenging the conventional giant impact theory.

One possible solution to this challenge is that Theia and proto-Earth formed at similar distances from the Sun, i.e., from material of similar chemical composition. Various studies have explored and tested this hypothesis by tracking the composition of Earth and Theia in large sets of solar system formation simulations. While [227, 228] found this to be a low-probability event, [229, 230] have demonstrated how late giant impacts frequently occur between a proto-Earth and a last large impactor of approximately identical composition, offering a plausible solution to the giant impact challenge. This finding implies that the resemblance in composition between the Earth and the Moon may naturally arise as a consequence of a late giant impact.

In addition, several variations of the giant impact scenario have been proposed to reconcile the theory with observations. Those include a hit-and-run impact with an even more massive impactor [231, 232], an impact between two proto-planets of comparable masses [233], impacts with a fast-spinning proto-Earth [234], multiple impacts [235] and other more complex scenarios leading to a “synestia”, that is the vaporization of all material involved in the
impact that settles into a torus to then evolve in the Earth-Moon system [236]) (see figure 26⁸ for a representation of the different models).

All these scenarios aim to achieve a significant mixing fraction between proto-Earth and Theia material, intending to address the challenge associated with the Earth-Moon composition similarity. However, each scenario is influenced by the need for ad hoc assumptions (e.g. the necessity to quickly dissipate a large amount of angular momentum) and the inherent low probability that characterizes them (for instance, the probability of having an impact between two bodies of the same size is extremely low, see e.g. [230]). Despite numerous proposals, no individual or combined scenarios fully meet all Earth-Moon system constraints. Further studies, encompassing a broader range of parameters and addressing concerns related to angular momentum, isotopic constraints, and disk masses, are essential to comprehensively understand the formation of our satellite. However, different scenarios leave different signatures in the internal structure and composition of the Moon and the Moon's internal structure and its formation history are closely interconnected.

In all scenarios involving an impact to create the Moon, it is believed that this event generated sufficient heat to form an initially predominantly molten Moon from the materials involved in the impact. As this magma ocean cooled, different minerals crystallized and sank or floated to different depths, depending on their density. This process of fractional crystallization led to the formation of the Moon's distinct layers. As mentioned above, seismic data from LGWA will be instrumental in mapping these layers and understanding their composition, density variations, and structural characteristics.

Moreover, seismically detected anomalies have indicated the presence of relics of Theia in the Earth's mantle, offering constraints on the giant impact scenario [237]. Seismology of the Moon conducted with LGWA will likely yield similar results, exploring the lunar mantle and potentially providing future insights into its structure and the presence of primordial anomalies related to its formation mechanism. The detection of unexpected structures or materials will indeed serve as a test for existing theories or will help to refine them, offering a more comprehensive understanding of the Moon's formation and the role of specific impactors.

In conclusion, the formation of the Moon remains an open question, and seismic data from LGWA will be crucial in exploring the internal structure and composition of our satellite, providing important constraints on the various formation scenarios.

### 3.1.4 Geologic processes

*Main contributors:* Francesco Mazzarini, Goro Komatsu, Luciano Zuccarello, Alessandro Frigeri

The main geological processes on the Moon are impact cratering and regolith gardening [238], volcanism [239], mass-wasting/landslides [240], and tectonics.

The interpretation of composition and morphology of the Moon suggests that effusive and explosive volcanism took place in the past [239]. Radio-isotopic dating of first returned lunar samples suggests a volcanism age between 3.1 to 3.8 Gyr ago [241], while recent volcanic

<footnote n="8">⁸The cartoon image of the Moon formation scenarios is from https://letstalkscience.ca/educational-resources/backgrounders/origin-earths-moon.</footnote>
rocks sampled by Chang'e 5 show younger ages, of about 2 Ga [242]. While there is no evidence for active volcanoes on the surface of the Moon, this does not exclude the presence of magmatic bodies at depth.

Tectonics on the Moon are studied through charaterization of inactive fault systems [243] and by investigating any possible recent activity [195]. Impact cratering and landslides are directly amenable to seismic observations with LGWA. Landslides are widespread on the Moon and have been generally considered old in the Lunar geologic record [244, 245]. Studies on recent tectonics [195, 246] are supporting the existence of recent mass wasting processes.

In the following, points 1 to 3 are about the contribution of the LGWA to the knowledge of the Moon's interior (see also section 3.1.2) in terms of the definition of mechanical layering and regolith formation process using the seismic array of LGWA as "seismic antenna". Points 4 to 5 are focused on the definition and analysis of the main tectonic processes in the area of the deployment site as well as on the cratering processes in terms of crater morphology and frequency.

1) The regolith represents the surface where the seismic array will be deployed in the LGWA experiment. The seismic LGWA array can be used as a seismic antenna that can investigate the seismic "velocity stratigraphy" of the site by analyzing the seismic noise [247, 248]. The "velocity stratigraphy" may provide information on the subsurface layering and the geometry of the bedrock-regolith interface. Moreover, the analysis of seismic-acoustic signals (e.g., [249]) of the seismic array in the near side polar region will likely provide new insights about the lunar seismicity (see also section 3.1.1) as well as its mechanical stratigraphy providing new clues about the issues of the cooling of the pristine Moon's crust [250].

2) Seismic noise cross-correlation applied at pairs of stations unveil information on the Earth's crust characteristics and their variations with time [251]. This noise-based methodology enhances the common features hidden in the seismic recordings coming from different stations. We would apply this methodology to implement new protocols and techniques to perform for retrieving information about the process of the continuous flow of micrometeorites that govern the resurfacing of the Moon landscape as well as the production and evolution of regolith.

3) The LGWA array configuration will guarantee us to analyze the kinematic properties of the seismic wavefield, based on the common waveform model (e.g., [248]). In particular, the array methods permit the estimation of the phase velocity and propagation azimuth of the analyzed signals. The array analysis will allow researchers to characterize surface waves in terms of dispersion curves, phase velocity, and their variability with depth. Through the use of a second array, it will be possible to better constrain the seismic source(s), especially in terms of depth, increasing the knowledge of the Moon's interior. In particular, the detectable frequency band of the seismic antenna depends on the sensitivity of the sensors and on the maximum inter-distance between the nodes of the antenna [249].
4) Morphological and structural analysis along with crater counting may be performed at the LGWA site. The regolith production is mostly due to impacts and the amount of regolith produced is somehow linked to the size of the crater (see chapter 2.4.4 Regolith Composition; [114]). Thus, these studies about the cratering size distribution and craters' morphology may provide new data for modeling the production rate of regolith and a possible estimation of the regolith thickness in the LGWA site and its surroundings.

5) The geological, morphological, and structural studies of the site of the LGWA will provide information on the deformation style of the area (compression vs. tension/strike-slip). The spatial distribution and the patterns of the structures in the area (for instance, the wrinkle ridges, and grabens) are linked to the mechanical layering of the crust (e.g., [195, 252–254]). Cooling and tidal despinning of the Moon suggest a tectonic model inferring compressive tectonics in the equatorial zones, strike-slip tectonics in the middle latitude belts, and extensional tectonics at the poles [255, 256]; the seismicity detected by the LGWA array may thus be used for better constraining this tectonic model. Additionally, LGWA observation may provide information about the complex relationships between tectonism and volcanism, which are for the moment inferred mostly from the surface geology [257].

## 3.2 Gravitational-wave science

The LGWA will observe GWs at frequencies from 1 mHz up to about 1 Hz, which makes it the sought-for missing link between the space-based detector LISA and future terrestrial detectors like the proposed ET and CE. No other GW detector can observe astrophysical events that involve WDs like tidal disruption events and SN 1a (sections 3.2.1 and 3.2.2). Only LGWA can observe IMBH binaries in the early Universe and understand their role in the formation of today’s SMBHs (see section 3.2.2). Only LGWA can provide early warnings weeks before the mergers of solar-mass compact binaries formed by NSs and BHs together with excellent sky localization (section 3.2.3). The observation of DWDs with precise estimation of their luminosity distance and having identified their host galaxies with known redshifts will provide a new and independent approach to measure the Hubble constant (section 3.2.3). Especially LGWA’s unique role as partner for multiband observations of GW sources together with terrestrial detectors (or space-based if present) enables a new level of precision in waveform measurements and searches for imprints of a new fundamental physics (section 3.2.4).

### 3.2.1 Astrophysical explosions and matter effects on waveforms

*Main contributors:* Alexey Bobrick, Martina Toscani, David Vartanyan, Tsvi Piran, Jan Harms, Suvodip Mukherjee, Sourav Roy Chowdhury, Aayushi Doshi, Suraj N K, Trisha V, Kiranjyot Gill

The decihertz band harbors signals from a multitude of astrophysical processes not accessible to the currently operating GW observatories. Their detection would transform the study of these objects. However, the GW signatures of many astrophysical objects are either uncertain or unknown, making it harder to estimate their expected rates and the
information one might extract from the signals. If no significant improvement of the models is made, it would be harder to detect and analyze the signals. With this caveat in mind, however, thanks to the diversity of the potentially observable sources, some will likely be observed during the mission lifetime, possibly in conjunction with EM observations, this way significantly impacting the respective fields. We also note that the rates of individual detectable astrophysical events are sufficiently low so that no complication from overlapping waveforms is expected. Below, we review the most likely such sources.

**Stellar mergers.** Stellar mergers are a prominent example where GWs may inform us about physical processes. The LGWA has the unique capability to observe WD/WD mergers. In the Galaxy, these mergers happen at a rate of about 3 times per century [258]. However, specifying the properties of two white dwarfs, it is currently not yet established with certainty what specific outcome their merger may produce [259–261]. The complexity arises because the nuclear detonation or deflagration conditions are extremely hard to resolve in simulations [262–264]. They also have a strong sensitivity to the geometry of the merger and the composition profiles, and yet, they play a decisive role in the outcome of the merger [265, 266]. In addition, these processes happen during the fairly complex gravitational interactions of the two stars [259, 267]. Moreover, following the onset of deflagration or detonation, the exact nucleosynthesis in the white dwarfs is also challenging to model [268, 269].

There are multiple classes of astrophysical transients and outcomes known to be produced by double white dwarf mergers [270]. As an example, it is known that some double white dwarf binaries may detonate fully and lead to bright supernovae such as normal SNe Type Ia, 91bg-like SNe, SNe Type 91T, or Super-Chandrasekhar SNe ([271], see also section 3.3.2). They happen at a Galactic rate of approximately 6 times less frequent than all DWD mergers, i.e., once per about two centuries [258]. However, due to their energetic nature, their GW signal is likely to be brighter [272]. Therefore, while it still remains to be studied, LGWA may potentially see such events extragalactically and hence more frequently. Similarly, some white dwarf binaries may experience a weak detonation and produce Ca-strong SNe, SNe Type Iax, 08ha-like SNe [271], with their deci-Hertz band GW signal being uncertain. In some other binaries, the ignition may be even more gentle, leaving behind remnants such as another, more massive, white dwarf, an sdB star or an RCorBor star [259]. The latter has been recently constrained to happen between once per 200–1000 years in the Galaxy [273]. LGWA observations may be transformative for our understanding of such events. Identifying the connection between the progenitor white dwarf masses and the transient event they produce would dramatically improve our understanding and modelling efforts for these systems. Moreover, deci-Hertz GW observations may be the only way of probing what happened to the binary material in the first seconds following the detonation, in particular shedding light on the fate of the surviving object and the physics of explosion. The main caveat in this regard is the relatively low rate of double white dwarf mergers in the Galaxy and the local universe, as well as the uncertainties related to their GW signal.

Less explored avenues involve the physics of mergers of white dwarfs with neutron stars, stellar black holes [274, 275] and intermediate-mass black holes [276]. WD-NS mergers, in particular, happen at Galactic rates of about once per few thousand years [277, 278], but would be observed more frequently if extragalactic events were detectable. Specifically
<figure><img src="image_30.png" /><figcaption>**Figure 27.** Top panel: 3-dimensional magnetohydrodynamic simulation of the merger between a 1.4 M☉ neutron star and a 1 M☉ carbon-oxygen white dwarf companion, as presented in [282]. Panels (a)–(j) depict density slices in the orbital plane, starting from the beginning of the simulation (panel a) and continuing until $t=242$ s (panel j). Bottom panel: corresponding gravitational wave signal assuming a distance of 50 kpc. The left plot shows the strain versus time, while the right plot presents the characteristic strain versus gravitational wave frequency. Reproduced from [282]. CC BY 4.0.</figcaption></figure>

for extragalactic events, the EM signal for the event may allow one to search for the GW counterpart using waveform templates, potentially enhancing GW detectability. In all these cases, such mergers are expected to produce an optical transient event and are governed by a complex interplay of nuclear evolution, magnetohydrodynamics and radiative transfer, especially in the vicinity of the compact object, which is the dominant feedback source in such events [279–281].

Figure 27 represents an example of the evolution of GW strain over the last ~250 seconds prior to the merger of a 1.4 M☉ NS with a 1 M☉ carbon-oxygen WD companion, as modeled within the 3-dimensional magnetohydrodynamic framework [282]. The simulation covers the last 100 seconds of the inspiral and ~150 seconds after the disruption of the WD. Contrary to
the “chirping” GW amplitude expected for NSNS or BHBH binaries (e.g., [283]), this example does not exhibit a chirp prior to the merger. However, small oscillations are noticeable, attributed to the binary’s eccentricity in the final stages before the merger (figure 27, panel a). The GW emission diminishes abruptly shortly after the tidal disruption of the WD. The authors estimate that the merger would not significantly contribute to the signal-to-noise ratio; thus, the inspiral phase will dominate the observed signal [284].

**Gravitational waves from tidal disruption events.** Tidal Disruption Events [285–288] occur when a star of mass and radius ($M_*$, $R_*$), orbiting a MBH of mass $M_\bullet$, is torn apart by the MBH tides which overcome the stellar self-gravity. After the disruption, roughly half of the stellar debris is expected to circularize around the MBH and eventually form an accretion disc. These occurrences lead to multimesenger emission, including GWs, electromagnetic radiation, and neutrinos, offering a comprehensive view of the event from the initial disruption to the later stages (see section 3.3.3 for further details).

In order for a star to be disrupted by the MBH, it needs to be in a region of the phase-space called *loss cone*. In terms of angular momentum, the loss cone is defined as [289]

$$L_{lc} \approx \frac{2GM_{\bullet}R_t}{\beta}, \qquad (3.1)$$

where $R_t$ is the tidal radius, i.e., the maximum distance from the MBH to have the disruption of the star

$$R_t \approx \left(\frac{M_{\bullet}}{M_*}\right)^{1/3} R_* \approx 2 \times 10^{-6} \text{pc} \left(\frac{R_*}{R_{\odot}}\right) \left(\frac{M_*}{M_{\odot}}\right)^{-1/3} \left(\frac{M_{\bullet}}{10^6 M_{\odot}}\right)^{1/3}, \qquad (3.2)$$

(see [290] for relativistic corrections to this formula) and $\beta = R_t/R_p$ is the penetration factor, that is the ratio between the tidal radius and the stellar pericenter. In reality, the exact extent of the disruption depends on the specific characteristics and internal structure of the star itself [see, e.g., 291]. In general, we can categorize three distinct cases: when $\beta \gtrsim 1$ the star experiences full disruption; when $\beta \approx 1$ the star undergoes partial disruption, possibly leading to quasi-periodic eruptions (e.g., [292, 293]; see section 3.3.5, for details); and when $\beta \lesssim 1$ no disruption of the star occurs.

The main channel responsible for TDEs is two-body relaxation. Two-body relaxation occurs when a stellar orbit is altered by the gravitational interaction with another star. In the steep potential of the MBH this interaction is typically weak, meaning the stellar trajectory is usually not significantly affected by this deviation (collisionless system). However, in high-density stellar environments like globular clusters and nuclear stellar clusters, the cumulative effect of numerous collisions can considerably impact the star trajectory (collisional system). As a result, a star may have its pericenter falling within the tidal sphere, increasing the likelihood of a TDE occurrence.

While so far TDEs have been detected mainly through EM emission, with the advent of space-based GW observatories we are on the verge of witnessing the first observations of GW-TDEs [56]. In particular, the most interesting scenario would be the case of a WD revolving around a light massive BHs ($10^3 - 10^5$). This system would in fact produce a GW signal, which could be a single burst in case of full disruption of the star or a more continue emission in case of periodic stripping [294, 295]. This emission would present peak frequencies
around the deci-Hz, that is the frequency window where LGWA is the most sensitive. The detection of such a signal, together with the electromagnetic and neutrinos counterparts of these sources, could be a decisive factor for a full characterization of these systems.

Let us focus on the burst emitted during the star disruption, arising from the time variation of the mass quadrupole of the black hole-star system. Analytical order-of-magnitude estimates for the peak amplitude and frequency of this signal read [296, 297]

$$h_{\text{gw}} \approx 2 \times 10^{-22} \beta \times \left(\frac{M_*}{M_{\odot}}\right)^{4/3} \times \left(\frac{R_*}{R_{\odot}}\right)^{-1} \times \left(\frac{M_{\text{bh}}}{10^6 M_{\odot}}\right)^{2/3} \times \left(\frac{d}{16 \text{ Mpc}}\right)^{-1}, \quad (3.3)$$

$$f_{\text{gw}} \approx \beta^{3/2} \times 10^{-4} \text{Hz} \times \left(\frac{M_*}{M_{\odot}}\right)^{1/2} \times \left(\frac{R_*}{R_{\odot}}\right)^{-3/2}. \quad (3.4)$$

From these formulas, we see that a typical scenario involving a Sun-like star disrupted by a $10^6 M_{\odot}$ MBH at a distance of 20 Mpc produces a strain around $10^{-22}$ with frequencies ranging from $10^{-4} \sim 10^{-3}$ Hz depending on how much close the star is to the MBH. For WD-TDEs instead, considering as typical parameters describing the star a mass and radius of $M_* = 0.5 M_{\odot}$, $R_* = 0.01 R_{\odot}$, we expect a similar strain $h \sim 10^{-22}$ but at higher frequencies $10^{-2} \sim 1$ Hz, due to the huge compactness of the WD. Hence, WD-TDEs emit GWs in a region of the frequency interval where LGWA is the most sensitive.

To produce GW-TDE waveforms we need to study this signal numerically. Toscani et al. 2022 [297] have started exploring the huge parameter space describing this emission, which is described by nine parameters: the MBH mass and spin, the mass of the star, the penetration factor, the eccentricity and inclination of the stellar orbit, the viewing angle, the orbital orientation parameter and the source distance. In their work, Toscani et al. 2022 employed PHANTOM, a general relativistic smoothed particle hydrodynamics code [298, 299] to simulate TDEs and calculate the resulting GWs. They have studied how different parameters affect the signal and started to collect the waveforms in a catalog. However, to be fully prepared for the first observations of TDEs, it is crucial to expand this collection of theoretical waveforms by exploring a wider range of scenarios and parameter combinations.

**Interactions in binaries.** Interactions in stably transferring binaries are also physically rich, and involve accretion disc physics, hydrodynamics, possible jet and outflow formation, and still poorly understood mechanisms of mass loss [300–303]. With GW observations, it may be possible to constrain the mass transfer rates in these systems, this way at least indirectly constraining the nature of interactions [304]. Coupling such observations with optical, X-ray and radio data may be particularly constraining for understanding the interaction physics in such binaries [305, 306]. For the Galactic sources, the timescales in the inner accretion disc match the LGWA band and, therefore, for sufficiently massive accretion discs, such observations may potentially be important [307, 308]. However, both the GW signal and the rates of detectable mergers need to be studied in detail.

Mergers involving bigger objects may appear too slow to produce a measurable signal in the LGWA band. However, the compact central cores of geometrically large objects may have much shorter and much more relevant timescales. For example, common envelope merger events of giants and compact stars that initially happen on year-long timescales have been recently shown to produce a measurable GW signal for LISA [281, 309, 310]. Similarly, in
mergers of massive main sequence stars, which take place on tens of minutes timescales, the geometrically smaller cores may merge on the factor of tens timescales shorter [311]. Such mergers are common in the Galaxy and, for example, Renzo et al. [310] estimate that between 0.1 and 100 sources are detectable by LISA during its mission lifetime, implying comparable rates for LGWA. For similar reasons, mergers of white dwarfs with main sequence stars or white dwarfs with the cores of red giants or stars of the asymptotic giant branch may be visible, although modelling of their GW signatures and LGWA detection rates is still necessary. Generally, we envision that GW signatures of all types of stellar mergers mentioned here need to be studied in detail.

Tidal interactions in highly eccentric systems may also have their unique GW signature. Such binaries form in hierarchical triple stellar systems [312, 313]. While the effective timescale of the periaston passage may be in tens of minutes timescale, the tidal oscillations induced in the tidally deformed stars may have a factor of several higher frequency harmonics. Potentially detecting such signals will be informative both of the tidal interactions and the triple stellar dynamics for systems containing tidally interacting stars. However, the GW signatures of these systems also remain unknown so far.

**Gravitational waves from helium flashes.** Another unique avenue is the detection of GW signature from the helium flash at the tip of the red-giant branch. The ignition of helium is expected to be off-center, exhibit non-spherical formation, and occur over timescales of tens to hundreds of seconds [314, 315]. Due to the complexity of the helium flash onset, limited attempts have been made thus far at nucleo-hydrodynamic modeling [316, 317]. Given these flashes occur deep within the center, GWs and neutrino observations may be the only way to constrain these events. While the Galactic rates of these events can be easily estimated as the formation rate of the red giant stars in the Galaxy [318], thus being approximately once per decade, their GW strain amplitudes are far from being understood, necessitating further research.

**Core-collapse supernovae.** In the last two decades, significant efforts have been made in investigating the GW emission from CCSNe (see [319–323] for recent reviews). Non-spherical explosions are required to produce GWs, which happens during three distinct phases: a) immediately at bounce (through time-dependent rotational flattening and post-shock convection, lasting tens of ms); b) the growing neutrino-driven turbulence (lasting 50–200 ms); and through c) PNS modal oscillations [319, 324–331]. These phases, characterised by GW emission in the ~100–1000 Hz frequency range, are accompanied by an additional low-frequency (≈50 Hz) signal, henceforth known as the GW linear memory [332, 333] (see also section 3.2.2) that is generated through aspherical, large-scale matter ejecta motions coupled with anisotropic neutrino emission [334–339]. The neutrino memory signal shows a more secular time-evolution than the matter component, which is due to the cumulative time-integral of the anisotropy-weighted neutrino luminosity [340]. Sustained turbulent accretion in more massive progenitors results in higher neutrino luminosities and generally more anisotropic explosions. As with the matter component, the neutrino component is more pronounced for delayed explosions of models with higher compactness [341].
<figure><img src="image_31.png" /></figure>

**Figure 28.** Gravitational-wave spectra $2\sqrt{f}|\tilde{h}(f)|$ for CCSNe with different stellar masses as a function of time projected against strain noise curves $\sqrt{S_n}$ for various GW detectors (adapted from [322]). The simulations, extending out to ~6 seconds after the bounce, are unable to constrain the spectrogram in the region 0.1–1.0 Hz. The sources are assumed to be at a distance of 10 kpc. Reprinted figure with permission from [322], Copyright (2023) by the American Physical Society.

Large-scale SN ejecta asymmetries (where jet-like structures may emerge) are expected (see e.g. [342–346]) and are seen observationally using spectropolarimetry [347–352], but their GW emissions are associated with frequencies that are beyond the LGWA observation band (100–1000 Hz) [353–356] (see also figure 28).

While recent simulations do not cover the decihertz band (see for instance [322] and figure 28 for 10 kpc event signals) the linear and nonlinear memory effects can lead to detectable GW signals below 1 Hz [338, 357]. In this way, even with LGWA, one would be able to study the GW emission generated by the neutrino processes [322, 337, 358]. As discussed above, the range >50 Hz primarily arises from matter asymmetries while the range <10 Hz carries information regarding the anisotropy of the neutrino emission. Although these frequency ranges may overlap in reality, they are, in principle, distinguishable. The polarization of the signal provides insights into the asymmetries of the event along with the orientation of the source with respect to the line of sight. Notably, a simultaneous detection of the low-frequency memory signal by LGWA and the high-frequency component by terrestrial detectors would offer an invaluable, unprecedented understanding of CCSNe. The memory signal would provide information about the progenitor star while frequencies above 100 Hz would provide insight into the newly formed PNS. Although the exploration of lower-frequency CCSNe signals and their detectability has only begun in recent years, significant progress has been made in extending simulations to several seconds post-bounce. The near-future goal of extending these simulations to tens of seconds holds promise for producing consistent results at low frequencies.
**Gravitational waves from relativistic jets.** The acceleration of a relativistic jet is another source of gravitational radiation [359–361]. The resulting GW signal is a memory-type signal, namely, they take the form of a step leaving a permanent deformation of spacetime after they pass. The detailed features of the signal depend on the acceleration (and possible deceleration) of the jet, on its overall duration and orientation relative to the observer [362–364]. The overall amplitude of the GW signal is, as expected on dimensional grounds, of order $GE_{jet}/c^4d$, where $E_{jet}$ is the energy of the jet and $d$ the distance of the source. The frequency is the smaller of the inverse acceleration time and the jet duration. Natural candidates for jet-GWs are long GRB jets whose typical energy is of order $10^{51}$ erg and typical frequency of order tens of deciHz. Short GRB jets are somewhat weaker and have higher frequency. As those are more frequent, it might be easier to detect. Most remarkable are hidden jets that take place in some powerful supernovae [365]. Those jets are choked inside supernovae and are difficult to observe directly. Their unique GW signature might enable us to confirm their existence. The energies of choked supernovae jets are comparable to those of long GRB jets [365]. As supernovae are much more frequent than GRBs it might be expected to detect these signals first [364]. In particular, the GWs from a powerful hidden jet in supernovae are likely stronger than the GWs from the collapse event itself. A Jet-GW signal from a galactic supernova will have a strain of $\gtrsim 10^{-21}$ in the frequency range of LGWA.

### 3.2.2 Populations and formation channels of GW sources

*Main contributors:* Elisa Bortolas, Manuel Arca Sedda, Pau Amaro Seoane, Stefano Benetti, Marica Branchesi, Adam Burrows, Enrico Cappellaro, Roberto Della Ceca, Kiranjyot Gill, Ines Francesca Giudice, Elisabeth-Adelheid Keppler, Chiaki Kobayashi, Valeriya Korol, Francesco Longo, Ferdinando Patat, Sourav Roy Chowdhury, Roberto Serafinelli, Paola Severgnini, Martina Toscani, David Vartanyan

This section describes the astrophysical sources that could generate a GW signal accessible to the LGWA. We provide an overview of the main formation channels for each source and other astrophysical aspects crucial for LGWA’s source detection and interpretation. We start by detailing the astrophysics of compact stellar binaries, which can be stellar black holes, neutron stars, white dwarfs and any combination thereof. We then describe massive BHs and I/EMRIs: for the former, both bodies in the binary have a mass at least $> 100M_{\odot}$; for the latter, the mass of the secondary body is typically $< 10^{-2}$ times lighter than the primary. We then describe further possible LGWA sources as stellar tidal disruption events, asymmetric neutron stars and finally, GWs from type II supernovae via the memory effect. Table 4 summarizes the main LGWA sources with their properties. The detection horizons for equal mass binaries and I/EMRIs are shown in figure 5.

**Compact-binary mergers of stellar-mass compact objects.** Compact binary systems, comprising WDs, NSs and BHs populate our local Universe. Approximately $10^6$ yr before their merger, these systems emerge as prime targets for space-based GW observatories. Missions like LISA [366], TianQin [367], and Taiji [368], set to operate at milli-Hz frequencies, are anticipated to be functional in the 2030s. Lunar-based projects, such as LGWA (operating in the deci-Hz regime), although capable of producing exciting science by themselves, can
<table><caption>**Table 4.** Here we list the main GW sources for LGWA with their typical formation channels, together with the total mass, mass ratio accessible to the LGWA for each of them.</caption><thead><tr><th>Source</th><th>Formation channel(s)/cause</th><th>M<sub>tot</sub> [M<sub>☉</sub>]</th><th>q</th></tr></thead><tbody><tr><td>Stellar binaries</td><td>Stellar binary evolution, dynamical interactions</td><td>1–10<sup>2</sup></td><td>0.1 – 1</td></tr><tr><td>MBH binaries</td><td>Galaxy-galaxy mergers</td><td>10<sup>3</sup> – 10<sup>6</sup></td><td>0.01 – 1</td></tr><tr><td>IMRIs</td><td>Two-body relaxation, AGN disks</td><td>10<sup>2</sup> – 10<sup>5</sup></td><td>10<sup>−4</sup> – 10<sup>−2</sup></td></tr><tr><td>TDEs</td><td>Two-body/resonant relaxation</td><td>10<sup>3</sup> – 10<sup>6</sup></td><td>10<sup>−5</sup> – 10<sup>−3</sup></td></tr><tr><td>Asymmetric NSs</td><td>Non-axisymmetric rotating NS</td><td>1 – 4?</td><td>—</td></tr></tbody></table>

complement space-based missions, especially at the high-frequency end of their sensitivity window, effectively bridging the gap with terrestrial detectors. Furthermore, LGWA can enhance the scientific scope of compact binaries to approximately 1 Hz, enabling the detection of events like DWD and NS-WD mergers [10]. Notably, some of these mergers are not accessible to the terrestrial detectors nor to the lower-frequency space missions.

**Stellar black-hole binaries.** The detection of GWs by the LIGO-Virgo-Kagra (LVK) collaboration, led by the discovery of GW150914 [1], has provided proof of BHs, enriching our knowledge of known merging BHs up to the present population of nearly 100 objects with masses above 30 $M_{☉}$. This was well above the limit set by previous observations, supporting the evidence for the existence of binary BHs, and for the formation of new BHs as by-product of a BH mergers. Such a growing catalogue of events [55] allows constraints to be placed on the cosmic population of merging BHs. Among all observed mergers, there are several intriguing sources with properties that clearly deviate from the overall distributions. One of them is GW190521 [369, 370], the first GW source to leave behind an IMBH with a mass of $\sim 150 M_{☉}$.

With a primary mass of $\sim 85 M_{☉}$, GW190521 was also a challenging source to interpret. Stellar evolution models predict a gap in the BH mass spectrum roughly between 40–300 $M_{☉}$ owing to the onset of pair instability and PPISN in their progenitors [371]. Stars $\gtrsim 300 M_{☉}$ may collapse to BHs (see [372] for a review). The actual range of masses affected by pair instability and PPISN is highly uncertain, and it depends on the details in stellar evolution models. Also, star collisions and binary interactions can alter the stellar structure such that the star bypasses the pair instability and PPISN phases and instead undergoes direct collapse, possibly leaving a BH remnant with a mass in the gap. BHs in the gap could also originate from previous BH mergers, following the so-called hierarchical merger scenario.

It is important to understand the origin of merging BHs to interpret GW observations. From a theoretical standpoint, the main formation channels for compact binary mergers are via binary stellar evolution [373–385], dynamical interactions in star clusters [386–408], and primordial BH interactions [409–418].

Identifying the imprint of different formation channels is not trivial, owing to the many processes, and related uncertainties that can affect the merging BH population (see for example [405, 419–422]). The cosmic star formation, the metallicity distribution, the star-cluster formation and evolution, the natal BH mass, spin, kicks, and the parameters of BH binaries are only a few of such processes and quantities that can dramatically affect the
properties of observed merging BHs [405]. However, only a handful of parameters, like the binary eccentricity, the mass ratio, and the effective spin distribution, might be the key to understanding such population of merging objects.

Among all, the binary eccentricity is considered to be a quantity that can clearly tell whether a binary merger is formed dynamically or not [80, 81, 423, 424]. Several processes, like common envelope dynamics, mass transfer, and GW emission, are expected to dampen binary eccentricities and lead to almost circular orbits ($e < 10^{-3}$) even before the binary emits GWs in the frequency range of terrestrial detectors (> 10 Hz) (see e.g. [423, 425]). However, SN kicks or common envelope physics may lead to moderately eccentric binaries emitting high-frequency GWs [426, 427]. In dynamical environments, instead, binaries are assembled via strong dynamical interactions, which can naturally lead to the formation of highly eccentric binaries [404, 428-434], depending on the environment in which they develop. For example, eccentric binaries can form via GW captures, secular processes, and binary-single encounters in quiescent and active galactic nuclei [428, 435-437], or via three- and four-body interactions in young and globular clusters [386, 404, 429, 432, 433]. For dynamical mergers, the environment can also affect the critical value of the binary separation below which GW emission becomes the dominant evolutionary process and the binary decouples from the overall dynamics. This means that an eccentric merging binary forming in a young massive cluster will likely be circularised by the time it reaches the 1-10 Hz band, but can appear eccentric at lower frequencies observable with LGWA, whilst a binary forming in a massive and dense galactic nucleus may form with a sufficiently small separation to be detectable as eccentric source even with high-frequency detectors (e.g. [424, 433, 438]). Despite some of the detected GW sources could be eccentric [439-443], the effects of eccentricity on detected signals are very similar to those induced by binary precession, thus making it hard to place stringent constraints on the eccentricity [444, 445]. Advances in data analysis and waveform templates are recently enabling the premises to measure the eccentricity of binaries provided that it exceeds $O(10^{-2})$ [446-452]. With the possibility to follow the binary over many orbits, lower frequency detectors may be the key to untangle the two effects and robustly determine the binary eccentricity [358, 453], helping us to pin down the origin of at least some sub-population of observed sources [80, 81]. In these regards, multiband observations with different detectors can help to increase the accuracy of measured parameters. Multiband detections can be sub-threshold in LGWA becoming significant only with the help of the other GW detectors involved in the observation.

Another interesting, possibly distinctive, feature of merging BHs is the distribution of spins. Ideally, a merging BH binary formed from isolated binary stellar evolution is expected to lead to two BHs with aligned spins [454], although some level of misalignment can be induced during the BH formation process, e.g. during the supernova phase [454-459]. Conversely, dynamical BH mergers are expected to have spins isotropically distributed in space, owing to the chaotic nature of the interactions that drive their formation [425]. This suggests that a precise measurement of the BH spins and their mutual orientation would help identifying the binary formation origin. Spins in current GW data analysis are poorly constrained, and generally the spin orientation of merging binaries is inferred from the so-called effective spin parameter $\chi_{\text{eff}}$ [460], which is a projection of the spins onto the binary angular momentum,
weighted with the binary component masses. A population of mergers with aligned spins would be characterised by a $\chi_{\text{eff}}$ distribution clearly peaked around a positive value, whilst such a peak would be centered on zero for mergers with isotropically distributed spins.

Finally, identifying the location of the merger would definitely help to pin down the formation scenario. Combining observations performed with different detectors can significantly help reduce the localization area down to a few arcmin² (see section 2.2.2), possibly providing clues about the merger birth site, at least on a statistical basis and for relatively closeby sources.

The LGWA can play a crucial role in measuring the aforementioned quantities. Working in the deci-Hz frequency range, depending on its final sensitivity it could follow merging BHs for months and weeks before the merger, ensuring high precision measurements of the masses, the spins, and possibly the eccentricity evolution of the binary (see section 2.2.3). These are fundamental for further understanding the evolution of (single) massive stars, and the formation and evolution of massive star binaries.

*White-dwarf and neutron-star binaries.* Mergers of WDs and NSs are extremely important for understanding the origin of elements [461]. NS mergers are proposed for one of the astrophysical sites of the rapid neutron capture process [462], which has been confirmed by the detection of GW and EM transient 'kilonova' [463]. WDs mergers are thought to become sub-Chandrasekhar-mass Type Ia supernovae [464, 465], which are responsible for at least some of the Fe production particularly in dwarf galaxies [466]. Compact stellar systems composed of WDs and NSs are guaranteed GW sources, as some of them have been already discovered with electromagnetic (EM) telescopes (see also section 3.3.1). Some of the shortest period and better characterised of the known binaries have also been proposed for testing space-based GW detectors to maximise their scientific output (e.g. [467–470]). Some of such systems, known in literature as *verification binaries* [e.g., 467], can be detected by LGWA [10]. They are guaranteed multi-messenger sources offering an opportunity to study the astrophysics of compact sources using both their GW and EM emission (e.g. [305, 471–474]). They would also be ideal calibration sources for LGWA given their known location and well-modeled GW amplitudes eventually measured precisely by LISA (see section 2.1.4.

From a theoretical perspective, compact binaries are expected to be several orders of magnitude more abundant than currently observed by EM telescopes (e.g. [475, 476]), with binaries composed of two WDs being the most abundant in the Milky Way and its immediate neighbourhood. Their formation involves up to several mass transfer episodes; at least one of these episodes has to be unstable leading to a *common envelope*, a phase during which the binary can shrink dramatically [465, 477–480]. Even though this is one of the least understood phases in binary evolution, the fact that we do observe close double compact objects and mergers is a strong indication that something like a common envelope phase happens [481]. Based on these observations, several theoretical modelling efforts are being made (e.g. [482, 483]). Thus, the demographics of compact binaries observed via GW radiation will provide opportunities to learn new physics and answer key scientific questions related to the formation and evolutionary processes of close binary systems. Besides the common envelope physics, this includes questions related to the stability and efficiency of mass and angular momentum transfer, tides, and accretion onto compact objects, as well as details of their destruction in supernova explosions [for a review see 484, 485].
At frequencies < 0.1 mHz, binary population synthesis simulations predict $\mathcal{O}(10^7)$ double WDs, followed by $\mathcal{O}(10^5)$ NSWDs in the Milky Way alone [for a review see 484]. Studying these binary populations with EM facilities has proven to be technically challenging due to the compact size of these binaries and WD/NS stars themselves, and so GW detectors — characterised by different selection effects — are ideally suited for discovering and characterising them in bulk [486, 487]. Importantly, GW selection effects enable the study of EM-dim double compact objects at unprecedentedly large distances throughout the Milky Way, including its most massive satellites and possibly reaching out as far as the Andromeda galaxy, which otherwise impossible with EM telescopes [488–491]. Recent binary population synthesis studies forecast between 2 and 200 double WDs in the Milky Way with orbital periods of less than 200 seconds (GW frequencies greater than $10^{-2}$ Hz) that LGWA could potentially capture in the inspiral phase [472, 492–496]. Observation-based forecasts are even more optimistic, predicting up to 1000 inspiralling double WDs in the same frequency regime in the Milky Way alone [258, 487, 497].

*Supernovae Type Ia and white-dwarf binaries.* SNe Ia are believed to originate from WDs which, due to mass transfer or generally, interactions in close binary systems, grow above the Chandrasekhar limit ($M_{Ch} \sim 1.4 M_{\odot}$) and are incinerated by a thermonuclear explosion under degenerate matter conditions. This idea dates back to the early '70 [498] but the actual nature of the secondary star remains undetermined. Two alternative scenarios have been proposed: the donor is a hydrogen or helium main sequence or a giant star (the single degenerate scenario, or SD), or another WD (the double degenerate scenario, or DD), which would lose orbital momentum via GW radiation and eventually merge. In the case of SD systems, mass transfer onto the accreting WD occurs when the secondary donor star fills its Roche lobe. This sets a lower limit for the separation between the two stars and the orbital period (of the order of 10 minutes for the most compact, non-degenerate donors [499]). In this configuration, the GW emission is weak and does not significantly affect the binary evolution. On the contrary, in DD systems the orbital radius naturally shrinks as an effect of angular momentum loss via GW emission [465]. Because of the small tidal radius of WDs, this allows a minimum orbital period of tens of seconds (see below). Since the intensity of the GW emission increases with increasing frequency, this is also expected to produce a much stronger signal, falling in the 0.01–0.1 Hz domain, right in the frequency range where LGWA’s sensitivity is at its best. This difference in orbital periods creates a clear-cut case, in which GW detection can act as an effective discriminant between the two channels. Using Kepler’s third law relating the period $P$ and the semi-major orbital axis $a$, and considering that the GW frequency is given by $f_{GW} = 2/P$, it can be readily shown (see for instance [500]) that

$$f_{GW} = \frac{\sqrt{G}}{\pi} (M_1 + M_2)^{1/2} a^{-3/2} \approx 0.1 \text{Hz} \left(\frac{M_1 + M_2}{2M_{\odot}}\right)^{1/2} \left(\frac{a}{0.02 R_{\odot}}\right)^{-3/2}, \quad (3.5)$$

where $M_1$ and $M_2$ are the masses of the two stars. Given the total mass constraint ($M_1 + M_2 \gtrsim M_{Ch}$), the typical WD radius ($R_{WD} \sim 0.01 R_{\odot}$; [501]) and the minimum WD separation ($a \sim 3R_{WD}$; [502]), eq. (3.5) yields a maximum GW frequency $f_{GW,m} \sim 0.1$ Hz when the merger occurs (see also [259], figure 21 therein). The time it takes for a binary system to merge, under the simplifying assumption of a circular orbit and neglecting possible
mass transfer, hydrodynamical and radiative effects was computed by Peters [503] (see eqs. (5.9)-(5.10) therein), and can be expressed as:

$$t_m = \frac{5}{256} \frac{c^5}{G^3} \frac{a^4}{M_1 M_2 (M_1 + M_2)},$$

which, taking into account equation (3.5), can be rewritten as:

$$t_m(M_c, f_{WG}) = \frac{5}{256} \left(\frac{1}{\pi}\right)^{8/3} c^5 G^{-5/3} M_c^{-5/3} f_{GW}^{-8/3} \approx 9.3 \text{ yr} \left(\frac{M_c}{M_{\odot}}\right)^{-5/3} \left(\frac{f_{GW}}{0.1\text{Hz}}\right)^{-8/3} \quad (3.6)$$

where $M_c = (M_1 + M_2)^{-1/5} (M_1 M_2)^{3/5}$ is the chirp mass [500].

The SN Ia rate in the Galaxy is well known from direct observations in the local universe: $r_{Ia}=(5.4\pm1.2)\times10^{-3} \text{ yr}^{-1}$ [504]. This corresponds to an event every ~200 yr, which is definitely too low to provide a significant chance of detection of a WD binary merger during the lifetime of a GW campaign.

However, in order to understand the progenitor of SN Ia, statistical approach can be followed. If the bulk of SNe Ia comes from DD systems, there needs to be enough such systems with the suitable properties (mass, merging time) to account for the observed SN Ia rate. Let us assume that $n(M_c, f_{GW})$ is the probability density function describing the distribution of DD systems. Let us then also indicate with $M_{c,l}$ and $M_{c,h}$ the lower and upper chirp mass limits for having a total mass $M_1 + M_2 \gtrsim M_{Ch}$. These limits are set considering the maximum and minimum mass of a C-O WD: ~1.0$M_{\odot}$ [505] and ~0.3$M_{\odot}$ [506] ($M_1 = 0.4M_{\odot}$, $M_2 = 1.0M_{\odot}$ and $M_1 = M_2 = 1M_{\odot}$, corresponding to an approximate chirp mass range 0.5-0.9 $M_{\odot}$). Finally, let us indicate with $f_{GW,l}$ the lower limit of the frequency range covered by the GW detector, which corresponds to the maximum merging time $t_{m,h}$ and maximum orbital period $P_h$. With these settings, the total expected number of suitable DD systems found by the GW detector is:

$$N_* = \int_{M_{c,l}}^{M_{c,h}} \int_{f_{GW,l}}^{f_{GW,m}} n(M_c, f_{GW}) \, dM_c \, df_{GW},$$

where, as we have shown above, $f_{GW,m} \sim 0.1 \text{ Hz}$. Since, by construction, all these systems will have merged (and hence exploded) by $t = t_{m,h}$, the corresponding explosion rate is simply given by

$$r_{Ia} = \frac{N_*}{t_{m,h}}$$

Since $r_{Ia}$ is well known (see above), the argument can be reversed and one can predict $N_*$. For illustration purposes, using this relation and eq. (3.6), we have compiled table 5 for some representative values of $P_h$. For the sake of simplicity, we have assumed $M_1 = M_2 = 0.7M_{\odot}$ ($M_c \simeq 0.6M_{\odot}$). We note that the above calculations are a good approximation only for $P \gtrsim 100 \text{ s}$. For lower periods (50-100 s, depending on the WD masses) Roche lobe overflow ensues. Recent 3D hydrodynamical simulations show that for sufficiently massive primaries, the onset of unstable dynamical accretion of helium from the secondary white dwarf, just prior to the binary merger, heats up the helium shell on the primary white dwarf. As a result,
<table><caption>**Table 5.** GW frequency, merging time and number of DD systems with the suitable properties required to reproduce the observed Galactic SN Ia rate for some example values of the maximum orbital period. The largest period (~11 hours) corresponds to a merging time equal to the Hubble time.</caption><thead><tr><th>P<sub>h</sub><br>(s)</th><th>f<sub>GW,l</sub><br>(Hz)</th><th>t<sub>m,h</sub><br>(yr)</th><th>N<sub>*</sub></th></tr></thead><tbody><tr><td>40000</td><td>5.0×10<sup>-5</sup></td><td>1.3×10<sup>10</sup></td><td>(7.1±1.6)×10<sup>7</sup></td></tr><tr><td>3600</td><td>5.6×10<sup>-4</sup></td><td>2.2×10<sup>7</sup></td><td>(1.2±0.3)×10<sup>5</sup></td></tr><tr><td>2000</td><td>10<sup>-3</sup></td><td>4.6×10<sup>6</sup></td><td>(2.4±0.6)×10<sup>4</sup></td></tr><tr><td>200</td><td>10<sup>-2</sup></td><td>9.9×10<sup>3</sup></td><td>52±12</td></tr></tbody></table>

a thermonuclear runaway occurs, igniting a helium detonation on the surface of the primary white dwarf and eventually leading to the ignition of the carbon-oxygen core [e.g., 507–509]. This would lead to a merger timescale that is much shorter than what is predicted by eq. (3.6).

As shown in table 5, for $f_{GW,l}=0.01$ Hz, which corresponds to a maximum merging time $t_{m,h} \sim 10^4$ yr, $N_* = 52 \pm 12$. Therefore, to match the observed SN Ia rate, at any given time the Galaxy needs to host 40-60 double-WDs with $M_1 + M_2 \gtrsim M_{Ch}$ orbiting with a period of $\lesssim 200$ s. If the number of DD systems found in the frequency range 0.01–0.1 Hz is not enough to account for the observed rate, either SD contributes in a significant way to the census of progenitor systems, or SN Ia can originate also from smaller mass systems. These have longer merging times and hence one would need an even higher number of systems in the considered frequency range. On the other hand, they may remain undetected because the intensity of their GW emission is lower than for more massive systems. We notice that whereas the sub-Chandrasekhar scenario was not the favoured option to explain the majority of SN Ia [510], in recent years it gained support also in accounting for the observed SN Ia diversity, and it is considered as one of the possible scenarios [264, 511]. The simplified approach outlined above is meant only to illustrate the basic concept. In order to achieve an accurate prediction of the SN rate to be compared with the observed value, one needs also to consider the actual distribution of WD masses, the GW strain at a given frequency and the spatial distribution of sources.

The calculations presented above refer to possible detections within our own Galaxy. However, figure 7 shows a detection horizon for DWD binaries enabling us to detect DWD systems on the verge of merging in nearby galaxies. Even if the actual horizon limit depends on the details of the merging process, which is complex and not fully understood, it is possible to estimate a lower limit on the rate of DWD mergers detectable by LGWA from the local SN Ia rate, in the assumption that SN Ia originate from DWD binaries.

To derive the rate of SN Ia events in the Local Universe, we use the SN observed by ZTF and ATLAS from 2018 to 2023. These optical surveys continuously cover the sky and their nearby SN candidates are typically spectroscopically classified by programs such as PESSTO [512]. Collecting data from TNS<fnref n="9" /> and the Bright Supernova Catalogue,<fnref n="10" /> the

<footnote n="9">⁹https://www.wis-tns.org/.</footnote>

<footnote n="10">¹⁰https://www.rochesterastronomy.org/.</footnote>