# Cometary dust analogues for physics experiments

A. Lethuillier,1 C. Feller,3 E. Kaufmann,2,7 P. Becerra,3 N. Hänni,3 R.
Diethelm,1 C. Kreuzig,1 B. Gundlach,1 J. Blum,1 A. Pommerol,3 G. Kargl,2 E.
Kührt,4 H. Capelo,3 D. Haack,4 X. Zhang,6 J. Knollenberg,4 N. S. Molinski,1 T.
Gilke,1 H. Sierks,5 P. Tiefenbacher,2 C. Güttler,5 K. A. Otto,4 D. Bischoff,1
M. Schweighart,2 A. Hagermann,7 N. Jäggi,3
1Institut für Geophysik und extraterrestrische Physik (IGeP), TU Braunschweig,
Mendelssohnstr. 3, 38106 Braunschweig, Germany.
2Space Research Institute, Austrian Academy of Science, Schmiedlstraße 6, 8042
Graz, Austria.
3Physikalisches Institut, Universität Bern, Sidlerstrasse 5, 3012 Bern,
Switzerland.
4Deutsches Zentrum für Luft- und Raumfahrt, Rutherfordstraße 2, 12489 Berlin-
Adlershof, Germany.
5Max-Planck-Institut für Sonnensystemforschung, Justus-von-Liebig-Weg 3, 37077
Göttingen, Germany.
6Qian Xuesen Laboratory of Space Technology, China Academy of Space
Technology.
7Department of Computer Science, Electrical and Space Engineering, Lulea
University of Technology, Bengt Hultqvistsvag 1. 981 92 Kiruna, Sweden
E-mail<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

The CoPhyLab (Cometary Physics Laboratory) project is designed to study the
physics of comets through a series of earth-based experiments. For these
experiments, a dust analogue was created with physical properties comparable
to those of the non-volatile dust found on comets. This "CoPhyLab dust" is
planned to be mixed with water and CO2 ice and placed under cometary
conditions in vacuum chambers to study the physical processes taking place on
the nuclei of comets. In order to develop this dust analogue, we mixed two
components representative for the non-volatile materials present in cometary
nuclei. We chose silica dust as representative for the mineral phase and
charcoal for the organic phase, which also acts as a darkening agent. In this
paper, we provide an overview of known cometary analogues before presenting
measurements of eight physical properties of different mixtures of the two
materials and a comparison of these measurements with known cometary values.
The physical properties of interest are: particle size, density, gas
permeability, spectrophotometry, mechanical, thermal and electrical
properties. We found that the analogue dust that matches the highest number of
physical properties of cometary materials consists of a mixture of either
60%/40% or 70%/30% of silica dust/charcoal by mass. These best-fit dust
analogue will be used in future CoPhyLab experiments.

###### keywords:

comets: general – methods: laboratory : solid state – techniques:
miscellaneous

††pubyear: 2020††pagerange: Cometary dust analogues for physics
experiments–Cometary dust analogues for physics experiments

##  1 Introduction

The study of the physics of planetary analogue materials is essential for our
understanding of the objects of the Solar System. In particular, research on
the physics of cometary materials greatly benefits from laboratory
experiments, as in-situ measurements are difficult to obtain. Our knowledge of
comets and cometary nuclei has increased significantly in the last few
decades. With the help of numerical models, earth-based observations, and
especially ambitious space missions, a remarkable amount of information has
been collected, providing insights into the physical processes taking place on
comets.

The Rosetta mission in particular, spent more than two years studying comet
67P/Churyumov-Gerasimenko (hereafter 67P/C-G) and its nucleus from up close
with a wide array of instruments. In November 2014, the Philae lander detached
from the Rosetta orbiter and descended to land on the surface of the nucleus.
For three days, the lander measured many physical properties of the surface
before running out of power.

In order to interpret many of the measurements performed by the Rosetta
instruments, models had to be developed and assumptions on the materials that
make up the nucleus had to be made. Experimental studies of cometary analogues
in environments similar to those encountered in comets can help to validate
the models and limit the assumptions made about the composition of comets.
Support from laboratory experiments to cometary science has been ongoing since
the 1970’s. The first cometary experiment was done by Dobrovolsky & Kajmakov
(1977) who studied the sublimation of water ice/refractory mixtures in vacuum.
Similar experiments were conducted at the Jet Propulsion Laboratory in the
1980’s by Saunders et al. (1986) and Storrs et al. (1988). One of the most
ambitious cometary laboratory experiments was the KOSI ("Kometen-SImulation",
Comet-Simulation in English) experiments by Grün et al. (1992), in which
mixtures of dust and ice were cooled down to cryogenic temperatures before
being illuminated in vacuum. These experiments allowed the measurements of the
thermo-mechanical properties of cometary analogues and also showed that
thermal activity within the samples led to the formation of a desiccated
refractory layer with a low thermal conductivity (Spohn et al., 1989).
However, these experiments had many free parameters and the properties changed
between measurements, which complicated the interpretation of some of the
observations.

The data sent back by Rosetta from comet 67P/C-G provided us with an
unprecedented view of a comet and has given us access to the physical
properties of cometary material. Thanks to these recent measurements made by
all of the Rosetta instruments, it is now possible to create more accurate
refractory cometary dust analogues. These dust analogues will need to be mixed
with volatile components in order for earth-based experiments to shed light on
the physical processes happening on comets.

To this end, in the framework of the CoPhyLab (Comet Physics Laboratory,
Gundlach 2019) project, we present our cometary dust recipe. The main goal of
this refractory analogue is to reproduce the physical properties of actual
cometary material as accurately as possible while being procurable in large
enough amount for laboratory experiments. The sample should also be
representative of different comets, not just 67P/C-G. As the CoPhyLab
experiments are focused on physical and not chemical properties, we do not aim
to reproduce the chemical composition of comets with this analogue. We
acknowledge that chemical and physical composition are interdependent of each
other and at a later stage, to study more complex processes, a chemical
analogue might be desirable but is out of the scope of this paper.

In Section 2, we will present a brief overview of current cometary analogues,
we will also justify the development of the CoPhyLab comet refractory analogue
(hereafter CoPhyLab dust) and specifically the use of a two component mixture
of silica and charcoal. In Section 3, we put forward a detailed list of all
the physical properties of interest, a justification for their selection, and
the target values for these properties. Finally, in Section 4, we document the
procedure we use to mix the CoPhyLab dust, as well as the physical properties
of different mixing ratios of silica dust and charcoal.

##  2 Known cometary analogues

A few groups have developed and used cometary analogues in the past, with the
goal of studying the sublimation of volatiles from an illuminated dust/ice
mixture. These cometary analogues have a lot in common but also have some
significant particularities that depend mostly on the experiment they were
used in as we discuss below.

For the KOSI experiment (Grün et al., 1992), large quantities of samples of up
to a few kg had to be produced. Therefore, the material used as an analogue of
the refractory part had to be readily available. Stöffler et al. (1991)
mention the use of mixtures of silicate minerals and soot as the refractory
parts in a number of KOSI experiments. The silicate component was a mixture of
olivine, pyroxene, montmorillonite, and kaolinite originating from terrestrial
sources. They were chosen following observations made on comet Halley,
interplanetary dust particles, and carbonaceous chrondrites (Stöffler et al.,
1991). The soot was chosen as a carbon source and to control the albedo of the
samples. In total, 6 samples were created each one for one of the KOSI
experiments (Grün et al., 1991). Later experiments used olivine mixed with
soot for more complex sublimation experiments (Grün et al., 1993). Similar
cometary analogues were used in later studies, such as in Herique et al.
(2002), in which the dielectric properties of samples at radar frequencies
were investigated in preparation for the Rosetta mission.

Other mixtures of silicate minerals and carbon were analysed in preparation
for the arrival of Rosetta and for the analysis of cosmic dust measurements.
Rotundi et al. (2002) studied different mixtures of Mg and Fe bearing
silicates, carbon rich dust, and mixed carbon silicate dust. The samples were
then exposed to extraplanetary post-condensation processes, analysed with
electron microscopy, and spectroscopy to identify their textures,
morphologies, grain compositions, and crystallographic properties.

The KOSI samples were relatively complex, as they were made up of multiple
ground minerals mixed with soot. This could result in difficulties when
analysing various measurements quantitatively. More recent studies have tended
towards the use of simpler mixtures, e.g., Kaufmann & Hagermann (2018) used
carbon black as the refractory part of the cometary material, which served
mainly as a light absorbing agent to induce morphology changes under
illumination conditions. For the specific measurements presented in their
study, such as hardness measurements and morphology changes, this mixture was
sufficient. In Flandes et al. (2018), aerogel was used as a cometary dust
analogue to study the trajectory of a dust particle. Therefore, only the low
bulk density and Young’s modulus needed to be reproduced by the analogue.

Nevertheless, for some measurements more complex samples are necessary. For
example, in an effort to reproduce the spectroscopic and the photometric
properties of the nucleus’ surface of comet 67P/C-G, Poch et al. (2016a, b)
and Jost et al. (2017a, b) produced their own cometary analogue. The dust
component of this analogue were made of tholins as analogues of the complex
organic matter needed to reproduce the strong spectral slope in the visible
and carbon powder to control the albedo of the sample. Noting that the
presence of silicate materials appears to have little effect on the spectral
properties of such mixtures (Rousseau et al., 2018), silicates were not
included in these studies, in order to lower the number of components and make
the observations easier to interpret.

The CoPhyLab project comprises a great deal of experimental facilities
dedicated to investigating the physics of comets (Kreuzig et al., 2019;
Kreuzig & et al., 2021). Experiments are planned to study the sublimation of
ices, ejection of particles, heat transfer inside the surface layers, gas
diffusion through the material, mechanical properties, electrical properties,
morphology, and evolution of spectrophotometric properties (Gundlach, 2019).
Therefore, the dust analogues previously described are not suitable, as they
generally are aimed at studying one physical parameter in particular. Also,
the complex analogues used in the KOSI experiments are not suitable, because
they contain too many components with too many unknown physical properties,
which would make the interpretation of the measurements more difficult. In
order for these experiments to correctly reflect the physical processes
occurring on comets, a nucleus refractory analogue must be created and well
characterised. The properties that the CoPhyLab project is interested in
studying are physical and therefore we do not require a chemical match to the
estimated cometary composition. However, we note that the chemical composition
has a strong effect on key physical properties such as albedo/density and
therefore cannot completely be ignored. In the following Section, we describe
each physical parameter of interest, the values we are aiming for with our
dust analogue, and our methods of measurement.

##  3 Material properties

The samples studied in the CoPhyLab large chamber weigh several kg (Kreuzig et
al., 2019; Kreuzig & et al., 2021), therefore the comet analogue has to
consist of safe components purchasable in quantities in the kg range for an
affordable price. Our dust analogue is thus composed of a two phase mixture:

  * •

The first phase is made of silicon dioxide (S5631), otherwise known as silica,
from Honeywell Research Chemicals. This component simulates the silicate
materials. It comes in the form a white dust with a well controlled particle
size (99 % 0.5-10 µm) and can be purchased in 1 kg increments at a price of
currently $\sim$200 € Kg-1).

  * •

The second phase is Juniper charcoal dust purchased from (Pyropowders
Wacholderkohle). This component was chosen to represent the organic matter
known to be present on the surface of the comet, but also to act as a
darkening agent. It comes in the form of a dark powder with a larger particle
size than the silicon dioxide (<100 µm) and a lower cost (currently 12 €
Kg-1). Even if charcoal is known to not be present on comets, it is generally
used as an analogue for the dark organic material present on the surface as
will be described later. We will also see that it allows us to match many of
the physical properties of cometary dust. We were not able to find charcoal
with a similar particle size to the silica dust in the quantities necessary
for the CoPhyLab experiments. Grinding the charcoal, in the quantities needed
for the experiments, is feasible but would require a lot of work-power and
time. As the non ground charcoal allows us to fit many physical parameters,
grinding was not deemed necessary.

A total of eight physical properties were deemed essential for the CoPhyLab
physics experiments. For each property, a short description of the estimated
cometary values and how we measure them in our laboratory is presented below.

###  3.1 Particle size distribution

####  3.1.1 Cometary particle size distributions

The state of knowledge on the particle size distribution of cometary
refractories has greatly increased since Rosetta. Previous studies of
chondritic porous interplanetary dust particles from the Earth’s stratosphere
have shown particles with sub-micrometre sizes that generally follow log-
normal size-frequency distributions (Rietmeijer, 1993; Wozniakiewicz et al.,
2013). Studies of the particles collected by the Stardust mission also show a
strong presence of particles with sizes below the micrometre range that follow
log-normal distributions (Hörz et al., 2006; Zolensky et al., 2006).

Rosetta offered many opportunities to constrain the particle size distribution
of cometary dust. Visible and Infrared Thermal Imaging Spectrometer (VIRTIS)
observations of the coma and of outbursts have shown the presence of sub-
micrometre particles and a size distribution with a power-law index in the
range 2.5–3 (Bockelée-Morvan et al., 2017). In addition, an anomalous feature
observed by the Alice spectrograph can be explained by the presence of
nanometre grains close to the instrument (Noonan et al., 2016). Johansson et
al. (2017) observed a strong decrease in the photoelectric current measured by
the Langmuir Probe at perihelion that could be linked to the presence of
nanometre-sized grains.

Three instruments on board Rosetta were dedicated to the study of the cometary
dust: MIDAS (Micro-Imaging Dust Analysis System), GIADA (Grain Impact Analyser
and Dust Accumulator), and COSIMA (Cometary Secondary Ion Mass Analyser).
MIDAS is the instrument with the best size resolution and has allowed for a
classification of the collected dust particles in the coma into three
categories (Mannel et al., 2019):

  1. 1.

Large agglomerates ($\approx$10 µm) composed of micrometre sized particles in
a fragile arrangement.

  2. 2.

Large agglomerates ($\approx$10 µm) composed of micrometre sized particles in
a structure with fractal dimension less than two.

  3. 3.

Small particles ($\approx$1 µm) with subunits in the 100 nm range.

In addition, Mannel et al. (2019) also found that the size distribution of the
smallest particles follow a log-normal law with an average around 100 nm and a
power law index in the range 2.9 to 3.8.

The analysis of the COSIMA data has revealed the presence of agglomerates in
the range of 30 to 150 µm (Merouane et al., 2017) and that the power law index
of the particle size distribution changes as the comet orbits the sun (from
-1.6 after equinox to -2.8 at perihelion, Merouane et al. 2017). The lack of
small particles detected (below 30 µm) is interpreted as the fact that small
charged particles would have been deflected before reaching the instrument.
Large agglomerates (>500 µm) were also detected but they disappeared after
equinox (Merouane et al., 2017).

GIADA found compact particles ranging from 30 µm to 1 mm, and fluffy
agglomerates ranging from 0.2 mm to 2.5 mm (Fulle et al., 2015). GIADA also
found that the dust size distribution changes as the comet orbits the sun;
from a power law index of > -2 at 2.2 and 2.1 au inbound, to -3.7 at
perihelion (Fulle et al., 2016). By comparing dust coma models to OSIRIS data,
Marschall et al. (2020) found that the best fitting dust size distribution
power law index at perihelion is around 3.7${}^{0.57}_{-0.078}$ and that the
smallest dust particles should be "strictly smaller than 30 µm and nominally
even smaller than 12 µm." Marschall et al. (2020).

These values are mostly valid for the dust coma surrounding the comet.
Retrieving similar values for the refractory phase before it leaves the
surface is challenging. A derivation of a direct relationship between the coma
dust size and surface dust size is difficult, as an unknown selection of
mechanisms could take place in between (for example the sublimation of
volatiles after ejection, leading to further fragmentation). Nevertheless,
using images of the surface taken by the ROLIS instrument onboard Rosetta,
Mottola et al. (2015) derived a dust size distribution power law index of -2.2
for agglomerates ranging from 4 to 0.2 cm.

####  3.1.2 Conventions for the definitions of particles

For the definitions of the different types of particles we are analysing, we
will use the convention defined in Güttler et al. (2019). They define three
categories of particles:

  1. 1.

A "solid group", composed of irregular grains, monomers, and dense aggregates
of grains. They are mainly characterised by a strong tensile strength and by a
very low porosity (less than 10%).

  2. 2.

A "porous group", composed of porous agglomerates of grains and clusters of
porous agglomerates (porosity 10-95

  3. 3.

A "fluffy group", composed of fractal dendritic agglomerates, generally very
porous (porosity $>95\%$) and with a very low tensile strength, see Fulle &
Blum (2017) for more details.

For the CoPhyLab experiments, we want to match two of the particle categories
to the known cometary values, the solid group and the porous group. In the
solid group, we are unable to distinguish between an individual grain and a
dense agglomerate of grains with the measurement methods at our disposal (see
section below). We make the assumption, due to their low porosity and high
strength, that the dense agglomerates are indistinguishable from the
individual grains for most of our planned experiments. Thus, we hereafter use
"grain" to mean individual grains and dense agglomerates of grains. In a
similar way, we lack the ability to distinguish between porous agglomerates of
grains and clusters of porous agglomerates. They will be both referred to
hereafter as agglomerates, as the differences between them are not expected to
impact any of the individual experiments. We choose not to try and match the
fluffy group composed of fractal agglomerates, mainly because they are
difficult to produce in the quantities needed for the experiments.
Additionally it would complexify the comparison of numerical models to the
experiments.

####  3.1.3 Particle size measurement methods

Two methods were used to evaluate the grain size-frequency distribution of our
samples. The first method involved using a sieving tower with levels of
different-sized sieves. Using this method, the smallest size fraction
reachable is 44 µm. The second method involved using a microscope and
analysing the images of dust particles suspended in ethanol. The suspension
was exposed to an ultrasound bath in order to separate the agglomerates into
their individual grains. The images, taken at different zoom factors, were
then analysed with a shape recognition script that identified individual
grains and fitted a circle around them to provide an estimate of their size.
In order to determine the smallest sizes visible by this method, we calibrated
the microscope using a USAF 1951 Chart calibration target. Images of the
target demonstrated that we could observe particles as small as 0.43 µm. It
might be possible to observe smaller particles, but unfortunately we were not
able to verify this as we already reached the limit of our calibration target.
We therefore take 0.43 µm as our best resolution using this method, but assume
that we could resolve particles half that size.

In order to measure the agglomerate size-frequency distribution (agglomerates
that are formed from the shaking and combination of particles from both
phases), we combine the microscope method (for agglomerates in the micrometre
range) with a camera with a macro-lens (for agglomerates in the 100 micrometre
range up to the millimetre range). The camera observes a white piece of paper
on which we sprinkled the dust mixtures (see Figure 1). The images were
analyzed with a shape detection algorithm to estimate their number and size,
similarly to how the microscope images were analysed. Using this method the
resolution is 24 µm.

Figure 1: Example of one of the images of the dust taken with a camera and
macro-lens used to derive the agglomerate size-frequency distribution

####  3.1.4 CoPhyLab dust grain size-frequency distribution

The grain size-frequency distribution is known for both base materials. For
pure silica, the dust size-frequency distribution was previously measured by
Kothe et al. (2013, their Figure 3), in which the mass-frequency distribution
shows that most of the mass is contained in grains with sizes between 1 µm and
10 µm. The grain size of the charcoal was measured in this work by using the
microscope method described in the previous subsection. The particles were
quite irregular, so we systematically took the longest dimension to be
representative of the size of the particle.

Figure 2 displays the cumulative size-frequency distribution of the charcoal
grains observed with the help of our microscope (250 nm < r < 600 nm). This
size-frequency distribution can be compared to Rosetta estimates for the grain
size. For the charcoal grains we found a slope of the linear fit to our data
of $\alpha=2.8\,\times\,10^{-3}\,nm^{-1}$ (see Fig. 2), close to those found
by MIDAS ($\alpha=3.5\,\times\,10^{-3}\,nm^{-1}$ for particle G and
$\alpha=3.2\,\times\,10^{-3}\,nm^{-1}$ for particle D (Mannel et al., 2019)
and VIRTIS ($2.5-3.0\,\times\,10^{-3}\,nm^{-1}$ Bockelée-Morvan et al. 2017).

Figure 2: Cumulative size-frequency distribution of the grains (250 nm < r <
600 nm) of charcoal. The grain sizes are fitted with a linear function and the
average size (392 nm) is shown. We also indicated in the grey-shaded area the
sizes that are below our minimum calibration size.

The average grain size of the two components of the CophyLab dust are
compatible with the smallest values detailed in the previous section and with
the constraints given by Marschall et al. (2020) (grains with sizes less than
1 µm). Based on these results, we find that all possible mixtures of silica
dust and charcoal have the required grain size.

####  3.1.5 CoPhyLab dust agglomerate size distribution

The CoPhyLab dust agglomerates were measured with the method described in
Section 3.1.3 for mass fractions of silica dust reaching from 10 % to 90 %.
For each of the nine mixtures, the size-frequency distribution was fitted with
a power law in the 100 µm to 1 mm size range (two examples can be seen in
Figure 3 top). In the bottom of Figure 3, the resulting power law indices are
plotted as a function of the silica mass fraction and compared to values
derived from measurements of the Rosetta instruments. We found that most
mixtures (from 20 % to 90 % silica dust) have a power law index between -1.5
to -2.2, which is in good agreement with the dust size-frequency distribution
found by GIADA, ROLIS, and COSIMA at equinox. However, we do not reach the
indices determined by the instruments at perihelion. This implies that to
compare our results to the most active phases of the cometary orbit, different
size distributions are probably required.

Figure 3: Top: Agglomerate size-frequency distribution between the 100 µm and
2 mm for two charcoal/silica mass ratios. The shaded areas represent the
uncertainties of the fitted power law indices. Bottom: Index of the power law
fit as a function of the mass fraction of silica dust. The error bars show the
uncertainty of the fit parameters as shown in the top figure. The horizontal
lines represent estimated values of the power law index derived from multiple
Rosetta instruments described in Section 3.1.1.

However, this comparison has a few caveats. The COSIMA power law index was
determined mostly for particles with sizes between 30 µm to 150 µm, which is a
an order of magnitude lower than our agglomerate sizes Merouane et al. (2017).
Another possibility is that the agglomerates broke upon impact and only the
resulting fragments are observed. Additionally, all of these power law indices
are derived from dust that has left the cometary surface and thus does not
necessarily represent the properties of the dust on the nucleus. For these
reasons, we are more confident that the ROLIS power law index is the most
representative of the nucleus cometary dust. It is interesting to note that
GIADA equinox observations also find a similar power law index to that of
ROLIS (Fulle et al., 2016).

Taking all this information into account, we find that most of our mixtures
possess power law indices very close to those found by GIADA and ROLIS. In
four cases (20, 40, 60, and 70 % of silica dust), the error bars overlap with
the hypothesized surface dust power law index. In three cases (30, 80, and 90
% of silica dust), the values are found to be sufficiently close and thus are
considered acceptable mixtures. The only outlier is the 10 % silica dust
mixture. Therefore, we decided to not consider it further for our CoPhyLab
experiments.

###  3.2 Material density

####  3.2.1 Cometary dust densities

The material density of cometary dust is a fairly unknown quantity. The
Rosetta Radio Science Investigation (RSI) (Pätzold et al., 2016) measured that
the comet as a whole has a bulk density of 533$\pm$6 kg m-3, which implies a
high porosity of 72–74 %. In order to derive this porosity value, Pätzold et
al. (2016) used a value of 2600$\pm$400 kg m-3as the material density for the
cometary dust (density with no porosity). Jorda et al. (2016), using an
estimated global density of the comet of 532$\pm$7 kg m-3and a grain density
between 2000 to 3500 kg m-3, found that the comet has a porosity between 70 %
and 75 %. For their analysis of the data from the Comet Nucleus Sounding
Experiment by Radiowave Transmission (CONSERT), Kofman et al. (2015) used
material densities of 2500 to 3500 kg m-3(based on densities of ordinary and
carbonaceous chondrites) and found that the nucleus has a porosity of 75 to
85%. In a later study, the CONSERT team extended this range from 2000 to 3500
kg m-3(Herique et al., 2017). In order to be compatible with their
measurements, the authors hypothesized that a high fraction of carbonaceous
material is needed. This in turn led them to favour materials with densities
closer to 2000 than to 3500 kg m-3(see Table 7 in Herique et al. 2017 with the
compatible materials in bold). They find that CR2 chondrites could be
discarded due to the lack of hydrated minerals in 67P/C-G.

####  3.2.2 Density measurement method

In order to measure the intrinsic material density (or grain density) of our
analogue materials, we used a helium pycnometer (Upyc-1200e-V5.04, located at
the University of Bern) that measures the volume of helium needed to fill the
voids in a sample of known volume. This then allows us to calculate a material
density for the sample. This method has been previously used to measure the
material density of Lunar and Martian simulant regolith samples (Mattei et
al., 2014; Brouet et al., 2019; Pommerol et al., 2019).

####  3.2.3 CoPhyLab dust density

Using the method mentioned above, the material densities of the silica dust
and the charcoal end members were determined to be 2550-2600 kg m-3and
1500-1600 kg m-3, respectively. For the analogue mixtures, we used a linear
mixing law in order to determine the material densities. These densities are
plotted in Figure 4. In this Figure, we also indicated the range of allowable
material densities for our mixtures (those used by previous studies as
estimates for the 67P/C-G refractory grain density). In order to take into
account as many of the densities described in Section 3.2.1, we choose a range
from 2000 to 3000 kg m-3. We can see from Figure 4 that all mixtures with less
than 50 % silica dust by mass do not have the minimum density value required.
We also note that our densities are generally quite low (< 2600 kg m-3),
making them compatible with the values in Herique et al. (2017).

Figure 4: Density of the CoPhyLab silica-charcoal dust mixtures as a function
of the mass fraction of the silica dust. The grey-shaded area indicates the
allowable range for the material densities of a cometary dust analogue Kofman
et al. (2015); Jorda et al. (2016)

###  3.3 Gas permeability

Gas permeability is an important factor in numerical models for the activity
of comets as it describes how easily solid material allows gas (like
sublimated water molecules) to travel through the pores of the surface layers
(see Gundlach et al. 2020a for an example). The gas flow through a porous
material can be represented by two main parameters. The gas permeability that
represents the viscous flow of gas and the Knudsen diffusion coefficient.

####  3.3.1 Cometary dust gas permeability

The Philae lander was designed to measure various surface properties with
several sensors. Unfortunately, none of those were dedicated to the
measurement of gas permeability. Part of the CoPhyLab experiments are devoted
to better constrain this property for cometary physical analogues.
Consequently, the gas flow measured for the cometary-analogue candidates is
presented here but is not used to constrain the best analogue of all the
candidates.

####  3.3.2 CoPhyLab dust gas permeability measurement method

To measure gas permeability, we performed gas flow experiments using a
cylindrical sample container filled with CoPhyLab dust and mounted in the
middle of a vacuum chamber. The sample container separates the chamber into
two individual compartments (upstream and downstream compartment), connected
only via the sample. With this chamber configuration, the gas streaming into
the upstream compartment is directed through the sample into the downstream
compartment, which is evacuated by pumping. The gas used for the measurements
is cleaned oil-free air. The gas flow is controlled by a thermal mass flow
sensor, allowing for gas flow in the range of 0.15 mg s-1to 20 mg s-1. This
setup was previously used to measure the gas permeability for cometary
analogues (Schweighart et al., 2021).

Three different types of pressure sensors were used to achieve high-accuracy
measurements within different pressure ranges, one of each type connected to
the upstream and downstream compartment. A sieve at the bottom of the
cylindrical sample container supports the weight of the sample, holds it in
place and ensures that gas can pass from one compartment to the other. To
measure the gas permeability, a constant flow of gas is directed through a
sample of known volume and the pressure in the two compartments is measured as
a function of the gas flow. During the evacuation process, the difference in
pressure between the upper and lower compartment is kept as low as possible to
minimise mechanical changes in the sample (although the building up of
compacted layers at the bottom of the sample could still not be avoided).
After a minimum pressure of 10-2 mbar was obtained, the chamber was flooded
with gas, starting with a gas flow of 0.15 mg s-1. As the system adapted to
the change, the pressure approached a steady state. Whenever a steady pressure
level was reached, the mass flow was doubled (more details can be found in
Schweighart et al. 2021).

Although the influence of parts other than the sample are minimised, there is
still some influence from the sieve at the bottom of the container. Pressure
differences for an empty sample container with just the sieve were measured
and the pressure values obtained during the measurement with different samples
were corrected to account for the pressure differences caused only by the
sample. All measurements were done at room temperature.

Samples were prepared as described in Section 4.2. For the different samples,
the sizes of the individual dust agglomerates were in the range of 56 µm to
1000 µm.

Gas permeability and Knudsen diffusion coefficient were calculated from the
measured pressure values (see Schweighart et al. (2021) for further details).

####  3.3.3 CoPhyLab dust gas permeability

As mentioned above, there are no in-situ measurements of the gas flow through
cometary surface dust layers available. To get a first impression of possible
gas activities, we performed gas flow measurements with one of the
SiO2/charcoal mixtures (70 % / 30 %). The samples are difficult to handle and,
as will be seen later, the results show a strong dispersion. Samples with a
height >10 mm tend to build up a compacted layer at the outlet (downstream
side of the sample) and often channels are created close to the sidewalls of
the sample container, resulting in pits on the surface. Samples with a higher
amount of charcoal have cracks that build up in the middle of the sample. Such
measurements were excluded from further data evaluation.

Some of the changes in the samples take place during the evacuation process
before the gas flow is started. To minimise mechanical changes of the sample,
the pressure difference between the upper and the lower compartment should be
kept low, preferably at less than 1 mbar. This is hard to achieve with the
current set-up, therefore, the number of samples whose measured properties can
be used for data interpretation is limited. In the same way as the experiments
done with glass beads by Schweighart et al. 2021, one can see a dependency of
the gas flow on the size of the single agglomerates. Although the average
size-frequency distribution of samples is known (see Section 3.1.1), small
variations can lead to non negligible changes in the gas permeability
measurements.

For the CoPhyLab dust sample with $70\,\%SiO_{2}$ and $30\,\%$ charcoal
(sample height $8\,$mm, porosity = $75$$\pm$1.5 %, maximum agglomerate size in
the range $700\,\micron-900\,\micron$) we find an average gas permeability of
$B=2.04\cdot$ $10^{-11}$ $m^{2}$$\pm$$0.22\cdot$ $10^{-11}$ $m^{2}$ and a
Knudsen diffusion coefficient $D_{K}$ of $1.74\cdot$ $10^{-3}$ $m^{2}$
$s^{-1}$$\pm$$0.24\cdot$ $10^{-3}$ $m^{2}$ $s^{-1}$.

###  3.4 Spectral properties

####  3.4.1 Cometary dust spectral properties

The spectral properties of planetary bodies can help us to identify the
composition and physical properties of their uppermost surface layers.
Studying the spectral properties of cometary analogues, especially when mixed
with water ice and exposed to solar illumination, can help us to better
understand processes which take place on a comet. To this end, we plan to
study the spectral properties of our CoPhyLab dust samples exposed to
simulated cometary conditions (temperature, pressure and illumination).

The spectral reflectance of a closely-packed particulate medium is a function
of the viewing geometry, the optical properties of the scatterers that
constitute the medium and the physical properties of the medium itself (e.g.
the surface porosity and the surface roughness). Hence, for this study, we
aimed at characterizing the overall spectral properties of the pure samples
and mixtures.

The spectral properties of comets have been measured at multiple occasions.
For comparison to our analogues, we mainly focus on the spectra acquired by
VIRTIS of the Rosetta spacecraft as they are the most recent and detailed
spectral properties we have to this day. These studies have revealed the
presence of water ice among a complex mixture of organics and refractory
materials on the nucleus’ surface (Capaccioni et al., 2015; Quirico et al.,
2016; Poch et al., 2020). These VIRTIS measurements also allowed the detection
of overnight surface deposition of volatiles released during the local daytime
and in particular to characterise the diurnal cycle for water-ice (De Sanctis
et al., 2015).

####  3.4.2 Spectral properties measurement method

The spectral properties of the samples were investigated using the University
of Bern’s Mobile Hyperspectral Imaging System (MoHIS Pommerol et al. 2019).
This instrument uses a 250 W halogen lamp as a light source, to which a
monochromator (Oriel, MS257) is attached, with three gratings to sweep from
the NUV (Near UV) to VNIR (Very Near InfraRed) domains and select specific
wavelengths with a narrow bandpass. An optical fibre is placed after the
monochromator and set up to illuminate the sample perpendicularly to its
surface. A CCD camera is used for the observations in the visible domain
(380-940 nm) and an MCT (Mercury, Cadmium, Telluride) detector is used for the
infrared observations (950-2450 nm). Additional details on the setup can be
found in Kreuzig et al. (2019).

####  3.4.3 CoPhyLab dust spectral properties

Nine mixtures with a 10 % increment by mass of charcoal were prepared. The
sample holders were filled with the mixture using a standard kitchen sieve
(400-500 µm mesh) to achieve a smooth and featureless uppermost layer. The
spectral properties in the visible and near-infrared domains (from 380 to 2450
nm) are presented in Figure 5.

Figure 5: Top: Reflectance spectra of the pure phases of the Cophylab dust
with normalisation at 535 nm. The shaded area represents the dispersion
associated with these measurements (present for both SiO2 and charcoal but the
SiO2 normalised error is small). The 67P/C-G spectrum corresponds to a spot of
the Aswan terrace on comet 67P/C-G (Capaccioni et al., 2015). Bottom:
Reflectance spectra of Cophylab dust mixture with normalisation at 535 nm.
Symbols included for readability.

These measurements show an important difference between the SiO2 and the
charcoal powder in the visible and infrared domain (see Figure 5). Across the
400-2500 nm wavelength range, the reflectance factor of the SiO2 sample has a
median value of 0.96 and reaches close to unity near 1250 nm. SiO2 displays a
noticeable positive slope in the visible range and shows an overall $\sim$ 15
% decrease in reflectivity across the 1.2-2.5 µmwavelength range. We note the
presence of hydration and hydroxylation features around 1.4 µm ($\sim$ 7140
cm-1), 1.9 µm ($\sim$ 5250 cm-1), as well as around 2.2 µm ($\sim$ 4545 cm-1)
(see Elliott & Newns, 1971; Lipp, 1992; Pommerol & Schmitt, 2008, and
references therein). It is to be noted that the samples were measured at
ambient conditions. A thorough heating of the SiO2 material, and its
preservation in a desiccating oven prior to manipulations, could certainly
lead to a decrease of the intensity of these features. Overall, the spectrum
of pure SiO2 powder does not present any large variations and remains at most
within 15 % of its reflectivity value at 535 nm 111wavelength of the central
wavelength of the green filter of the Rosetta/OSIRIS Narrow Angle Camera.. We
also displayed in this figure the spectrum of comet 67P/C-G (specifically the
spectrum of the Aswan terrace on the nucleus (Capaccioni et al., 2015) and any
SiO2 relative spectral variations appear very moderate when compared to it.

The spectrum of the charcoal is characterised by its lack of features and its
low reflectivity, which remains below 5 % in the visible domain and increases
with a slope of 18$\pm$9 %/100 nm between 800 and 2400 nm, where it reaches a
reflectivity of 13$\pm$5 %. The normalisation of the spectrum at 535 nm
highlights this increase and also points to a slight reflectivity decrease in
the 400-500 nm region (with a spectral slope of -4$\pm$1 %/100 nm), as well as
the presence of a broad but shallow dip in the charcoal’s spectrum between 1
µmand 1.2 µm. This reflectance dip is compatible with the absorption band of
CH bonds present in organic compounds Izawa et al. (2014). While the spectrum
of charcoal and 67P/C-G are similar in the 400-550 nm and the 950-1200 nm
ranges, they differ across the 600-900 nm domain and throughout the
investigated infrared domain.

In examining the spectra of the mixtures (Figure 5, bottom), we observe that
the charcoal powder drives their spectral properties. This is illustrated by
the low reflectance of all mixtures, including those that have small
fractional contents of charcoal powder, as well as by the overall absence of
spectral features and the monotonically positive average spectral slope in the
near-infrared. The reflectance is close to 72 % for the 10 % charcoal mixture
and close to 88 % for the 20 % charcoal mixture. Comparing the spectra of the
mixtures with that of 67P/C-G, normalised at 535 nm, we are able to again
observe the same differences between the charcoal powder and 67P/C-G.

In the visible domain, the relative reflectance values of the mixtures are
comparable to that of 67P/C-G mostly around the 500-570 nm window, with an
overall mismatch in the near-infrared domain. However, all mixtures with more
than 20 % charcoal content appear to match the relative reflectance of 67P/C-G
at certain wavelengths: around 2 $\mu$m for the 30 % charcoal mixture, around
1.78 $\mu$m for the 50 % mixture, around 1.5 $\mu$m for the 70 % mixture, and
around 1.35 $\mu$m for the 90 % charcoal mixture.

For each sample, we computed spectral slopes between 535 nm and 882 nm, using
the formula from Delsanti et al. (2001). The results are reported in Table 1.
In general, the increase of the spectral slopes appears to follow the increase
in charcoal fraction. The difference between the spectral slope of the 80 %
charcoal mixture and its neighbours could be potentially explained by a
spatial inhomogeneity within the mixture, further enhanced by the low
reflectance of the mixture and the reflectance dispersion at each wavelength.
This would also explain its similarity to the spectral slope of the pure
charcoal. The spectral slopes of the 10 % and 20 % charcoal mixtures are lower
than even that of the pure SiO2 sample. Moreover, while the reflectances of
these mixtures transition down to the reflectance level of the pure charcoal
sample, their spectral slopes appear to be negative or neutral over the
visible range (Figure 5). However, they exhibit markedly positive spectral
slopes beyond 1.2 µm, similarly to the pure charcoal sample (Figure 5). The
lower-than-average spectral slopes of the 10 % and 20 % charcoal mixtures in
the visible could be explained by the scattering contribution of the SiO2,
which is then still the main species of the mixture.

Table 1:  Visible spectral slope of the pure CoPhyLab dust materials and their mixtures using the formula from Fornasier et al. (2015), and BVRI (Blue, Visual, Red and Infrared) colours computed using Bessell filters. Sample | 535–882 nm slope
---|---
| (%/100 nm)
0% (Pure SiO2) | 2.8$\pm$0.2
10.0 % | -1.4$\pm$0.2
20.0 % | 1.0$\pm$0.3
30.0 % | 3.8$\pm$0.9
40.0 % | 5.0$\pm$1.0
50.0 % | 4.0$\pm$1.0
60.0 % | 5.0$\pm$1.0
70.0 % | 5.0$\pm$1.0
80.0 % | 11.0$\pm$3.0
90.0 % | 7.0$\pm$2.0
100% (Pure charcoal) | 10.0$\pm$3.0

Compared to the nucleus of 67P/C-G, these computed spectral slopes are lower
than the average terrain of the comet. In the high-spatial observations of the
nucleus near opposition (Feller et al., 2016, 2019), the spectral slope of the
typical boulder-less terrain was close to 18 %/100 nm, i.e. about 2.6 times
greater than the spectral slope of the 90 % charcoal mixture. On the nucleus,
areas with low spectral slopes were also observed to be brighter than their
surroundings, and were typically associated with material fractionally
enriched in water-ice (Barucci et al., 2016; Hasselmann et al., 2017;
Deshapriya et al., 2018).

###  3.5 Photometric properties

####  3.5.1 Cometary dust photometric properties

The photometric properties of the considered end-members and mixtures were
investigated and are presented in the companion paper Feller et al. (in
preparation). We focus here on the single-scattering (wssa), the geometrical
(Ageo) and on the bidirectional albedo (Abd). These are important quantities
to the study of the physics of our samples as they describe how dark our
samples are and how much total energy is absorbed through illumination. The
single-scattering albedo corresponds to the propensity of grains/aggregates to
scatter light through simple reflection. The geometric albedo at incidence and
emergence zero corresponds to how much light is scattered at opposition.
Finally, the bidirectional albedo is the bond albedo before integration over
all wavelengths, it represents the reflectance integrated over the incidence
hemisphere and the emergence hemisphere.

In Table 2, we compare the albedos of selected CoPhyLab dust mixtures (see
below) with those of asteroids and comets, determined using the Hapke
reflectance model. Li et al. (2007a); Li et al. (2013) modelled the
photometric properties of comet 9P/Tempel 1 as observed in the Bessell V-Band
filter Bessell (1990) by the Deep Impact and Stardust-NExT cometary missions
respectively. Helfenstein & Veverka (1989) fitted the phase curves of a
collection C-type asteroids as observed from Earth in the V-Band filter. More
recently, the Rosetta mission allowed us to study the nucleus of comet 67P/C-G
at great detail, in particular Fornasier et al. (2015) used low- and large-
phase angle observations acquired with a V-band equivalent broadband filter
during the orbiting with the nucleus to determine its photometric properties.

Table 2:  Single-scattering (wssa), geometric (Ageo), and bidirectional (Abd)
albedos at, or close to, 550 nm for selected CoPhyLab dust mixtures compared
to values of comets and asteroids.

|  wssa (%) |  Ageo (%) |  Abd (%)
---|---|---|---
10 % charcoal |  47.8$\pm$0.3 |  34$\pm$2 |  22.7$\pm$0.1
30 % charcoal |  11.7$\pm$0.1 |  9$\pm$1 |  5.3$\pm$0.1
50 % charcoal |  9.0$\pm$0.1 |  6$\pm$1 |  3.7$\pm$0.1
70 % charcoal |  7.6$\pm$0.1 |  5$\pm$1 |  3.2$\pm$0.1
90 % charcoal |  5.7$\pm$0.2 |  4$\pm$1 |  2.5$\pm$0.1
9P/Tempel 1a,b |  3.9$\pm$0.5 | 5.6 | 1.3
67P/C-Gc |  3.7$\pm$0.2 |  5.9$\pm$0.3 |  1.23$\pm$0.01
Average C-typed | 2.5 | 4.9 | 0.8*

References - a:Li et al. 2007b; b: Li et al. 2013; c: Fornasier et al. 2015;

d: Helfenstein & Veverka 1989

*: anisotropic case estimation, using Eq. 11.21 of Hapke 1993

####  3.5.2 Photometric properties measurement method

The photometric phase curves of our samples were measured using the
PHysikalisches Institut Radiometric Experiment 2 (PHIRE-2) radiogoniometer. We
refer the reader to Pommerol et al. (2011) for a complete description of the
instrument and the calibration process. The measurements were acquired in the
principal plane (i.e. the azimuth angle equals either 0∘ or 180∘) using the
instrument’s 550$\pm$ 10 nm broadband filter. The light source was set at an
incidence angle of 0∘ and measurements were acquired every 5∘ in the plane of
emergence from 5∘ to 75∘. The phase curves of the samples cover thus the
5∘–75∘ phase angle range.

####  3.5.3 CoPhyLab dust photometric properties

Fitting an implementation of the so-called Hapke photometric model Hapke
(1993) to the obtained phase curves (see the companion paper Feller et al. (in
preparation), we were able to derive the single-scattering, geometrical and
bidirectional albedo values of the end-members and the CoPhyLab dust mixtures.
As noted previously with their respective spectra, the single-scattering
albedos highlight the respective brightness and dimness of the two pure
materials (w${}_{\mathrm{ssa,SiO_{2}}}~{}\simeq~{}$97.5$\pm$0.1 and
w${}_{\mathrm{ssa,charcoal}}~{}\simeq~{}$5.6$\pm$0.3). For comparison, the
SiO2 value is almost as large as that of ice (Warren & Brandt, 2008; Yoldi et
al., 2015), while the juniper charcoal’s wssa is almost four times lower than
that of lunar Maria (Sato et al., 2014).

Generally the single-scattering albedo values decrease sharply with the
increase of charcoal content, such that adding 10 % by mass of charcoal to a
pure SiO2 sample slashes its bidirectional albedo (83.4$\pm$0.1) while adding
30 % by mass of charcoal reduces it by about 94 %. This sharp brightness
decrease, also noted for the mixtures’ spectra, is consistent with the
findings by Warren & Wiscombe (1980); Pommerol & Schmitt (2008) and Jost et
al. (2017a), which respectively considered mixtures of snow (or fine-grained
water ice) and soot (or ground anthracite) and pointed to the driving
influence of the fine opaque particles over the photometric properties of the
mixtures, even when amounting to a few percent of the total mass. This trend,
which clearly stands out for bidirectional albedos, holds as well for the
single-scattering and geometric albedo values of these dust mixtures.

Based on the determined geometrical albedos, while prepared dust mixtures with
a charcoal fraction lesser than 50 % would, in comparison, appear brighter
than the nucleus surface of 9P/Tempel 1 or 67P/C-G, those with a higher
fraction of charcoal would appear at opposition as dark as their nuclei’s
surfaces. The further consideration of the bidirectional albedos points out
that the investigated mixtures are inherently slightly better scatterers than
the surfaces of these comets under all viewing geometries, as emphasised by
the larger single-scattering albedo values of these mixtures. This apparent
discrepancy between the geometrical and bidirectional albedo values of the
dust mixtures and their cometary counterparts can be explained through a more
extended consideration of the photometric behaviour of these surfaces (see
Feller et al., in preparation). In essence, the comparable geometrical albedo
value of the 67P/C-G surface with respect, for instance, to the 70 % charcoal
dust mixture, is due to the strong backward-scattering nature of the nucleus
surface reinforced at small phase angles the marked disappearance of shadows
cast by dust grains and aggregates on the nucleus surface itself (i.e. the
shadow-hiding contribution of the opposition effect, Fornasier et al. 2015;
Feller et al. 2016). By comparison to other small bodies of the Solar System,
at this wavelength, the prepared mixtures would be brighter than the average
primitive C-type asteroid.

While the non-linear reflectance surge of the opposition effect is positively
correlated with a surface roughness and particle grain size (Déau et al. 2013
and references therein), the mixture’s scattering asymmetry is a function of
the material driving the mixture’s photometric properties (Pilorget et al.,
2015) and therefore not only dependant on its physical properties, but also on
its chemical composition, which in the case of 67P/C-G is still the subject of
research (Quirico et al., 2016; Poch et al., 2020). Alternatively, in order to
lower the dust mixtures’ albedos to better match the values of cometary
nuclei, more absorbent material, such as carbon black, can be used.
Unfortunately, such a material is difficult to handle safely, due to its small
particle size, and would present a potential danger for little gain. We
therefore argue that the low albedos reached by mixture with a carbon mass
content higher than 30 % are close enough (less than 5 % difference) to
cometary values to allow us to model correctly the corresponding physics
knowing the intensity of the illumination input.

###  3.6 Mechanical properties

Characterising the mechanical properties of cometary material is important to
understand the activity of comets, planetary formation, and the evolution of a
comet’s morphology. For example, dust ejection is only possible when the gas
pressure created by the sublimation of volatiles in the nucleus of comets
exceeds the tensile strength of the material (Skorov & Blum, 2012; Fulle et
al., 2020; Gundlach et al., 2020b). These mechanical properties can also
control the collapse of cliffs observed on the surface of the nucleus
(Groussin et al., 2015; Prialnik & Sierks, 2017; Attree et al., 2018; Kappel
et al., 2020). It is important to distinguish between two possible tensile
strengths. First, the inner-agglomerate tensile strength (referred to
hereafter as inner tensile strength), which represents the strength of the
binding of the solid particles inside the pebbles, and second, the inter-
agglomerate tensile strength (referred to hereafter as inter tensile
strength), which represents how strongly the agglomerates are bound to each
other.

####  3.6.1 Cometary dust mechanical properties

With the arrival of Rosetta at comet 67P/C-G, knowledge on the mechanical
properties of cometary matter has greatly increased. Two instruments located
on the Philae lander were dedicated to the study of these properties on the
surface close to the lander. First, the MUPUS penetrometer was not able to
penetrate the surface at Abydos and Spohn et al. (2015) concluded that the
uniaxial compressive strength of the material had to be at least 2 MPa in
order to prevent the penetration of MUPUS. Second, the Acoustic Surface
Sounding Experiment (CASSE) was used to determine the mechanical properties at
the first landing location, Agilkia. Based on its measurements, a compressive
strength between 3.5 and 12 kPa was determined (Möhlmann et al., 2018). CASSE
was also used to listen to the MUPUS penetrator as it attempted to penetrate
the surface. This allowed estimates of the sheer modulus between 3.6 MPa and
346 Mpa, and of the Young’s modulus between 7.2 MPa and 980 MPa (Knapmeyer et
al., 2018).

Another method used to determine the mechanical properties was based on
geomorphological observations by the OSIRIS cameras to infer appropriate
values based on analytical or numerical models. Geomorphological models of
boulders and cliffs on the surface resulted in estimates of the inter tensile
strength on the order 1-10 Pa (Kappel et al., 2020). Using OSIRIS observations
and examining the relationship between gravitational slopes and surface
morphology, Groussin et al. (2015) estimated the compressive strength to be
between 30 and 150 Pa and the inter tensile strength to be between 3 and 15
Pa. Vincent et al. (2017) performed a statistical analysis of large
geomorphological features on the surface to calculate values of the inter
tensile strength of 1-2 Pa at a ten-metre scale. Comparatively, analyses of
the morphology of overhanging cliffs on the nucleus constrained the range of
possible inter tensile strengths to between 0.02-1.02 Pa (Attree et al.,
2018). In a recent study of the multiple landings of Philae, O’Rourke et al.
(2020) found that the compressive strength of the surface material was lower
than 12 Pa. Theoretical values for the inter tensile strengths were derived by
Skorov & Blum (2012) in their Figure 4.

####  3.6.2 Mechanical properties measurement method

A complete study of the mechanical properties of the CoPhyLab dust analogues
is outside of the scope of this paper, as this will be performed through a
dedicated experiment in a future study (see Blum et al., 2014, for details).
At the time of writing, only the inner tensile strength of the CoPhyLab
samples can be measured with the setup available. The method used by CoPhyLab
is the Brazilian Disk Test (BDT) in which a cylindrical sample of material is
formed and compressed on a scale with a thin metal loading bar. The force
exerted on the sample is measured until the cylinder fractures. The inner
tensile strength $\sigma$ can then be derived by

$\sigma=\frac{2F}{\pi dl},$ (1)

$F$ is the maximum exerted force at break-up, $l$ is the thickness of the dust
cylinder, and $d$ is the diameter of the sample, respectively. This method has
been previously used to study protoplanetary and cometary analogues (see Haack
et al. 2020; Bischoff et al. 2020; San Sebastián et al. 2020).

####  3.6.3 CoPhyLab dust tensile strength

The inner tensile strengths of four of the CoPhyLab mixtures plus the two pure
materials were measured 10 times each. The average and standard deviations
(small with regard to the values, nearly invisible in the Figure) for each
sample are shown in Figure 6. All the samples had varying porosities, in
general between 65 and 75 %. As these values are close to those expected for
the comet (70 to 80 %), we can use the values measured with only a small
linear correction (see Bischoff et al., 2020, for details). Although not
directly comparable, Figure 6 also displays the cometary values of the inter
tensile strength in the greyed area (equivalent to 67P/C-G tensile strength
between 0.02 and 15 Pa,). The inner tensile strengths of the candidate
analogues are higher by at least one order of magnitude compared to the inter
tensile strengths derived for 67P/C-G which is to be expected as agglomerates
are not as strongly bounded together when compared to grains. If we correct
for temperature, we would expect a higher inner tensile strength for the
candidates and if we correct for porosity, we should see a slight drop. It has
been shown by experimental studies that comets could indeed be made of
agglomerates with an inner agglomerate tensile strength on the order of 1 kPa
and an agglomerate tensile strength in the Pa range (Blum et al. 2014;
Gundlach et al. 2018, Figure 7 in Groussin et al. 2019, and references
therein).

Figure 6: Tensile strengths of the CoPhyLab dust mixtures as a function of the
mass fraction of silica dust with error bars (for some mixtures these are very
small and therefore barely visible). We also indicate the allowable range for
the inter-agglomerate tensile strengths of a cometary dust analogue in the
grey-shaded area. The two theoretical cometary dust aggregates tensile
strength (star and diamond) are derived from the values presented in Figure 4
of Skorov & Blum (2012).

Using the measured tensile strengths, we can try and limit the possible
candidates. If we assume that we need an internal tensile strength of around 1
kPa at approximately 70 % porosity, then all samples with a silica dust mass
fraction higher than 0.7 would have the required tensile strength. However, as
our measurements were done at room temperature -– and at cometary temperatures
the tensile strength is expected to change (this will be investigated in the
future) –- the candidates with a silica dust mass ratio below 70 % cannot be
completely discarded.

###  3.7 Thermal properties

The evolution of the nucleus, from changes in morphology to the observed
activity, is strongly linked to the thermal properties of cometary dust. Both
modelling and instrument data analysis would greatly benefit from a better
understanding of these quantities. The three main properties of interest are
the thermal conductivity $k$, the heat capacity at constant pressure $C_{p}$,
and the thermal inertia $I$, the latter defined through

$I=\sqrt{kC_{p}\rho},$ (2)

with $\rho$ being the mass density of the sample.

These three parameters have a strong dependency on composition, porosity and
temperature. Often their mixing laws are not linear. In-depth measurements of
these properties at low temperatures, relevant to cometary environments, is
out of the scope of this paper. Instead, an overview of these properties at
room temperature is presented here, in order to attempt to constrain the best
candidates.

####  3.7.1 Cometary thermal properties

Three instruments were able to assess the thermal properties of the cometary
material. The MUPUS penetrometer thermal mapper was equipped to measure the
thermal inertia of the upper layers. A local thermal inertia of 85$\pm$35 J
K-1 m-2 s-1/2was required to reproduce the MUPUS-TM measurements Spohn et al.
(2015). Using data from VIRTIS, Leyrat et al. (2016) found that the best-fit
thermal inertia for certain regions of 67P/CG is around 25-170 J K-1 m-2
s-1/2. Additionally, Marshall et al. (2018) fit a thermal model to the VIRTIS
observations and found a thermal inertia of 80 J K-1 m-2 s-1/2. The Microwave
Instrument for the Rosetta Orbiter (MIRO) has also helped to constrain the
thermal properties of the upper subsurface. Gulkis et al. (2015) found a low
thermal inertia of 10 to 50 J K-1 m-2 s-1/2by analysing the surface radiation
emitted from the nucleus. Later, slightly different best-fit values to the
MIRO measurements, equal to 10-30 J K-1 m-2 s-1/2and 10-60 J K-1 m-2 s-1/2,
were calculated (Choukroun et al., 2015; Schloerb et al., 2015).

Another approach to constrain the thermal conductivity of cometary analogue
dust candidates is to examine the thermal conductivity of carbonaceous
chrondrites, which could be good analogues to the cometary refractory
material. Henke et al. (2016) modelled the thermal conductivity of porous
chondritic material based on the properties of the individual mixture
components. They were able to derive a formula for the porosity dependence of
the thermal conductivity

$k(\phi)=((k_{b}\mathrm{max}((1-2.216\phi),0))^{4}+(k_{b}e^{1.2-\phi/0.167})^{4})^{1/4},$
(3)

where $\phi$ is the porosity and $k_{b}$ the bulk thermal conductivity at 0 %
porosity. Using this formula, we find a thermal conductivity between 0.05 and
0.2 W m-1 K-1for porosities between 70 % and 80 % and a bulk heat conductivity
between 4.0 and 4.9 W m-1 K-1.

Grott et al. (2019) used two formulas to derive the thermal conductivity of a
boulder located on asteroid Ryugu (observed by the Hayabusa 2 spacecraft).
These formulas are based on fits to experimental data of the thermal
conductivity of carbonaceous chrondrites and read

$k(\phi)=\frac{0.11(1-\phi)}{\phi}$ (4)

and

$k(\phi)=4.3e^{-\phi/0.08}.$ (5)

With these formulas, we find a thermal conductivity between 6.8 10-4 and 3.6
10-2 W m-1 K-1for porosities between 70 % and 80 %.

####  3.7.2 Thermal properties measurement method

The thermal properties of our dust candidates were measured using a KD2 Pro
thermal Analyser. This device has the ability to measure both the thermal
conductivity and the heat capacity of samples. We produced compressed
cylinders with 2.5 cm radius and varying heights (between 6 and 10 cm) and
inserted the device’s 6 cm needle inside the samples. For each mixture, we
produced six samples with slightly varying porosities ranging from 60 to 75 %.

####  3.7.3 CoPhyLab dust thermal properties

The measured thermal properties are for samples with a porosity in the range
60 to 75 %. In order to compare the measured values to the estimated cometary
values described previously, we would need to know these properties in the
porosity range 70 to 80 %. Making samples with porosities larger than 75 % is
difficult and not possible with the current setup. Therefore we decided to fit
the thermal properties with a linear fit and then extrapolate the measured
values from the sample porosities (60 to to 75 %) to the cometary porosities
(70 to 80 %). We make the assumption that this extrapolation is possible given
that the porosities measured for the comet are very close to those of our
samples. Additionally, though it would help to derive a more accurate mixing
law, we lack measurements over a larger porosity range.

The measured properties extrapolated to a porosity of 70-80 % are shown in
Figure 7. The top figure shows the thermal conductivity as a function of the
silica dust mass fraction in the mixture. We also display the ranges of
possible porous chondritic mixtures determined by the mixing laws presented in
Section 3.7.1, for a porosity of 70-80 %.

Figure 7: Top: Heat conductivity of the CoPhyLab cometary dust analogues as a
function of the silica dust content. The two grey-shaded areas represent the
thermal conductivity of carbonaceous chrondrites with a porosity between 70-80
% based on mixing models. Bottom: Thermal inertia of the CoPhyLab cometary
dust analogues as a function of the silica dust content. The grey-shaded area
represents the thermal inertia values constrained by Rosetta described in the
text.

We observe that the thermal conductivity at such high porosities has no
visible dependencies on the silica dust ratio. This is most likely due to the
fact that the porosity of the sample is the main factor determining the
thermal properties for two main reasons. (i) The measurements were done at
atmospheric pressure. The high porosity of our samples means that air
contributes strongly to the global thermal conductivity of our sample (see
below). (ii) Radiation between particles in the sample also contributes to the
global thermal conductivity, particularly for high porosities. All the
candidates have a thermal conductivity in the ranges determined by Henke et
al. (2016) and slightly higher than Grott et al. (2019).

The bottom plot of Figure 7 shows the thermal inertia of the samples as a
function of the silica dust content. The grey-shaded area represents the range
of thermal inertia measured on comet 67P/C-G by the Rosetta instruments. The
measured thermal inertia for our samples is higher by a factor of 1.5 - 2 and
does not overlap with the cometary range. However, our analogue-material
values are generally overestimated for three main reasons. (i) The
measurements were not performed in vacuum due to experimental constraints (the
measurement device is not adapted to work in a vacuum environment) and
therefore the voids in our samples were filled with air. In a vacuum
environment, this would tend to reduce the thermal conductivity of our
candidates, as air has a thermal conductivity of k = 0.026 W m-1 K-1 at 298 K.
(ii) The thermal properties were measured at room temperature and, in general,
geological materials will see their thermal inertia reduced as their
temperature drops. This can be seen for example in Figure 10 of Opeil et al.
(2020) for carbonaceous chondrites, in which the thermal inertia drops by
15-20 % when the temperature drops from 300 K to 150 K. By applying the same
thermal inertia change to our samples, we obtain the blue crosses in Figure 7.
This puts our measured values in the range of the values measured by Rosetta.
(iii) One additional change that impacts the thermal properties is the
presence of water ice. Rosetta determined that the presence of water ice is
likely in the areas studied and granular water ice has a thermal inertia
between 10 and 100 J K-1 m-2 s-1/2 at low temperatures and high porosities
(Ferrari & Lucas, 2016). The hatched area in Figure 7 denotes this range.
Therefore, we interpret that any mixture of our candidates and water ice would
probably have a thermal inertia well in the range measured by the Rosetta
instruments.

The thermal properties are thus constrained by porosity, temperature, and the
presence of volatiles. An in-depth study of these parameters (in vacuum and
mixed with water ice at low temperature) for the chosen CoPhyLab dust is
planned, but is out of the scope of this paper, as it most likely will have
little to no impact on the selection of an appropriate candidate for a
cometary physical analogue, as the porosity and temperature are well
controlled properties for our samples.

###  3.8 Electrical properties

The electrical properties of a material are described by its relative electric
permittivity. This number is a complex, dimensionless factor

$\epsilon_{r}=\epsilon_{\mathrm{r}}^{\prime}-i\epsilon_{\mathrm{r}}^{\prime\prime}$
(6)

that measures how an electric field decreases relative to vacuum when it
passes through a material.

The real part $\epsilon_{\mathrm{r}}^{\prime}$ (also known as the dielectric
constant) represents the capacity of the material to change polarisation as an
imposed electric field changes (i.e. it relates to energy storage), while the
imaginary part $\epsilon_{\mathrm{r}}^{\prime\prime}$ represents the ability
of the material to transmit the electrical charge through charged particles
(i.e. it relates to energy attenuation). In practice, an electromagnetic wave
changes its velocity (depending on $\epsilon_{\mathrm{r}}^{\prime}$) and
magnitude (depending on the loss tangent
$\tan(\delta)=\epsilon_{\mathrm{r}}^{\prime\prime}/\epsilon_{\mathrm{r}}^{\prime}$)
as it travels through a material. Thus, instruments that can measure these
changes in the wave can provide direct information about the permittivity of a
material.

Both the real and imaginary parts of the complex permittivity depend strongly
on the composition, porosity, and temperature of the material. This makes
permittivity an extremely useful physical property in the characterisation of
planetary surfaces. There are many remote and in-situ instruments that can
measure the permittivity of a planetary surface material with varying degrees
of resolutions in space and frequency. Most of these instruments operate in
the microwave frequency range, where the dependence of the permittivity on
frequency is weaker than at other spectral ranges. For example, by increasing
order of frequency ranges, permittivity probes, echo-sounding radars, surface
imaging radars, and microwave radiometers are all able to constrain the
complex permittivity of a planetary surface.

####  3.8.1 Electrical properties of comets

The electrical properties of cometary matter have been studied by earth-based
telescopes, orbiting spacecrafts, and in-situ landed instruments. Kamoun et
al. (2014) used the Arecibo radio-telescope to constrain the real part of the
permittivity of the top 2.5 meters of comet 67P/C-G to be between 1.9 - 2.1 at
a frequency of 2.38 GHz. Initial measurements by the CONSERT bistatic radar on
Rosetta estimated $\epsilon_{\mathrm{r}}^{\prime}=1.27$ at 90 MHz, valid for
depths up to 100 m (Kofman et al., 2015). However, with the subsequent
determination of the exact location of the Philae lander (that carried one of
the CONSERT antennas, cf. Kofman et al. 2007),
$\epsilon_{\mathrm{r}}^{\prime}$ was found to range between 1.7 and 1.95 in
the shallow subsurface of 67P/C-G (< 25 m) and between 1.2 and 1.32 in the
deeper interior (25 – 150 m Kofman et al. 2020), in better agreement with
Kamoun et al. (2014). Finally, data collected at 409 Hz by the SESAME-PP probe
on board Philae led to values of $\epsilon_{\mathrm{r}}^{\prime}$ of no less
than 2.45 for the top few meters of the surface beneath the landing site
(Lethuillier et al., 2016). The $\epsilon_{\mathrm{r}}^{\prime}$ of most
geologic materials lose their frequency dependency at the low temperatures
relevant to cometary environments (Brouet et al., 2016). Thus, the difference
observed in the values of $\epsilon_{\mathrm{r}}^{\prime}$ at high (Arecibo
and CONSERT) and low (SESAME-PP) frequencies is most likely due to the
presence of a porosity gradient inside the nucleus of the comet (Lethuillier
et al., 2016).

The imaginary part of the permittivity is difficult to estimate from these
measurements, due not only to technical constraints, but also to the fact that
it has a much stronger temperature and frequency dependency than the real
part, complicating its prediction outside of the measured range. Nevertheless,
based on the materials that we expect to be present (e.g. ices) and its
probable high porosity, attenuation should be low within the nucleus and thus
$\epsilon_{\mathrm{r}}^{\prime\prime}$ is also likely to be low (Kofman et
al., 2015).

####  3.8.2 Electrical properties measurement method

The laboratory setup (Epsimu (R) from Multiwave) we used for the electrical
characterisation of our CoPhyLab dust mixtures consists of a conical coaxial
cell connected to a 2-port Vector Network Analyzer (VNA; Anritsu Master
MS2038C) equipped with a central cylindrical sample holder, which we filled
with the various dust simulant samples. The samples were contained by two
dielectric walls of polytetrafluoroethylene (PTFE). We used this system
(Sabouroux & Ba, 2011) to measure the permittivity of the samples between 80
MHz and 3 GHz. This choice of frequency range does not include the lower
frequencies at which SESAME-PP operated, as the measurement system would fail
to operate appropriately at such long wavelengths. However, the higher
frequency values, rather than the lower ones, were those used to probe deep
into the nucleus of 67P/C-G and are thus more relevant to this study, since
they are characteristic of the entire comet. They also have the advantage of
having a higher accuracy (the SESAME-PP values are only an upper limit to the
real part of the electrical properties). All measurements were made at ambient
temperature (23∘ C) and under ambient air pressure. A full description of our
experimental setup can be found in Brouet et al. (2015), and further examples
of its use for planetary regolith studies can be found in Brouet et al.
(2016); Brouet et al. (2019).

The sample preparation consists of completely filling the sample container
with the sample. In order to achieve different porosities within the sample
holder, the sample was compressed throughout the filling process with varying
degrees of pressure, using a cylinder cut precisely to fit the dimensions of
the sample holder. Once filled, the sample holder was weighed to determine the
mass and bulk density of the sample, using the known volume of the sample
containment volume (1.291 ± 0.288 cm3). Using the grain densities determined
for the components and their mixtures (see Section 3), we calculated the
porosities of each sample measured with this setup. We limited our
measurements to two porosities for each dust mixture, one high (70$\pm$7 %)
and one low (59$\pm$3 %). Lower porosities are difficult to achieve for dry
granular samples, but these relatively high porosities are more relevant to
the observed porous nature of comets.

The permittivity is obtained by first measuring the scattering parameters (the
reflection and transmission coefficients) of the cell loaded with the relevant
sample over 1000 frequencies between 3 MHz and 3 GHz. The permittivity of the
sample at each frequency is then determined with the Nicolson-Ross-Weir
procedure (Nicolson & Ross, 1970) applied to the sample scattering parameters.
As there is little variability in permittivity in the frequency range between
80 MHz and 3 GHz, we calculated the average permittivity in this frequency
range for each sample, and took this to be the representative value of the
sample. Further details on the calculation procedure and its use with this
setup can be found in Georget et al. (2014).

####  3.8.3 Electrical properties of CoPhyLab dust

The measured real and imaginary parts of the permittivity of the end member
components and selected mixtures are shown in Figure 8. In order to obtain
these values, we took the results found for both the high (70$\pm$7 %) and low
(59$\pm$3 %) porosities, then performed a linear fit to obtain the porosity
dependence of the electrical properties. Using this linear relation, we
extrapolated the electrical properties for the porosity of the nucleus of
67P/C-G (70 to 80 %). The error bars represent both the uncertainty of the
measurements and the range of porosities to which we extrapolated to (70 to 80
%). Many mixing laws exist that are used to extrapolate the electrical
permittivity of granular samples (e.g. Sihvola, 2000; Brouet et al., 2016).
However, given the low measured permittivities and, importantly, given that
the cometary porosities are close to those measured for the lab samples, we
decided to extrapolate linearly. A future in-depth study of the electrical
properties of the CoPhyLab dust will investigate the possible mixing laws to
be used and will compare these with an empirical law devised specifically for
the CoPhyLab dust components.

Figure 8 shows that all samples with a silica dust content higher than 30 % by
mass have values of $\epsilon_{\mathrm{r^{\prime}}}$ compatible with those
measured for 67P/C-G (grey-shaded area). As cometary matter is assumed to be a
mixture of water ice and dust, the permittivity measured at 67P/C-G must
include the contribution of water ice. Thus, we also indicated in Figure 8 the
theoretical $\epsilon_{\mathrm{r^{\prime}}}$ of cold (150 K) and porous
(between 70 and 80 %) water ice, which ranges between 1.25 and 1.50 (based on
the Debye model, Debye 1929). Any mixture of this water ice with CoPhyLab dust
of more than 30 % silica dust by mass would still be compatible with the
measured cometary values. We therefore consider all dust analogues with more
than 30 % silica by mass to be valid from the viewpoint of their electrical
properties.

Figure 8: Top: Real part of the permittivity of porous (70 – 85 %) CoPhyLab
dust candidates as a function of the silica dust content. The grey-shaded area
represents the range of values observed for the nucleus of 67P/C-G (Kamoun et
al. 2014; Kofman et al. 2015) and the hatched area represents the range of
$\epsilon_{\mathrm{r^{\prime}}}$ for cold, porous (70-85 %) water ice. The
error bars take into account both the uncertainty of the measurements combined
with the range of porosities that we extrapolated to (70 to 80 %). Bottom:
Imaginary part of the permittivity of porous (70 – 85 %) CoPhyLab dust
candidates as a function of the silica dust content.

##  4 Cophylab dust

Using the constraints on all the physical properties described throughout this
paper, it is possible to build a physical analogue for cometary dust. In this
Section, we describe the method we used to determine this analogue and
summarise the physical properties of the chosen mixture.

###  4.1 Choosing the best ratio

Table 3 shows all of the physical properties described above for each mass
ratio between silica and charcoal dust. The values are indicated with the
target necessary to build a plausible cometary non-volatile physical analogue.
Values indicated in green are optimal, values in orange are less desirable,
and values in pink are to be avoided. For each mixture, we associated a
numerical value to the quality of the fitting (1 for green, 0.5 for orange,
and 0 for pink) and when adding up these values, we obtained a total
compatibility for this mixture. This implies that the optimal mixing ratio for
a dust analogue to plausibly simulate cometary regolith in physical
experiments is 60/40 % or 70/30 % of silica dust/charcoal by mass.

Table 3: Physical properties of all investigated dust analogue candidates with target ranges indicated in the second column. The cells in green represent values that fall within the constraints; the orange cells have values that fall outside the desired ranges, but could still be acceptable, and the pink cells denote unacceptable values. For each mixture, we associated a numerical value to the quality of the fitting (1 for green, 0.5 for orange, and 0 for pink) and when adding up these values, we obtained a total compatibility for this mixture (bottom row). The mixtures with a 60/40 % and 70/30 % SiO2/charcoal both have the highest total compatibility and therefore represent the best candidate dust analogue. Physical property | Target values | 0/100 | 10/90 | 20/80 | 30/70 | 40/60 | 50/50 | 60/40 | 70/30 | 80/20 | 90/10 | 100/0
---|---|---|---|---|---|---|---|---|---|---|---|---
Grain size |  $<$ 1 µm |  $<$ 1 µm
1-2 Agglomerates |  Power law index: -1.8 to -2.3 | NM | -1.05 | -1.81 | -1.86 | -1.97 | -2.22 | -2.26 | -2.23 | -1.83 | -1.79 | NM
1-2 Density | 2-3 g cm-3 | 1.55 | 1.65 | 1.75 | 1.86 | 1.96 | 2.06 | 2.17 | 2.27 | 2.37 | 2.47 | 2.58
1-2  Albedo (550 nm) | 1.47 | 3.00 | 3.08 | 3.38 | 3.86 | 3.79 | 4.43 | 3.47 | 6.48 | 7.52 | 25.26 | 85.12
1-2 Thermal inertia |  10 - 170 J m-2 K-1 s-1/2 | 127.0 | 128.2 | 127.2 | 128.3 | 129.1 | 136.8 | 131.6 | 129.4 | 130.0 | 138.5 | 146.8
1-2  Inter Tensile strength |  $>$1 kPa | 109 | NM | NM | NM | NM | 309 | 551 | 932 | 1427 | NM | 8667
1-2  Electric permittivity (real part) | 1.27-2.1 | 2.81 | NM | NM | 1.88 | 1.84 | NM | 1.58 | 1.72 | NM | NM | 1.57
Total compatibility |  | 3.5 | 2.5 | 3.5 | 4.5 | 5 | 5 | 6 | 6 | 5 | 4 | 5

###  4.2 Dust recipe

In order to create a visibly homogeneous dust in which both components are
intimately mixed, we used the following recipe:

  1. 1.

Weigh 60 % (or 70 %) of the total desired mass in silica dust and 40 % (or 30
%) of it in charcoal.

  2. 2.

Roughly mix both components in a container.

  3. 3.

Pour a chosen liquid in another container (e.g., a nitrogen dewar if using
liquid nitrogen as the mixing liquid). This step in necessary to dissolve
previously formed agglomerates.

  4. 4.

Spoon the mixed dust into the liquid while stirring.

  5. 5.

Once all the dust is in the liquid, continue stirring until all agglomerates
are broken down and both components are well mixed.

  6. 6.

Let the mixture air dry. Some frost may form but can removed by putting the
dust in a desiccator.

  7. 7.

Shake the mixture with an automatic shaker or by hand for 10 minutes to form
new agglomerates formed of grains from the two components.

Distilled water, ethanol or liquid nitrogen can all be used as the mixing
liquid. However, this will affect the drying time and handling of the dust. In
all cases, a dust-protection mask is required to avoid breathing in the
smallest dust particles and gloves are suggested as the charcoal can be messy
when handled. Additional caution must be taken when liquid nitrogen is used as
it will disperse the dust in the air more easily than water or ethanol,
especially during step (iv). Finally, the handling should be done in an air-
suction hood (first because of the powder and second because of the
evaporating nitrogen that displaces the air)

An image of the resulting dust is shown in Figure 9. Its low reflectance and
the presence of large agglomerates surrounded by smaller aggregates and grains
are visible. Samples only composed of agglomerates can be obtained by sieving
gently the CoPhyLab dust.

Figure 9: Image of the CoPhyLab cometary dust analogue.

###  4.3 Physical properties

Table 4 summarises the measured physical properties of our chosen dust
analogues. They mostly match the constraints presented in Section 3. Both
candidates have an albedo higher than that of comets, but the 60/40 % has the
lowest value out of both (3.47 compared to 1.47 for 67P/C-G). We therefore
decided to use slightly higher albedo values, as this should not impact the
results in a significant way given that the value is well characterised and
can be modelled in numerical simulations.

The inner tensile strength of the 60/40 % mixture is lower than the value
aimed for (551 Pa compared to around 1 kPa (see Section 6), whereas the 70/30
% has a good match (932 Pa). The inner tensile strength is not a strong
constraint, because the inter tensile strength is hard to measure for this
dust analogue (see Blum et al., 2014, for details) and the inner tensile
strength of the comet is not known.

It is important to note here that one of the biggest facing in cometary
experiments trying to reproduce the activity is the presence of earth gravity.
One possibility to overcome this limitation is to use a micro-g environment as
given in a drop tower or during a parabolic flight. But both is beyond the
scope of the CoPhyLab arrangements. Another option to adapt the experiments to
gravity on Earth is the scaling of the guiding force ratios - gravity/cohesion
and gravity/gas drag - by reducing the grain size distribution compared to a
real comet and by increasing the strength of sample illumination. However, we
are limited in these aspects as reducing the grain sizes is quite difficult
and a strong radiation source, as would be needed, is currently not available
. Upcoming papers using the CoPhyLab dust will discuss in much more depth the
gravity issue.

For most of the other physical properties, both dust candidates are very
similar. The choice of which ratio would be better for a cometary physics dust
analogue depends on which experiments are planned. In general, we favour the
60/40 % for all experiments with the exception of gas flow measurements (the
70/30 % was easier to handle for these experiments) and for tensile strength
measurements (the 70/30 % is a better match).

Table 4: The physical properties of the best fitting dust analogues. Physical property | 60/40 % | 70/30 %
---|---|---
Average grain size | 392 nm | 364 nm
Agglomerate size power law index | -2.12 | -2.23
Density | 2.17 g/cm3 | 2.27 g/cm3
Albedo (550 nm) | 3.47 | 6.48
535-880 nm slope | 4.89 | 4.89
Gas permeability | N/A | 2.0415e-11 m
Knudsen diffusion coefficient | N/A | 1.7366e-03 m2/s
Thermal inertia (J/m2s1/2K) | 129.4 | 131.6
Tensile strength | 551 Pa | 923 Pa
Electric Permittivity (real part) | 1.58$\pm$0.4 | 1.75$\pm$0.4
Electric Permittivity (imaginary part) | 0.011$\pm$0.08 | 0.023$\pm$0.08

##  5 Conclusions

In this paper, we described in detail the measured physical parameters of the
non-volatile part of cometary dust. We then compared these values to the
physical properties of cometary dust analogues with the objective of finding
the analogue that would allow us to study the physics of comets in the most
accurate way possible. For this, we made a dust analogue composed of silica
dust to represent the siliceous material present in cometary dust and ground
charcoal to represent the organic and dark material observed on the nucleus of
comets. For most properties, we produced samples ranging from 10/90 % to 90/10
% in mass ratio of silica dust/charcoal and compared their properties to the
measured cometary values. Once this was done, we attributed a match descriptor
(1 for a good match, 0.5 for an average match and 0 for a poor match) and were
able to concluded that a ratio of either 60/40 % or 70/30 % of silica
dust/charcoal represents good analogues for the physical properties of the
non-volatile part of cometary material. We generally favour the 60/40 % ratio,
because it has a better matching albedo, which is an important parameter that
controls how much of the insolation power is absorbed.

We also presented the laboratory protocol we used in order to produce the
CoPhyLab dust as this should allow the scientific community to make use of it
as well.

In conclusion, we find that the CoPhyLab dust is a good analogue that will be
used in many future experiments planned for the study of the Physics of
comets.

## Acknowledgements

This work was carried out in the framework of the CoPhyLab project funded by
the D-A-CH programme (DFG: GU 1620/3-1 and BL 298/26-1 / SNF: 200021E 177964 /
FWF: I 3730-N36). The team from the University of Bern is supported by the
Swiss National National Science Foundation, in part through the NCCR PlanetS

## Data Availability

The data for Sections 3.2, 3.4, 3.5, 3.6, 3.7 and 3.8 are available in the
article. The data for Sections 3.1 and 3.3 will be shared on request to the
corresponding author.

## References

  * Attree et al. (2018) Attree N., et al., 2018, A&A, 611, A33
  * Barucci et al. (2016) Barucci M. A., et al., 2016, A&A, 595, A102
  * Bessell (1990) Bessell M. S., 1990, PASP, 102, 1181
  * Bischoff et al. (2020) Bischoff D., Kreuzig C., Haack D., Gundlach B., Blum J., 2020, Monthly Notices of the Royal Astronomical Society, 497, 2517
  * Blum et al. (2014) Blum J., Gundlach B., Mühle S., Trigo-Rodriguez J., 2014, Icarus, 235, 156
  * Bockelée-Morvan et al. (2017) Bockelée-Morvan D., et al., 2017, Monthly Notices of the Royal Astronomical Society, 469, S443–S458
  * Brouet et al. (2015) Brouet Y., Levasseur-Regourd A. C., Sabouroux P., Encrenaz P., Thomas N., Heggy E., Kofman W., 2015, Astronomy & Astrophysics, 583, A39
  * Brouet et al. (2016) Brouet Y., et al., 2016, Monthly Notices of the Royal Astronomical Society, 462, S89
  * Brouet et al. (2019) Brouet Y., Becerra P., Sabouroux P., Pommerol A., Thomas N., 2019, ICARUS, 321, 960
  * Capaccioni et al. (2015) Capaccioni F., et al., 2015, Science, 347, aaa0628
  * Choukroun et al. (2015) Choukroun M., et al., 2015, A&A, 583, A28
  * De Sanctis et al. (2015) De Sanctis M. C., et al., 2015, Nature, 525, 500
  * Déau et al. (2013) Déau E., Flandes A., Spilker L. J., Petazzoni J., 2013, Icarus, 226, 1465
  * Debye (1929) Debye P., 1929, Journal of the Society of Chemical Industry, 48, 1036
  * Delsanti et al. (2001) Delsanti A. C., Boehnhardt H., Barrera L., Meech K. J., Sekiguchi T., Hainaut O. R., 2001, A&A, 380, 347
  * Deshapriya et al. (2018) Deshapriya J. D. P., et al., 2018, A&A, 613, A36
  * Dobrovolsky & Kajmakov (1977) Dobrovolsky O. V., Kajmakov E., 1977, International Astronomical Union Colloquium, 39, 37–46
  * Elliott & Newns (1971) Elliott C. R., Newns G. R., 1971, Appl. Spectrosc., 25, 378
  * Feller et al. (2016) Feller C., et al., 2016, MNRAS, 462, S287
  * Feller et al. (2019) Feller C., et al., 2019, A&A, 630, A9
  * Ferrari & Lucas (2016) Ferrari C., Lucas A., 2016, A&A, 588, A133
  * Flandes et al. (2018) Flandes A., et al., 2018, Icarus, 302, 1
  * Fornasier et al. (2015) Fornasier S., et al., 2015, A&A, 583, A30
  * Fulle & Blum (2017) Fulle M., Blum J., 2017, Monthly Notices of the Royal Astronomical Society, 469, S39
  * Fulle et al. (2015) Fulle M., et al., 2015, The Astrophysical Journal, 802, L12
  * Fulle et al. (2016) Fulle M., et al., 2016, The Astrophysical Journal, 821, 19
  * Fulle et al. (2020) Fulle M., Blum J., Rotundi A., Gundlach B., Güttler C., Zakharov V., 2020, Monthly Notices of the Royal Astronomical Society, 493, 4039
  * Georget et al. (2014) Georget E., Abdeddaim R., Sabouroux P., 2014, Comptes Rendus Physique, 15, 448
  * Grott et al. (2019) Grott M., et al., 2019, Nature Astronomy, 3, 971
  * Groussin et al. (2015) Groussin O., et al., 2015, A&A, 583, A32
  * Groussin et al. (2019) Groussin O., et al., 2019, Space Sci. Rev., 215, 29
  * Grün et al. (1991) Grün E., Kochan H., Seidensticker K. J., 1991, Geophysical Research Letters, 18, 245
  * Grün et al. (1992) Grün E., Benkhoff J., Gebhard J., 1992, Annales Geophysicae, 10, 190
  * Grün et al. (1993) Grün E., et al., 1993, Journal of Geophysical Research: Planets, 98, 15091
  * Gulkis et al. (2015) Gulkis S., et al., 2015, Science, 347
  * Gundlach (2019) Gundlach B., 2019, in EPSC-DPS Joint Meeting 2019. pp EPSC–DPS2019–429
  * Gundlach et al. (2018) Gundlach B., et al., 2018, MNRAS, 479, 1273
  * Gundlach et al. (2020a) Gundlach B., Fulle M., Blum J., 2020a, Monthly Notices of the Royal Astronomical Society, 493, 3690
  * Gundlach et al. (2020b) Gundlach B., Fulle M., Blum J., 2020b, Monthly Notices of the Royal Astronomical Society, 493, 3690
  * Güttler et al. (2019) Güttler C., et al., 2019, A&A, 630, A24
  * Haack et al. (2020) Haack D., Otto K., Gundlach B., Kreuzig C., Bischoff D., Kührt E., Blum J., 2020, A&A, 642, A218
  * Hapke (1993) Hapke B., 1993, Theory of reflectance and emittance spectroscopy, 1 edn. Cambridge University Press
  * Hasselmann et al. (2017) Hasselmann P. H., et al., 2017, MNRAS, 469, S550
  * Helfenstein & Veverka (1989) Helfenstein P., Veverka J., 1989, in Binzel R. P., Gehrels T., Matthews M. S., eds, Asteroids II. pp 557–593
  * Henke et al. (2016) Henke S., Gail H.-P., Trieloff M., 2016, A&A, 589, A41
  * Herique et al. (2002) Herique A., Gilchrist J., Kofman W., Klinger J., 2002, Planetary and Space Science, 50, 857
  * Herique et al. (2017) Herique A., et al., 2017, Monthly Notices of the Royal Astronomical Society, 462, S516
  * Hörz et al. (2006) Hörz F., et al., 2006, Science, 314, 1716
  * Izawa et al. (2014) Izawa M. R. M., Applin D. M., Norman L., Cloutis E. A., 2014, Icarus, 237, 159
  * Johansson et al. (2017) Johansson F. L., et al., 2017, Monthly Notices of the Royal Astronomical Society, 469, S626
  * Jorda et al. (2016) Jorda L., et al., 2016, Icarus, 277, 257
  * Jost et al. (2017a) Jost B., et al., 2017a, Planet. Space Sci., 145, 14
  * Jost et al. (2017b) Jost B., Pommerol A., Poch O., Brouet Y., Fornasier S., Carrasco N., Szopa C., Thomas N., 2017b, Planetary and Space Science, 148, 1
  * Kamoun et al. (2014) Kamoun P., Lamy P. L., Toth I., Herique A., 2014, A&A, 568, A21
  * Kappel et al. (2020) Kappel D., Sachse M., Haack D., Otto K. A., 2020, A&A, 641, A19
  * Kaufmann & Hagermann (2018) Kaufmann E., Hagermann A., 2018, Icarus, 311, 105
  * Knapmeyer et al. (2018) Knapmeyer M., Fischer H.-H., Knollenberg J., Seidensticker K., Thiel K., Arnold W., Faber C., Möhlmann D., 2018, Icarus, 310, 165
  * Kofman et al. (2007) Kofman W., et al., 2007, Space Science Reviews, 128, 413
  * Kofman et al. (2015) Kofman W., et al., 2015, Science, 349
  * Kofman et al. (2020) Kofman W., Zine S., Herique A., Rogez Y., Jorda L., Levasseur-Regourd A.-C., 2020, Monthly Notices of the Royal Astronomical Society, 497, 2616
  * Kothe et al. (2013) Kothe S., Blum J., Weidling R., Güttler C., 2013, Icarus, 225, 75
  * Kreuzig & et al. (2021) Kreuzig C., et al. 2021, Review of Scientific Instruments, submitted
  * Kreuzig et al. (2019) Kreuzig C., Kargl G., Pommerol A., Gundlach B., Blum J., 2019, in EPSC-DPS Joint Meeting 2019. pp EPSC–DPS2019–1319
  * Lethuillier et al. (2016) Lethuillier A., et al., 2016, A&A, 591, A32
  * Leyrat et al. (2016) Leyrat C., et al., 2016, in Joint 48th meeting of the Division for Planetary Sciences (DPS) and 11th European Planetary Science Congress (EPSC). pp 219.02–219.02, https://elib.dlr.de/107190/
  * Li et al. (2007a) Li J.-Y., A’Hearn M. F., McFadden L. A., Belton M. J. S., 2007a, Icarus, 188, 195
  * Li et al. (2007b) Li J.-Y., et al., 2007b, Icarus, 191, 161
  * Li et al. (2013) Li J.-Y., A’Hearn M. F., Belton M. J. S., Farnham T. L., Klaasen K. P., Sunshine J. M., Thomas P. C., Veverka J., 2013, Icarus, 222, 467
  * Lipp (1992) Lipp E. D., 1992, Applied Spectroscopy Reviews, 27, 385
  * Mannel et al. (2019) Mannel T., et al., 2019, A&A, 630, A26
  * Marschall et al. (2020) Marschall R., Markkanen J., Gerig S.-B., Pinzón-Rodríguez O., Thomas N., Wu J.-S., 2020, Frontiers in Physics, 8, 227
  * Marshall et al. (2018) Marshall D., et al., 2018, A&A, 616, A122
  * Mattei et al. (2014) Mattei E., Lauro S. E., Vannaroni G., Cosciotti B., Bella F., Pettinelli E., 2014, Icarus
  * Merouane et al. (2017) Merouane S., et al., 2017, Monthly Notices of the Royal Astronomical Society, 469, S459
  * Mottola et al. (2015) Mottola S., et al., 2015, Science, 349
  * Möhlmann et al. (2018) Möhlmann D., et al., 2018, Icarus, 303, 251
  * Nicolson & Ross (1970) Nicolson A. M., Ross G. F., 1970, IEEE Transactions on Instrumentation and Measurement, 19, 377
  * Noonan et al. (2016) Noonan J., et al., 2016, Acta Astronautica, 125, 3
  * O’Rourke et al. (2020) O’Rourke L., et al., 2020, Nature, 586, 697
  * Opeil et al. (2020) Opeil C. P., Britt D. T., Macke R. J., Consolmagno G. J., 2020, Meteoritics & Planetary Science, 55
  * Pätzold et al. (2016) Pätzold M., et al., 2016, Nature, 530, 63
  * Pilorget et al. (2015) Pilorget C., Fernando J., Ehlmann B. L., Douté S., 2015, Icarus, 250, 188
  * Poch et al. (2016a) Poch O., Pommerol A., Jost B., Carrasco N., Szopa C., Thomas N., 2016a, Icarus, 266, 288
  * Poch et al. (2016b) Poch O., Pommerol A., Jost B., Carrasco N., Szopa C., Thomas N., 2016b, Icarus, 267, 154
  * Poch et al. (2020) Poch O., et al., 2020, Science, 367, aaw7462
  * Pommerol & Schmitt (2008) Pommerol A., Schmitt B., 2008, Journal of Geophysical Research: Planets, 113
  * Pommerol et al. (2011) Pommerol A., Thomas N., Affolter M., Portyankina G., Jost B., Seiferlin K., Aye K.-M., 2011, Planetary Space Science, 59, 1601
  * Pommerol et al. (2019) Pommerol A., et al., 2019, Space Science Reviews
  * Prialnik & Sierks (2017) Prialnik D., Sierks H., 2017, Monthly Notices of the Royal Astronomical Society, 469, S217
  * Quirico et al. (2016) Quirico E., et al., 2016, Icarus, 272, 32
  * Rietmeijer (1993) Rietmeijer F. J., 1993, Earth and Planetary Science Letters, 117, 609
  * Rotundi et al. (2002) Rotundi A., Brucato J. R., Colangeli L., Ferrini G., Mennela V., Palomba E., Palumbo P., 2002, Meteoritics & Planetary Science, 37, 1623
  * Rousseau et al. (2018) Rousseau B., et al., 2018, Icarus, 306, 306
  * Sabouroux & Ba (2011) Sabouroux P., Ba D., 2011, Progress In Electromagnetics Research B, 29, 191
  * San Sebastián et al. (2020) San Sebastián I. L., Dolff A., Blum J., Parisi M. G., Kothe S., 2020, Monthly Notices of the Royal Astronomical Society, 497, 2418
  * Sato et al. (2014) Sato H., Robinson M. S., Hapke B., Denevi B. W., Boyd A. K., 2014, Journal of Geophysical Research: Planets, 119, 1775
  * Saunders et al. (1986) Saunders R. S., Fanale F. P., Parker T. J., Stephens J. B., Sutton S., 1986, Icarus, 66, 94
  * Schloerb et al. (2015) Schloerb F. P., et al., 2015, A&A, 583, A29
  * Schweighart et al. (2021) Schweighart M., Macher W., Kargl G., Gundlach B., Capelo H., 2021, MNRAS
  * Sihvola (2000) Sihvola A., 2000, Subsurface Sensing Technologies and Applications, 1, 393
  * Skorov & Blum (2012) Skorov Y., Blum J., 2012, Icarus, 221, 1–11
  * Spohn et al. (1989) Spohn T., Seiferlin K., Benkhoff J., 1989, in Hunt J. J., Guyenne T. D., eds, ESA Special Publication Vol. 302, Physics and Mechanics of Cometary Materials. pp 77–81
  * Spohn et al. (2015) Spohn T., et al., 2015, Science, 349
  * Storrs et al. (1988) Storrs A., Fanale F., Saunders R., Stephens J., 1988, Icarus, 76, 493
  * Stöffler et al. (1991) Stöffler D., Düren H., Knölker J., Hische R., Bischoff A., 1991, Geophysical Research Letters, 18, 285
  * Vincent et al. (2017) Vincent J.-B., et al., 2017, Monthly Notices of the Royal Astronomical Society, 469, S329
  * Warren & Brandt (2008) Warren S. G., Brandt R. E., 2008, Journal of Geophysical Research (Atmospheres), 113, D14220
  * Warren & Wiscombe (1980) Warren S. G., Wiscombe W. J., 1980, Journal of Atmospheric Sciences, 37, 2734
  * Wozniakiewicz et al. (2013) Wozniakiewicz P. J., Bradley J. P., Ishii H. A., Price M. C., Brownlee D. E., 2013, ApJ, 779, 164
  * Yoldi et al. (2015) Yoldi Z., Pommerol A., Jost B., Poch O., Gouman J., Thomas N., 2015, Geophys. Res. Lett., 42, 6205
  * Zolensky et al. (2006) Zolensky M. E., et al., 2006, Science, 314, 1735