11institutetext: Space Research Institute of the Austrian Academy of Sciences,
Schmiedlstrasse 6, 8042 Graz, Austria
11email<EMAIL_ADDRESS>22institutetext: Department of Physics,
University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, UK 33institutetext:
Centre for Exoplanets and Habitability, University of Warwick, Gibbet Hill
Road, Coventry CV4 7AL, UK 44institutetext: IRAP, Université de Toulouse,
CNRS, CNES, UPS, 9 avenue Colonel Roche, FR-31400, Toulouse, France
55institutetext: Istituto Nazionale di Astrofisica, Istituto di Astrofisica e
Planetologia Spaziali, via Fosso del Cavaliere 100, I-00133 Rome, Italy
66institutetext: European Space Astronomy Centre, Camino Bajo del Castillo,
s/n., Urb. Villafranca del Castillo, 28692 Villanueva de la Cañada, Madrid,
Spain 77institutetext: Scientific Support Office, Directorate of Science,
European Space Research and Technology Centre, 2201 AZ Noordwijk, The
Netherlands

# Cometary dust collected by MIDAS on board Rosetta††thanks: Table
LABEL:table:_MIDAS_particle_shape_descriptor_full_table is only available in
electronic form at the CDS via anonymous ftp to cdsarc.cds.unistra.fr
(130.79.128.5) or via https://cdsarc.cds.unistra.fr/cgi-bin/qcat?J/A+A/. MIDAS
dust coverage, clustering, and shape descriptor maps can be found
https://minjaegasparkim.github.io/Rosetta-MIDAS_dust_maps

II. Particle shape descriptors and pristineness evaluation

M. Kim Cometary dust collected by MIDAS on board Rosetta††thanks: Table is
only available in electronic form at the CDS via anonymous ftp to
cdsarc.cds.unistra.fr (130.79.128.5) or via https://cdsarc.cds.unistra.fr/cgi-
bin/qcat?J/A+A/. MIDAS dust coverage, clustering, and shape descriptor maps
can be found https://minjaegasparkim.github.io/Rosetta-MIDAS_dust_mapsCometary
dust collected by MIDAS on board Rosetta††thanks: Table is only available in
electronic form at the CDS via anonymous ftp to cdsarc.cds.unistra.fr
(130.79.128.5) or via https://cdsarc.cds.unistra.fr/cgi-bin/qcat?J/A+A/. MIDAS
dust coverage, clustering, and shape descriptor maps can be found
https://minjaegasparkim.github.io/Rosetta-MIDAS_dust_mapsCometary dust
collected by MIDAS on board Rosetta††thanks: Table is only available in
electronic form at the CDS via anonymous ftp to cdsarc.cds.unistra.fr
(130.79.128.5) or via https://cdsarc.cds.unistra.fr/cgi-bin/qcat?J/A+A/. MIDAS
dust coverage, clustering, and shape descriptor maps can be found
https://minjaegasparkim.github.io/Rosetta-MIDAS_dust_mapsCometary dust
collected by MIDAS on board Rosetta††thanks: Table is only available in
electronic form at the CDS via anonymous ftp to cdsarc.cds.unistra.fr
(130.79.128.5) or via https://cdsarc.cds.unistra.fr/cgi-bin/qcat?J/A+A/. MIDAS
dust coverage, clustering, and shape descriptor maps can be found
https://minjaegasparkim.github.io/Rosetta-MIDAS_dust_mapsCometary dust
collected by MIDAS on board Rosetta††thanks: Table is only available in
electronic form at the CDS via anonymous ftp to cdsarc.cds.unistra.fr
(130.79.128.5) or via https://cdsarc.cds.unistra.fr/cgi-bin/qcat?J/A+A/. MIDAS
dust coverage, clustering, and shape descriptor maps can be found
https://minjaegasparkim.github.io/Rosetta-MIDAS_dust_mapsCometary dust
collected by MIDAS on board Rosetta††thanks: Table is only available in
electronic form at the CDS via anonymous ftp to cdsarc.cds.unistra.fr
(130.79.128.5) or via https://cdsarc.cds.unistra.fr/cgi-bin/qcat?J/A+A/. MIDAS
dust coverage, clustering, and shape descriptor maps can be found
https://minjaegasparkim.github.io/Rosetta-MIDAS_dust_maps T. Mannel Cometary
dust collected by MIDAS on board Rosetta††thanks: Table is only available in
electronic form at the CDS via anonymous ftp to cdsarc.cds.unistra.fr
(130.79.128.5) or via https://cdsarc.cds.unistra.fr/cgi-bin/qcat?J/A+A/. MIDAS
dust coverage, clustering, and shape descriptor maps can be found
https://minjaegasparkim.github.io/Rosetta-MIDAS_dust_mapsCometary dust
collected by MIDAS on board Rosetta††thanks: Table is only available in
electronic form at the CDS via anonymous ftp to cdsarc.cds.unistra.fr
(130.79.128.5) or via https://cdsarc.cds.unistra.fr/cgi-bin/qcat?J/A+A/. MIDAS
dust coverage, clustering, and shape descriptor maps can be found
https://minjaegasparkim.github.io/Rosetta-MIDAS_dust_maps J. Lasue Cometary
dust collected by MIDAS on board Rosetta††thanks: Table is only available in
electronic form at the CDS via anonymous ftp to cdsarc.cds.unistra.fr
(130.79.128.5) or via https://cdsarc.cds.unistra.fr/cgi-bin/qcat?J/A+A/. MIDAS
dust coverage, clustering, and shape descriptor maps can be found
https://minjaegasparkim.github.io/Rosetta-MIDAS_dust_mapsCometary dust
collected by MIDAS on board Rosetta††thanks: Table is only available in
electronic form at the CDS via anonymous ftp to cdsarc.cds.unistra.fr
(130.79.128.5) or via https://cdsarc.cds.unistra.fr/cgi-bin/qcat?J/A+A/. MIDAS
dust coverage, clustering, and shape descriptor maps can be found
https://minjaegasparkim.github.io/Rosetta-MIDAS_dust_maps A. Longobardo
Cometary dust collected by MIDAS on board Rosetta††thanks: Table is only
available in electronic form at the CDS via anonymous ftp to
cdsarc.cds.unistra.fr (130.79.128.5) or via https://cdsarc.cds.unistra.fr/cgi-
bin/qcat?J/A+A/. MIDAS dust coverage, clustering, and shape descriptor maps
can be found https://minjaegasparkim.github.io/Rosetta-MIDAS_dust_mapsCometary
dust collected by MIDAS on board Rosetta††thanks: Table is only available in
electronic form at the CDS via anonymous ftp to cdsarc.cds.unistra.fr
(130.79.128.5) or via https://cdsarc.cds.unistra.fr/cgi-bin/qcat?J/A+A/. MIDAS
dust coverage, clustering, and shape descriptor maps can be found
https://minjaegasparkim.github.io/Rosetta-MIDAS_dust_maps M. S. Bentley
Cometary dust collected by MIDAS on board Rosetta††thanks: Table is only
available in electronic form at the CDS via anonymous ftp to
cdsarc.cds.unistra.fr (130.79.128.5) or via https://cdsarc.cds.unistra.fr/cgi-
bin/qcat?J/A+A/. MIDAS dust coverage, clustering, and shape descriptor maps
can be found https://minjaegasparkim.github.io/Rosetta-MIDAS_dust_mapsCometary
dust collected by MIDAS on board Rosetta††thanks: Table is only available in
electronic form at the CDS via anonymous ftp to cdsarc.cds.unistra.fr
(130.79.128.5) or via https://cdsarc.cds.unistra.fr/cgi-bin/qcat?J/A+A/. MIDAS
dust coverage, clustering, and shape descriptor maps can be found
https://minjaegasparkim.github.io/Rosetta-MIDAS_dust_maps R. Moissl Cometary
dust collected by MIDAS on board Rosetta††thanks: Table is only available in
electronic form at the CDS via anonymous ftp to cdsarc.cds.unistra.fr
(130.79.128.5) or via https://cdsarc.cds.unistra.fr/cgi-bin/qcat?J/A+A/. MIDAS
dust coverage, clustering, and shape descriptor maps can be found
https://minjaegasparkim.github.io/Rosetta-MIDAS_dust_mapsCometary dust
collected by MIDAS on board Rosetta††thanks: Table is only available in
electronic form at the CDS via anonymous ftp to cdsarc.cds.unistra.fr
(130.79.128.5) or via https://cdsarc.cds.unistra.fr/cgi-bin/qcat?J/A+A/. MIDAS
dust coverage, clustering, and shape descriptor maps can be found
https://minjaegasparkim.github.io/Rosetta-MIDAS_dust_maps the MIDAS team

(Received 13 June, 2023 / Accepted 10 August, 2023)

###### Abstract

Context. The MIDAS (Micro-Imaging Dust Analysis System) atomic force
microscope on board the Rosetta comet orbiter investigated and measured the 3D
topography of a few hundred of nm to tens of $\mu$m sized dust particles of
67P/Churyumov-Gerasimenko with resolutions down to a few nanometers, giving
insights into the physical processes of our early Solar System.

Aims. We analyze the shapes of the cometary dust particles collected by MIDAS
on the basis of a recently updated particle catalog with the aim to determine
which structural properties remained pristine.

Methods. We develop a set of shape descriptors and metrics such as aspect
ratio, elongation, circularity, convexity, and particle surface and volume
distribution, which can be used to describe the distribution of particle
shapes. Furthermore, we compare the structure of the MIDAS dust particles and
the clusters in which the particles were deposited to those found in previous
laboratory experiments and by Rosetta/COSIMA. Finally, we combine our findings
to calculate a pristineness score for MIDAS particles and determine the most
pristine particles and their properties.

Results. We find that the morphological properties of all cometary dust
particles at the micrometer scale are surprisingly homogeneous despite
originating from diverse cometary environments (e.g., different collection
targets that are associated with cometary activities/source regions and
collection velocities/periods). There is only a weak trend between shape
descriptors and particle characteristics such as size, collection targets, and
cluster morphology. We next find that the types of clusters found by MIDAS
show good agreement with those defined by previous laboratory experiments,
however, there are some differences to those found by Rosetta/COSIMA.
Furthermore, our pristineness score shows that almost half of MIDAS particles
suffered severe alteration by impact, which indicates structural modification
by impact (e.g., flattening and/or fragmentation) is inevitable despite the
very low collection speeds (i.e., $\sim$ 3 - 7 m s-1). Based on our result, we
rate 19 out of 1082 MIDAS particles at least moderately pristine that is they
are not substantially flattened by impact, not fragmented, and/or not part of
a fragmentation cluster.

###### Key Words.:

comets: 67P/Churyumov-Gerasimenko – space vehicles: Rosetta – space vehicles:
instruments – planets and satellites: formation – techniques: miscellaneous –
protoplanetary disks

##  1 Introduction

Since the formation of comets, asteroids, planetesimals, and planets is
expected to start with the aggregation of the smallest interstellar dust
particles (Tielens et al., 2005; Li & Greenberg, 2003; Weidenschilling &
Cuzzi, 1993; Blum & Wurm, 2008), the properties of the smallest dust grains in
the early solar system are of great importance. These have been the focus of
various studies, for example, the sample return mission flying by comet
81P/Wild 2, Chondritic Porous Interplanetary Dust Particles collected in the
stratosphere, as well as the ultracarbonaceous Antarctic micrometeorites
(Brownlee et al., 2006; Flynn et al., 2013; Noguchi et al., 2015; Duprat et
al., 2010). In particular, cometary material is the result of aggregation
processes known to take place in extremely low gravity conditions that can
result in aggregates with low tensile strength (Sierks et al., 2015; Attree et
al., 2018). These fragile structures are suspected to have been stored in
comets and to be lifted into the coma by cometary activity (e.g., Blum et al.,
2017). However, these investigations are hampered by the severe alteration of
the dust particles between their time of release from the comet and their
investigation, for example, due to heating to temperatures above the melting
point of silica as well as due to the capturing process (Hörz et al., 2006),
and the passage through Earth’s atmosphere (Flynn et al., 2013).

To obtain structural information on pristine cometary dust particles, a unique
opportunity to sample the dust and gas environment of the inner coma of comet
67P/Churyumov-Gerasimenko (hereafter 67P) was pioneered by the Rosetta mission
between 2014 and 2016. The Micro-Imaging Dust Analysis System (MIDAS; Riedler
et al. 2007; Bentley et al. 2016a), one of three in-situ dust instruments on
board, is the first generation Atomic Force Microscope (AFM) that was launched
into space to collect the smallest cometary dust particles with sizes from
hundreds of nanometers to tens of micrometers. It recorded the 3D
topographic/textural information with nanometer resolution and collected
statistical parameters (Kim et al., 2023). Most importantly, dust particles
were collected close to the comet (less than $\sim$ 30 km afar) with low
relative velocities between spacecraft and nucleus, roughly between some cm
s-1 and 10 m s-1 (e.g., Della Corte et al., 2015), which enables to collect
dust particles with only a small degree of alteration. In particular, small
particles are assumed to be aggregates of subunits (Bentley et al., 2016b)
that have a higher internal strength so their sizes and shapes might be
possibly still pristine (Hornung et al., 2016).

Depending on the particle strength and the collection velocity, dust particles
hitting a collection target either undergo alteration such as break up or
compaction, or they stay intact (Ellerbroek et al., 2017; Hornung et al.,
2016). The secondary ion mass spectrometer COSIMA (Cometary Secondary Ion Mass
Analyser; Langevin et al., 2016), using a similar ‘hit and stick’ collection
technique to MIDAS but for particles one to two orders of magnitude larger,
observed that the majority of dust particles would fragment upon collection
and create large scatter fields of fragments (Langevin et al., 2016). This
finding was confirmed by a laboratory experiment for particles larger than
about 80 micrometers (Ellerbroek et al., 2017). It is, however, still an open
question to understand to what extent the one order of magnitude smaller MIDAS
particles were altered during the collection process, and which of the MIDAS
particles show pristine structures. The straightforward dust collection
strategy with MIDAS (i.e., the dust particles from 67P entered the MIDAS
instrument via a funnel and simply hit the targets; Bentley et al., 2016a)
could lead to an unknown degree of collection alteration. Consequently, dust
alteration during the collection process has to be understood to retrieve the
properties of pristine and more realistic cometary particles. Furthermore, the
flow properties of bulk materials (e.g., flowability) are influenced by
particle shape and particle size, amongst others (Mellmann et al., 2013).
Thus, the investigation of unaltered and thus more realistic particles could
open up new possibilities for unraveling unresolved questions in space
science, particularly in gas flow experiments in cometary environments (Laddha
et al., 2023). The importance of shape descriptors of the non-spherical MIDAS
particles (Bentley et al., 2016b; Kim et al., 2023) is further enhanced as
traditional models using purely spherical particles might not be sufficient to
significantly improve gas flow models further.

In this paper, a ‘pristine’ particle is a particle that was not altered by the
collection that is a particle as it was moving through the cometary coma.
Depending on its history between its formation in the early solar system and
its collection, this particle may or may not be modified by its flight through
the coma, ejection from the cometary surface, storage, or incorporation into
the comet. Thus, it has to be judged case by case in which sense a particle’s
properties reflect properties of cometary dust in the coma, the comet, or even
in the early solar system.

Using the final MIDAS particle catalog that contains all cometary dust
particles collected by MIDAS together with their basic properties, called
particle catalog V6111ESA planetary science archive of MIDAS/Rosetta (PSA
6.2.4), dataset identifier: RO-C-MIDAS-5-PRL-TO-EXT3-V3.0,
https://archives.esac.esa.int/psa/#!Table%20View/MIDAS=instrument (Kim et al.
2023), we focus on the development of MIDAS particle shape descriptors to
understand the degree of dust alteration and we determine the structural
properties of the MIDAS dust particles that remained pristine. This
paper222The present study follows a dust classification scheme (i.e., the
definition of language for all the different dust pieces) that has already
been unified with a clearly defined vocabulary within the Rosetta dust studies
(Mannel et al. 2019; Güttler et al. 2019; Kim et al. 2023). is organized as
follows: We provide a description of the MIDAS instrument and its collection
procedure in Sect. 2. Next, we discuss the development of MIDAS particle shape
descriptors and the MIDAS cluster classifications. We describe the evaluation
of MIDAS particles and clusters based on MIDAS shape descriptors and compare
them to previous studies in Sect. 3. Based on these results, we investigate
the development of a pristineness descriptor of MIDAS particles. We summarize
our findings and address the outlook of this study in Sect. 4.

##  2 Methods

###  2.1 The MIDAS AFM and its dust collection

MIDAS was a unique instrument designed to collect and investigate the size,
shape, texture, and microstructure of cometary dust particles down to the 10s
of nanometers scale (Riedler et al., 2007; Bentley et al., 2016a). The MIDAS
dust intake system consisted of a funnel and a shutter that could be opened to
allow dust particles to fall into the collection targets mounted onto a wheel.
After the collection of a dust particle, the wheel was rotated to transport
the dust particle to the AFM, which physically scanned over the particles.

A scientific sequence of MIDAS was started with a prescanning of an area of a
target, exposing it to the dust flux of the comet, and rescanning of the same
area with low resolution. If a dust particle was detected, it was then scanned
with optimized parameters (Bentley et al., 2016a). There are two operating
modes (i.e., amplitude-modulated ‘dynamical mode’ and ‘contact mode’) in
MIDAS, while MIDAS mainly utilized an amplitude-modulated mode, which
effectively avoided feedback issues (e.g., most AFMs that operate in a vacuum
use frequency modulation, potentially causing damage and fragmentation,
especially with large particles having high Z gradients; Hecht et al., 2008;
McSween et al., 2010) by performing software-controlled point approaches to
each pixel of the image (Bentley et al., 2016a). This approach is slower than
traditional AFMs, but minimizes damage at each pixel position of particles,
making it ideal for studying delicate or sensitive samples.

The force arising from the tip-sample interaction in MIDAS causes the
deflection of the piezo-resistive cantilevers. These cantilevers, attached to
the sharp tip, can electrically detect their own deflection without the need
for additional sensing elements. Specifically, when the tip-sample separation
is small (around 5–10 nm), the electron orbits interact, resulting in a weak
attractive force. Consequently, the resonance frequency of the cantilever
changes due to a virtual increase in its spring constant. When excited close
to their resonant frequency ($\sim$ 80 - 100 kHz) the cantilevers have an
amplitude of cantilever vibration on the order of 40 - 100 nm. The tip-sample
interaction arises from a combination of short-range, repulsive atomic forces,
and long-range Van der Waals force (Riedler et al., 2007). When operated in
the contact mode, which operates close to the repulsive force regime where the
very sharp tip (i.e., tip radius $\sim$ 10 to 15 nm) physically touches the
surface of particles, the force applied by the tip to the sample is
approximately 10-7 – 10-6 N (Riedler et al., 2007), translating to a pressure
range during measurements spanning approximately 100 MPa to 2500 MPa. However,
when operated in dynamic mode, the expected force is reduced to 10-8 N
(Riedler et al., 2007), corresponding to the pressure values during the
measurements that lie within the range of around 10 MPa to 25 MPa. This
relatively small force and the absence of lateral forces minimize the
likelihood of damaging the tip or sample. In addition, the approach (force-
distance) curve of the MIDAS instrument can be recorded throughout an image,
providing valuable information about the physics of the tip-sample interaction
and the physical properties of the sample.

Rastering over the particles’ surface, a 3D image of cometary dust was
created, which enabled the determination of the particle structure, and thus
an insight into the properties of micro- to nanometer-sized dust particles. In
particular, the high-resolution MIDAS images allow us to determine particle
shape factors and descriptors. We note that the volume estimate in MIDAS may
be susceptible to over-estimation due to several factors (e.g., tip dilation
and concave surfaces; see Sect. 3.1.1), which can lead to incomplete imaging
of certain particles, potentially resulting in inaccuracies in the volume
measurements. In the retrieved scans identifying dust grains and marking them
with a mask is performed by hand with the open-source package Gwyddion (Nečas
& Klapetek, 2012). More detailed information about MIDAS and its dataset can
be found in previous MIDAS studies (e.g., Riedler et al., 2007; Bentley et
al., 2016a; Mannel et al., 2016, 2019; Kim et al., 2023).

MIDAS collected nano- to micrometer-sized cometary dust particles on 4
different small (1.4 mm x 2.4 mm) and sticky targets (i.e., target 11, target
13, target 14, and target 15)333Note that previous studies (e.g., Longobardo
et al., 2022; Kim et al., 2022) adopt different indexing, which comes from the
number of telemetries counted from 1 to 64. However, the MIDAS particle
catalog (Kim et al., 2023) and browse images count the targets from 0 to 63.
Thus, target numbers 10, 12, 13, and 14 in the previous studies correspond to
target numbers 11, 13, 14, and 15, respectively, in this study., where each
target collected dust in different periods. For example, the dust particles on
Target 11, Target 13, and Target 15 were collected before perihelion and the
ones on Target 14 were collected in an outburst after perihelion. Furthermore,
the average compact dust speed was estimated for exposition periods of each
MIDAS target via speed measurements of GIADA (Longobardo et al., 2022). In
particular, the mean velocities for the particle collections on targets 11 and
13 are slower (i.e., 3.1 $\pm$ 1.5 and 2.7 $\pm$ 0.3 m s-1, respectively),
while the velocities of the particles collected on target 14 and 15 are faster
(i.e., 7.21 $\pm$ 0.09 and 7.2 $\pm$ 0.2 m s-1, respectively; Longobardo et
al., 2022). The standard deviation range corresponds to each MIDAS target 1-2
m s${}^{-}1$. Furthermore, the standard deviation of the entire GIADA-MIDAS
dataset is 6 m s${}^{-}1$. The detailed list of target exposure history and
duration can be found in Appendix Table B.1. in Kim et al. (2023).

Assuming the same source region of particles detected by GIADA and MIDAS in
the same period, Longobardo et al. (2022) determined which MIDAS particles
stem from which source area of the comet based on a traceback algorithm
applied to GIADA data (Longobardo et al., 2020). In particular, MIDAS
particles on target 14 originated from rough terrains (or deeper layers),
implying that these particles are expected to be more pristine. On the other
hand, particles on target 15 were ejected from smooth terrains, which are
thought to originate from dust particles falling back to the cometary surface
after ejection, creating smooth plains that can be as much as a few meters
thick (Longobardo et al., 2020). Since ejection, travel through the coma,
backfall, and re-ejection are likely to result in particle alteration,
particles on target 15 may not be as pristine as those on target 14.
Furthermore, particles collected on targets 11 and 13 originated from both
types of terrain.

###  2.2 Development of MIDAS particle shape descriptors

Since particle shape descriptors represent a range of properties, for
instance, a spatial variation on a large scale or irregularity/surface
textures on a small scale (Berrezueta et al. 2019), they are well suited to
evaluate and classify our particle collection. Thus, we develop MIDAS particle
shape descriptors to determine particles preserving their pristineness.

We start from 3523 MIDAS particle identifications based on the updated MIDAS
particle catalog V6 (Kim et al. 2023). For further investigation, we select
particles only usable for further investigation (e.g., only particles of
cometary origin, particles with a preferably low amount of alteration,
particles not shown to be fragments of particles, particles were not
susceptible to being multiple fragments, particles not suspected to have
fallen off a tip), which is necessary to ensure the integrity and reliability
of the dataset. Additionally, we remove duplicates as many MIDAS dust
particles were scanned several times and thus select the best representation
of particles (Kim et al. 2023). Next, we again exclude particles with a very
small number of pixels in images (e.g., ¡ 10) due to the physical difficulties
of further analysis with a small number of pixel particles. After applying
these selection criteria, 1082 MIDAS particles are used for the analysis of
shape descriptors in total. These selected particles will serve as the basis
for our in-depth analysis and study of cometary particles and their properties
including shape descriptors. More detailed information about MIDAS particle
selection for further investigation can be found in previous MIDAS studies
(e.g., Kim et al., 2023).

For the development of MIDAS particle shape descriptors, we first apply
several pre-processing procedures, most importantly, rotation of the data to
align the scan direction to the horizontal direction, correction of horizontal
scars in scan files, alignment of rows in scan files using the median of
differences algorithm, leveling of the data by means of a plane subtraction,
and the rotation of scan files in the opposite direction of the first rotation
with the Gwyddion Python module called
Pygwy444http://gwyddion.net/documentation/user-guide-en/pygwy.html to all scan
files to clean up the MIDAS data. This is necessary to avoid falsification of
the result by AFM image artifacts.

We consider several independent 2D or 3D shape descriptors and
shape/morphological parameters, for example, aspect ratio (Lasue et al. 2019),
elongation (Bentley et al. 2016b), circularity (often called 2D sphericity;
Berrezueta et al. 2019), and convexity (often called solidity parameter or 2D
roughness; Berrezueta et al. 2019). In the present section, we introduce the
shape descriptors and correlate them with already derived particle properties.
We note that there are limitations (e.g., resolution) and possible sources of
uncertainty that must be considered when performing particle shape analysis as
with all imaging/measurement techniques. Furthermore, AFM measurements provide
only a 2D projection of the particle’s surface. As a result, the actual 3D
shape is not directly determined by the applied method; rather, only the 3D
topology is obtained. Therefore, this limitation should be considered in the
following analyses.

Aspect ratio: We calculate the aspect ratio $\frac{H}{\sqrt{A}}$, where $H$ is
the height (i.e., subtraction of the median height value to all pixels
surrounding a particle from the maximal z value of that particle) and $A$ is
the projected 2D area of the dust particle/cluster on the target. The aspect
ratio is used as a tool to assess the degree of flattening of MIDAS dust
particles (Lasue et al. 2019). For example, higher aspect ratio particles
indicate that particles are less flattened. In particular, we assume particles
with ratios over about 0.8 are unflattened based on the aspect ratio
distribution of MIDAS particles (see Sect. 3.1.2).

In the present work, we determine the aspect ratio for MIDAS particles and
clusters (Kim et al., 2023), compare them with those found for COSIMA
particles and clusters in Lasue et al. (2019), and check if the aspect ratio
can be used as a proxy for particle pristineness (i.e., investigate whether
results from Lasue et al. (2019) are also valid for MIDAS particles).

Elongation: We calculate two elongations of MIDAS particles to determine how
much the shape deviates from a sphere: i) the major axis to the height
$\frac{a}{h}$, where $a$ is the major axis of the 2D projection and $h$ is the
height of the particle, called ‘3D elongation’ and ii) the major axis to the
minor axis $\frac{a}{b}$, where $b$ is the minor axis of 2D projection, called
‘2D elongation’, where all axes and heights have to be in 90 degrees angle to
each other in the coordinate system based on the target after leveling work
(Bentley et al., 2016b). An elongation value larger than 1 indicates that the
shapes of the particles deviate from a spherical form. The final elongation
value is chosen as the bigger elongation between the 2D and 3D elongation.

Circularity: We calculate a circularity $\frac{4\,\pi\,A}{P^{\rm{\,2}}}$,
where $A$ is the area of the particle of the 2D projection and $P$ is the 2D
projection perimeter of the particle, to quantify roundness. Physically, a
circularity value of 1 corresponds to a circle.

Convexity: We calculate a convexity $\frac{A}{A_{\rm{convex}}}$, where $A$ is
the area of the particle and $A_{\rm{convex}}$ is the area defined by the
convexity produced by the irregularity of the edge of the particle, to
describe how fringed the rims are. This parameter is defined as the ratio
between the area of the silhouette and the convex hull of the silhouette.
Thus, it represents the 2D projection roundness of particles. For example, a
convexity value of 0.5 corresponds to 100$\%$ of the convex hull area occupied
by perimeter concavities. A brief sketch of an example is given in Fig. 1.

Figure 1: Brief sketch of the comparison between the area of the silhouette
and the convex hull of the silhouette on the example of an original MIDAS
particle (Particle ID: 2015-11-22T165903$\\_$P01$\\_$T15; Kim et al., 2023).
The value of the convexity of this particle shows 0.456.

Particle surface and volume distribution: Since the impact residue strongly
depends on the size of the initial particle and velocity (Ellerbroek et al.,
2017), the deposit left by such an impact can be investigated to understand
how the impact on the target modified the particles and thus determine the
degree of alteration of its structure. We aim to link the amount of dust
deposited to the distance from the center of the deposit by refining previous
ideas (Guarino, 2019) and applying them to MIDAS particles. This allows an
understanding of the shape of a deposit (e.g., pyramidal or rectangular) and
the nature of its rims (e.g., steep cliff-like or shallow sloped, asymmetric
curved rim or straight edge).

The residue from the impact covered by dust is computed as the number of
pixels with dust as the volume (or height) associated with those pixels. The
algorithm of the two developed deposit studies is described below:

\- Particle surface distribution: We investigate the area of the particle on
the 2D projection. For each particle, the image is divided into N rings (where
N is the total number of rings from the center to the outermost possible ring
with each ring being 1 pixel thick) from the center of the deposit. This
center is computed as the mean value of the x and y coordinates of the pixels
of the mask (i.e., left & right and up & down, Sect. 2.1). We compute the area
of the particle laying inside each i-th ring (i.e., summing the number of
pixels with dust). Finally, we calculate for each ring the percentage of
pixels with dust (i.e., that belonging to the particle) in that ring.

\- Particle volume distribution: We investigate the volume of the particle by
weighing the particle surface distribution by the height of each pixel. Note
that the value of the particle volume distribution plot can be smaller than
the one of particle surface distribution because the unit of height values is
in micrometer (e.g., in case the height value is below 1 $\mu$m).

Based on the particle surface and volume distribution, a clear distinction
between solid and roundish particle bulks with defined rims (the so-called
‘MIDAS Single’ particles) and other shapes (e.g., elongated shapes with
fringed rims; so-called ‘MIDAS Pile’) become apparent. The name convention is
adopted from the work of Ellerbroek et al. (2017) because ‘MIDAS Single’
particles look like ‘single morphology’ from Ellerbroek et al. (2017).
Examples of the results from the two algorithms (particle surface and volume
distribution) along with 3D images of the investigated particles are given in
Fig. 2.

Figure 2: Example of particle surface and volume distribution of ‘MIDAS
Single’ (e.g., typically a solid, roundish bulk and shows a plateau in the
particle surface distribution; left column) and ‘MIDAS Pile’ (e.g., elongated
shapes, fringed rims, and no plateau visible in the surface distribution and
thus less steep slope than one for the MIDAS Single particles; right column)
particles. 3D images of the MIDAS Single and MIDAS Pile particles are marked
with red circles in the left and right bottom images.

###  2.3 MIDAS cluster/particle classification

We investigate possible similarities between the MIDAS dataset and previous
studies that classified shapes of cometary dust particles (e.g., Ellerbroek et
al. 2017; Langevin et al. 2016). This classification work is a cornerstone to
determine particle pristineness because particle properties that were already
connected to alteration or pristineness in other studies could be identified
in MIDAS data as well and be similarly interpreted.

Ellerbroek et al. (2017) investigated the footprint of cometary dust analogs
in laboratory experiments using low-velocity impacts of analog materials and
compared these with COSIMA and MIDAS data. They found that the degree of
alteration is strongly determined by the initial particle size and the impact
velocity. In particular, for certain combinations of size and velocity, only a
part of the dust particle is left on the target and the amount of mass
transferred increases with the impact velocity. Thus, the velocity is the main
driver of the appearance of the resulting deposits for most collisions. For
example, for velocities $v$ below $\sim$ 2 m s-1, initial parent particles
either stick without visible alteration and leave a ‘single’ deposit on the
target plate, or the parent particles bounce, leaving a shallow ‘footprint’
that is a flat layer of monomers. At velocities $v$ ¿ 2 m s-1 and initial
parent particle sizes ¿ 80 $\mu$m, particles fragment upon collision,
transferring up to 50 percent of their mass in a rubble-pile-like deposit
named ‘pyramid’ morphology on the target.

In the case of MIDAS particle collection, we investigate possible
fragmentation of the collected particles using a sophisticated algorithm (the
mean-shift algorithm method; Kim et al. 2023) to identify dust pieces
belonging together, so-called MIDAS clusters. The algorithm was cautiously
tested in Kim et al. (2023), for example, the expected size of the clusters
for each target and thus the optimal cluster number was validated by the
k-nearest neighbors algorithm (Cover & Hart, 1967) and silhouette analysis
(Rousseeuw, 1987), the assignment of particles into clusters was shown to be
statistically significant, similar results were obtained by a different
algorithm described in Longobardo et al. (2022), and the identified cluster
morphologies are comparable to those found in other experiments (Ellerbroek et
al., 2017; Langevin et al., 2016).

Table 1: Mean velocity, orbital epoch of collection, type of terrains, and the number of the different cluster types (deposits) listed for each MIDAS target. Target | Mean | Orbital | Type | MIDAS | MIDAS | MIDAS
---|---|---|---|---|---|---
velocity | epoch of | of | Single | Footprint | Pyramid
[m s -1] | collection | terrains | Cluster | Cluster | Cluster
11 | 3.1 $\pm$ 1.5 | Pre-perihelion | Rough + Smooth | 31 | 14 | 7
13 | 2.7 $\pm$ 0.3 | Pre-perihelion | Rough + Smooth | 10 | 4 | 0
14 | 7.21 $\pm$ 0.09 | Post-perihelion | Rough | 48 | 61 | 17
15 | 7.2 $\pm$ 0.2 | Pre-perihelion | Smooth | 3 | 0 | 1
Total |  |  |  | 92 | 79 | 25

Using this identification, we investigate whether the morphologies of MIDAS
deposits are qualitatively similar to those found by previous laboratory
studies (Ellerbroek et al., 2017). The automatic algorithm determined clusters
with characteristics that are strongly aligned with the three morphological
groups defined in Ellerbroek et al. (2017). In particular, we consider the
number of all fragments in one cluster (MIDAS single cluster vs. MIDAS
footprint and MIDAS pyramid clusters), the existence of a dominant central
fragment (MIDAS footprint cluster vs. MIDAS pyramid cluster), and the diameter
of the scattering field compared to the size of the central fragment or
deposit (MIDAS footprint cluster vs. MIDAS pyramid cluster). In conclusion, we
summarize the MIDAS classification into three different morphological types
defined based on Ellerbroek et al. (2017) as follows:

-MIDAS single cluster555We note that the ‘MIDAS single cluster’ term should not be confused with ‘MIDAS Single’ from particle surface and volume distribution in Sect. 2.2: Deposits should have a clearly defined central component with only a few ($\leq$ 2) or no scattered fragments, resulting from the sticking of the entire aggregate upon impact with little or no fragmentation.

-MIDAS footprint cluster: The most important morphological characteristic is that there is a collection of monomers with no dominant central fragment, resulting from the bouncing of the parent particle upon impact. The scattered field is about twice the size of the left central fragment due to the bouncing effect.

-MIDAS pyramid cluster: Deposits should have a clearly defined central fragment with a lot of scattered debris around it, resulting from the fragmentation upon impact. The diameter of the scattering field is about twice the central deposit.

An example of the classification of MIDAS clusters, e.g., a MIDAS single
cluster, a MIDAS footprint cluster, and a MIDAS pyramid cluster, and the
appearance of different morphological types from Ellerbroek et al. 2017 (right
top in each sub-figure) are shown in Fig. 3.

Figure 3: An example showcasing the classification of MIDAS clusters is
presented, highlighting three distinct morphological classes: MIDAS single,
MIDAS footprint, and MIDAS pyramid clusters. Each class is depicted through 2D
representations featuring four MIDAS morphologies (clusters). For comparison
purposes, a confocal microscope image showing a dust deposit, which exhibits
corresponding morphological features observed by Ellerbroek et al. (2017), is
displayed in the bottom-right corner of each sub-figure. The white scale bar
accompanying the image indicates a length of 100 $\mu$m, providing a reference
for size.

We find that the majority of morphological types of individual clusters in all
targets are single or footprint deposits. According to Ellerbroek et al.
(2017), small (¡ 80 $\mu\rm{m}$) particles leave single deposits, thus a large
number of MIDAS Single deposits underline the small parent particle size.
Additionally, the dominance of MIDAS footprints suggests that if larger
particles arrived they had slow impact velocities (Ellerbroek et al., 2017). A
summary of a number of different morphological types of all targets based on
the mean shift method (Kim et al., 2023) and the target mean velocity
(Longobardo et al., 2022) is given in Table 1.

Furthermore, we compare MIDAS clusters to COSIMA studies (Langevin et al.,
2016; Merouane et al., 2016; Hornung et al., 2016), which showed the typology
and optical properties of cometary particles collected by the COSIMA mass
spectrometer in the inner coma of 67P. They found four different morphological
classes of particles: ‘compact’, ‘shattered clusters’, ‘glued clusters’, and
‘rubble piles’. However, we find that only the compact particles, which are
particles with well-defined boundaries with only a very small number of
satellite particles, are relatively easy to identify in the MIDAS data. The
lack of a numerical definition of the different shapes found by COSIMA and the
different particle sizes (COSIMA in the hundreds of micrometer range, MIDAS in
the tens of micrometer range) precludes the application of comparative
algorithms. Consequently, we only use the MIDAS cluster classification based
on Ellerbroek et al. (2017) for further investigations in the present study.

We note that all these morphological classes of the particles detected by
MIDAS and COSIMA belong to the GIADA ‘compact’ particles, although GIADA also
defined a second category called ‘fluffy’ that was not found by COSIMA and
only once by MIDAS (Longobardo et al., 2020, 2022; Mannel et al., 2016).

##  3 Results and discussion

###  3.1 Evaluation of MIDAS particles

####  3.1.1 MIDAS particle shape descriptor

We calculate the shape descriptors described in Sect. 2.2 to all MIDAS
particles usable for analysis. A summary of the statistics of the MIDAS
particle shape descriptors is given in Table 2. The detailed information on
all MIDAS particle characteristics and shape descriptors can be found in Table
LABEL:table:_MIDAS_particle_shape_descriptor_full_table of Appendix A.

Table 2: Overview of the mean and standard deviation of the shape descriptors of MIDAS particles for each target. Target | Number of particles | Aspect ratio | Elongation | Circularity | Convexity
---|---|---|---|---|---
11 | 250 | 0.47 $\pm$ 0.27 | 3.68 $\pm$ 1.95 | 0.60 $\pm$ 0.17 | 0.47 $\pm$ 0.02
13 | 40 | 0.39 $\pm$ 0.13 | 4.54 $\pm$ 2.31 | 0.53 $\pm$ 1.86 | 0.47 $\pm$ 0.03
14 | 785 | 0.57 $\pm$ 0.44 | 4.00 $\pm$ 2.41 | 0.57 $\pm$ 0.20 | 0.47 $\pm$ 0.03
15 | 7 | 0.45 $\pm$ 0.09 | 2.83 $\pm$ 1.02 | 0.67 $\pm$ 0.18 | 0.47 $\pm$ 0.01
MIDAS Total | 1082 | 0.54 $\pm$ 0.40 | 3.93 $\pm$ 2.31 | 0.58 $\pm$ 0.19 | 0.47 $\pm$ 0.03

First, we find that the value of the aspect ratio of all the MIDAS particles
is found around 0.53 $\pm$ 0.40, which is smaller than expected since one
would expect the value of 1 for unflattened particles. According to the
finding from Ellerbroek et al., 2017, smaller and slower arriving particles
(e.g., MIDAS particles) seem to show almost no alteration. Thus, we conclude
that MIDAS particles seem to be flattened upon the impact, indicating not
enough internal strength to stay unaltered based on our results. Additionally,
we find that the value of the aspect ratio of all the MIDAS particles is
higher than the one of COSIMA particles showing 0.36 $\pm$ 0.21 (Langevin et
al., 2016; Lasue et al., 2019, which indicates higher strength of smaller
particles.

Furthermore, we find that the majority of MIDAS particles have an elongation
larger than 1 with the value of elongation 3.93 $\pm$ 2.31 (i.e., the largest
axis is about 4 times longer than the smallest one). This means that their
shapes highly deviate from a sphere, which shows good agreement with previous
studies (e.g., Fulle et al. 2017). We note that the elongation of the
particles on target 15 appears to be significantly smaller compared to the
other targets. However, considering the uncertainty of one of target 15, this
difference becomes less significant.

The link between interstellar dust grains and MIDAS dust particle can be found
via their approximate shapes. For example, linear polarisation of the light
(Hiltner, 1949; Mathis, 1990) suggests that the interstellar dust grains
should be both elongated and partially aligned. Furthermore, the presence of
elongated grains is also considered in various cometary dust models (e.g.,
Greenberg & Gustafson, 1981; Levasseur-Regourd et al., 2007; Lasue &
Levasseur-Regourd, 2006). In particular, Greenberg & Gustafson (1981) proposed
that cometary dust comprises agglomerations of elongated submicrometer-size
interstellar dust with aspect ratios of 2-4, which showed a satisfactory
agreement between light scattering experiments and observations.

We also find that 3D elongation is bigger than 2D elongation in most cases,
meaning that the shortest axis between the height and the semi-minor axis is
the height. These results show consistency with Bentley et al. (2016b), where
most particles had an elongation of about $\sim$ 3, which mostly means that
the height of the particle is three times smaller than the maximum diameter.
Both results may imply either the particles had a natural elongation and are
more probable to stick on MIDAS targets when arriving with the flattest side
up-wards (i.e., having the largest cross-section sticking to the target), they
collided with the target in an arbitrary alignment but turned their shortest
axis upwards upon impact, or the particles are flattened upon impact. This
result is also consistent with the statistics of the MIDAS particle catalog
(Kim et al., 2023), with the bigger mean value of equivalent radius on the 2D
projection compared to the radius derived from the volume of the particle. On
the assumption that the fractal particle E (Mannel et al., 2016) is not
heavily altered by the impact since it preserved its fractal structure, it is
suggested that the elongation of its sub-units forming particles is natural
and not created by the impact (Bentley et al., 2016b). However, sub-units of
particle E mostly show an elongation around 3 with their height as the
shortest axis (Bentley et al., 2016b), suggesting that the sub-units may have
suffered flattening upon impact. If a rotation of the sub-units cannot happen
to keep the fractal structure intact, the aspect ratio (and/or 3D elongation)
could be a reasonable parameter to find particles with the most pristine
morphology.

Additionally, we find that the value of the circularity of MIDAS particles is
0.58 $\pm$ 0.19, indicating MIDAS particles deviate from being circular. On
the other hand, we find that the value of the convexity of MIDAS particles
showed 0.47 $\pm$ 0.19, meaning that most of the convex hull area of MIDAS
particles is occupied by their perimeter concavities and thus showed the
rather smooth particle shape on 2D projection view. In particular, all MIDAS
particles show a similar value of convexity.

We note that these shape descriptors are particularly tip convolution
dependent, which is an inherent feature of all AFMs (e.g., Vijendran et al.,
2007) and hard to be fully removed as all AFM images are the convolution of
the tip shape and the particle shape, particularly for rough surfaces. For
example, multiple points on the tip may be simultaneously in contact with the
surface and so the shape and geometry of the tip has an effect on the accuracy
of the imaging. This has the effect of making protruding features appear wide,
while holes appear smaller with a broader tip. More specifically, the
variation in particle height leads to considerable uncertainties in tip
convolution (Mannel et al., 2019), with a calculated uncertainty ranging from
0.4 to 178 percent (using the equation in Mannel et al. 2019) for the dataset
of all MIDAS particles. The smallest and largest uncertainties are associated
with the flattest and roughest particles, respectively. Therefore, due to the
broad tip used in the MIDAS instrument (with a half-opening angle of 25∘ $\pm$
5∘), very small fringes on the particles may not be effectively imaged.

####  3.1.2 Relation between shape descriptors and particle characteristics,
collection target, and cluster morphology, and MIDAS shape descriptor maps

In the present section, we investigate possible relationships between the
discussed shape descriptors and particle characteristics (e.g., size), MIDAS
collection targets (i.e., here related to collection velocities/periods and
cometary source regions with dust activities; see Sect. 2.1), and cluster
morphology derived from laboratory experiments (Ellerbroek et al., 2017) to
find similarities/differences between the particles. In particular, we aim to
find particles that preserved at least some properties pristinely (i.e., as
they were when stored in the comet and/or as they formed in the early solar
system).

Shape descriptors vs. particle size We first investigate the relation between
MIDAS shape descriptors and particle size. Furthermore, we further investigate
the correlation between large particles (e.g., r ¿ 8 $\mu$m) and small
particles (e.g., r ¡ 8 $\mu$m) as indicated by the size distribution of MIDAS
particles. For example, particles larger than 8 $\mu$m in radius show lower
aspect ratios. In particular, we find no large particles with an aspect ratio
larger than 0.8.

The scattered plot of the relation between all MIDAS shape descriptors and
particle size can be found in Fig. 4. We find no clear trend between shape
descriptors and particle size, in particular, only weak correlations between
shape descriptors and size.

Figure 4: Relations between MIDAS particle shape descriptors and sizes of
particles.

We first find that larger MIDAS particles within low standard deviation (i.e.,
0.26 $\pm$ 0.09) show a tendency to lower aspect ratios, which can also be
explained by their larger size and therefore expected weaker strength. We also
find that the aspect ratio of larger MIDAS particles shows a rather similar
value of COSIMA particles (see Sect. 3.1.1), compared to the one of smaller
MIDAS particles. On the other hand, small particles are the only candidates
with extremely large aspect ratios, however, they show a large variance as
well (i.e., 0.49 $\pm$ 0.41). Based on this finding, it is reasonable to
conclude that particles with a high aspect ratio have undergone less
alteration or deformation upon impact and thus have retained their original
morphology compared to particles with lower aspect ratios.

We next find that larger MIDAS particles show relatively smaller elongation
values, showing again the degree of flattening as the shortest axis between
the height and the semi-minor axis in the particle is mostly the height in our
analysis (see Sect. 3.1.1).

Furthermore, we find that larger MIDAS particles show smaller values of
circularity and convexity. As Kimura et al., 2020 indicated that dust
aggregates in the early stage of comet formation may grow under BCCA
(ballistic cluster-cluster aggregation), corresponding to the decreasing
density as the particle size increases (e.g., Kozasa et al., 1992; Mukai et
al., 1992; Kataoka et al., 2013) up to scales of 10 $\mu$m (i.e.,
corresponding to MIDAS size scale) due to the motion of dust particles that
are controlled by Brownian motion, where dust particles of similar size hit
and stick to each other (Weidenschilling et al., 1989; Weidenschilling &
Cuzzi, 1993), and then by BPCA (ballistic particle-cluster aggregation) once
aggregate particles grow to the size of 10 to 100 $\mu$m. Based on this
finding, MIDAS particles would show the change in different shape descriptors
(e.g., circularity, convexity, and elongation) for the larger particles, if
larger MIDAS particles consist of a few agglomerates (e.g., relatively few
large sub-particles) of the next smaller hierarchical step. For example,
larger MIDAS particles would naturally deviate from a spherical shape and lead
to more fringed rims. Consequently, we suggest that our findings with smaller
values of circularity and convexity for larger MIDAS particles are possibly
explained by a hierarchical growth process and would show consistency with the
fractal growth process as it may be expected by models of early cometary dust
accretion (e.g., Weidenschilling et al., 1989; Kimura et al., 2020). This
finding also aligns with the previous finding of a higher fragmentation or
alteration for larger MIDAS particles (Mannel et al., 2019), indicating a
relatively lower internal strength keeping the larger particles together.
During the particle selection for further investigation (see Sect. 2.2), we
also find that out of 135 particles larger than 10 $\mu$m in total, only 22
particles remained unfragmented, indicating around 85% of larger particles
underwent fragmentation during the collection and/or scanning process. This
indicates that fragmentation of the particle in subunits is easier than
fragmentation of the subunits in grains, which also underlines the suggested
hierarchical dust structure with characteristic subunit size regimes (Mannel
et al., 2019).

Shape descriptors vs. collection targets Next, we investigate the relation
between MIDAS shape descriptors and collection targets. The distributions of
the four MIDAS shape descriptors for each dust collection target, which is
here a proxy for the source region (i.e., particles on target 14 originated
from rough terrains/deeper layers, particles on target 15 originated from
smooth terrains, and particles on targets 11 and 13 originated from both types
of terrains; see Sect. 2.1; Longobardo et al., 2022), the collection velocity
(i.e., target number 11 equates to a mean collection velocity of 3.1 $\pm$ 1.5
m s-1, target number 13 to 2.7 $\pm$ 0.3 m s-1, target number 14 to 7.21 $\pm$
0.09 m s-1, and target number 15 to 7.2 $\pm$ 0.2 m s-1 (Longobardo et al.,
2020), and/or the period of dust emission from the comet (i.e., particles on
target 11, 13, 15 were collected when comet showed a nominal activity, while
particles on target 14 were collected when comet showed an outburst), can be
found in Fig. 5.

Figure 5: Density plots of MIDAS particle shape descriptors for each dust
collection target. The graph of target 15 shows narrow high spikes due to low
statistics, contrary to the smooth graph of target 14 resulting from a high
number of data points. Overall, the particle shapes seem to be similarly
distributed independently from the collection target, i.e., the collection
velocity, the cometary source region, or the period of dust emission from the
comet.

We find that there is no clear trend between target and shape descriptors even
for the unflattened (thus potentially less altered) particles (see Sect. 2.2).
Although the statistics on target 15 are very poor, the data still shows
similar behavior in this investigation. Thus, we conclude that particles
coming from different terrain and activity are similar in their investigated
shape properties. This means dust activity such as dust ejection, partial dry-
out (loss of volatiles), and recycling of dust material (backfall and
subsequent ejection) did not alter the structure of particles on the
micrometer scale. These results indicate that dust parameters associated with
the collection target, such as dust activities, cometary source regions, and
collection velocities and periods, do not play a significant role in the
alteration of particle structure at the micrometer scale. We note that our
finding about the homogeneity of MIDAS particles in their properties may show
the consistency with globally uniform Martian soil all but the coarsest
components (e.g., larger fragments, clasts, and spherules) at widely separated
sites (McSween et al., 2010).

Shape descriptors vs. cluster morphologies We finally investigate the relation
between MIDAS particle shape descriptors and cluster morphologies according to
the definition of Ellerbroek et al. (2017) and Sect. 2.3. The distributions of
the four MIDAS shape descriptors for each cluster morphology can be found in
Fig. 6.

We find that cometary dust particles of different cluster morphology are
rather homogeneous in properties. More specifically, we find that the aspect
ratio distributions of the particles are very similar and independent of the
cluster type (see the left top panel of Fig. 6). This may imply that the sub-
units of different cluster types are very similar in their shape and
composition. On this assumption, different cluster types may not be created by
differently composed parent particles. A similar situation of surprisingly
homogeneous properties of the sub-units of cometary dust particles down to the
sub-micrometer scale was found for IDPs (Bradley et al., 2014) and material
collected by Stardust (Hörz et al., 2006). Following the results from Lasue et
al. (2019), the different cluster morphologies detected by MIDAS, COSIMA, or
in simulations are not only created by a change in sub-unit properties (e.g.,
different particle structure and/or composition) but also by different impact
velocities. Thus, based on our findings, which indicate the similar
composition and internal cohesive strength of the parent particles, the
variations in impact velocities during the collection process might lead to
distinct cluster morphologies. This result is in good agreement with the
laboratory experiments of Ellerbroek et al. (2017), where MIDAS (and in a
wider sense also COSIMA) cluster types were reproducible by using one simple
cometary analog material (SiO2 spheres with a polydisperse size distribution)
with different impact velocity.

Figure 6: Density plots of MIDAS particle shape descriptors depending on the
cluster morphology. The similar particle shapes independent from the cluster
morphology suggest that the collected parent particles were homogeneous in
particle properties and consisted of similar subunits.

However, we find that the different mean velocities of the MIDAS dust
collection (approximately between 3 and 7m s-1; Longobardo et al. 2020; see
also Sect. 2.1) did not alter the mean deposit morphology (see Fig. 5). This
discrepancy with Ellerbroek et al. (2017) can be interpreted as a result of
different material compositions that, in particular, lead to different
cohesive strengths and thus different threshold velocities for the creation of
different cluster morphologies. This is not surprising as the material used by
Ellerbroek et al. (2017) was extremely simple SiO2 aggregates. On the
contrary, compositional analysis of dust of comet 67P (e.g., by the COSIMA
instrument) indicated a more varied composition, in particular with a share of
about 45 mass percent of the particles consisting of a long-chained organic
material (Bardyn et al., 2017). The expected different cohesiveness of SiO2
aggregates and dust of comet 67P might be confirmed by the MIDAS results.

Based on the investigation in Sect. 2.2, we create maps combining dust
clustering (Kim et al., 2023) and MIDAS shape descriptors, which can be found
in Appendix B. MIDAS shape descriptor maps allow a quick overview of dust
distribution and properties.

We find that the least altered particles (e.g., higher aspect ratio particles)
can occur even in large clusters (e.g., MIDAS footprint cluster or MIDAS
pyramid cluster). This contradicts the finding from Ellerbroek et al. (2017),
which indicated that the smaller and slower a particle arrives at the target
the higher the chance that it sticks without alteration. No alteration would
mean the particle does not fragment, making it a cluster with only a single
particle inside, a so-called single-particle-cluster (SPC). Thus, the aspect
ratio of SPCs is expected to be higher. However, high aspect ratio MIDAS
particles seem to be randomly scattered over the target and mostly be part of
clusters (see Figs. 12, 13, 14, and 15). As Hornung et al. (2016) suggested,
unflattened particles are possibly fragments that are pre-existing in parent
particles. To be specific, on the assumption that the force that holds the
grains in the subunits together is stronger than the force that holds the
subunits of the particle together (Mannel et al., 2019), the impact energy may
first be used for fragmentation (i.e., breaking the bonds between the pre-
existing sub-units) when the parent particle hit the target, and if all impact
energy is used up before compaction of the sub-units could happen some sub-
units are set free unaltered. In other words, the impact energy at dust
collection did only suffice to destroy the bonds between the sub-units in the
parent particle but did not alter the internal structure of the sub-units
(i.e., easier fragmentation of the particle in subunits compared to one of the
subunits in grains). This may lead to MIDAS particles with high aspect ratios
so thus MIDAS particles with unaltered structures can be found in clusters as
well. This finding again aligns well with the hierarchical agglomerate
structure for cometary dust as the tensile strength of the porous dust layer
would decrease with increasing aggregate size (see also discussion in the
relation between shape descriptors and particle characteristics such as size;
Skorov & Blum, 2012; Kimura et al., 2020) and could lead to differences in the
cohesive strength of particle units and subunits at MIDAS scales (e.g., 10
micrometers or less) if the cometary dust is characterized by a hierarchical
structure of fractal aggregates derived from the coagulation process in the
solar nebula. Furthermore, Kimura et al. (2020) indicated an outer layer of
organic material that may be of interest for the bond strength between
particle subunits, implying that different processes of aggregation could lead
to more differences in the cohesive strength of particle units at these
different scales, supporting the MIDAS measurements.

####  3.1.3 MIDAS cluster morphology – aspect ratio classification compared to
COSIMA results

Lasue et al. (2019) conducted a numerical simulation of aggregate impact
flattening to interpret the initial properties of particles/clusters collected
by COSIMA. They found that the particle morphologies observed by COSIMA and
those generated by the laboratory experiments of Ellerbroek et al. (2017) are
consistent. Thus, it is of interest to compare MIDAS cluster structures to
those found by COSIMA and laboratory experiments, and check if the same
structures are present, although the size of COSIMA particles is one to two
orders of magnitude larger. Furthermore, the laboratory study and the COSIMA
images yield insight into parent particle alteration, which might help to
determine the least altered MIDAS particles.

Following the approach taken in Lasue et al. (2019) allows a quantitative
comparison of the morphological cluster classification between COSIMA and
MIDAS in terms of aspect ratio calculations. As discussed in Sect. 2.3, the
MIDAS cluster morphology classification appears to follow Ellerbroek et al.
(2017) such that the dust can be categorized into one of three classes: MIDAS
single, MIDAS footprint, or MIDAS pyramid cluster morphology.

The radius of clusters $r_{\rm{cluster}}$ is calculated by taking half of the
mean value between the length in the x-direction (right position of the right-
most particles in a cluster – left position of the left-most particle in a
cluster) and length in the y-direction (upwards position of the uppermost
particles in the cluster - downwards position of the lowermost particles in
the cluster) on the assumption that clusters are circular/spherical shapes.
Furthermore, the height of the cluster $h_{\rm{cluster}}$ is chosen as the
highest height of the particles within the cluster. Calculated aspect ratios
(i.e., $\frac{h_{\rm{\,cluster}}}{\sqrt{\,\pi\,r_{\rm{\,cluster}}^{2}}}$) and
their density plots of all MIDAS clusters and of COSIMA particles (Lasue et
al., 2019) can be found in Table 3 and Fig. 7.

Table 3: The mean value and standard deviation of calculated aspect ratios of all MIDAS clusters MIDAS Cluster | Aspect ratio $\frac{h_{\rm{\,cluster}}}{\sqrt{\pi\,r_{\rm{\,cluster}}^{2}}}$
---|---
Single cluster | 0.38 $\pm$ 0.25
Footprint cluster | 0.13 $\pm$ 0.17
Pyramid cluster | 0.14 $\pm$ 0.05
Total | 0.22 $\pm$ 0.16

Figure 7: Comparison between calculated aspect ratios of MIDAS clusters (left)
and the COSIMA clusters (right; Lasue et al. 2019). Both graphs show a peak at
smaller ratios and a long shoulder towards higher ratios, but overall the
COSIMA data show higher ratios.

MIDAS single cluster We find that the aspect ratio distributions of COSIMA and
MIDAS are not similar although the MIDAS single cluster morphology looks very
similar to the COSIMA compact morphology (i.e., particles with well-defined
boundaries). The values of the aspect ratio of MIDAS single and COSIMA compact
morphologies are 0.38 $\pm$ 0.25 (see Table 3) and 0.73 $\pm$ 0.24 (Langevin
et al., 2016), respectively. This discrepancy is basically definition-
dependent that is COSIMA and MIDAS classification used different definitions
for compact and single morphology. The COSIMA compact particles have, by
definition, a high aspect ratio and present only well-defined boundaries
without smaller satellite particles and with an apparent height above the
collecting plane of the same order of magnitude as their x and y dimensions
(Langevin et al., 2016). However, we find that MIDAS cluster analysis shows
that several high aspect ratio MIDAS particles are contained in MIDAS
footprint and even MIDAS pyramid clusters (see Sect. 3.1.2). Thus, we suggest
that contrary to the COSIMA classification high aspect ratio particles should
not be treated as a unique cluster class. Furthermore, the MIDAS
classification strictly follows the definition from Ellerbroek et al. (2017),
resulting in only particles with clearly defined central components or no
scattered fragments being labeled as single (see Sect. 2.3).

We also find a slight deficit of high aspect ratio particles in the MIDAS
Single morphology collection compared to COSIMA’s compact collection (see Fig.
7). There is no apparent reason for this behavior at the present state of the
work, thus this may be an effect due to the low statistics of COSIMA and MIDAS
(167 COSIMA clusters of over $\sim$ 30,000 COSIMA detections were analyzed,
compared with 196 MIDAS clusters). Consequently, it would be of great interest
to include the rest of the COSIMA data set, possibly even re-classified
following the Ellerbroek et al. (2017) definition, and to check how the
density plot of COSIMA is changed.

MIDAS footprint cluster According to the aspect ratio calculation, COSIMA
shattered clusters and MIDAS footprints show similar behavior, for example, a
strong overlap to other cluster types and a wide distribution of ratios
covering the smallest up to values of $\sim$ 0.5. The mean ratio of the COSIMA
shattered cluster and MIDAS footprints show similar behavior as well (i.e.,
0.22 $\pm$ 0.10; Langevin et al., 2016) for COSIMA shattered cluster (see Fig.
7) and 0.13 $\pm$ 0.17 for MIDAS footprints (see Table 3). In particular,
images of COSIMA shattered clusters show a depression in the central part of
the deposit, similar to those found in scans of MIDAS footprint clusters.
Thus, we may conclude that the closest resemblance to the MIDAS footprints can
be found in COSIMA shattered clusters, although the morphology of MIDAS
footprints does not have a direct counterpart in the COSIMA data set.

MIDAS pyramid cluster MIDAS pyramids may show similar behavior to COSIMA
rubble piles (i.e., the value of the aspect ratio is 0.37 $\pm$ 0.13; Langevin
et al., 2016) and glued clusters (i.e., the value of aspect ratio is 0.27$\pm$
0.09; Langevin et al., 2016), with the difference that MIDAS pyramids show a
lower aspect ratio (i.e., the value of aspect ratio is 0.14 $\pm$ 0.05; see
Table 3). This can be explained by the fact that MIDAS had a 10-micrometer
absolute height detection limit, and in most practical cases the limit is less
than 5 micrometers. If a pyramidal cluster has a diameter over 10 micrometers,
a ratio 1 pyramidal cluster could not be detectable by MIDAS. Therefore,
pyramids are biased towards flattened deposits resulting in artificially low
ratios. We note that this is a limitation common to all AFMs of current in-
situ planetary exploration instruments, more so those capable of higher
resolutions. For example, AFM investigation of Martian soil FAMARS was able to
provide data on the parameters including particle heights up to 6 - 12
micrometers. To address this limitation, future developments in AFM technology
or the use of complementary imaging techniques are required to obtain a more
comprehensive analysis of particles with diverse surface features, including
those exceeding the current height limitations.

Furthermore, we find that the class of MIDAS pyramids might contain some
borderline cases due to the complex appearance of clusters (except for the
clearly detectable ones with compact morphology). The boundary between MIDAS
footprints and pyramids is fluid. As a result, the MIDAS pyramid class
contains COSIMA’s glued clusters and rubble piles. We note that glued clusters
may be the outcome of particles with slightly different material composition
(Langevin et al., 2016). Furthermore, a slight angle during deposition might
also help to create slightly asymmetric features such as those found for glued
clusters or rubble piles.

According to the results from the comparison of MIDAS parent particle
structures to those detected by COSIMA and laboratory experiments, we find
that MIDAS morphologies and aspect ratio show both similarities and
differences to those found by COSIMA. Classification differences can be
understood when taking into account the difference in resolution and imaging
technique. Ellerbroek et al. (2017) showed that the single morphology may
contain the particles to be least altered, which implies particles found in
MIDAS single cluster morphology can also be the candidates for least altered
particles. Furthermore, using the similarities between MIDAS clusters and
COSIMA clusters as well as the aspect ratio calculation of each cluster, we
suggest that the MIDAS single clusters are the least altered among MIDAS
morphologies. This conclusion shows agreement with the results of laboratory
experiments Ellerbroek et al. (2017) and the observations of COSIMA.

###  3.2 Pristineness descriptor

Current gas flow models in experiments and simulations (e.g., Laddha et al.,
2023) have an indication that cometary activity can be strongly associated
with the cometary surface and microphysical properties (e.g., structures).
Thus, less altered and thus more pristine shape descriptors that are used for
particle classification of dust in space science will yield valuable clues on
the effect of more realistic grain shape on the gas flow in the cometary
environment.

For this purpose, we now combine shape descriptors and knowledge about
seemingly pristine morphologies to determine their level of alteration,
ultimately deriving a final pristineness descriptor based on the previous
findings on the deposition of dust on MIDAS targets by the identification of
dust clusters and their morphology. Thus, the aim of the present section is to
identify the particles that have undergone the least amount of alteration and
provide a comprehensive description of their properties.

####  3.2.1 Development of MIDAS particle pristineness descriptors

We calculate a final cumulative pristineness score by weighting one point if
an individual particle satisfies each parameter that indicates pristineness
that is if the particle surface and volume distribution of MIDAS particle
classified as ‘MIDAS Single’ (see Sect. 2.2), a particle shows a moderately
high aspect ratio (¿ 0.5; motivated by $\sim$ mean value of aspect ratio of
whole MIDAS particles; see Sect. 3.1.1), a particle shows a higher aspect
ratio (¿ 0.8; see Sect. 3.1.1), or if a particle is found in the MIDAS single
cluster (i.e., SPC; see Sect. 3.1.3; Ellerbroek et al., 2017). Consequently,
the final pristineness score starts from 1 (‘severely altered’), 2
(‘altered’), 3 (‘possibly altered’), 4 (‘moderately pristine’), and 5 (‘highly
pristine’). The flow chart on how to calculate dust particle pristineness is
described in Fig. 8. This approach allows us to assess and describe the
properties of the particles that have experienced minimal alteration.

Based on the result from pristineness calculator, we create maps combining
dust clustering (Kim et al., 2023) and the pristineness score of MIDAS
particles, which can be found in Appendix B.6.

Figure 8: Flow chart on how to calculate dust particle pristineness.

####  3.2.2 Statistics of the pristineness descriptor

The final pristineness scores and the related histogram can be found in Fig.
9.

Figure 9: Distribution of the final pristineness score of MIDAS particles,
where 1 stand for ‘severely altered’ and 5 for ‘highly pristine’. Only 1
particle is found to be highly pristine and 29 candidates are rated with 4
‘moderately pristine’.

We find that out of 1082 investigated particles, there is only one particle
rated as highly pristine with a score of ‘5’. This result is mainly because
particles with very high aspect ratios are predominantly found in MIDAS
footprints and pyramid clusters, rather than in MIDAS single clusters (SPCs:
single-particle-cluster; see Sect. 3.1.2). Additionally, several particles
with intermediate aspect ratios were detected as SPCs. The findings from Sect.
3.1.1, where flattened sub-units were either compressed upon impact or turned
into the target direction on impact despite the parent particle not being
fragmented, support that those SPCs with low aspect ratios have likely
undergone some alteration, such as flattening due to the impact. This suggests
that SPCs could be either subunits of the MIDAS footprint cluster or particles
that have remained pristine, which differs from the expectations proposed by
Ellerbroek et al. (2017), where SPCs were presumed to be pristine. However, we
note that the SPCs in Ellerbroek et al. (2017) are at the edge of their
resolution capability, and thus an alteration such as flattening is likely not
identified. Based on the current data analysis, we conclude that SPCs are
susceptible to flattening, including even high degrees of alteration.

Furthermore, we find that there are 29 particles rated as ‘4’ in terms of
pristineness calculation and thus 30 particles in total as the most pristine
particles (particles rated ‘4’ or ‘5’). Interestingly, no single particle
rated ‘4’ or ‘5’ is found on target 13, where particles were collected at
nominal activity with slower speed from smooth and rough terrains, and target
15, where particles were collected at nominal activity with faster speed from
smooth terrain (see Sect. 2.1). Most importantly, we find that 11 ‘MIDAS Pile’
particles were included in moderately pristine particles (pristineness rated
‘4’). Given that the appearance of MIDAS Pile particles is expected to result
from the target impact, we thus exclude 11 ‘MIDAS Pile’ particles from the
final list of most pristine particles (particle rated ‘4’ and ‘5’) and thus
reasonably rescale the pristineness score (i.e., 19 most pristine MIDAS
particles in total). On the other hand, we find that there are 474 particles
rated ‘1’, indicating that nearly half of the MIDAS particles have undergone
significant alteration due to impact, while 222 and 354 particles were rated
‘3’ and ‘2’, respectively.

Overall, our findings reveal the presence of only one highly pristine
particle, a small number of moderately pristine particles, and a substantial
proportion of altered particles within the MIDAS dataset. These results
emphasize that dust alteration is an unavoidable process, even at the
relatively slow collection speeds achieved by the Rosetta spacecraft.

####  3.2.3 Characteristics of pristine particles

A summary of characteristics and shape descriptors of the 19 particles rated
‘4’ or ‘5’, sorted by the number of pixels on the pristineness descriptor, is
given in Appendix B.5. Furthermore, the 3D appearance, surface and volume
distribution, and characteristics of the selected examples of most pristine
particles (particle rated ‘4’ and ‘5’) can be found in Figs. 10 and 11.

Figure 10: Appearance, surface and volume distribution, and characteristics of
the most pristine particle (particle rated 5, Particle ID:
2016-08-21T211728_P03_T14). Figure 11: Selected examples of appearance,
surface and volume distribution, and their characteristics of particles rated
4, i.e. moderately pristine, on the pristineness scaling.

We find that $\sim$ 40 % of most pristine MIDAS particles (7 of 19 particles)
that are rated 4 and 5 are found in MIDAS single clusters (i.e., SPCs). This
implies again that moderately pristine particles can be found even in
footprints or pyramids (resembling COSIMA glued cluster, shattered cluster, or
large rubble pile morphology), which is thought to be initial sub-clusters of
the particles that did not get modified by the collection. We also find these
candidates for pristine particles are not that elongated, showing the mean
value of elongation $\sim$ 1.8. This value is close to the one from
observations and simulation of ISM grains (Hiltner, 1949; Voshchinnikov et
al., 1999), compared to the average elongation of all MIDAS particles, showing
the mean value of elongation $\sim$ 3.93 (see Table 2 and Sect. 3.1.1). This
finding may indicate that a relatively higher value of elongation of all MIDAS
particles is possibly created by impact rather than subunits turning in one
direction when deposited (i.e., particles have a natural elongation and
preferentially stick with their longer side on the targets; Bentley et al.,
2016b).

##  4 Summary and outlook

The MIDAS AFM on board the Rosetta comet orbiter investigated the 3D
topography of about 3523 cometary dust particles with sizes between a few
hundreds of nm to tens of $\mu$m based on images with resolutions down to a
few nanometers. Based on the updated version of the MIDAS particle catalog
(Kim et al., 2023), we analyzed the shapes of the cometary dust particles. In
particular, we developed MIDAS particle shape descriptors such as aspect
ratio, elongation, circularity, convexity, and particle surface and volume
distribution. Next, we compared the structure of the MIDAS dust particles and
clusters (i.e. fragments of a parent particle that broke up upon collection)
to those found in laboratory experiments (Ellerbroek et al., 2017) and by
COSIMA onboard Rosetta (Lasue et al., 2019). Finally, we calculated a
pristineness score for the MIDAS particles and determined the most pristine
particles and their properties. Based on the particle shape descriptors and
pristineness calculator, we created dust maps combining clustering and the
derived parameters, as well as the pristineness score. We finally established
the microphysical properties of pristine cometary materials in the present
study, which have drawn on a wide range of shape descriptors. The key results
are as follows:

  * •

We found that the mean value of the aspect ratio of all the MIDAS particles is
found around 0.53 $\pm$ 0.40, which is implying the degree of flattening and
is smaller than expected since one would expect the value of 1 for unflattened
particles. We also found that the mean value of all MIDAS particles’
elongation is 3.93 $\pm$ 2.31, meaning that their shapes highly deviate from a
sphere. Additionally, we found that the value of the circularity of MIDAS
particles is 0.58 $\pm$ 0.19, meaning that MIDAS particles deviate from being
circular. Finally, we found that the value of the convexity of MIDAS particles
showed 0.47 $\pm$ 0.19, meaning that most of the convex hull area of MIDAS
particles is occupied by their perimeter concavities.

  * •

We found no clear trend between shape descriptors and particle size, only weak
correlations between aspect ratio and size, for instance, larger particles
within low standard deviation (i.e., 0.26 $\pm$ 0.09) showing a tendency to
lower aspect ratios and small particles being the only candidates with
extremely large aspect ratios. However, small particles show a large variance
as well (i.e., 0.49 $\pm$ 0.41). We found that large particles show relatively
smaller elongation values, implying again the degree of flattening. Large
particles show smaller circularity and convexity, which may possibly be
explained by a hierarchical growth process.

  * •

We found that there is no clear trend between shape descriptors and the
properties related to the target (and thus dust activities/cometary source
region). These results imply that various dust activities depending on the
cometary source region and different velocities of the MIDAS dust collection
do not play a role in the structural alteration of the particles on the
micrometer scale.

  * •

We found that cometary dust particles of different cluster morphology (i.e.,
MIDAS single, footprints, and pyramid clusters) are rather homogeneous in
properties. We found that the aspect ratio distributions of the particles are
very similar and independent of the cluster type, implying that the sub-units
of different cluster types are very similar in their shape and composition.

  * •

We made a quantitative comparison between the data of COSIMA and MIDAS
clusters. We found that MIDAS clusters and their aspect ratio distribution
show both similarities and differences to those found by COSIMA. Based on the
finding and results from Ellerbroek et al. (2017), we concluded that the MIDAS
Single cluster may contain the particles to be least altered.

  * •

We calculated a final pristineness score by weighting based on combined shape
descriptors and knowledge about seemingly pristine morphologies. We found that
there is only 1 particle rated as highly pristine and 18 particles rated as
moderately pristine, while 222 and 354 particles are rated as possibly altered
and altered. We also found that there are 474 particles rated as severely
altered. This finding indicates dust alteration is inevitable even at the slow
collection speeds that were available at the Rosetta spacecraft.

The particle catalog (Kim et al. 2023) and shape descriptor in the present
study will serve as references for future scientific projects such as the
development of more realistic analog materials, and the design of dust
particles in simulations for comets and early solar system studies. The
database will also be a landmark for any future cometary or interplanetary
dust investigation, be it a re-consideration of Stardust data, the analysis of
returned material of asteroids, or even - in the far future - of a comet. Gas
flow properties are significantly influenced by the shape of the grains.
Therefore, adopting a more quantitative approach that correlates with shape
descriptors, particularly for realistic (and thus pristine) cometary dust
particles used in particle classification, can provide valuable insights into
how grain shape affects the characteristics of gas flow through the medium
(e.g., packed beds).

There are still possibilities to improve the particle’s structural
description, for instance, an investigation of 3D shape descriptors such as
roughness calculation (Kim et al. in preparation) can be applied to increase
our understanding of the microphysical properties of pristine cometary
materials. Furthermore, subunit size investigation could be taken into account
to further understand particle growth (e.g., Mannel et al. 2019). Finally, an
estimation of particle strength similar to that given in Hornung et al. (2016)
can be studied to verify the microphysical properties of cometary materials.
These studies are in preparation and will further increase our knowledge about
cometary dust.

###### Acknowledgements.

This paper is dedicated to the memory of MIDAS Co-I Prof. Anny-Chantal
Levasseur-Regourd, a true Renaissance person. The authors gratefully thank our
referee and editor for the constructive comments and recommendations which
definitely help to improve the readability and quality of the paper. M. Kim
and T. Mannel acknowledge funding by the ESA project ”Primitiveness of
cometary dust collected by MIDAS on-board Rosetta” (Contract No. 4000129476).
M. Kim also acknowledges the funding from the Royal Society. J. Lasue
acknowledges funding by CNES and the PNP INSU CNRS for working on the Rosetta
data. This research was supported by the International Space Science Institute
(ISSI) through the ISSI International Team “Characterization of cometary
activity of 67P/Churyumov-Gerasimenko comet”.

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##  Appendix A Shape descriptor of MIDAS particles

The MIDAS particle shape descriptor presented in this paper contains in total
of 1082 scans of particles (see Sect. 3.1.1). This table is an excerpt only
and the full table of the ultimately chosen 1082 particles is available at the
CDS.

Table 4: Summary of characteristics and shape descriptors of all MIDAS particles. Particle ID | Target | Area | Radius | Height | Aspect | Elongation | Circularity | Convexity | PSVD666Particle surface and volume distribution | Cluster | Ellerbroek777MIDAS Cluster classification according to Ellerbroek et al.2017 | COSIMA888MIDAS Cluster classification according to the COSIMA classification (e.g., Langevin et al. 2016) | Pristineness
---|---|---|---|---|---|---|---|---|---|---|---|---|---
|  |  [$\mu{m}^{2}$] |  [$\mu{m}$] |  [$\mu{m}$] | Ratio |  |  |  |  | Number |  |  | score
2014-11-18T032520_P01_T11 | 11 | 1.991 | 0.796 | 0.870 | 0.617 | 1.900 | 0.796 | 0.481 | MIDAS Single | 44 | Single | Compact | 4
2014-11-18T131924_P01_T11 | 11 | 0.664 | 0.460 | 0.320 | 0.393 | 2.732 | 0.871 | 0.480 | MIDAS Pile | 8 | Footprint | Shattered cluster | 1
2014-11-18T131924_P02_T11 | 11 | 2.757 | 0.937 | 1.190 | 0.717 | 1.653 | 0.838 | 0.461 | MIDAS Single | 8 | Footprint | Shattered cluster | 3
2014-11-18T131924_P03_T11 | 11 | 0.357 | 0.337 | 0.110 | 0.184 | 5.963 | 0.739 | 0.500 | MIDAS Pile | 8 | Footprint | Shattered cluster | 1
2014-11-18T131924_P04_T11 | 11 | 0.408 | 0.361 | 0.230 | 0.360 | 3.648 | 0.553 | 0.500 | MIDAS Pile | 37 | Single | Compact | 2
2014-11-18T131924_P05_T11 | 11 | 1.225 | 0.625 | 0.530 | 0.479 | 2.662 | 0.650 | 0.479 | MIDAS Single | 5 | Pyramid | Large Rubble pile | 2
2014-11-18T131924_P06_T11 | 11 | 2.195 | 0.836 | 0.760 | 0.513 | 2.539 | 0.839 | 0.420 | MIDAS Pile | 5 | Pyramid | Large Rubble pile | 2
2014-11-18T131924_P07_T11 | 11 | 0.204 | 0.255 | 0.100 | 0.221 | 4.844 | 0.577 | 0.500 | MIDAS Pile | 8 | Footprint | Shattered cluster | 1
2014-11-18T131924_P10_T11 | 11 | 0.306 | 0.312 | 0.110 | 0.199 | 5.908 | 0.577 | 0.500 | MIDAS Pile | 8 | Footprint | Shattered cluster | 1
2014-11-27T193208_P02_T11 | 11 | 0.141 | 0.212 | 0.170 | 0.453 | 2.921 | 0.706 | 0.492 | MIDAS Single | 39 | Single | Compact | 3
2014-11-28T034542_P02_T11 | 11 | 0.197 | 0.250 | 0.100 | 0.225 | 5.305 | 0.886 | 0.471 | MIDAS Single | 27 | Single | Compact | 3
2014-11-28T034542_P03_T11 | 11 | 0.150 | 0.218 | 0.140 | 0.362 | 3.791 | 0.694 | 0.443 | MIDAS Single | 27 | Single | Compact | 3
2014-11-29T222402_P06_T11 | 11 | 0.313 | 0.315 | 0.440 | 0.787 | 1.967 | 0.568 | 0.460 | MIDAS Single | 6 | Footprint | Compact | 3
2014-11-29T222402_P07_T11 | 11 | 0.221 | 0.266 | 0.290 | 0.616 | 1.883 | 0.988 | 0.464 | MIDAS Single | 6 | Footprint | Compact | 3
2014-11-29T222402_P08_T11 | 11 | 0.049 | 0.125 | 0.110 | 0.496 | 2.990 | 0.558 | 0.475 | MIDAS Single | 6 | Footprint | Compact | 2
2014-11-29T222402_P09_T11 | 11 | 0.049 | 0.125 | 0.120 | 0.541 | 3.162 | 0.442 | 0.450 | MIDAS Single | 6 | Footprint | Compact | 3
2014-11-29T222402_P10_T11 | 11 | 0.081 | 0.161 | 0.170 | 0.597 | 2.393 | 0.629 | 0.457 | MIDAS Single | 6 | Footprint | Compact | 3
2014-11-29T222402_P11_T11 | 11 | 0.256 | 0.285 | 0.280 | 0.553 | 2.293 | 0.811 | 0.464 | MIDAS Single | 6 | Footprint | Compact | 3
2014-11-30T141103_P02_T11 | 11 | 0.059 | 0.137 | 0.120 | 0.494 | 2.652 | 0.749 | 0.460 | MIDAS Single | 6 | Footprint | Compact | 2
2014-12-02T113032_P02_T11 | 11 | 0.532 | 0.411 | 0.310 | 0.425 | 2.875 | 0.874 | 0.466 | MIDAS Single | 6 | Footprint | Compact | 2
2014-12-02T113032_P03_T11 | 11 | 0.037 | 0.108 | 0.120 | 0.625 | 2.313 | 0.619 | 0.429 | MIDAS Single | 6 | Footprint | Compact | 3
2015-01-24T051029_P07_T11 | 11 | 0.588 | 0.433 | 0.870 | 1.134 | 3.337 | 0.300 | 0.400 | MIDAS Pile | 14 | Footprint | Shattered cluster | 3
2015-01-24T051029_P08_T11 | 11 | 0.706 | 0.474 | 0.190 | 0.226 | 5.752 | 0.382 | 0.455 | MIDAS Pile | 14 | Footprint | Shattered cluster | 1
…999This table is an excerpt only and the full table is available at the CDS.

##  Appendix B MIDAS shape descriptor maps

MIDAS dust maps combining shape descriptors that is aspect ratio, elongation,
circularity, and convexity, are in general 2D images (e.g., white: lower
value, red: intermediate value, and black: higher value) showing their shape
descriptors at the respective locations on the individual target. Furthermore,
particle clustering with a sophisticated clustering algorithm (i.e., mean
shift method) is described to identify fragments with a common origin (Kim et
al. 2023).

###  B.1 MIDAS shape descriptor maps - aspect ratio

Figure 12: Map showing the aspect ratio distribution of dust particles and the
particle clustering of target 11. The pink circles represent an approximate
size estimation of individual MIDAS clusters. Figure 13: Map showing the
aspect ratio distribution of dust particles and the particle clustering of
target 13. The pink circles represent an approximate size estimation of
individual MIDAS clusters. Figure 14: Map showing the aspect ratio
distribution of dust particles and the particle clustering of target 14. The
pink circles represent an approximate size estimation of individual MIDAS
clusters. Figure 15: Map showing the aspect ratio distribution of dust
particles and the particle clustering of target 15. The pink circles represent
an approximate size estimation of individual MIDAS clusters.

###  B.2 MIDAS shape descriptor maps - elongation

Figure 16: Map showing the elongation distribution of dust particles and the
particle clustering of target 11. The pink circles represent an approximate
size estimation of individual MIDAS clusters. Figure 17: Map showing the
elongation distribution of dust particles and the particle clustering of
target 13. The pink circles represent an approximate size estimation of
individual MIDAS clusters. Figure 18: Map showing the elongation distribution
of dust particles and the particle clustering of target 14. The pink circles
represent an approximate size estimation of individual MIDAS clusters. Figure
19: Map showing the elongation distribution of dust particles and the particle
clustering of target 15. The pink circles represent an approximate size
estimation of individual MIDAS clusters.

###  B.3 MIDAS shape descriptor maps - circularity

Figure 20: Map showing the circularity distribution of dust particles and the
particle clustering of target 11. The pink circles represent an approximate
size estimation of individual MIDAS clusters. Figure 21: Map showing the
circularity distribution of dust particles and the particle clustering of
target 13. The pink circles represent an approximate size estimation of
individual MIDAS clusters. Figure 22: Map showing the circularity distribution
of dust particles and the particle clustering of target 14. The pink circles
represent an approximate size estimation of individual MIDAS clusters. Figure
23: Map showing the circularity distribution of dust particles and the
particle clustering of target 15. The pink circles represent an approximate
size estimation of individual MIDAS clusters.

###  B.4 MIDAS shape descriptor maps - convexity

Figure 24: Map showing the convexity distribution of dust particles and the
particle clustering of target 11. The pink circles represent an approximate
size estimation of individual MIDAS clusters. Figure 25: Map showing the
convexity distribution of dust particles and the particle clustering of target
13. The pink circles represent an approximate size estimation of individual
MIDAS clusters. Figure 26: Map showing the convexity distribution of dust
particles and the particle clustering of target 14. The pink circles represent
an approximate size estimation of individual MIDAS clusters. Figure 27: Map
showing the convexity distribution of dust particles and the particle
clustering of target 15. The pink circles represent an approximate size
estimation of individual MIDAS clusters.

###  B.5 Pristineness of MIDAS particles

A summary of characteristics and shape descriptors of 19 selected particles
rated 4 and 5 are listed.

Table 5: Summary of characteristics and shape descriptors of 19 most pristine MIDAS particles, i.e., pristineness score rated 4 and 5 (marked in boldface). Particle ID | Area | Radius | Height | Aspect Ratio | Elongation | Ellerbroek | COSIMA | Particle surface and | Pristineness
---|---|---|---|---|---|---|---|---|---
| [$\mu$m2] | [$\mu$m] | [$\mu$m] |  |  | classification | classification | volume distribution | score
2014-11-18T032520_P01_T11 | 1.99 | 0.8 | 0.87 | 0.62 | 1.9 | Single | Compact | MIDAS Single | 4
2015-12-13T120938_P14_T11 | 0.29 | 0.3 | 0.47 | 0.87 | 1.47 | Footprint | Shattered cluster | MIDAS Single | 4
2016-04-17T082628_P07_T14 | 1.36 | 0.66 | 0.78 | 0.88 | 1.82 | Footprint | Shattered cluster | MIDAS Single | 4
2016-06-03T062540_P06_T14 | 25.27 | 2.84 | 3.29 | 0.91 | 1.68 | Footprint | Shattered cluster | MIDAS Single | 4
2016-06-03T062540_P09_T14 | 34.69 | 3.32 | 3.72 | 0.88 | 1.89 | Footprint | Shattered cluster | MIDAS Single | 4
2016-06-06T053711_P03_T14 | 7.6 | 1.56 | 1.67 | 0.61 | 1.93 | Single | Compact | MIDAS Single | 4
2016-06-19T161200_P06_T14 | 12.39 | 1.99 | 2.34 | 0.66 | 2 | Single | Compact | MIDAS Single | 4
2016-06-24T072745_P32_T14 | 7.43 | 1.54 | 1.93 | 0.98 | 1.6 | Footprint | Shattered cluster | MIDAS Single | 4
2016-07-06T073351_P14_T14 | 0.33 | 0.32 | 0.4 | 0.95 | 1.58 | Footprint | Shattered cluster | MIDAS Single | 4
2016-07-08T002124_P13_T14 | 5.95 | 1.38 | 2.46 | 1.01 | 1.78 | Pyramid | Large Rubble pile | MIDAS Single | 4
2016-08-15T223355_P03_T14 | 7.43 | 1.54 | 1.6 | 0.88 | 1.85 | Footprint | Shattered cluster | MIDAS Single | 4
2016-08-18T123122_P01_T14 | 11.89 | 1.95 | 2.1 | 0.61 | 2.04 | Single | Compact | MIDAS Single | 4
2016-08-18T220423_P01_T14 | 19.82 | 2.51 | 2.39 | 0.54 | 2.29 | Single | Compact | MIDAS Single | 4
2016-08-21T211728_P02_T14 | 33.7 | 3.28 | 2.68 | 0.72 | 2.67 | Single | Shattered cluster | MIDAS Single | 4
2016-08-21T211728_P03_T14 | 30.72 | 3.13 | 3.32 | 0.93 | 2.09 | Single | Compact | MIDAS Single | 5
2016-09-08T122335_P12_T14 | 0.34 | 0.33 | 1.83 | 3.15 | 1.21 | Footprint | Shattered cluster | MIDAS Single | 4
2016-09-08T122335_P23_T14 | 0.41 | 0.36 | 1.75 | 2.74 | 1.49 | Footprint | Shattered cluster | MIDAS Single | 4
2016-09-08T122335_P24_T14 | 0.21 | 0.26 | 1.69 | 3.66 | 1.7 | Footprint | Shattered cluster | MIDAS Single | 4
2016-09-12T200834_P06_T14 | 1.9 | 0.78 | 2.32 | 1.68 | 1.34 | Footprint | Shattered cluster | MIDAS Single | 4
Mean value | 10.72 | 1.52 | 1.98 | 1.23 | 1.81 |  |  |  |

###  B.6 MIDAS pristineness maps - pristineness evalution

MIDAS dust maps combining pristineness scores are in general 2D images (e.g.,
white: lower value, red: intermediate value, and black: higher value) showing
their pristineness score at the respective locations on the individual target.
Furthermore, particle clustering with a sophisticated clustering algorithm
(i.e., mean shift method) is described to identify fragments with a common
origin (Kim et al. 2023).

Figure 28: Pristineness map combining dust clustering of target 11. The pink
circles represent an approximate size estimation of individual MIDAS clusters.
Figure 29: Pristineness map combining dust clustering of target 13. The pink
circles represent an approximate size estimation of individual MIDAS clusters.
Figure 30: Pristineness map combining dust clustering of target 14. The pink
circles represent an approximate size estimation of individual MIDAS clusters.
Figure 31: Pristineness map combining dust clustering of target 15. The pink
circles represent an approximate size estimation of individual MIDAS clusters.