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

Parameswaran Ajith  0000-0001-7519-2439 Pau Amaro Seoane  0000-0003-3993-3249
Manuel Arca Sedda  0000-0002-3987-0519 Riccardo Arcodia  0000-0003-4054-7978
Francesca Badaracco  0000-0001-8553-7904 Enis Belgacem  0000-0003-4920-0911
Stefano Benetti  0000-0002-3256-0016 Alexey Bobrick  0000-0002-4674-0704
Alessandro Bonforte  0000-0003-0435-7763 Elisa Bortolas  0000-0001-9458-821X
Valentina Braito  0000-0002-2629-4989 Marica Branchesi  0000-0003-1643-0526
Adam Burrows  0000-0002-3099-5024 Enrico Cappellaro  0000-0001-5008-8619
Roberto Della Ceca  0000-0001-7551-2252 Chandrachur Chakraborty
0000-0003-4380-3033 Shreevathsa Chalathadka Subrahmanya  0000-0002-9207-4669
Michael W. Coughlin  0000-0002-8262-2924 Stefano Covino  0000-0001-9078-5507
Andrea Derdzinski  0000-0001-9880-8929 Aayushi Doshi  0009-0006-2205-3391
Maurizio Falanga  0000-0003-3095-6065 Stefano Foffa  0000-0002-4530-3051
Alessia Franchini  0000-0002-8400-0969 Alessandro Frigeri  0000-0002-9140-3977
Yoshifumi Futaana  0000-0002-7056-3517 Oliver Gerberding  0000-0001-7740-2698
Kiranjyot Gill  0000-0003-4341-9824 Matteo Di Giovanni  0000-0003-4049-8336
Ines Francesca Giudice  Margherita Giustini  0000-0002-1329-658X Philipp
Gläser  0000-0002-7552-5800 Jan Harms111Corresponding author.
0000-0002-7332-9806 Joris van Heijningen  0000-0002-8391-7513 Francesco
Iacovelli  0000-0002-4875-5862 Bradley J. Kavanagh  0000-0002-3634-4679 Taichi
Kawamura  0000-0001-5246-5561 Arun Kenath  0000-0002-2183-9425 Elisabeth-
Adelheid Keppler  0000-0003-3453-2606 Chiaki Kobayashi  0000-0002-4343-0487
Goro Komatsu  0000-0003-4155-108x Valeriya Korol  0000-0002-6725-5935 N. V.
Krishnendu  0000-0002-3483-7517 Prayush Kumar  0000-0001-5523-4603 Francesco
Longo  0000-0003-2501-2270 Michele Maggiore  0000-0001-7348-047X Michele
Mancarella  0000-0002-0675-508X Andrea Maselli  0000-0001-8515-8525 Alessandra
Mastrobuono-Battisti  0000-0002-2386-9142 Francesco Mazzarini
0000-0002-3864-6558 Andrea Melandri  0000-0002-2810-2143 Daniele Melini
0000-0002-5383-2375 Sabrina Menina  0000-0003-1044-6877 Giovanni Miniutti
0000-0003-0707-4531 Deeshani Mitra  0000-0002-1350-019X Javier Morán-Fraile
0000-0002-8918-5130 Suvodip Mukherjee  0000-0002-3373-5236 Niccolò Muttoni
0000-0002-4214-2344 Marco Olivieri  0000-0002-7333-8809 Francesca Onori
0000-0001-6286-1744 Maria Alessandra Papa  0000-0002-1007-5298 Ferdinando
Patat  0000-0002-0537-3573 Tsvi Piran  0000-0002-7964-5420 Silvia Piranomonte
0000-0002-8875-5453 Alberto Roper Pol  0000-0003-4979-4430 Masroor C.
Pookkillath  0000-0002-7199-8037 R. Prasad  0000-0002-6602-3913 Vaishak Prasad
0000-0001-6712-2457 Alessandra De Rosa  0000-0001-5668-6863 Sourav Roy
Chowdhury  0000-0003-2802-4138 Roberto Serafinelli  0000-0003-1200-5071
Alberto Sesana  0000-0003-4961-1606 Paola Severgnini  0000-0001-5619-5896
Angela Stallone  0000-0002-8141-017X Jacopo Tissino  0000-0003-2483-6710
Hrvoje Tkalčić  0000-0001-7072-490X Lina Tomasella  0000-0002-3697-2616
Martina Toscani  0000-0001-5997-7148 David Vartanyan  0000-0003-1938-9282
Cristian Vignali  0000-0002-8853-9611 Lucia Zaccarelli  0000-0002-4053-7625
Morgane Zeoli  0009-0007-1898-4844 Luciano Zuccarello  0000-0003-0094-9577

###### 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.

###### Contents

  1. 1 Introduction
    1. 1.1 Science traceability matrices
      1. 1.1.1 Gravitational-wave science and multi-messenger astronomy
      2. 1.1.2 Lunar science
  2. 2 The Lunar Gravitational-wave Antenna
    1. 2.1 Mission Concept
      1. 2.1.1 Payload description
      2. 2.1.2 Main instrument-noise contributions
      3. 2.1.3 Reduction of the seismic background
      4. 2.1.4 Lunar response to GWs and calibration
      5. 2.1.5 Sensitivity models of LGWA
      6. 2.1.6 Outlook: LGWA upgrades
    2. 2.2 Observational capabilities
      1. 2.2.1 Detection horizons
      2. 2.2.2 Localization of GW sources in space and time
      3. 2.2.3 Estimates of spin and mass parameters
      4. 2.2.4 Multiband GW observations
    3. 2.3 Studies of the Lunar Surface Environment and of the Deployment Site
      1. 2.3.1 Geologic models
      2. 2.3.2 Solar illumination and surface temperature
      3. 2.3.3 Regolith composition
      4. 2.3.4 Ground tilt response
      5. 2.3.5 Seismic background noise
      6. 2.3.6 Magnetic fluctuations on the lunar surface
    4. 2.4 Soundcheck and Other Relevant Lunar Missions
  3. 3 Science Objectives
    1. 3.1 Lunar science
      1. 3.1.1 Seismic sources
      2. 3.1.2 Lunar internal structure
      3. 3.1.3 Moon’s formation history
      4. 3.1.4 Geologic processes
    2. 3.2 Gravitational-wave science
      1. 3.2.1 Astrophysical explosions and matter effects on waveforms
      2. 3.2.2 Populations and formation channels of GW sources
      3. 3.2.3 GW cosmology
      4. 3.2.4 Fundamental physics with GWs
    3. 3.3 Multi-messenger observations
      1. 3.3.1 Compact binaries with white dwarfs and neutron stars
      2. 3.3.2 Supernovae
      3. 3.3.3 Tidal Disruption Events
      4. 3.3.4 Intermediate and Massive Black Hole Binaries
      5. 3.3.5 Extreme/Intermediate Mass-ratio Inspirals

## List of abbreviations

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

##  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, 4, 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 outside
our galaxy. 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 222ESA SciSpacE white papers,
the Decadal Survey in Astrophysics 333Astro Decadal 2020 report, in Biological
and Physical Sciences Research in Space444BPS Decadal 2023 report, and in
Planetary Science and Astrobiology 555Planetary Decadal 2023 report 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 deployment scenarios, which will be provided
with a dedicated document.

###  1.1 Science traceability matrices

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

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

####  1.1.2 Lunar science

Science goals |  Science questions |  Observational requirements |  Instrument requirements |  Top-level mission requirements
---|---|---|---|---
Understanding of the internal structure of the Moon |  What are the resonance frequencies and Q-values of the lunar normal modes? |  Observe ringdown of normal modes produced by moonquakes. |  Sensitivity better than 0.1 $\mu$m/Hz1/2 at 1 mHz and better than 0.1 nm/Hz1/2 at 0.1 Hz |  1 yr mission lifetime
|  What is the level of fracturing in the megaregolith? |  Observe the effect of seismic scattering on the wavefield generated by moonquakes and GW signals. |  Sensitivity better than 0.1 nm/Hz1/2 at 0.1 Hz and better than 0.1 pm/Hz1/2 at 1 Hz |  1 yr mission lifetime
|  What are the rheological and thermal properties and composition of the Moon’s core? |  Discriminate and model P- and S-waves travelling through the Moon’s core and interacting with its boundary. |  Sensitivity better than 1 pm/Hz1/2 from 0.1 Hz to 1 Hz |  1 yr mission lifetime; possibly as part of a lunar seismic network
Understanding the nature of lunar seismicity |  What is the origin of moonquakes (e.g., tectonic, thermal or tidal) and how to determine their locations (latitude, longitude, and depth)? |  Perform array analysis of at least a few 100 moonquake waveforms. |  Sensitivity better than 0.1 nm/Hz1/2 at 0.1 Hz and better than 0.1 pm/Hz1/2 at 1 Hz |  3 yr mission lifetime; possibly as part of a lunar seismic network
|  Is the Moon a competitive platform for GW detection beyond LGWA? |  Determine the seismic noise level in PSRs and its daily and seasonal variation. |  Sensitivity better than 1 pm/Hz1/2 at 0.1 Hz and better than 1 fm/Hz1/2 at 1 Hz |  1 yr mission lifetime
Observing geological processes through their seismic signatures |  How to characterize the Moon’s surface and crustal structure from tectonic and meteoroid impact events? How does it change in time? |  Ambient noise and event coda imaging and interferometry through autocorrelations and cross-correlations. |  Continuous recordings in the frequency range 0.1–5 Hz |  $>1$ yr mission
Understanding the Moon’s formation history and evolution |  What can the deep internal structure of the Moon tell us about its formation history? |  Observe the lowest-frequency normal modes. |  Sensitivity better than 0.1 $\mu$m/Hz1/2 at 1 mHz and better than 3 nm/Hz1/2 at 10 mHz |  1 yr mission lifetime

##  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
666Radioisotope thermoelectric generator concept. 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 Fig. 1. The aim is to achieve a displacement
sensitivity of 10-12 m/$\surd$Hz at 0.1 Hz and 10-15 m/$\surd$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.

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. Figure adjusted from [20].

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 104 and 106,
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. Fig. 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/$\surd$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 platform accurate to within 10
$\mu$rad 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 Fig. 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]

$x_{\rm{th}}^{2}=\frac{4k_{\rm{B}}T}{m\omega\big{[}\big{(}\omega_{0}^{2}-\omega^{2}\big{)}^{2}+\big{(}\omega_{0}^{2}/Q\big{)}^{2}\big{]}}\frac{\omega_{0}^{2}}{Q}$
(2.1)

where $k_{\rm{B}}$ 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

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

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

$i_{\rm{RIN}}=i_{\rm{sn}}\sqrt{\frac{\omega_{\rm{c}}}{\omega}+1},$ (2.3)

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

$x_{\rm{f}}=\frac{\nu_{\rm{L}}}{\nu_{\rm{0}}}\Delta L_{0},$ (2.4)

where $\nu_{\rm{L}}$ represents the laser-frequency noise,
$\nu_{\rm{0}}=c/\lambda$ the central laser frequency and $\Delta L_{0}$ the
static arm length difference.

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

$x_{\rm{squid}}^{2}=\frac{2E_{\rm{A}}(1+f_{\rm{c}}/f)}{m\omega_{0}\eta\beta},$
(2.5)

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

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

$x_{\rm{act}}=\frac{\alpha n_{\rm{DAC}}}{R_{\rm{s}}m\omega^{2}},$ (2.6)

where $\alpha$ denotes the actuator strength in N/A and $R_{\rm{s}}$ the shunt
resistance. It will depend on the lunar SBN if actuation on the proof mass of
the inertial sensor is necessary.

(a)

(b)

Figure 2: Minimum detectable inertial displacement for the two LGWA concepts:
2(a) a niobium Watt’s linkage with laser-interferometric readout and 2(b) a
silicon Watt’s linkage with superconductive readout. All readout noises are
corrected by the mechanical transfer function of the proof mass suspension.

####  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.

####  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 [32]
and later analyzed for a spherically symmetric body in the normal-mode
formalism [33]. 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 [34]. The Dyson model was
used in [18, 35] and the normal-mode formalism was used in [36, 10] 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 [37, 38],
and to extend the Dyson model to a horizontally layered half space [39].

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.

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 [40, 41]. 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 [42] and any errors will not be a
dominating factor. Calibration procedures have also been developed for a
superconducting coil + SQUID readout [43, 44], 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 [45, 46, 47]. 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 repository777GWFish git repository. 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 (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.

Figure 4: Models of characteristic strain sensitivities.

####  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 [48, 28, 49].

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 [50, 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 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 –

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 $M_{\rm IMBH}$ 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).

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 $M=(1+z)M_{\rm src}$ ($z$ is the
redshift). At 1000 $M_{\odot}$, 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 [55, 2].
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 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.

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 Gpc3 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⊙ BNS is about 100 Mpc, and for 30+30 M⊙ BBH about 1.9 Gpc
($z=0.4$).

##### 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.

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.

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 band. 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).

Figure 8: Maximum distance $d_{\max}$, at which LGWA can see a WD-TDE
($M=0.5\text{M}_{\odot}$, $R_{*}=0.01\text{R}_{\odot}$) 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).

####  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 to
months. 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 appearing in the signal at a detector: $\exp({\rm
i}(\vec{k}\cdot\vec{r}(t(f))-2\pi ft_{\rm c}))$, where $t_{\rm c}$ 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.

Since for LGWA the motion of the Moon around the Earth and around the Sun
needs to be simulated together with its rotation, the natural choice for LGWA
seems to be to use a solar-centered system. However, this is just convenient
from a simulation perspective, and does not solve the problem. For these
reasons, we do not present a detailed assessment of sky-localization and
merger-time errors here, and leave it instead to a future study.

Heuristically, one may select the reference frame in order to get as close as
possible to the expected result. This was done to analyze the localization of
GW170817 with LGWA using the Fisher-matrix approximation [14], and it was
shown that few-arcmin2 sky-localization errors can be obtained. Similar sky-
localization capabilities should be expected for any GW signal that has
similar SNR and can be observed with LGWA over months to years like galactic
DWDs and solar-mass BBHs. The order of magnitude of this result is not
dependent on our (still uncertain) Fisher-matrix analyses alone, but can also
be estimated analytically under simplified assumptions, e.g., neglecting
changing antenna patterns and correlations between sky-location parameters and
other waveform parameters [60, eq. (52)].

####  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 results in figure 9 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).

Figure 9: 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.

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 10. 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 10: 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.

####  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) [62, 63, 64, 65] and in the USA with
the Cosmic Explorer (CE) [66, 64, 7, 67]. They may be further complemented by
observatories in the southern hemisphere [68]. 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 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 [69] 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 [70, 71].

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 [72, 73, 74]; parameter estimation can either be
performed jointly, or sequentially, using results from detectors at lower
frequencies as priors for data analysis at higher frequencies [75]; detections
in ground-based interferometers can also be used to look back in LGWA/LISA
data to find events at lower SNR [76].

Figure 11: 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⊙, $M_{2}=8\times 10^{5}$ M⊙ and
$d_{L}=1.7$ Gpc, while the IMBH binary has source masses $M_{1}=10^{3}$ M⊙,
$M_{2}=4\times 10^{2}$ M⊙ and $d_{L}=2$ Gpc.

An illustration of multi-band GW sources is provided in Fig. 11, 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 $\sim 90$ sources already
observed [2]. Their multi-band potential is actively studied in the context of
LISA and ground-based interferometers [69, 77, 78, 79, 80, 81, 82, 83, 84,
85]. 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 $\sim
0.016\,\rm Hz$ $5\,\rm yrs$ before merger, well inside the LISA band. The same
system $1$ day before merger emits at $\sim 0.26\,\rm Hz$, 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.

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
[86], where the source-frame mass distribution is described by the
“PowerLaw+Peak” (PLP) model [87], the spin distribution by the “Default” spin
model of [87], and the evolution of the merger rate with redshift by a Madau-
Dickinson profile [88]. We refer to Appendix A of [89] 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. $\mathcal{R}_{0}=17\,\rm
Gpc^{-3}\,yr^{-1}$. With these assumptions, we expect $\sim 6600$ sources per
year up to redshift $\sim 1$, which is approximately the LGWA horizon at
$100\,M_{\odot}$ 888We remind that the maximum BBH mass in the PLP mass
distribution is $m_{\rm max}=87\,M_{\odot}$ . 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 $[10^{-5},10]\,\rm yrs$.
The time to coalescence $\tau$ and the chirp mass $\mathcal{M}_{c}$ of the
system determine the initial frequency of each GW source according to the GR
prediction, $f_{\rm in}=134\times(1.21\rm
M_{\odot}/\mathcal{M}_{c})^{5/8}\times(1\rm s/\tau)^{3/8}\,\rm Hz$. We compute
the SNR of each source assuming a maximum observing time of $10\,\rm yrs$ in
ET in its triangular configuration, LGWA and LISA. We use the public package
gwfish [90]. With a single realization of the population according to the
above prescriptions, we obtain $\sim 960$ sources observed by both ET and LGWA
with $\rm SNR>8$, 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 minimun of 8 to a maximum of
$\sim 20$, while those in ET are always $>100$, with the best events reaching
$\rm SNR\sim\mathcal{O}(10^{3})$. 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 [82].

  * •

_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
$\mathcal{M}_{c}=1.188\,M_{\odot}$, corresponding to the value measured for
GW170817 [91] was emitting at $\sim 0.05\rm Hz$, 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
$\sim 0.27\,\rm Hz$, 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 [89]. 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 $\sim
0.09\,\rm Hz$. 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 $\mathcal{R}_{0}=105^{+190}_{-83}\,\rm Gpc^{-3}\,yr^{-1}$.
Using the central value of $105\,\rm Gpc^{-3}\,yr^{-1}$, a flat mass
distribution between $[1.1,2.5]\,\rm M_{\odot}$, and values for the Madau-
Dickinson profile obtained as described in Appendix A of [89], we obtain $\sim
36$ sources per year within redshift $z\sim 0.1$, which corresponds to the
LGWA horizon at $\sim\rm few\,M_{\odot}$. Over a period of $10\,\rm yrs$, we
obtain 5 joint detections between LGWA and ET with $\rm SNR>8$. Given the
large uncertainty on the local merger rate, we also compare to the results
obtained using the upper and lower values of $295\,\rm Gpc^{-3}\,yr^{-1}$ and
$22\,\rm Gpc^{-3}\,yr^{-1}$, that 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 allow in particular their precise localization prior to
merger, which is a key need for potential multimessenger observations. Also,
long-duration multi-band studies using LGWA and ground-based GW detectors [71,
92] can improve the estimation of parameters, in particular the tidal
deformability [70]. This will lead to better constraints, ruling out many more
theoretical EOS models [92].

  * •

_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 Fig. 11 emits at $\sim
0.002\,\rm Hz$ 5 years before the merger, and at $\sim 0.27\,\rm Hz$ 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 $\sim 10$. For example, Ref. [93] finds between $\approx 25$ and
$\approx 75$ 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
[94, 95]. 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 [96], though
its detection might be challenging. Indeed, eccentricity dampens the
characteristic amplitude of each harmonic compared to a circular one. Figure
12 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 [97],
so most of the GW power is radiated at the peak frequency of $f_{\rm
peak}=2.16(1-e)^{-3/2}P^{-1}$.

Figure 12: 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.

A useful figure-of-merit to assess multi-band capabilities of LGWA is the
detection horizon. In Figures 13 and 14 we show the joint detection horizons
for LGWA-ET and LGWA-LISA respectively, for binary systems between
10–10${}^{7}\,M_{\odot}$. In general, the horizon is dominated by the least
sensitive detector. For stellar-origin BBHs ($\sim 5-100\,\rm M_{\odot}$), 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 $\geq\mathcal{O}(100)$. 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 $\sim\mathcal{O}(10^{3})$ in LISA. Finally, we note that an
interesting ”sweet spot” exists for IMBHs around $10^{3}\rm M_{\odot}$ 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 $[2-5]\times 10^{3}\,\rm M_{\odot}$ 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 13: 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. Figure 14: Multiband horizon for
a network of LISA and LGWA, computed as in figure 13.

###  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 15 shows the geological map for the Moon’s southern polar region.
Initially compiled after the Apollo program by Wilhelms et al [98], it has
recently been updated by Fortezzo et al [99]. The map’s fundamental components
are surface portions classified 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
[100] and progresses towards multi-dimensional and multi-resolution models
(See Section 2.3.5).

Figure 15: Top: Global-scale geological map of the Moon’s southern polar
region, displaying how the geological units are spatially distributed [98,
99]. 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.

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 $1.5^{\circ}$ 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 [101, 102].
Based on the resulting illumination maps, PSRs and extensively illuminated
spots can be identified (compare blue and red areas in Fig. 16). 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 $\approx 10$ m
above ground. The illumination at the surface and 2 m above ground of one of
the PSRs is shown in figure 16a+b.

Figure 16: 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. Figure adapted from [101].

Illumination maps also serve as an input for a thermal model to derive
(sub-)surface temperature estimates for the uppermost 2 m of regolith [103].
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 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 Fig. 17.

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.

Figure 17: 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.

####  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 [104]. 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 [105, 106]. The regolith has been
estimated to be 5 m to 20 m thick globally, with a shear velocity of less than
100 m/s [107, 108].

Regolith in the Moon forms by high‐energy physical weathering processes (e.g.,
[109]) 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 ([106] and references therein). In general, the continuous
impacts of large and small asteroids led to the formation of the lunar
regolith [110, 106]. The impact on the pristine bedrock surface generates
breccia lens within the crater and a blanketing by ejecta around the crater
(Figure 18).

Figure 18: Conceptual model of the regolith formation by impact modified after
[106]. 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.

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 ([109] and references therein).

The strength of bedrock significantly affects the crater size and hence the
volume of regolith produced especially for sub-decameter impactors. The
regolith volume produced by an individual impact crater is quantitatively
characterized as a function of crater diameter and pre-impact regolith
thickness [106].

For the lunar maria, the surface structure can be modelled as a fine-grained
regolith layer atop the underlying coherent bedrock (Figure 18). Depending on
the ratio of crater rim-to-rim diameter (D) to pre-impact regolith thickness
(T) different morphologies may form ([106] 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 [111].

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 [112, 113]. 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 [112]. In the south pole of the Moon
are present both pristine crust as well as basalts filling craters [114].

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 [115]. 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 meter beneath the surface, SAR processed radar
recordings highlighted the occurrence of well-defined layering formed by
levels having the dielectric constant ($\epsilon=3.3$) typical of that lunar
regolith [116].

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 the site underwent remodelling for
multiple impacts [114]. Similar multiple regolith layers are interpreted to
exist also from Chang’e-3 Yutu rover data [117].

At satellite scale, seismic evidence suggests that the cumulative ejecta
thickness on the lunar highlands is possibly tens of kilometres thick [115].
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 [118]. (Figure 19).

Figure 19: Highly idealized cross-section through the internal structure of
the megaregolith and the upper lunar crust (modified after [115]). The depth
scale is highly uncertain because regional variations are expected depending
on the degree to which basin-sized impacts have influenced a region.

In the upper 1–2 km of the lunar maria, multiple layers of thick lava with
regolith on top have been identified [119].

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 (section 2.3.3 is crucial to determine the bearing capacity at the
landing site [120]. The latter reflects also in soil stability when planning
rover’s use for siting the instrumentation at distance from 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
[121]. 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 [122, 123]. 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 [124,
125] and because of the relevance of tidal deformation in estimating the lunar
orbital evolution [126]. Today, accurate models of the tidal potential are
available on the basis of ground-based or space-borne selenodetic observations
[127], 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 $\sim\pm
5^{\circ}$. Fourier analysis of the tidal potential [127] 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 $\sim 0.1$ m level, peak tilt (relative to the local plumb line) at the
$\sim 5\times 10^{-6}$ rad level, and peak disturbance to the gravitational
acceleration at the $\sim 0.5$ 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., 127]. 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 [128, 129].

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 $5\cdot 10^{-9}$ m/s2 during a
partial Phobos eclipse, which reduced the surface temperature in 1 m distance
by 2 K over 10s. [130] 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 $10^{-10}\,\rm{m\,Hz^{-1/2}}$
between 0.1 Hz and 1 Hz, corresponding to the instrument noise of the Apollo
seismometers[131, 35]. A modeled estimate of the SBN was set at about $2\times
10^{-14}\,\rm{m\,Hz^{-1/2}}$ 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 [132].

With more than 7000 events recorded [132, 133], 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 [132]. 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 [134, 133], each nest having
dimensions of 2 km or less[135, 134]. 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 [132, 134]. 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 [132, 133,
134, 136]. The most active nest, identified as $A_{1}$, counts more than 400
recorded events in the years 1969–1977 [135, 137].

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 [134]. 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 [134].

To date, the exact origin of DMQ remains unclear, and the presence of fluids
[138] or partial melts [133] in the Moon’s interior has been hypothesized.
Recently [139], 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 [140, 136].

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 [132, 137, 141]. 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 [142], 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, [143] released a mass-dependent
meteoroid flux estimate between $1.1\times 10^{-4}\,\rm hr^{-1}\,km^{-2}$ and
$1.1\times 10^{-7}\,\rm{1/(hr\,km^{2})}$. [144] completed the picture using
long-period seismic data issuing a rate between $1\times
10^{-7}\,\rm{1/(hr\,km^{2})}$ and $1.1\times 10^{-9}\,\rm{1/(hr\,km^{2})}$.
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 $7.00\times
10^{-8}\,\rm{1/(hr\,km^{2})}$ [145]. Between 2018 and 2020 [146], Near Earth
Orbit Lunar Impacts and Optical Transients (NELIOTA) detected 79 events with a
rate of $2.05\times 10^{-7}\,\rm{1/(hr\,km^{2})}$ for sporadic events and
$3.9\times 10^{-7}\,\rm{1/(hr\,km^{2})}$ for events during meteor showers. The
combined rate was found to be $2.3\times 10^{-7}\,\rm{1/(hr\,km^{2})}$.
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 [145, 146].
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
[145, 146]. 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[146].

Concerning the morphology of the seismic signals generated by impacts,
seismograms recorded by ALSEP show two distinct parts, high-frequency, and
low-frequency components [143]. 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 [132, 137] 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 [137]. 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 forth class of seismic events is thermally triggered. [147] 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, [148] 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 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 [149]. 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 [150, 151]. 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 [152]. The principal domains are
shown in figure 20.

Figure 20: Sketch of the plasma and magnetic environment around the lunar
orbit.

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 [153]. Wave activity is manifested in the foreshock region
[154], 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 [155], 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 [156]. 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 ([157]; [158]). This structure is
called mini-magnetosphere, and is one of the main scientific topics for the
lunar plasma environment ([159]).

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) [160]. Recent numerical simulations
reproduced the limb compression signature when the mini-magnetosphere reflects
the solar wind protons back into space ([161]).

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 [162]. A global proton reflection from the
lunar surface also excites such wave activities [163]. In addition, [164],
[165] 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 [166] 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 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
[167]. 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., [168]. 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 21.

Figure 21: 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.

Soundcheck is expected to reach sub-pm/Hz1/2 inertial sensitivity above 0.1 Hz
and probe the SBN with unprecedented precision.

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 [169], 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/$\surd$Hz sensitivity. There are several options, such as homodyne
quadrature interferometry [e.g. 170] and deep frequency modulation
interferometry [e.g. 171]. While both are theoretically similar in performance
[172], the homodyne quadrature interferometric readout is less computationally
demanding and therefore preferred for Soundcheck given its more stringent
power budget.

Figure 22: Minimum detectable inertial displacement for the Soundcheck using a
3 kg niobium Watt’s linkage with an interferometric readout. More details in
the text.

#### 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 [173]. 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 [174] at
the following DOI:$\rm{10.7914/SN/XA\\_1969}$. 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
[137].

Concerning Earth-based observations, there are currently two active
collaborations, namely MEO [145] at NASA and NELIOTA [146] 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
[175]. 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) [176],
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 [121]. 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 [177]. 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
[178]. The catalog has been constantly updated with state-of-the-art methods
applied to the data [179, 180], and even today, new events are discovered from
the data [e.g 181]. 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
[182].

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
[132, 134]. 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. 183]. 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. 184, 185]. These may result in variations of
the seismicity rate and spatial distribution, and to elucidate this open
question, new observation at different location 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

Figure 23: 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 [132]).

The different types of moonquakes are generally classified with their source
depth and mechanism (see Figure 23). The first type is deep moonquakes, which
are most frequently observed seismic event on the Moon, and more than 7000
events were reported [178, 179, 180]. 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 [132].
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 [132, 133, 179] 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 [140, 186, 139, 187]. 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 [118]. 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 [132, 118]. 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 [188].
Watters et al. [189] 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. [189] 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 a 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 [190] 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. [183]
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 originates 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) [191, 192]. 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 [193, 194]. Finally,
the seismic signal of a small primordial black hole with mass of $10^{15}$ g
traversing the Moon was studied [195], and primordial black holes of mass
$>10^{19}$ g would form impact craters with a distinct morphology [196]. 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,
[197]) 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, [198]), 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) [100]. This model has been recently updated
through a thorough review of seismic data and events [136, 180].

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 mantle-crust boundary below the
station [199, 200]. 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 [201]. The lunar ’Moho’ discontinuity (the
crust–mantle interface) is set at a depth of $40\,$km [202] to fit geodetic
observations. This, in turn, imposes a constraint on the density contrast
between crust and mantle, resulting in about $\sim 0.55$. 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 [203].

The average reference model of the Moon describes physical properties,
including core radius and density. A core radius of $380\pm 40\,$km and an
average core mass density of $5200\pm 1000\,\text{kg/m}^{3}$ 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
Fig. 24, which also features the VPREMOON model by [100], represented in cyan.
These models are overall consistent up to a depth of $\sim 1200\,$km. At