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: European Space Astronomy Centre,
Camino Bajo del Castillo, s/n., Urb. Villafranca del Castillo, 28692
Villanueva de la Cañada, Madrid, Spain 55institutetext: Istituto Nazionale di
Astrofisica, Istituto di Astrofisica e Planetologia Spaziali, via Fosso del
Cavaliere 100, I-00133 Rome, Italy 66institutetext: 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: Tables 7 and 8
are 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/

I. Dust particle catalog and statistics

M. Kim Cometary dust collected by MIDAS on board Rosetta††thanks: Tables 7 and
8 are 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/Cometary dust collected by MIDAS on board Rosetta††thanks:
Tables 7 and 8 are 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/Cometary dust collected by
MIDAS on board Rosetta††thanks: Tables 7 and 8 are 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/Cometary dust collected by MIDAS on board Rosetta††thanks:
Tables 7 and 8 are 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/Cometary dust collected by
MIDAS on board Rosetta††thanks: Tables 7 and 8 are 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/Cometary dust collected by MIDAS on board Rosetta††thanks:
Tables 7 and 8 are 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/ T. Mannel Cometary dust
collected by MIDAS on board Rosetta††thanks: Tables 7 and 8 are 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/Cometary dust collected by MIDAS on board Rosetta††thanks:
Tables 7 and 8 are 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/ P. D. Boakes Cometary dust
collected by MIDAS on board Rosetta††thanks: Tables 7 and 8 are 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/Cometary dust collected by MIDAS on board Rosetta††thanks:
Tables 7 and 8 are 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/ M. S. Bentley Cometary dust
collected by MIDAS on board Rosetta††thanks: Tables 7 and 8 are 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/Cometary dust collected by MIDAS on board Rosetta††thanks:
Tables 7 and 8 are 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/ A. Longobardo Cometary dust
collected by MIDAS on board Rosetta††thanks: Tables 7 and 8 are 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/Cometary dust collected by MIDAS on board Rosetta††thanks:
Tables 7 and 8 are 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/ H. Jeszenszky Cometary dust
collected by MIDAS on board Rosetta††thanks: Tables 7 and 8 are 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/Cometary dust collected by MIDAS on board Rosetta††thanks:
Tables 7 and 8 are 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/ R. Moissl Cometary dust
collected by MIDAS on board Rosetta††thanks: Tables 7 and 8 are 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/Cometary dust collected by MIDAS on board Rosetta††thanks:
Tables 7 and 8 are 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/ the MIDAS team

(Received 21 October 2022 / Accepted 15 February 2023)

###### Abstract

Context. The Micro-Imaging Dust Analysis System (MIDAS) atomic force
microscope (AFM) on board the Rosetta comet orbiter has been dedicated to the
collection and 3D topographical investigation of cometary dust in the size
range of a few hundreds of nanometers to tens of micrometers with a resolution
down to a few nanometers.

Aims. We aim to catalog all dust particles collected and analyzed by MIDAS,
together with their main statistical properties such as size, height, basic
shape descriptors, and collection time. Furthermore, we aim to present the
scientific results that can be extracted from the catalog, such as the size
distribution and statistical characteristics of cometary dust particles.

Methods. Through a careful re-analysis of MIDAS AFM images, we make a
significant update and improvement to the existing MIDAS particle catalog,
resulting in the addition of more particles and newly developed shape
descriptors. The final product is a comprehensive list of all possible
cometary dust particles detected by MIDAS. The catalog documents all images of
identified dust particles and includes a variety of derived information
tabulated one record per particle. Furthermore, the best image of each
particle was chosen for subsequent studies. Finally, we created dust coverage
maps and clustering maps of the MIDAS collection targets and traced any
possible fragmentation of collected particles with a detailed algorithm.

Results. The revised MIDAS catalog includes 3523 MIDAS particles in total,
where 1857 particles are expected to be usable for further analysis (418 scans
of particles before perihelion + 1439 scans of particles after perihelion,
both after the removal of duplicates), ranging from about 40 nm to about 8
$\mu$m in size. The mean value of the equivalent radius derived from the 2D
projection of the particles is 0.91 $\pm$ 0.79 $\mu$m. A slightly improved
equivalent radius based on the particle’s volume coincides in the range of
uncertainties with a value of 0.56 $\pm$ 0.45 $\mu$m. We note that those sizes
and all following MIDAS particle size distributions are expected to be
influenced by the fragmentation of MIDAS particles upon impact on the
collection targets. Furthermore, fitting the slope of the MIDAS particle size
distribution with a power law of ${a\cdot r}^{\rm{\,b}}$ yields an index
$\rm{\,b}$ of $\sim$ -1.67 to -1.88. Lastly, based on the created dust
coverage maps and clustering maps of the MIDAS collection targets, we
determined the particle fragmentation ratio of 4.09 for nominal activity and
11.8 for the outburst, which underlines that parent particles with faster
impact velocity are more likely to be fragmented during dust collection.

###### Key Words.:

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

##  1 Introduction

Since comets are small bodies with orbits generally far from the Sun, they
store material that remains almost entirely unaffected by gravitational
pressure and solar irradiation. Consequently, comets are thought to have
preserved dust from the very beginning of the Solar System’s formation. In
particular, the smallest cometary dust grains are of great importance as they
represent the building blocks of planetesimals and planets and, thus, they
contain information on their earliest growth processes thought to start with
collisional aggregation of the smallest dust grains (Tielens et al., 2005; Li
& Greenberg, 2003; Weidenschilling & Cuzzi, 1993; Blum & Wurm, 2008).

The microscopic properties of the smallest dust particles have been studied in
a variety of ways, for instance, samples returned from comet 81P/Wild 2
(Brownlee et al., 2006), chondritic porous interplanetary dust particles (CP-
IDPs) collected in the stratosphere (Flynn et al., 2013), and Antarctic
(Noguchi et al., 2015), as well as ultracarbonaceous Antarctic Micrometeorites
(Duprat et al., 2010). However, these investigations either suffer from
significant dust alteration between the time of release from the comet and
their analysis or their provenance is unknown. Although it is generally
difficult to obtain structural information of pristine cometary dust
particles, a unique opportunity to sample the dust and gas environment of the
inner coma of a comet, namely, 67P/Churyumov-Gerasimenko (hereafter 67P), was
offered by the Rosetta mission between 2014 and 2016. In particular, dust
particles were collected with low relative velocities (roughly between some cm
s-1 and tens of m s-1; Della Corte et al., 2015; Fulle et al., 2015) enabling
dust particles to be collected with only a small degree of alteration after
their release. One of three in situ dust instruments on board, Micro-Imaging
Dust Analysis System (MIDAS; Riedler et al., 2007; Bentley et al., 2016a) was
the first atomic force microscope (AFM) that was launched into space to
collect and investigate the properties of cometary dust. It collected
particles with sizes from hundreds of nanometers to tens of micrometers and
recorded their 3D topographic and textural information and statistical
parameters (Bentley et al., 2016a, c). We note that AFMs have been developed
for planetary science applications to study extraterrestrial samples such as
Martian soil particles (Phoenix/NASA; Vijendran et al., 2007; Smith et al.,
2009), lunar samples (Apollo 11/NASA; Hammond et al., 2007), and atmospheric
aerosol particles (Lee & Tivanski, 2021) as well.

The findings of MIDAS presented in this work are set in relation to those of
the other dust analysis instruments on board Rosetta: COmetary Secondary Ion
Mass Analyzer (COSIMA; Langevin et al., 2016), which was dedicated to the
chemical analysis of cometary particles $\sim$ 10 ${\mu}m$ to submillimeter in
size and delivered optical microscope images with resolutions down to about 10
micrometers, and Grain Impact Analyser and Dust Accumulator (GIADA; Colangeli
et al., 2007), which derived the number, mass, momentum, and velocity of dust
particles from comet 67P.

The goal of the current study of MIDAS data is to present the revised MIDAS
particle catalog, together with the main statistics and scientific
results111The definition of language used in this study can be found in
Appendix A. that can be extracted. This paper is organized as follows: we
provide a description of the MIDAS instrument and the mechanism of dust
collection in Section 2. Furthermore, we discuss a sophisticated clustering
algorithm to understand the fragmentation of dust particles during collection.
In Section 3, we give a general description of the MIDAS particle catalog and
its main statistics. Based on the results, we show the size distributions of
MIDAS particles and fragments. Furthermore, we present dust coverage maps and
clustering maps showing the distribution of fragments and parent particles. We
summarize our findings in Section 4.

##  2 Methods

###  2.1 Description of the MIDAS AFM, its dust collection and imaging

MIDAS was the first in situ AFM launched into space. MIDAS had a passive dust
intake system and collector as presented in Figure 1. It consisted of a funnel
leading the particles through a shutter that controlled the particle flux and
thus the exposure time onto the collection targets (sized 1.4 mm x 2.4 mm with
an area of about 3.5 mm2) mounted on the circumference of a sample wheel
(Bentley et al., 2016a). The targets could be transported to an AFM stage
equipped with 16 small, very sharp tips that rastered the surface of the
targets and the collected dust particles. The amplitude-modulated AFM obtained
resolutions down to a few nanometers per pixel (Bentley et al., 2016b).

Figure 1: MIDAS instrument parameters in detail (based on Bentley et al.,
2016b).

The resulting data product is a 2D array where every entry stands for the
relative height measurement at a certain location by the change in amplitude
of the AFM oscillating cantilever. We note that the assessed 3D topographies
are the convolution of the structure of the particle and the tip shape, where
the smallest influence can be expected for particles with rims (i.e., vertical
topography with a gradient shallower than the tip opening angle), much flatter
than the steepness of the tip’s apex, as for all AFM measurements. As a
result, MIDAS acquired 3D images of cometary dust that can be used to analyze
the shape, volume, topographic structure and morphology, and other parameters
of individual particles.

Dust particles entering MIDAS had to pass a funnel with a 30-degree field of
view that narrowed in steps (see Figure 1) and ended in a shutter with a hole
sized like a MIDAS target (1.4 mm $\times$ 2.4 mm). Thus, no particles larger
than a millimeter could enter MIDAS and only small particles are assumed to
finally collide with the collection target and thus be collected.
Additionally, the maximal scan size was about $\sim$ 80 $\mu{\rm{m}}$ $\times$
80 $\mu{\rm{m}}$, such that the largest detected particle was several tens of
micrometers in size. We note that MIDAS targets are fixed relative to the
spacecraft’s movement and orientation because the Rosetta spacecraft kept its
orientation relative to the spacecraft velocity vector with an operational
requirement of the OSIRIS cameras for the Sun illumination to always be coming
from the same direction.

In total, 61 targets were available for dust collection, with 3 pre-mounted
targets used for in-flight calibration. After the arrival of the Rosetta
spacecraft at comet 67P, 8 targets were exposed and scanned for dust
collection (15 targets were exposed in total from the start of the mission),
but only 4 targets (i.e., targets 11, 13, 14, and 15222Note: Previous studies
(e.g., Longobardo et al., 2022; Kim et al., 2022) have adopted different
indexing methods, which comes from the number of telemetries counted from 1 to
64. However, the MIDAS particle catalog 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.)
were found to have detectable dust deposits of cometary origin. The detailed
list of target exposure history can be found in Table 7 of Appendix B. Other
targets (e.g., target 07) were found to show features that are similar to
cometary dust but are probably not of cometary origin. The most likely reason
is contaminant particles on the target being imaged with a tip that has
cometary dust stuck to it (due to the previous scanning on a target with
cometary dust). Tip sample convolution then leads to features similar looking
to cometary dust particles despite no cometary dust being collected on the
target. Furthermore, each target collected dust in a different time period
with differing arriving particle speeds $v$ (Longobardo et al., 2020). For
example, targets 11 and 13 collected tiny dust particles in three periods
before perihelion (Sep. – Nov. 2014, Dec. 2014 – Feb. 2015, and Feb. – Mar.
2015, respectively) with arriving particle speed $v$ about 3m s-1; whereas the
dust particles collected on target 14 were released in an outburst after
perihelion (Feb. 2016), with an arriving particle speed, $v,$ about 7m s-1
(Grün et al., 2016; Longobardo et al., 2022). The different periods again
correspond to different activities of the comet as well, for instance, nominal
activity at pre-perihelion and the February 16, 2016 outburst at post-
perihelion (Grün et al., 2016).

We note that these velocities are measured by GIADA (Rotundi et al., 2015),
whose detected particle size ranges from about 50 $\mu{\rm{m}}$ to several
millimeters (up to two orders of magnitude larger than MIDAS’ particles).
However, the constant dust flux ratio measured by GIADA regardless of periods
(nominal activity and outburst) and the results from the activity model
(Longobardo et al., 2022) concluded that the particles detected by MIDAS are
fragments of hundreds-micron- to mm-sized particles detected by GIADA. Thus,
we assume that the speed of MIDAS parent particles is similar to those
detected by GIADA. We also note that individual small particles may have
arrived with much higher velocities (Agarwal et al., 2007; Della Corte et al.,
2015; Merouane et al., 2016; Hilchenbach et al., 2017). However, small
individual particles are rarely found in the MIDAS dataset, thus, we assume
that the majority of particles arrived with velocities of several meters per
second as measured by GIADA.

A typical 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; Levasseur-
Regourd et al., 2018). To perform the grain identification, analysis, and
calibration, the open-source package Gwyddion222http://gwyddion.net was used
throughout this study. In particular, we drew the mask by hand, judging by
eyes, but cross-checked it iteratively (Bentley et al., 2016c) More detailed
information about the MIDAS instrument can be found in previous MIDAS
publications (Riedler et al., 2007; Bentley et al., 2016a).

###  2.2 Description of the MIDAS clustering algorithm: Identification of
fragments with common origins

When a dust particle entered the MIDAS instrument, it collided with the
collection target with a certain speed, so the particles could be fragmented
upon impact. A fragmentation resulted in a characteristic pattern of dust
distribution on the target, producing so-called clusters, where all particles
in the same cluster are expected to have a common origin (i.e., coming from
the same parent particle). In particular, the initial particle size (and
structure) and particle velocity (Ellerbroek et al., 2017), as well as the
composition can strongly determine how far the fragments of clusters were
spread.

We aim to determine which MIDAS individual particles are fragments of the same
parent particle. In principle, the proximity (i.e., the distance between the
data points to each other; centroid to fragments) of dust particles was taken
into account in this work to identify all fragments of one parent particle.
This can be done by hand, but to avoid bias and facilitate repeatability, a
clustering algorithm was considered.

Given a set of data points, a clustering algorithm classifies each data point
into a specific group. Among a broad variety of available classification
algorithms, it is critical to choose the most suited one for the given data
set. In particular, the clustering result should find cluster centers that
minimize conditional variance (i.e., an appropriate representation of data)
and be repeatable and consistent. Furthermore, a non-parametric algorithm
(i.e., no assumption of any prior shape of the final cluster such as
spherical, elliptical, or similar) was used. Thus, the clustering result is
not sensitive to the initial parameters and is not dependent on too many
parameters. Lastly, the clustering result should not be sensitive to outliers;
outliers have to be considered as single particles forming their own cluster,
not one of the components in a wrong cluster. Based on these requirements, we
chose the mean shift-clustering method (Fukunaga & Hostetler, 1975) among
several clustering algorithms and approaches. In particular, mean shift
clustering does not need the number of clusters to be specified in advance
because the number of clusters will be determined by the algorithm with
respect to data unlike in most other algorithms, such as $k$-means clustering
or the Gaussian mixture model (MacQueen, 1967; Press et al., 2007). In the
mean shift-clustering method, given $n$ data points $x_{\,\rm{i}}$, on a
d-dimensional space $R^{\,\rm{d}}$, and (as the only free parameter ) the
window radius (called the bandwidth), $h$, the multivariate kernel density,
$f(x),$ estimate obtained with kernel K($x$) can be described as:

$f(x)=\frac{1}{n\cdot
h^{\,\rm{d}}}\,\Sigma\,\mathrm{K}\,\bigg{(}\frac{x-x_{\,\rm{i}}}{h}\bigg{)}.$
(1)

Based on the kernel density estimation, the mean shift algorithm assigns the
data points to the clusters iteratively by shifting points (a so-called
sliding-window-based algorithm) towards the highest density of data points
(i.e., cluster centroid). The choice of a sensible bandwidth, $h,$ is
described in Section 3.2 and Table 5. The resulting clusters and implications
for MIDAS dust collection and comparison to other data are discussed in
Section 3.2 and Appendix D. Visualizations of the final clustering results can
be found in Appendix F.

##  3 Results and discussion

###  3.1 MIDAS particle catalog

####  3.1.1 Description of the MIDAS particle catalog

In the MIDAS particle catalog, all particles detected by MIDAS together with
all available information about them are documented and displayed as a table.
Each particle is described in one line where its (meta) data are collected in
columns, for instance, images of single particles and various statistical
evaluations of the particles according to size, volume, and basic shape
descriptors. In particular, each cometary dust identification in every MIDAS
AFM scan is masked using the open-source Gwyddion AFM software (Nečas &
Klapetek, 2012) and a link to the particle mask file in the catalog is
provided along with the 3D topographic data of each particle. Additionally,
several flags highlighting their origin are given, the quality and/or
confidence of the identification and image and scan quality, as well as
additional parameters describing the particle and image properties. In the
present study, we improve on the first public version of the MIDAS catalog
(MIDAS particle catalog V5333ESA planetary science archive of MIDAS/Rosetta
(PSA 6.2.3), dataset identifier: RO-C-MIDAS-5-PRL-TO-EXT3-V2.0, Server
https://www.cosmos.esa.int/web/psa/ftp-browser#rosetta) and update it to V6 by
adding more particles, correcting several manual errors, and adding newly
developed shape descriptors (Kim et al., 2022; Kim et al. in preparation).

This update is extremely important because all scientific data and statistics
about the particle (e.g., its location, size, and height) were extracted from
the masked areas, which were stored as separate data products in the archive.
In the following, we present the most important entries in the particle
catalog for this project.

Particle ID: a unique identifier for each particle that consists of the start
time of the scan containing the particle (in the format year-month-day T hour
minutes seconds), a particle number corresponding to the mask number in its
mask file (e.g., each particle was given its own pixel mask so that one mask
file could label many particles), and the target number on which the particle
was detected. For example, the particle ID 2015-12-12T144849$\\_$P01$\\_$T11
in the catalog shows the scan on which the particle was detected started on
the day 12 Dec. 2015 at the time 14:48:49. The number after ”P” in the
particle ID indicates the number of the mask, which is the number of the dust
particle marking starting with one in each scan. The last entry in the
particle ID is the number of the target on which the particle was detected
(e.g., T11 for a particle on target 11).

Linked Particle ID: describes a link between different observations of the
same particle and provides the particle ID of the previous scan of the same
particle. This is important because particles were often scanned several times
(e.g., to optimize the scanning parameters). For further studies, such as the
creation of dust coverage maps and clustering maps in Section 3.1.3 and the
planned shape descriptor work, we only select the best representation of each
particle. Figure 2 describes an example of the selection for the best
representation of each particle.

Master ID: gives the particle ID of the first time a particle was scanned.
Thus, it is possible to obtain the particle IDs of all apparitions of the same
particle via the same master ID.

Prescan Flag: indicates whether the presence of the visible and/or identified
particle feature was already exposed in a previous scan. We note that only for
$\sim$ 6% (221/3523) of the particles’ prescans are available. Since pre-
scanning, dust collection, and search for dust particles on the target was
heavily time-consuming and the mission time-limited, not all areas on the
exposed targets could be pre-scanned (Bentley et al., 2016a). However, all
dust particles that were detected in scans with pre-scans were clearly
distinct from the contamination pattern on the targets (flat, about 50-100 nm-
sized bumps) and showed a typical morphology. Features larger than the typical
contamination are expected to be cometary. This flag also represents the
special cases when there was no exposure of the target between the prescan and
the scan in which the particle is seen, which likely have previously attached
themselves to the cantilever tip during scanning of a particle and have
subsequently fallen from the tip onto the target.

Particle Flag: indicates whether the particle is cometary in origin, based on
several sets of criteria (e.g., not present prior to the previous exposure of
the target, too big to be contamination, the clear ”splatter” pattern of many
small particles seen as fragmentation of larger particles on impact or during
collection, etc.) or if a different origin is assumed (e.g., contamination on
the target). In this study, we select and investigate only cometary particles.

Imaging Quality Flag: indicates whether a particle was imaged without issues.
Examples of issues that caused a scan to be rejected include when the particle
was not completely in the scanning range (e.g., a part of the particle lies
outside of the boundaries of the image), parts of the particle are hidden by
failed regions in the scan (e.g., a cantilever has reached maximum extension
such that not the entire particle could be scanned), or strong artifacts
appeared as, for instance, tip convolution333As usual for AFM images, all
MIDAS topographic images are a convolution of the tip and the particle surface
shapes, with the strength of the effect depending on the condition of the tip
(sharpness, shape, contamination) and the morphology of the particle. Note: a
full-tip deconvolution was not possible due to the unexpectedly large cometary
particles. For instance, MIDAS features a tip imaging target that allows the
first 700 nm of the MIDAS tips to be imaged, however, the cometary particles
imaged by MIDAS were mostly found to be much larger.. We considered only those
particles that were fully imaged without issues to determine their shapes in
further studies.

Multiple Fragments Flag: indicates whether the mask of the particles seems to
contain multiple fragments that are lying over each other, such that a
separation of the fragments was not possible. Such cases must be disregarded
during further studies such as shape descriptor calculation to avoid
falsification of the determined particle shape. Thus, we flagged multiple
fragments when there were clearly multiple fragments contained within the
particle mask or identification that were too hard to separate.

Trust Height Flag: indicates whether the measured height of the particle
(i.e., defined as the difference between the highest pixel in the mask and the
median of the heights of all pixels surrounding the particle mask) can be
trusted. If the particle is not fully imaged or has one of a variety of
imaging issues (e.g., artifacts, failed imaging covering part of the particle
due to the reached maximum or minimum cantilever extension, a too-low image
resolution), the estimation of the particle height may not be reliable.
Furthermore, the majority of not fully imaged particles, possibly caused by
the saturation of the maximal cantilever extension, were found to be larger
than about 1.2 micrometers. Thus, here we define 1.2 micrometers as having
”poor resolution,” meaning that the height of the particle cannot be trusted.
We select only particles with trusted height for further study because the
height is expected to be a crucial input value for the size distribution, dust
coverage, and clustering maps, as well as the calculation of shape
descriptors.

Scientific data: to date, these entries mostly indicate the area, the height
in pixels, and micrometers, and the volume of the particle in cubic
micrometers. The height information (e.g., height and the mean height of the
surrounding area of the particle, the minimum and maximum height of pixels in
the mask in micrometers) together with the meta data about the X-axis and
Y-axis resolution (step size) of the scan, the number of steps, the X-axis and
Y-axis coordinate of the first pixel in the scan (top left pixel in all
images) in target coordinates, as well as the X and Y length of the image in
micrometers, allow the 3D topography of the particles to be recreated.
Together with the known location of each particle, this opens the opportunity
to draw MIDAS dust collection maps solely using the particle catalog.

Figure 2: Three scans of the same particle (particle ID of the left image:
2016-08-13T204242$\\_$P06$\\_$T11, of the middle image:
2016-08-14T112540$\\_$P06$\\_$T11, and of the right image:
2016-08-31T011432$\\_$P11$\\_$T11) with the master ID
2015-12-14T155236$\\_$P02$\\_$T11. For our studies, we selected the left image
as the best representation because it has the best resolution (194.51 nm
compared to the 781.84 nm and 389.01 nm resolution for the middle and right
image) and shows the earlier scan, meaning that the risk of alteration during
scanning is lower.

In addition to the scientific data, the catalog includes the tip number and
target number used in scanning, the filename and start time of the last image
of the tip made on the tip imaging target, as well as a bounding box
containing the pixel coordinates which can be used to extract individual
particles and masks from the image and mask files.

The MIDAS particle catalog provides a unique and useful tool for identifying
and investigating the structural properties of micrometer-sized cometary dust
particles. Most importantly, the catalog allows quick access to a variety of
particle characteristics, properties, and statistics. Furthermore, the catalog
is a resource for future studies of cometary dust such as the development of
MIDAS particle shape descriptors (Kim et al. in preparation). The most recent
version of the catalog (discussed here) can be found in the ESA’s Planetary
Science Archive (PSA)444ESA 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.

####  3.1.2 Basic statistics of MIDAS particles

The updated version of the MIDAS catalog V6 includes 3523 MIDAS dust particle
identifications in total. The selection of particles usable for further
investigation falls into two main steps: i) particle selection by using the
particle catalog and additional analysis of the MIDAS AFM scans and ii)
duplicate removal to ensure only the best representation of the particle among
multiple scans of the same particle is used. Details can be found below.

For the particle selection, only particles of cometary origin and with a
preferably low amount of alteration and thus clear appearance are of interest.
Thus, we used the following selection criteria: Particles were probably
cometary in origin (particle flag = 1) and imaged such that their height can
be derived, for instance, exhibiting no strong image artifacts (trust height
flag = 1) or fully imaged particle (imaging quality flag = 1). Furthermore,
particles were not susceptible to being multiple fragments (multiple fragments
flag = 0) and not suspected to have fallen off a tip, meaning that they were
previously scanned, picked up with the tip, and dropped at different locations
(prescan flag $\neq$ 4). Lastly, particles were not shown to be fragments of
particles previously scanned (linked particle flag $\neq$ 3).

With the particle selection work, we choose 2088 particles (493 particles
before perihelion + 1595 particles after perihelion) that are usable for shape
descriptor investigation in further analysis. A summary of how many particles
fall within which selection criteria for each target together with their total
number is given in Table 1.

Table 1: Number of MIDAS particles depending on selection criterion for each target. Selection criterion | Target
---|---
all | 11 | 13 | 14 | 15
Cometary origin | 3199 | 705 | 104 | 2377 | 13
Not multiple fragment | 3170 | 568 | 137 | 2443 | 17
Fully imaged | 2780 | 507 | 108 | 2148 | 15
Height trusted | 2421 | 497 | 108 | 2443 | 10
Not fallen off the tip, |  |  |  |  |
no fragment of prior scan | 3347 | 759 | 116 | 2451 | 16
All conditions | 2088 | 410 | 73 | 1595 | 10

With regard to duplicate removal, we note that many MIDAS dust particles were
scanned several times. The scientific reason for the duplication was to
optimize the scanning parameters to obtain a better image with the highest
possible resolution and optimized scanning area. However, we find that the
dust particles often show signs of alteration from the scanning process (e.g.,
fragmentation due to a breaking-off of subunits and dragging them along the
scanning direction). Thus, choosing the best image of a particle is a trade-
off between optimal scanning parameters and a low amount of alteration as a
result of scanning. Deciding on a case-by-case basis which scans of a particle
are the best usable for shape descriptor development is a cornerstone of this
study. In general, we chose the particle representation with higher resolution
and/or the earlier scan (showing or at least implying the lowest amount of
alteration or scanning artifacts). We find that in total 1857 particles (418
particles before perihelion + 1439 particles after perihelion) are unique
within 2088 particles. Thus, we used 1857 particles for further investigation.
Based on the selection process described above, the detailed list of best
representations of each particle depending on targets can be found in Table 8
of Appendix C.

In terms of the statistics of MIDAS particles, Table 2 shows how many unique
particles were collected in total depending on the exposure period for each
target. It also contains two equivalent radii (i.e., defined as the radius of
a disk or sphere with the same area or volume) and the volume of MIDAS
particles together with some simple statistics. The standard dust equivalent
radius on the 2D projection of the particles is calculated via Gwyddion and
Pygwy555Pygwy is a Python binding to Gwyddion’s objects, methods, and
functions, http://gwyddion.net/documentation/user-guide-en/pygwy.html as it
was done in previous publications, for instance, Bentley et al. (2016c).
However, we find that most MIDAS particles after impact show a flattened
conical or cylindrical shape with an elongation (Bentley et al., 2016c), thus
deviating from the simple 2D projection of a sphere assumed for the 2D
equivalent radius. Therefore, we suggest improving the calculation of the
equivalent radius of the particles before impact by taking into account
available 3D information via the volume of MIDAS particles. For each particle,
we first calculate the mean height of all surrounding pixels and subtract this
value from all the height values in the mask to set the zero level and thus
arrive at proper height values. Next, we multiplied the measured height of a
pixel by the area of the pixel and sum over all pixels to measure the volume
of all MIDAS particles. Finally, we calculated the 3D equivalent radius
through the mean volume of the deposited particle on the assumption that the
original particle was a sphere and was flattened by impact without any mass
loss. In conclusion, the 3D equivalent radius presumably gives a better
impression of the initial size of the particle before it hit the target than
the 2D equivalent radius based on the 2D projected area of the particles. We
note that the volume mean could systematically result in a smaller estimate of
the radius since it does not account for the lowered particle volume into the
surface of the target, in contrast to the estimate of the lower limit radius
based on a 2D projection.

Table 2: Number of particles collected depending on the period for each target. Target | Target 11 | Target 13 | Target 14 | Target 15 | All
---|---|---|---|---|---
Period |  | Sep. 2014 -
---
Nov. 2014
| Dec. 2014 -
---
Feb. 2015
Feb. 2016 |  | Feb. 2015 -
---
Mar. 2015
| Sep. 2014 -
---
Feb. 2016
| Pre-perihelion | Pre-perihelion | Post-perihelion | Pre-perihelion |
| Number of particles scanned
---
usable for shape descriptor
410 | 73 | 1595 | 10 | 2088
| Number of unique particles
---
usable for shape descriptor
350 | 61 | 1439 | 7 | 1857
| Particle equivalent radius
---
on the 2D projection
mean $\pm$ standard deviation [$\mu$m]
0.92 $\pm$ 0.75 | 0.64 $\pm$ 0.64 | 0.91 $\pm$ 0.81 | 1.61 $\pm$ 0.93 | 0.91 $\pm$ 0.79
| Particle equivalent radius
---
derived from volume
mean $\pm$ standard deviation [$\mu$m]
0.55 $\pm$ 0.42 | 0.37 $\pm$ 0.35 | 0.57 $\pm$ 0.46 | 0.95 $\pm$ 0.50 | 0.56 $\pm$ 0.45
| Volume of particle
---
mean $\pm$ standard deviation [${\mu}m^{3}$]
2.44 $\pm$ 7.00 | 1.11 $\pm$ 3.48 | 3.40 $\pm$ 14.89 | 6.21 $\pm$ 6.77 | 3.15 $\pm$ 13.49

We find that the calculated equivalent radii range from about 80 nm to 8.5
$\mu$m. In particular, the mean equivalent radius derived from the 2D
projection of the particles measures 0.91 $\pm$ 0.76 $\mu$m, which is larger
compared to the value derived by the volume 0.56 $\pm$ 0.45, showing
overlapping results in the range of the uncertainty. This may indicate either
MIDAS particles are flattened by impact already, thus showing a larger
particle size in the 2D projection or particles have a natural elongation and
preferentially stick with their longer side on the targets (Bentley et al.,
2016c).

Comparing the equivalent radii of particles collected pre-perihelion (mostly
collected on target 11, few particles on targets 13 and 15) to those radii
derived for particles from post-perihelion (target 14, all particles
originating from the outburst on February 16, 2016; Grün et al., 2016) shows
overlapping results in the range of the uncertainty as well. We do not find
that the calculated values themselves show a noticeable difference: both the
mean values of the 2D projection-based and volume-based equivalent radius are
similar for pre-perihelion and the outburst. Taking those facts together,
particles have similar projected areas and volume regardless of cometary
activities, leading to the conclusion that different cometary activities
(e.g., nominal activity or outburst) are not related to the either size of the
particle or the degree of compression.

The mean deposition velocities measured by the GIADA instrument for the
related MIDAS collection periods are lower for pre-perihelion (about 3 m s-1
for pre-perihelion and 7 m s-1 for the outburst; Longobardo et al., 2020).
Thus, we may conclude that the difference in impact velocity between 3 m s-1
and 7 m s-1 is not the main driver for different particle sizes in MIDAS
particle collection. Furthermore, dust source difference (Longobardo et al.,
2020) seems to be unrelated to the dust particle size as well because
particles collected in targets 11 and 14 are expected to stem from different
cometary terrain types. Although Longobardo et al. (2022) observed a dust
density variation (e.g., higher density particles $\rho$ ¿ 1000 g cm-3 during
the time MIDAS collected the particles on target 11 pre-perihelion, but lower
density particles $\rho$ ¡ 1000 g cm-3 during the time MIDAS collected the
particles of the outburst on target 14) that can be explained by different
dynamics of lighter and heavier particles (slower velocities for heavier
particles, thus more spread in the coma, hence lower detection rates), MIDAS
particle sizes seem not to be affected by density differences. Thus, we
conclude that different cometary parameters (e.g., cometary activities with
different impact velocities) do not lead to a different behavior of fragments
of parent particles during deposition, which shows consistency with previous
studies (e.g., Longobardo et al., 2022).

According to Fulle et al. (2020), micrometer-sized particles are too small to
be ejected from a cometary source by simple gas pressure. This finding is in
agreement with the observation of the COSIMA instrument, detecting a lack of
tens of micrometer-sized or smaller dust particles in the coma of comet 67P
(Merouane et al., 2017). Thus, it seems probable that the size of the
particles observed by MIDAS is mainly created by fragmentation, which should
depend on the initial size before impact, impact speed (Ellerbroek et al.,
2017), and the interconnected properties such as density and porosity, as well
as cohesion (Lasue et al., 2019). Thus, it should be noted that all size
distributions discussed in Sect. 3.1.4 may not reflect the particle sizes of
cometary dust in the coma but, rather, the particle sizes after collection by
MIDAS.

Lastly, we compare the measured volume of MIDAS particles to the calculated
volumes of commonly found shapes. Table 3 shows the measured volume, along
with the volumes calculated for a cone and a cylinder with the same radius as
the mean equivalent radius derived from the 2D particle projection, as well as
the derived equivalent radius based on the volume. We find that the mean value
of the volume of MIDAS particles (3.15 $\pm$ 13.49 $\mu$m 3) lies between the
mean value of a cylinder shape (8.81 $\pm$ 42.69 $\mu$m 3) and a cone shape
(2.94 $\pm$ 14.23 $\mu$m 3), but is more similar to a cone shape. The cone
shape slightly underestimates the volume, thus the average real shape might be
close to a cone shape but with a rounded tip. Since we did not find any other
rather irregular shape of MIDAS particles, we conclude that the natural
appearance of MIDAS particles resembles a pyramid and more like an upper
segment of an elongated ellipsoid (elongated by 2.87${}^{+1.90}_{-0.44}$,
lying flat on the target, as found by Bentley et al., 2016c).

Table 3: Measured volume, the calculated volumes on the assumption of cone-shaped and cylinder-shaped MIDAS particles, and the resulting 3D equivalent radius. | Measured | Cone shape | Cylinder shape
---|---|---|---
Volume |  |  |
mean $\pm$ standard deviation [$\mu$m 3] | 3.15 $\pm$ 13.49 | 2.94 $\pm$ 14.23 | 8.81 $\pm$ 42.69
Radius derived from volume |  |  |
mean $\pm$ standard deviation [$\mu$m] | 0.56 $\pm$ 0.45 | 0.51 $\pm$ 0.45 | 0.73 $\pm$ 0.65

####  3.1.3 Dust coverage maps

Based on the selection of the best representation of each dust particle, that
is, the removal of duplicates within the updated particle catalog, as
described in Section 3.1.2, we create dust coverage maps. These are extremely
useful visual aids to assess not only the spread of dust particles on the
MIDAS targets but also to check the results of the clustering algorithm. The
maps can also be used to derive results, such as the percentage of the scanned
area, the area covered by particles, ratios of numbers of fragments versus
parent particles, and so on (see Section 3.2).

We prepare dust coverage maps of the four different MIDAS targets with
cometary dust detection (i.e., targets 11, 13, 14, and 15) for all particles
(without duplicates) in 2D and 3D. For each dust coverage map, we provide two
versions, namely: with and without particles that are not fully imaged
(imaging quality = 1 for entirely imaged particles, 2 for particles not imaged
completely). In particular, dust coverage maps with all selected particles,
regardless of whether they are fully scanned or not, were created because
parent particles are expected to be too large to be fully scanned; thus, a
relation between fragments and their parent may only become visible in a map
including partially scanned dust particles. We also created maps with an
indication of the scanned area, where for overlapping scans only the bounding
box of the scanned area is shown to avoid overcrowding of the plot. This is
highly useful because MIDAS could only scan its collection targets in stripes
that were separated by about 80 $\mu$m-sized inaccessible areas vertically and
horizontally, stitched together by patches of maximally 80 $\mu$m x 80
$\mu$m-sized scans (Bentley et al., 2016a). Thus, a seeming cluster must
always be checked against the scanned area around it to avoid false cluster
identification. Additionally, we investigated 3D versions of the maps to allow
a better assessment of the particle heights. The maps are in general 2D
grayscale images showing the exact particle topographies at their respective
locations on the target, where darker color means higher height.

Examples of the dust coverage maps (e.g., 2D grayscale images with the
indicated scanned area and 3D grayscale images) are presented in Appendix E.
The data used in this paper (e.g., mask data and the location of particles in
the MIDAS particle catalog, scan files, and their location in the target) are
available in the ESA/PSA4.

####  3.1.4 Size distribution of the MIDAS dust particles

To investigate the MIDAS particle size distribution, we used 1857 unique MIDAS
particles that are usable for further analysis. For each size distribution, we
evaluate a series of shape descriptors and calculate both the equivalent radii
of dust particles by their 2D projection and the one derived from the measured
volume of MIDAS particles; we note that the latter is expected to give a more
accurate size of the dust particles (see Section 3.1.2). In the fit of the
size distribution, we excluded the smaller bins (up to equivalent radii $\leq$
500 nm) due to the resolution limit of the MIDAS instrument. This is because
almost half of the individual scans have resolution limits above $\sim$ 500
nm, which causes particles smaller than 500 nm to be hardly distinguishable
from noise. Thus, their number is possibly underestimated. Additionally,
following the idea of hierarchical particles suggested by Mannel et al. (2016)
and Blum et al. (2017), setting free such small particles should be a rare
event, for instance, that is only to occur at high-impact velocities or
especially loosely bonded small subunits. In conclusion, a low number of
nanometer-sized individual particles is expected due to scarcity and detection
bias.

Figure 3 shows the size distribution based on the equivalent radii of the 2D
projection (blue line) and the one derived from the volume (red line) of the
MIDAS particles, the error stated is one sigma. We derive that the size
distribution of the MIDAS particles can be described with a power law,
${r}^{\rm{\,b}}$, fitted with an index $\rm{\,b}$ of -1.88 $\pm$ 0.04 (volume
based) to -1.67 $\pm$ 0.11 (projection-based). In particular, we find that the
data are similar for radii larger than about 1 micrometer, but the slope of
the distribution based on the 2D projection of the particles is slightly
steeper and contains a larger scatter in the data points, whilst the radii
based on the volume show less spread and the fitted slope is shallower.
Furthermore, we find a slight underpopulation of larger-size bins, where the
low statistics leads to a larger uncertainty of the fitted slope. An
explanation could be a fragmentation mechanism during collection, where larger
(weaker) particles fragment more frequently than smaller ones.

Figure 3: MIDAS particle size distributions with equivalent radii based on the
particle’s 2D projection (blue line) combined with a power law ${a\cdot
r}^{\rm{\,b}}$ fit with an index $\rm{\,b}$ of $\sim$ -1.67 and the one
derived from volume (red line) with an index $\rm{\,b}$ of $\sim$ -1.88.

Figures 4 and 5 show the size distributions with the equivalent radius on the
2D projection of MIDAS particles (left) and the one derived from the volume
(right) depending on targets and different periods, respectively, and the
error stated is one sigma. We find that the slope of the size distributions
with the equivalent radius based on the particle’s 2D projection shows a
slight difference for different targets and periods. To be exact, the post-
perihelion data set is coincident with the target 14 dataset, thus there is no
difference in the fitting result. The pre-perihelion data set is consisting of
the data from targets 11, 13, and 15, however, targets 13 and 15 have low
statistics, thus the fitting result of target 11 is not much different from
that for pre-perihelion (a power law index of -1.12 $\pm$ 0.13 for target 11
and of -1.05 $\pm$ 0.10 for pre-perihelion). Investigating the size
distribution of equivalent radius based on the 2D projection and the one
derived from the particle’s volume, we find overlapping uncertainties for all
cases for pre- and post-perihelion. The relative similarity of the slopes of
the size distributions for each collection period may imply that different
cometary activities and impact velocity may not play the driving role in the
fragmentation of larger particles, but only in the number of collected parent
particles. This confirms the findings from Table 2 (see also Sect. 3.1.2).

We note that the equivalent radii based on 2D projection follow the fits less
well than those based on the volume. In particular, there is a slight
overpopulation of smaller particles and an underpopulation of radii larger
than a micrometer. We suggest that the deviation for the 2D projection case is
correlated to different compaction processes at different size scales, which
again implies inevitable dust alteration by impact.

Figure 4: Size distributions of the equivalent radius based on the 2D
projection depending on targets combined with a power law ${a\cdot
r}^{\rm{\,b}}$ fit (green and blue lines for target 11 and 14) with an index
$\rm{\,b}$ of $\sim$ -1.12 to -1.23 (left). Size distributions of the
equivalent radius derived from volume depending on targets combined with a
power law ${a\cdot r}^{\rm{\,b}}$ fit (green and blue lines for target 11 and
14) with an index $\rm{\,b}$ of $\sim$ -1.17 to -1.28 (right).

Figure 5:  Size distributions of the equivalent radius based on the 2D
projection depending on collection periods combined with a power law ${a\cdot
r}^{\rm{\,b}}$ fit (orange and blue lines for pre- and post-perihelion) with
an index $\rm{\,b}$ of $\sim$ -1.05 to -1.23 (left). Size distributions of the
equivalent radius derived from volume depending on collection periods combined
with a power law ${a\cdot r}^{\rm{\,b}}$ fit (orange and blue lines for pre-
and post-perihelion) with an index $\rm{\,b}$ of $\sim$ -1.19 to -1.28
(right).

###  3.2 Fragmentation and MIDAS parent particles (cluster)

While the previous sections discussed the properties of the dust particles and
fragments in the particle catalog, in this section, we described how we use
the data to discuss potential parent particle sizes and fragmentation
mechanisms.

####  3.2.1 Dust collection process

The main question in the present section is whether it is possible to deduce
the arriving MIDAS parent particle size before fragmentation. The idea is to
roughly understand dust particle deposition on the MIDAS targets and relate it
to the cluster size found by the mean shift clustering algorithm described in
Section 2.2.

The size of the clusters determined by the algorithm strongly depends on the
$h$ value (the bandwidth) in Equation 1. As the choice of $h$ is crucial, but
since the expected MIDAS cluster size is unknown, we orientate on the results
of other Rosetta dust instruments and laboratory experiments to set a
reasonable value. The bandwidth should be a strong function of the impact
velocities as well as initial particle sizes and material strengths
(Ellerbroek et al., 2017; Lasue et al., 2019). However, Ellerbroek et al.
(2017) found that a large mass loss of the parent particle on impact can be
expected in certain cases. In particular, they developed a mass transfer
function TF, which is defined as the ratio between the mass of the post-impact
deposit ($M_{\rm{\,post}}$) and the mass of the particle pre-impact
($M_{\rm{\,pre}}$), that is: TF = $\frac{M_{\rm{\,post}}}{M_{\rm{\,pre}}}$.

For larger particles (80 $\mu$m ¡ $d_{\rm{\,pre}}$ ¡ 410 $\mu$m), which are
comparable to the dust particle size investigated by COSIMA and GIADA, they
observed two different cases depending on the impact velocity. At low
velocities ($v$ ¡ 2 m s-1), the majority of these particles leave deposits
with a ”shallow footprint” morphology, namely, a circular or ellipsoidal line
of small fragments encompassing a sparsely covered or even empty area with a
typical TF ¡ 0.2 (i.e., less than 20 percent of the mass of the parent
particle was observed to be deposited on the target). Around 10$\%$ of the
incoming particles leave a ”single” morphology, where most of the parent
particle mass is expected to have stuck on the target and the particle seems
to be without (major) alteration. At velocities above 2 m s-1, a ”pyramid-
shaped” deposit is left on the target with 0.2 ¡ TF ¡ 0.5, that is, maximally
50 percent of the mass of the incoming particles was deposited on the targets.
The deposit looks as if the particle structure partially broke down,
scattering fragments around the bulk of the particle.

Particles smaller than 80 $\mu$m seemed to stick without alteration (creating
”single” morphologies). It is possible that dust particles that are just small
enough can stick without (strong) alteration, in particular without large mass
loss, however, it is not known from which sizes this effect takes place for
real cometary particles because the material composition of cometary dust is
expected to be different from that used in Ellerbroek et al. (2017), that is,
pure SiO2. Furthermore, the 80 $\mu$m threshold might be biased by the
resolution limit for the determination of the size and, hence, the estimated
mass of the incoming particles. Nevertheless, the observations of Ellerbroek
et al. (2017) suggest that if the size of MIDAS parent particles is larger
than a certain value, potentially around 80 $\mu$m but maybe also much
smaller, a substantial loss of parent particle mass, that is, a TF value much
smaller than 1, has to be taken into consideration.

A further reduction of the actually detected particle mass by MIDAS may be
caused by technical limitations. MIDAS could only fully image particles with
heights much less than 10 $\mu$m and it could only scan its targets in about
80 $\mu$m high stripes separated by about 80 $\mu$m high areas (Bentley et
al., 2016a). If fragments of a parent particle are higher than 10 $\mu$m or
were scattered in an unaccessible target area, they were not detected.
Furthermore, particle loss of particles already stuck to the MIDAS target
seemed to occasionally happen at the Flight Spare unit (a structurally
identical MIDAS instrument operated on Earth), especially when changing the
target located in front of the AFM unit.

####  3.2.2 Retrieval of the MIDAS parent particle sizes

We carried out two complementary approaches to the approximate idea of the
MIDAS parent particle size. In both cases, we used the clusters determined by
the algorithm described in Section 2.2. The first one is based on a visual
comparison of the patterns in the MIDAS clusters, in particular, when they are
similar to the shallow footprint dust deposit structures found in the
laboratory experiment of Ellerbroek et al. (2017). The second one attempts to
calculate the parent particle size from the total volume deposited in the
clusters.

The shallow footprint morphology determined in the Ellerbroek et al. (2017)
laboratory experiments stands out relatively well on dust collection targets
since it shows a circular or ellipsoidal line around a (nearly) empty area. It
is expected that a dust agglomerate arrived slowly and bounced on the target,
leaving only some dust fragments falling off its rim. This implies that the
size of the empty area should be roughly comparable to the parent particle
size. A visual inspection of MIDAS dust collection targets shows features that
look very similar to shallow footprints, for instance, as shown in Figure 6.
The empty area encircled by the fragments has a radius of about 15 - 25 $\mu$m
micrometers. We note that these radii are just drawn by eye and not a result
of the clustering algorithm. Judging from the shallow footprint-like MIDAS
deposits, the parent particle size would fall more into the tens of micrometer
regime with a mean size around 20 $\mu$m in radius. This would be well in
agreement with the smaller end of COSIMA and GIADA measurements, for example,
Merouane et al. (2016); Fulle et al. (2016); Levasseur-Regourd et al. (2018);
Longobardo et al. (2020). We note that larger particles of a millimeter to a
centimeter size are not part of the MIDAS data set due to the size of targets
(see Sect. 2.1).

Figure 6: Exemplary clusters of fragments deposited on MIDAS targets that show
a shallow footprint-like morphology. The empty area encircled by the fragments
is approximately marked with red circles and has a radius of about 15 - 25
$\mu$m.

In a second, complementary and straightforward attempt, we calculated the
MIDAS parent particle radius based on the assumption that a spherical parent
particle entered MIDAS and deposited its whole mass as fragments on the
target, similarly to the approach taken in Merouane et al. (2016). In
particular, summing up the volume of all fragments in one cluster, namely,
adding the height (i.e., peak height above the surrounding background pixels)
times pixel area for each cluster member, leads to the parent particle radius
given in Table 4.

Table 4: Parent particle radius derived from the volumes of all particles in each cluster. Target |  | Derived
---
parent
particle radius [$\mu$m]
| Mean and std of
---
parent
particle radius [$\mu$m]
11 | 0.32 – 6.28 | 4.68 $\pm$ 1.31
13 | 0.45 – 4.11 | 3.07 $\pm$ 0.84
14 | 0.58 – 9.86 | 7.34 $\pm$ 2.05
15 | 1.01 – 3.40 | 2.59 $\pm$ 0.61

We find that the MIDAS parent particle radii derived from their volume as
given in Table 4 are 2.59 to 7.34 micrometers in size, which is smaller than
the estimated few tens of micrometer parent particle radius derived from the
diameter of shallow footprint-like MIDAS deposits. These small sizes of parent
particles are not expected to be able to create the observed dust deposit
patterns, especially not the shallow footprints. Thus, this finding confirms
the observation in Ellerbroek et al. (2017) that a vast majority of the parent
particle mass is not transferred to the targets. It also emphasizes that MIDAS
lost an unknown part of the mass of cometary parent particles during dust
collection. In conclusion, the true MIDAS parent particle sizes can only be
roughly estimated and the measured volume of MIDAS particles presents a lower
limit of it.

Figure 7 shows the roughly estimated parent particles as size distribution
before and after perihelion and whole MIDAS particles, the error stated is one
sigma. We found the slope of MIDAS parent particle sizes before and after
perihelion is similar (i.e., -1.06 to -1.51 with an unknown but large
uncertainty attached to both slopes), which confirms the previous finding from
Sect. 3.1.4 that the dust particles are similar for different collection
periods. Furthermore, the slope of whole MIDAS parent particles shows $\sim$
-1.44, which indicates reasonable consistency with the finding from COSIMA for
the smaller particles (e.g., the size distribution of smaller particles
between 15 and 75 $\mu$m, which are comparable to MIDAS parent particle size
ranges, has a power index of $\sim$ -1.6 to 2.8; Merouane et al., 2016, 2017).

Figure 7: MIDAS parent particle size distributions with a power law ${a\cdot
r}^{\rm{\,b}}$ fit with an index $\rm{\,b}$ of $\sim$ -1.06 before perihelion
(blue line), the one with an index $\rm{\,b}$ of $\sim$ -1.51 after perihelion
(red line), and the one with an index $\rm{\,b}$ of $\sim$ -1.44 for whole
MIDAS particles (green line). We note that the parent particle sizes are
roughly estimated at lower limits and the uncertainty given in the graphs is
only that of the fitting routine, hugely underestimating the real uncertainty
of the size measurement.

####  3.2.3 Size of MIDAS clusters

To obtain sensible results about the MIDAS cluster size from the clustering
algorithm a reasonable value for the bandwidth, $h,$ in Equation 1 must be
chosen. In the previous section, we developed the idea that the MIDAS parent
particles may have a roughly estimated size of a few tens of micrometers;
thus, they seem to be similar in size to the smaller particles used in the
laboratory study of Ellerbroek et al. (2017), and similar to the smaller
particles detected by COSIMA and GIADA. Then, we decided to determine the $h$
value and the cluster size by an approximated cluster size of deposits found
in Ellerbroek et al. (2017). However, Ellerbroek et al. (2017) showed that the
degree of dust alteration and the cluster size by “hit and stick” collection
depends not only on the parent particle size but also on impact velocity. As a
result, the expected cluster size on the different MIDAS targets is assumed to
be dependent on the estimated mean velocities of the particles hitting each
target. Those mean velocities can be assumed from speed measurements of GIADA
(Longobardo et al., 2020) taken for compact particles in the related MIDAS
collection periods.

Table 5 shows that targets 11 and 13, holding particles from early pre-
perihelion (around lander delivery in November 2014), collected particles with
relatively slow velocities around 3 m s-1. Target 14 collected particles
during the February 16, 2016 post-perihelion outburst with slightly higher
velocities around 7 m s-1 (which is still a slow velocity compared to particle
speeds around perihelion). Target 15 only holds a negligible amount of
particles collected late pre-perihelion (March 2015) with an impact speed of
roughly 7 m s-1. Those impact velocities are both in the range used by
Ellerbroek et al. (2017) and, thus, a visual inspection of the deposits in
their study leads to expected cluster radii between 25 micrometers for slower
deposited particles and 35 micrometers for faster-deposited ones. This seems
to be a reasonable approach because the resulting variation is only a function
of the relative velocity between the spacecraft and dust particles with the
fixed MIDAS targets relative to the spacecraft movement and orientation (see
Section 2.1), which might be possibly causing dust particle distribution shown
in Figures 17 and 20 (i.e., not uniform across the shown area).

Table 5 gives an overview of the measured mean velocities of GIADA for the
related collection periods of each MIDAS target with cometary dust, the
determined cluster diameters based on the work of Ellerbroek et al. (2017),
and the applied bandwidth value, $h$. For the chosen bandwidth value, $h$, we
also carried out internal (e.g., k-nearest neighbors algorithm and silhouette
analysis; Fix & Hodges, 1989; Rousseeuw, 1987) as well as external validations
(e.g., comparison of the resultant cluster number based on the mean shift
method to the one with the random distribution), which can be found in
Appendix D. Running the clustering algorithm described in Section 2.2 with the
determined $h$ values results in a satisfying clustering of particles that is
visualized in the particle clustering maps in Appendix F.

Table 5: Mean particle velocities measured by GIADA, the applied bandwidth value $h$ in the mean-shift algorithm and corresponding cluster sizes. Target |  | Target
---
mean
velocity $v$
[m s-1]
| Applied
---
band
width $h$
| corresponding
---
cluster radius
[$\mu$m]
11 | 3.1 $\pm$ 1.5 | 14 |  $\sim$25
13 | 2.7 $\pm$ 0.3 | 14 |  $\sim$25
14 | 7.21 $\pm$ 0.09 | 24 |  $\sim$35
15 | 7.2 $\pm$ 0.2 | 24 |  $\sim$35

Table 6 shows a summary of the number of particles and parent particles
(clusters) per target together with their ratio. We find that the average
ratio between fragments and parent particles (clusters) is $\sim$ 4.1 much
smaller for targets 11 and 13 (and 15, however, the statistics of target 15
are negligible) than with $\sim$ 11.8 for target 14. In particular, a
comparison of the circumstances of dust collection showed that particles on
targets 11 and 13 were collected during nominal comet activity pre-perihelion
in late 2014 and early 2015 with lower collection velocities, but particles on
target 14 were gathered during a post-perihelion outburst on February 2016
with some meters per second higher impact speed.

Furthermore, the clustering results achieved with this algorithm are assumed
to be reasonable as they match with the results from complementary studies
(Ellerbroek et al., 2017; Longobardo et al., 2022). In particular, Longobardo
et al. (2022) carried out a complementary approach to derive MIDAS cluster
sizes: assuming that dust particles clustered within two times the fragment’s
size (lying on the same target and detected in the same exposure period)
belong to the same parent particle, they find similar results concerning the
cluster sizes and fragmentation ratios. In agreement with Longobardo et al.
(2022), we find that the parent particles collected during the outburst are
easier fragmented than those collected during nominal comet activity pre-
perihelion. We suggest that the reason is not only driven by the higher impact
speed but also higher particle compaction with lower deposition speed (see
Section 3.1.2; Longobardo et al., 2022). We would like to open up the
possibility that the difference in density detected by GIADA (Longobardo et
al., 2022) is a driver of higher fragmentation ratios, where lower density
particles are more prone to fragmentation either due to higher porosity or
different material composition.

Table 6: Number of particles and parent particles (clusters), and MIDAS fragmentation ratio for each target. Target |  | Number of
---
particles
| Number of
---
parent particles
(cluster)
| MIDAS
---
fragmentation
ratio
11 | 350 | 55 | 6.36
13 | 61 | 15 | 4.1
14 | 1471 | 125 | 11.8
15 | 7 | 4 | 1.8

##  4 Summary

The Micro-Imaging Dust Analysis System (MIDAS) atomic force microscope on
board the Rosetta comet orbiter investigated and measured the 3D topography of
a few hundred of nanometer- to tens of micrometer-sized cometary dust
particles with resolutions down to a few nanometers. We updated and enhanced a
MIDAS particle catalog of all detected MIDAS dust particles together with
their main properties such as size, height, basic shape descriptors, and
collection time. We present scientific results directly extracted from the
catalog such as the size distribution and statistical characteristics of
cometary dust particles.

The majority of the MIDAS particles are assumed to be fragmented upon
collection. This is not only supported by the herein presented clustering maps
but also suspected through observations of the two complementary dust analysis
instruments COSIMA and GIADA on board Rosetta. Thus, the following dust
particle sizes and size distributions may be heavily influenced by
fragmentation during dust collection and are not easily comparable to
unaltered particles in the cometary coma. The key results are as follows:

  * •

We updated the MIDAS particle catalog to version V6 to contain all dust
particles detected by MIDAS and displayed them as a table with a row for each
particle and columns for the (meta) data. The new version of the MIDAS catalog
includes 3523 particles in total. We carefully selected 2088 particles (493
particles before perihelion + 1595 particles after perihelion), whose image
quality is high enough that they can be used in further studies and selected
the best representation for each multiply scanned particle, which left us with
1857 particles for the presented studies.

  * •

We determined the equivalent radius based on the 2D projection of MIDAS
particles to range from about 80 nm to about 8.5 $\mu$m in size. In
particular, the mean value of particle equivalent radius on the 2D projection
is 0.91 $\pm$ 0.79 $\mu$m. As an improvement to the commonly used equivalent
radius, we developed an equivalent radius that takes into account the 3D
nature of the MIDAS data set, namely an equivalent radius based on the volume
measurement of the particles. This volume-derived equivalent radius with a
mean value of 0.56 $\pm$ 0.45 $\mu$m does agree with the 2D projection-based
equivalent radius within the uncertainty.

  * •

We compared the equivalent radii of particles collected pre-perihelion to
those radii derived for particles from post-perihelion and found that the
calculated values themselves do not show a noticeable difference. This implies
that particles have similar projected areas and volume regardless of cometary
activities, leading to the conclusion that different cometary activities
(e.g., nominal activity or outburst) do not relate to either particle sizes or
the degree of compression.

  * •

We compared the measured volume of MIDAS particles to the calculated volumes
of commonly found shapes such as cone shapes and cylinder shapes. A comparison
of the derived volume-based equivalent radius suggested that the average MIDAS
particle shape looks like a cone shape but with rounded tips.

  * •

We determined the size distribution for the two types of equivalent radii. We
found that the slope of the size distribution of the equivalent radius based
on the 2D projection shows a similar behavior to the one derived from volume.
Both follow a power law ${r}^{\rm{\,b}}$ fit with an index $\rm{\,b}$ of
$\sim$ -1.67 $\pm$ 0.11 to -1.88 $\pm$ 0.04, respectively. The slight
differences in slope for the two equivalent radii may reflect lower compaction
of small fragments: the projected area of the particles shrinks faster than
the related volume of the particles. There seems to be a population of less
compressed small particles, potentially fragments that avoided compression
because the impact energy was consumed by fragmentation or different material
composition.

  * •

The relative similarity of the slopes of the size distributions for each
period (with an index of -1.23 $\pm$ 0.10 to -1.28 $\pm$ 0.08 for outburst
activity in post-perihelion versus an index of -1.05 $\pm$ 0.10 to -1.19 $\pm$
0.08 for nominal activity in pre-perihelion) may imply that different cometary
activities and impact velocity may not play the driving role in the
fragmentation of larger particles, but only in the number of collected parent
particles.

  * •

We investigated fragmentation mechanisms during dust collection with the goal
of determining the arriving MIDAS parent particle sizes. We found indications
for substantial loss of parent particle mass upon collection and thus could
only roughly estimate MIDAS parent particle sizes to be in the tens of
micrometer range. The created cluster sizes by fragmentation of such a parent
particle were roughly approximated to be about 25 to 35 $\mu$m in radius
depending on the impact velocity. The slope of the size distribution for the
MIDAS parent particle size is $\sim$ 1.44, showing consistency with the
finding from COSIMA for smaller particles.

  * •

Based on the newly updated MIDAS particle catalog, we created dust coverage
maps of the MIDAS collection targets to obtain an easily accessible overview
of dust deposition. We ran a sophisticated mean-shift algorithm to determine
clusters of particles on the dust coverage maps. On this basis, we created
dust clustering maps to trace possible fragmentation of collected particles.
We determined the fragmentation ratio, namely, how many fragments were created
per parent particle, to be 4.09 for nominal activity and 11.8 for the February
16, 2016 outburst. With the help of GIADA data about particle velocities and
densities, we could determine that parent particles seem to undergo heavier
fragmentation if they have higher deposition velocities and/or lower
densities.

The comprehensive MIDAS catalog is a unique and useful tool for identifying
and investigating micrometer-sized cometary dust particles, allowing for quick
access to a variety of particle characteristics, properties, and statistics,
and it has been made available and updated in the ESA/PSA. This catalog can be
the basis for all following scientific investigations, for instance, the
development of more sophisticated MIDAS particle shape descriptors.

###### Acknowledgements.

We deeply miss our passed away MIDAS Co-I Prof. Anny-Chantal Levasseur-
Regourd. We were grateful to have her in our team as her energy and enthusiasm
truly inspired us. The authors gratefully thank our referee 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). 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 Terminology

Despite the complexity of cometary dust structures, a dust classification
scheme has already been unified with a clearly defined vocabulary in the
Rosetta dust studies (Mannel et al. 2019; Güttler et al. 2019). Here, we
present the terminology for all the different components of dust referred to
in this study and as they apply to collection and detection by MIDAS, in
particular:

  * •

Particle: a subordinate term that describes any type of dust unit (grain,
fragment, subunit, and/or cluster). If the type of dust is not known (e.g.,
whether it is a fragment), we suggest using this term.

  * •

Fragment: indicates that a larger particle was broken into pieces. A fragment
can be pre-existing in the dust collection (e.g., as a natural subunit formed
in the dust growth processes) or created by impact and/or other processes.

  * •

Parent particle: describes a particle as it enters the MIDAS instrument before
hitting the collection target. The parent particle can either stay intact
(i.e, unaltered by collection) or be altered (e.g., compression,
fragmentation).

  * •

Cluster: Cluster indicates a collection of several fragments spatially so
close to each other that they are expected to originate from the same parent
particle. Clusters always consist of fragments, which can also be called
particles because the particle is a subordinate term. The fragments may
contain subunits, which are either clusters of grains or grains.

  * •

Grain: the smallest and fundamental building blocks. They need to be
morphologically closed entities but can be chemically diverse (e.g., hard
spheres).

  * •

Grain cluster: describes a conglomerate of grains. It may be possibly grown by
hierarchical patterns in the early Solar System.

  * •

Subunit: indicates a morphologically distinct part in a particle. It can
either be a grain or a conglomerate of grains. In some cases, differentiation
is not possible due to low resolution or imaging artifacts.

##  Appendix B Target exposure history

From the start of the Rosetta mission, 15 targets were exposed in total. We
note that this does not necessitate that any dust is collected at this time.
However, only 8 targets were exposed and scanned for dust collection after the
arrival of the Rosetta spacecraft at comet 67P and only 4 targets (i.e.,
targets 11, 13, 14, and 15) were found to have detectable dust deposits of
cometary origin. The full table of the MIDAS target exposure history is
available at the CDS.

Table 7: Target exposure history with start and end time, and duration, for each target with comet activities. Start | End | Duration | Target | Note
---|---|---|---|---
2004-04-04 22:58:07 | 2004-04-04 23:04:38 | 0 days 00:06:31 | 33 |
2005-03-27 00:35:15 | 2005-03-27 00:38:13 | 0 days 00:02:58 | 33 |
2005-04-19 13:03:24 | 2005-04-19 13:06:23 | 0 days 00:02:58 | 33 |
2005-10-05 00:42:16 | 2005-10-05 00:44:14 | 0 days 00:01:57 | 33 |
2006-03-04 19:00:17 | 2006-03-04 19:03:16 | 0 days 00:02:58 | 33 |
2006-03-08 18:00:17 | 2006-03-08 18:03:15 | 0 days 00:02:58 | 33 |
2006-08-26 18:00:15 | 2006-08-26 18:03:13 | 0 days 00:02:57 | 33 |
2006-08-30 17:00:15 | 2006-08-30 17:03:13 | 0 days 00:02:57 | 33 |
2006-11-23 10:00:17 | 2006-11-23 10:03:15 | 0 days 00:02:57 | 33 |
2007-05-19 14:00:16 | 2007-05-19 14:03:14 | 0 days 00:02:58 | 34 |
2007-05-23 13:00:16 | 2007-05-23 13:03:14 | 0 days 00:02:58 | 33 |
2007-09-16 13:00:18 | 2007-09-16 13:03:16 | 0 days 00:02:58 | 33 |
2007-10-04 19:02:17 | 2007-10-04 19:07:15 | 0 days 00:04:58 | 34 |
2008-01-05 12:34:14 | 2008-01-05 12:37:12 | 0 days 00:02:57 | 2 |
2008-01-09 14:34:15 | 2008-01-09 14:37:11 | 0 days 00:02:55 | 2 |
2008-07-05 04:15:17 | 2008-07-05 04:18:17 | 0 days 00:02:59 | 33 |
2009-01-29 09:51:17 | 2009-01-29 09:54:16 | 0 days 00:02:58 | 3 |
2009-02-02 15:51:18 | 2009-02-02 15:54:16 | 0 days 00:02:58 | 33 |
2009-09-20 17:45:17 | 2009-09-20 17:47:17 | 0 days 00:02:00 | 33 |
2010-04-24 21:15:17 | 2010-04-24 21:17:17 | 0 days 00:02:00 | 35 |
2010-07-10 11:09:19 | 2010-07-10 22:51:18 | 0 days 11:41:58 | 37 |
2010-12-03 23:00:20 | 2010-12-03 23:02:18 | 0 days 00:01:58 | 5 |
2010-12-07 00:30:20 | 2010-12-07 00:32:18 | 0 days 00:01:58 | 33 |
2010-12-07 02:25:21 | 2011-03-05 01:02:19 | 87 days 22:36:58 | 33 |
2011-03-05 02:55:21 | 2014-09-03 21:58:18 | 1278 days 19:02:57 | 33 |
2014-09-17 12:27:20 | 2014-09-21 12:15:21 | 3 days 23:48:00 | 11 |
2014-09-28 00:06:20 | 2014-09-29 10:35:22 | 1 days 10:29:02 | 11 |
2014-09-30 12:16:21 | 2014-10-01 13:17:22 | 1 days 01:01:01 | 11 |
…
2016-02-16 23:25:25 | 2016-02-20 05:55:19 | 3 days 06:29:54 | 14 | Outburst
2016-02-21 08:07:26 | 2016-02-22 21:08:20 | 1 days 13:00:54 | 14 |
2016-02-23 23:19:26 | 2016-02-24 04:55:01 | 0 days 05:35:35 | 14 |
2016-03-03 11:18:17 | 2016-03-05 07:23:31 | 1 days 20:05:14 | 12 |
2016-03-08 10:50:38 | 2016-03-09 05:57:11 | 0 days 19:06:33 | 12 |
…333The full table is available at the CDS.

##  Appendix C Best representation of each particle

The MIDAS particle catalog presented in this paper contains in total of 3523
scans of particles. Since a part of those scans are suffering from artifacts,
low resolution, or represent the same particle just with different scanning
parameters, there was a cautious selection of particles used for further
scientific analysis necessary. In Sect. 3.1.2, the steps of this selection
process are described. The full table of the ultimately chosen 1857 particles
is available at the CDS.

Table 8: Scanning time, 2D and 3D radius, location of dust particles, and the cluster number (i.e., a reference to the assumed cluster or parent particle family) of best representation of each particle. Particle ID | Target | Start time | Duration | End time | 2D radius444the equivalent radius based on the 2D projection | 3D radius555the equivalent radius derived from volume | Location666from the center of the individual target | Cluster
---|---|---|---|---|---|---|---|---
Number | Y-M-D H:M:S | Days H:M:S | Y-M-D H:M:S | [$\mu$m] | [$\mu$m] | Left | Right | Up | Down | Number
[$\mu$m] |  [$\mu$m] |  [$\mu$m] |  [$\mu$m]
2014-11-18T032520_P01_T11 | 11 | 2014-11-18 03:25:20.311766 | 0 days 06:48:49.008102 | 2014-11-18 10:14:09.319868 | 0.80 | 0.51 | -130.20 | -128.52 | 28.11 | 26.85 | 49
2014-11-18T131924_P01_T11 | 11 | 2014-11-18 13:19:24.323539 | 0 days 06:53:45.008200 | 2014-11-18 20:13:09.331739 | 0.46 | 0.26 | 63.31 | 64.15 | 53.70 | 52.65 | 11
2014-11-18T131924_P02_T11 | 11 | 2014-11-18 13:19:24.323539 | 0 days 06:53:45.008200 | 2014-11-18 20:13:09.331739 | 0.94 | 0.67 | 63.31 | 65.40 | 57.06 | 54.96 | 11
2014-11-18T131924_P03_T11 | 11 | 2014-11-18 13:19:24.323539 | 0 days 06:53:45.008200 | 2014-11-18 20:13:09.331739 | 0.34 | 0.18 | 65.82 | 66.45 | 52.23 | 51.60 | 11
2014-11-18T131924_P04_T11 | 11 | 2014-11-18 13:19:24.323539 | 0 days 06:53:45.008200 | 2014-11-18 20:13:09.331739 | 0.36 | 0.21 | 35.83 | 36.67 | 40.49 | 39.86 | 44
2014-11-18T131924_P05_T11 | 11 | 2014-11-18 13:19:24.323539 | 0 days 06:53:45.008200 | 2014-11-18 20:13:09.331739 | 0.62 | 0.40 | 72.75 | 73.80 | 30.00 | 28.53 | 8
2014-11-18T131924_P06_T11 | 11 | 2014-11-18 13:19:24.323539 | 0 days 06:53:45.008200 | 2014-11-18 20:13:09.331739 | 0.84 | 0.52 | 73.17 | 74.84 | 28.11 | 26.22 | 8
2014-11-18T131924_P07_T11 | 11 | 2014-11-18 13:19:24.323539 | 0 days 06:53:45.008200 | 2014-11-18 20:13:09.331739 | 0.25 | 0.13 | 69.18 | 69.60 | 41.33 | 40.91 | 11
2014-11-18T131924_P08_T11 | 11 | 2014-11-18 13:19:24.323539 | 0 days 06:53:45.008200 | 2014-11-18 20:13:09.331739 | 0.18 | 0.15 | 67.29 | 67.50 | 49.09 | 48.67 | 11
2014-11-18T131924_P09_T11 | 11 | 2014-11-18 13:19:24.323539 | 0 days 06:53:45.008200 | 2014-11-18 20:13:09.331739 | 0.22 | 0.15 | 72.75 | 72.96 | 31.89 | 31.26 | 8
2014-11-18T131924_P10_T11 | 11 | 2014-11-18 13:19:24.323539 | 0 days 06:53:45.008200 | 2014-11-18 20:13:09.331739 | 0.31 | 0.17 | 63.52 | 64.15 | 54.33 | 53.70 | 11
2014-11-18T131924_P11_T11 | 11 | 2014-11-18 13:19:24.323539 | 0 days 06:53:45.008200 | 2014-11-18 20:13:09.331739 | 0.18 | 0.13 | 63.10 | 63.31 | 54.33 | 53.91 | 11
2014-11-27T193208_P02_T11 | 11 | 2014-11-27 19:32:08.587771 | 0 days 07:12:05.008563 | 2014-11-28 02:44:13.596334 | 0.21 | 0.15 | -16.91 | -16.43 | 2.39 | 1.98 | 46
2014-11-28T034542_P02_T11 | 11 | 2014-11-28 03:45:42.597553 | 0 days 07:08:14.008487 | 2014-11-28 10:53:56.606040 | 0.25 | 0.14 | -3.70 | -3.15 | 12.35 | 11.87 | 33
2014-11-28T034542_P03_T11 | 11 | 2014-11-28 03:45:42.597553 | 0 days 07:08:14.008487 | 2014-11-28 10:53:56.606040 | 0.22 | 0.14 | -0.13 | 0.42 | 14.89 | 14.47 | 33
2014-11-29T222402_P06_T11 | 11 | 2014-11-29 22:24:02.648255 | 0 days 13:54:45.016543 | 2014-11-30 12:18:47.664798 | 0.32 | 0.18 | -79.03 | -78.19 | 19.20 | 18.66 | 13
2014-11-29T222402_P07_T11 | 11 | 2014-11-29 22:24:02.648255 | 0 days 13:54:45.016543 | 2014-11-30 12:18:47.664798 | 0.27 | 0.19 | -76.00 | -75.46 | 24.96 | 24.41 | 13
2014-11-29T222402_P08_T11 | 11 | 2014-11-29 22:24:02.648255 | 0 days 13:54:45.016543 | 2014-11-30 12:18:47.664798 | 0.13 | 0.08 | -75.86 | -75.46 | 24.16 | 23.96 | 13
2014-11-29T222402_P09_T11 | 11 | 2014-11-29 22:24:02.648255 | 0 days 13:54:45.016543 | 2014-11-30 12:18:47.664798 | 0.13 | 0.08 | -75.81 | -75.41 | 24.16 | 23.96 | 13
2014-11-29T222402_P10_T11 | 11 | 2014-11-29 22:24:02.648255 | 0 days 13:54:45.016543 | 2014-11-30 12:18:47.664798 | 0.16 | 0.11 | -76.50 | -76.20 | 24.81 | 24.41 | 13
2014-11-29T222402_P11_T11 | 11 | 2014-11-29 22:24:02.648255 | 0 days 13:54:45.016543 | 2014-11-30 12:18:47.664798 | 0.29 | 0.19 | -72.43 | -71.79 | 32.44 | 31.75 | 13
2014-11-30T141103_P02_T11 | 11 | 2014-11-30 14:11:03.667023 | 0 days 13:50:28.016458 | 2014-12-01 04:01:31.683481 | 0.14 | 0.09 | -67.28 | -66.98 | 26.44 | 26.15 | 13
…777The full table is available at the CDS.

##  Appendix D Estimating the value of bandwidth $h$

Estimating the value of scaling factor bandwidth, $h,$ is significantly
important as choosing this value crucially impacts the cluster size and
interpretation. We calculated the estimated value of bandwidth, $h,$ in the
mean shift method with the k-nearest neighbors (kNN) algorithm from
estimate_bandwidth 888https://scikit-
learn.org/stable/modules/generated/sklearn.cluster.estimate_bandwidth.html
function in Python module sklearn.cluster, evaluating the isolation and
connectivity of the delineated clusters. A non-parametric KNN algorithm (Fix &
Hodges 1989; Cover & Hart 1967) relies on observable data similarities and
sophisticated distance metrics (e.g., Euclidean, Manhattan distance, or
Minkowski Distance; default and standard choice is the Euclidean distance)
from new unclassified or unlabeled data points to existing classified or
labeled data points to generate accurate predictions of the value of
bandwidth, $h,$ in the mean shift method (Comaniciu & Meer 2002). The distance
metrics can be described as:

${\rm{Euclidean\,distance}}\,(x,\,y)=\bigg{(}\,\sum_{i=1}^{n}\left|{x_{\rm{\,i}}-y_{\rm{\,i}}}\right|^{p}\bigg{)}^{\frac{1}{p}}:p=2,$
(2)

where $n$ is the number of dimensions (2 for our analysis), $x$ is the data
point from the dataset, and $y$ is the new data point to be predicted. Since
the kNN is a type of classification where the function is approximated locally
and MIDAS particle detection is scanning region-dependent (e.g., see Figure
9), we thus divided MIDAS particle detection in target 11 into locally ($\sim$
100 $\times$ 100 ${\mu}$m), namely, regions 1 to 8 (see Table 9 for details).
Estimated bandwidth values from estimate_bandwidth function and the
corresponding number of clusters in the local regions can be found in Table 9.

The bandwidth, $h,$ and thus cluster number can be also validated by an
alternative method such as the silhouette analysis (Rousseeuw 1987). This
method estimates the average distance between clusters’ so-called silhouette
coefficient $S_{\rm i}$ (also: silhouette width or score) for each observation
$i$ and a measure of how close each point in one cluster is to points in the
neighboring clusters, validating the optimal number of clusters. Even though
the silhouette coefficient mostly used the clustering algorithm to configure
the number of clusters in advance, the optimal cluster number from this method
could be compared to the one from the result of the mean-shift method with the
estimated value of bandwidth $h$ by the kNN algorithm. The silhouette
coefficient, $S_{\rm{i}}$, can be described as follows:

$S_{\rm i}=\frac{b_{\rm\,i}-a_{\rm\,i}}{\rm{max}\,(a_{\rm\,i},\,b_{\rm\,i})},$
(3)

where $a_{\,\rm i}$ is the average dissimilarity between $i$ and all other
points of the cluster to which $i$ belongs and $b_{\,\rm i}$ is the smallest
of $d\,(i,\,C)$ for all other clusters $C$ to which $i$ does not belong. Its
value ranges from -1 (i.e., clusters are assigned in the wrong way) to 1
(i.e., clusters are well apart from each other and clearly distinguished). The
optimal cluster numbers from the silhouette analysis can be found in Table 9.

We find that the optimal cluster numbers that are calculated by the k-nearest
neighbors algorithm and the silhouette coefficient analysis match well in a
reasonable range (at least with the local maxima of the silhouette
coefficient; see Table 9 and Figure 8).

Finally, we compared our results to the random distribution of particles
(e.g., the same number of particles within the same local area) to see if all
MIDAS dust fragments are in reality fragments of parent particles that are not
randomly distributed over the target. We used the same bandwidth (i.e., the
same size of Kernel distribution) and checked that the results vary
substantially. In particular, the result with the random distribution
underestimates the number of clusters. Thus, we concluded that our cluster
interpretation is more statistically significant than the random distribution
interpretation.

Even though these methods provide metrics calculating the goodness of a
clustering technique, we mainly investigate a more qualitative inspection
(e.g., comparing the cluster size that is derived from the bandwidth, $h,$ by
the kNN algorithm and the number of clusters from silhouette coefficient to
the previous experimental study of Ellerbroek et al. 2017) and chose the one
that looks the most reasonable (see also Section 2.2 and 3.2.3). Therefore, we
decide to use 14 as a bandwidth, $h,$ for the case of Target 11.

Region | Location from the center | Estimated bandwidth | Corresponding | Optimal number of cluster
---|---|---|---|---
Number | [$\mu$m] | $h_{\rm{\,estimated}}$ | number of cluster | from the silhouette coefficient
Region 1 | -50 ¡ X ¡ 50, 500 ¡ Y ¡ 600 | 3.55 | 2 |  $\sim$ 2
Region 2 | -100 ¡ X ¡ 0, 150 ¡ Y ¡ 250 | 9.14 | 4 |  $\sim$ 3
Region 3 | 0 ¡ X ¡ 150, 100 ¡ Y ¡ 250 | 24.94 | 11 |  $\sim$ 10
Region 4 | -150 ¡ X ¡ -50, -50 ¡ Y ¡ 50 | 14.32 | 5 |  $\sim$ 5-7
Region 5 | 50 ¡ X ¡ 150, -50 ¡ Y ¡ 50 | 14.54 | 5 |  $\sim$ 3
Region 6 | 200 ¡ X ¡ 300, 0 ¡ Y ¡ 100 | 11.57 | 3 |  $\sim$ 3, 8-10
Region 7 | -150 ¡ X ¡ -50, 0 ¡ Y ¡ -100 | 26.44 | 11 |  $\sim$ 11-13
Region 8 | 0 ¡ X ¡ 100, -250 ¡ Y ¡ -150 | 9.52 | 6 |  $\sim$ 4
| Mean $\pm$ std | 14.25 $\pm$ 7.36 |  |
Table 9:  Estimated value of bandwidth and the corresponding number of
clusters for Target 11 with the k-nearest neighbors algorithm and silhouette
coefficient analysis. Figure 8: Result from the silhouette coefficient
analysis to find an optimal number of clusters. The corresponding number of
clusters derived from the bandwidth, $h,$ is listed in the legend and Table 9,
which shows consistency with the optimal number of clusters with the highest
silhouette coefficient for the individual areas (see Table 9).

##  Appendix E Visualization of the MIDAS dust coverage maps

Overall, MIDAS dust coverage maps are 2D and 3D grayscale images showing the
exact particle topographies at their respective locations on the target. As
described in Section 3.1.3 a variety of maps were created and in the following
the most important ones for good visualization of the MIDAS data set are
shown: the 2D dust coverage maps including only the fully imaged particles
usable for further analysis (as selected in Section 3.1.2) with indicated
scanning area, and the 3D dust coverage maps including the same particles. We
note that we explicitly exaggerate the height of particles (i.e., Z plane)
compared to the X-Y plane in the 3D dust coverage maps to show the
topographies of MIDAS particles clearly.

###  E.1 2D MIDAS dust coverage maps

Figure 9: 2D dust coverage map of target 11 only including fully imaged
particles as selected in Section 3.1.2 with an indicated scanned area (red
boxes; overlaying scans create darker red color, thus more intense color
indicates iterative scanning). Figure 10: 2D dust coverage map of target 13
only including fully imaged particles as selected in Section 3.1.2 with an
indicated scanned area (red boxes; the darkness of red color indicates
iterative scanning). Figure 11: 2D dust coverage map of target 14 only
including fully imaged particles as selected in Section 3.1.2 with an
indicated scanned area (red boxes; the darkness of red color indicates
iterative scanning). Figure 12: 2D dust coverage map of target 15 with fully
imaged particles as selected in Section 3.1.2 with an indicated scanned area
(red boxes; the darkness of red color indicates iterative scanning.

###  E.2 3D MIDAS dust coverage maps

Figure 13: 3D dust coverage map of target 11 including only fully imaged
particles as selected in Section 3.1.2. Figure 14: 3D dust coverage map of
target 13 including only fully imaged particles as selected in Section 3.1.2.
Figure 15: 3D dust coverage map of target 14 including only fully imaged
particles as selected in Section 3.1.2. Figure 16: 3D dust coverage map of
target 15 including only fully imaged particles as selected in Section 3.1.2.

##  Appendix F Visualization of the MIDAS dust clustering maps

The MIDAS dust clustering maps were created based on the MIDAS dust coverage
maps (see Section 3.2.3) after running the mean shift clustering algorithm as
described in Section 2.2 and 3.2. The maps are generally 2D images of the
MIDAS targets with the 2D projection of the dust particles color-coded after
their affiliation to a cluster. The cluster center is indicated by a semi-
transparent red circle. The circle size does not indicate the cluster size as
it is the same size for each cluster, namely, it only indicates the centroid
(i.e., the center of mass with uniform density). For large clusters, some
fragments can lie outside the red circle. Particles with the same color belong
to the same cluster (the same parent particle) on the respective target.

Figure 17: Particle clustering map of target 11. Particles in the same cluster
are depicted in the same color and red circles indicate the approximated
location of the clusters. Figure 18: Particle clustering map of target 13.
Particles in the same cluster are depicted in the same color and red circles
indicate the approximated location of the clusters. Figure 19: Particle
clustering map of target 14. Particles in the same cluster are depicted in the
same color and red circles indicate the approximated location of the clusters.
Figure 20: Particle clustering map of target 15. Particles in the same cluster
are depicted with the same color and red circles indicate the approximated
location of the clusters.