In the research presented, a quantitative assessment is conducted on multiple publicly available methods for generating random porous media. The creation and examination of such media are fundamental to various models that offer a more advanced level of physical analysis concerning the transfer of energy and matter. These foundational models of porous media facilitate the quantification of crucial parameters like radiative thermal conductivity and volumetric absorption of external radiation. These parameters, in turn, play a critical role in simulating heat transfer within porous surface layers, like those found on comets or asteroids, influencing the effective brightness temperature of these layers. Therefore, the modelling of random porous media directly influences the analysis of remote microwave observations and the derivation of constraints on the characteristics of the objects under investigation.

The comparison among various open-source codes intended for generating porous layers is carried out. These methods can be categorised based on different criteria. For instance, they can be distinguished by methods that regulate contacts between elementary units (like YADE) and those that lack such control. The methods can also be classified by the particle types forming the structure, which can include spheres of different sizes, porous clusters composed of such spheres, or solid non-spherical particles. In the analysis of polydisperse media, a consistent application of particle size distribution laws and size value constraints is ensured for comparison purposes. Furthermore, packings consisting of cubes, tetrahedrons, octahedrons, and irregularly shaped particles are considered for non-spherical particles. In the case of hierarchical layers, aggregates of various sizes and degrees of nonsphericity are evaluated. The generated layers are compared based on parameters such as porosity, average pore size, permeability, and the depth distribution of the first and last particle collisions with the dust skeleton. The last parameter is vital to estimate gas heating upon passing through the layer and the resultant gas yield. Additionally, the computational performance associated with implementing the selected methodologies is thoroughly examined.

How to cite: Skorov, Y., Reshetnyk, V., Lukyanyk, I., Grynko, Y., Macher, W., Schuckart, C., and Blum, J.: Quantitative Assessment of Open-Source Methods for Generating Random Porous Media, Europlanet Science Congress 2024, Berlin, Germany, 8–13 Sep 2024, EPSC2024-698, https://doi.org/10.5194/epsc2024-698, 2024.

Introduction:

Cometary acitivity models (such as used in: Skorov et al. 2023, Gundlach et al. 2020, Bischoff et al. 2023 and Fulle et al 2020) depend on an accurate permeability prediction of surface near materials. The refractory to ice ratio of this material is studied extensively, but little is known about the structure of the porous layer or the shape of the icy regolith and how it might affect surface activity. To support cometary erosion models with an improved gas-flow prediction, we study various models which are used to describe the flow of rarefied gases through porous materials. These diffusion models are usually expressed for mono-disperse packed beds of spherical and simulations and experiments have confirmed the dependency on grain size and porosity (Güttler et al., 2023). But observations using Rosetta have shown, that cometary particles might be of elongated, non-spherical shape. Therefore, we generalised the current models to be applicable to polydisperse and non-spherical particles (Zivithal et al., in revision) and performed experiments which identified the gas flow parameters, Knudsen diffusion coefficient and viscous permeability, of different granular packings.

Measurements and results:

We use a dedicated measurement setup that allows to measure the gas flow parameters in the transition regime. To study the effects of angularity and polydispersity we conducted measurements with mono- and bi-disperse spherical packings, packings of elongated metal pins in different orientation, and highly porous packings. Special attention had to be paid to biases in measuring the porosity and the pressure drop in the sample. The conducted measurements confirm that the Knudsen diffusion coefficient is inversely proportional to the specific surface area of the grains and that the viscous permeability is inversely proportional to the specific surface area squared. This was not only valid for the mono-disperse but also for the bi-disperse packings measured. Further, we were able to identify a relation between the gas flow parameters, represented by a parameter 𝛽, which seems to be an indicator for the mean orientation of the grains. The findings give further evidence of the importance of the grain size distribution, the grain shape and the orientation for rarefied gas flow and how sensitive it is to changes within those parameters.

Discussion:

Cometary surfaces as seen by Rosetta and other space mission have a diverse morphology. Our results suggest that different morphological structures (consisting of packings of various grain size distributions and grain shapes) will have vastly different outflow behaviours and therefore, the findings could help to explain different erosion patterns. Most importantly the findings of this work emphasise the importance of further research about cometary surface composition and the interacting, sensitive gas flow.

References

Skorov, Y. et al., 2021. MNRAS 501.2, pp. 2635-2646.

Gundlach, B. et al., 2020. MNRAS 493, pp. 4690-3715.

Bischoff, D. et al., 2023 MNRAS, pp. 5171-5186.

Fulle, M. et al., 2020 MNRAS 493, pp. 4039-4044.

Güttler, C. et al., 2023. MNRAS 524, pp. 6114-3123.

Zivithal, S. et al., in revision. MNRAS

How to cite: Zivithal, S., Kargl, G., Macher, W., Güttler, C., Gundlach, B., Sierks, H., and Blum, J.: Angularity and Polydispersity effects on gas-flow and possible implications for cometary activity, Europlanet Science Congress 2024, Berlin, Germany, 8–13 Sep 2024, EPSC2024-732, https://doi.org/10.5194/epsc2024-732, 2024.

Introduction

The molecular diffusion of gas is an essential process in our understanding of cometary activity. Gas that is produced through sublimation in active sub-surface layers builds up a pressure, while at the same time diffusing towards the comet’s surface and escaping into space. The governing diffusion constant is strongly dependent on the microscopic structure of the material, i.e., its grain size and porosity (Güttler et al., 2023) but also grain shape and arrangement (Zivithal et al., accepted). Its detailed understanding is therefore bridging between the observed activity of comets with space probes and also analogue material (Kreuzig et al., 2021 and others) on one side and the microscopic material structure on the other side. Through the knowledge of diffusion and gas transport in the near surface layers, we aim to learn about the microscopic structure, thus the nature and formation of comets.

Experiment and Simulation

We have performed laboratory experiments on gas diffusion in the molecular-flow regime through very clean and controlled samples consisting of 0.5 mm diameter steel beads. These simulations were successfully reproduced using a Direct Simulation Monte Carlo (DSMC) approach with the PI-DSMC code (Rose, 2014). The simulations then allowed a broad variation of gas velocity (temperature and molar mass), particle diameter and porosity, confirming the analytic descriptions of Derjaguin (1946) and Asaeda et al. (1974). Residual deviations from absolute values were found on a level comparable to those by Asaeda et al. (1974; they introduced a scaling factor q=1.41) and moreover to be linear dependent on porosity. On a microscopic level, by tracing individual particles, the description of mean path lengths and their distribution by Derjaguin (1946) could also be confirmed.

Further Application of the DSMC Model

After successful application of the DSMC model, as confirmed by our experiments, literature experiments and analytical models, we are now applying it now to more complex geometries.

One aspect is the introduction of macroscopic voids of different geometries to study their effect on the gas-flow field. In particular, we look at the force applied on individual particles (which we consider as pebbles on a comet’s surface; Blum et al., 2017). We look at their lifting force, with and without voids, counteracting their cohesion.

Second, we simulate a gas source (sublimation front) as a plane below the comet surface but with granular material below. This allows the gas to diffuse into space as well as into the interior. We then let the gas that diffuses into the interior adsorb as a function of depth. We find that a substantial fraction of gas that is sublimated in the described plane does not escape into space but rather re-adsorbs in layers below the sublimation plane. This material transport builds up vertical layering, which will be studied in further depth for its eventual application to thermophysical models (Gundlach et al., 2020).

References

Asdaeda, M. et al., 1974. J. Chem. Eng. Jpn. , 7, 93.

Blum, J. et al., 2017. MNRAS 469, S755-S773.

Gundlach, B. et al., 2020. MNRAS 493, p4690-3715.

Güttler, C. et al., 2023. MNRAS 524, pp6114-3123.

Derjaguin, B.Y., 1946. Dokl. Akad. Nauk SSSR, 4, 687.

Kreuzig, C. et al., 2021. RSI 92:115102.

Rose, M., 2014. AIP Conf. Proc. “29th Int. Symp. on Rerefied Gas Dynamics”. Vol 1628.

Zivithal, S. et al., submitted. MNRAS

How to cite: Güttler, C., Rose, M., Sierks, H., Schuckart, C., Macher, W., Zivithal, S., Blum, J., Kargl, G., and Gundlach, B.: Gas diffusion and transport in cometary surface material, Europlanet Science Congress 2024, Berlin, Germany, 8–13 Sep 2024, EPSC2024-741, https://doi.org/10.5194/epsc2024-741, 2024.

For the thermal modelling of the activity and evolution of cometary nuclei, it is of utmost importance to understand the heat transfer in granular media. To help with the understanding of the underlying physical processes, laboratory cometary simulation experiments were conducted within the Comet Physics Laboratory (CoPhyLab) project [1]. A three-dimensional thermophysical model was developed to simulate selected CoPhyLab experiments and to better understand the underlying microphysics.

Samples of granular media were illuminated with a halogen lamp either continuously or in sinusoidal cycles and temperatures were measured with Pt1000 temperature sensors.

The thermophysical model is capable of solving the heat-transfer equation and the gas-diffusion equation via a finite-volume scheme. Furthermore, it includes effects that are important for the description of granular media, especially a thermal conductivity calculation that is dependent on both contact and radiative heat transfer [2], volumetric energy absorption [3] and sintering [4].

Figure 1: The temperature over time plots showing the best match between simulation (black curves) and selected temperature sensors (coloured curves). The laboratory sample was constantly illuminated in the first part of the experiment, after which it cooled down and finally got illuminated in sinusoidal cycles. The simulation parameters are a bolometric albedo of 0.7, a thermal conductivity of 0.008 W m^-1 K^-1 and a light-absorption length scale of 1 mm.

As a first test, the simulation results were compared to a pure sand sample as a simple representation of a non-active granular medium. The sample was continuously irradiated over multiple days, after which it was cooled down and finally irradiated again in a day-night-cycle pattern. With only the albedo, heat-conductivity and light-absorptionlength scale as free parameters, very good agreement between the laboratory measurements and the simulations to below 5 K difference could be achieved (Figure 1).

Figure 2: The temperature over time plots showing the best match between simulation (black curves) and selected temperature sensors (coloured curves). It can be seen that the simulation on the left doesn’t match the qualitative trend of the function, which is due to non-matching crater-wall temperatures. After artificially increasing the crater wall temperatures in the simulation on the right, a better match between simulation and the experimental data could be achieved.

Figure 3: The final temperature profile of the best fitting simulation of the ice samples in a 3D representation. The walls of the formed crater are colder than they were in the experiments.

Further experiments with pure granular water ice [5] were performed and simulated. The sample, which was irradiated with a day-night-cycle pattern, showed the formation of a steep crater over multiple days. The influence of the crater growth shows significant impact on the temperature profiles. Hence, these dynamic processes must be accurately described in order to match simulations to the laboratory experiments (Figures 2 and 3). It was found that possible sintering effects are seemingly negligible on the time scales and temperature regimes in which these experiments were conducted.

Lastly, a brief discussion on difficulties of modelling small-scale laboratory samples with thermophysical models shall be given, pertaining especially to the influence of the laboratory environment. It was shown that even small differences of the assumed background temperature could lead to variation in the simulation results by multiple Kelvins. Thus, special care has to be taken to account for these influences correctly.

In conclusion, laboratory experiments can provide much needed validation cases for thermophysical models and can be used to refine said models. In turn, these models can be used to help better understand and design laboratory experiments.

References:

[1] Kreuzig, C. et al. (2021). “The CoPhyLab comet-simulation chamber”. Review of Scientific Instruments 92.11, S. 115102.

[2] Gundlach, B. und Blum, J. (2012). „Outgassing of icy bodies in the Solar System - II: Heat transport in dry, porous surface dust layers“. Icarus 219.2, S. 618–629.

[3] Wurm, G. und Krauss, O. (2006). „Dust Eruptions by Photophoresis and Solid State Greenhouse Effects“. Physical Review Letters 96.13, S. 134301.

[4] Gundlach, B. et al. (2018). „Sintering and sublimation of micrometre-sized water-ice particles: the formation of surface crusts on icy Solar System bodies“. Monthly Notices of the Royal Astronomical Society 479.4, S. 5272–5287.

[5] Kreuzig, C. et al. (2023). „Micrometre-sized ice particles for planetary science experiments - CoPhyLab cryogenic granular sample production and storage“. RAS Techniques and Instruments 2.1, S. 686–694.

How to cite: Schuckart, C., Kreuzig, C., Meier, G., Brecher, J. N., Timpe, M., Knoop, C., Gundlach, B., and Blum, J.: 3D heat transfer simulation of laboratory measurements of granular media, Europlanet Science Congress 2024, Berlin, Germany, 8–13 Sep 2024, EPSC2024-108, https://doi.org/10.5194/epsc2024-108, 2024.

Maximum dust-to-gas mass flux ratio in spherically expanding dusty-gas flow.

In the context of an increasing number of complex multiparametric dusty-gas coma models it is convenient to address the analysis of complex physical phenomena in a step-by-step manner. We construct a set of elementary models with a minimum number of parameters selected to represent the key processes acting in a dusty gas coma. Such kind of models enables studies of generic processes occurring in variety of particular cases in order to reveal their characteristic features.

In many models of dusty-gas atmosphere of comets the dust-to-gas mass flux ratio is a free parameter. In order to constraint the range of possible values of this parameter, in the present work we propose an estimate of its maximum value. We consider a “pedagogic” case which assumes a homogeneous spherical nucleus and spherical expansion of dusty-gas (as an elementary model of the coma). The dust grains are assumed to be homogeneous spheres with size distribution given by a power law n(a_d) ∝ a_d^-β.

After ejection from the surface dust grain is accelerated by the gas flow in the gravitational field of the nucleus. In the present consideration we assume that the radiation pressure due to solar illumination of the grain is negligibly small. With increasing distance to the nucleus the gas drag and the nucleus gravitational attraction decrease and decoupling of gas and dust flows occurs at some distance. In absence of other forces, the dust grains continue motion with constant “terminal velocity”. As was shown in [1], the dust grains reach 90% of the terminal velocity at cometocentric distance about 6 comet radii.

The numerical integrated terminal velocity of dust grains in a spherically expanding flow is given in [1] for a wide range of conditions. The terminal velocity (v_d) can be approximated as:

v_d(a_d)/v_max=A_i Iv^Bi, i=1,2,3,

where Iv is a dimensionless parameter characterizing the efficiency of entrainment of the particle within the gas flow (see [1]), v_max is the theoretical maximal velocity of gas expansion, and A_i, B_i are coefficients of approximation defined for three non-overlapping ranges of parameter Iv variation.

To escape the gravitational attraction of the nucleus terminal velocity of the dust particles should exceed the escape velocity v_esc. This condition combined with the approximation for the terminal velocity allows us to derive the maximum size of the grains that reach escape velocity.

The dust mass loss rate q_d of grain size a_d and the gas production rate q_g are related via:

q_d(a_d)=χf_md(a_d) q_g da_d,

where χ=Q_d/q_g is the dust-to-gas mass loss rate, Q_d is the dust mass loss rate integrated over all grain sizes, and f_md is the normalized mass distribution of dust grains.  

Considering the foregoing, for the cometocentric distances greater than 6 comet radii it is easy to derive the energy fluxes of gas and dust flows.

The dust flow gets energy from the gas flow. Therefore, the maximum dust-to-gas mass loss rate corresponds a certain fraction of gas flow energy (κ<<1) being transferred in the dust flow energy.

In simplified form the expression for the maximum dust-to-gas mass loss rate is:

χ=κ(v_max/v_esc)² (a_max/a_esc)^4-β (3-β)/(4-β) [1-(a_min/a_max)^4-β]/[1-( a_min/a_esc)^3-β].

Fig.1 shows dust-to-gas mass flux ratio χ as a function of size distribution (β) for the case of a comet with nucleus radius R_n=1 km, mass M_n=10¹² kg, v_max=1 km/s, and κ=1. Note, that complete transfer of gas energy to the dust (κ=1) is not physically possible. In addition, in our reasoning it was assumed that the dust does not affect the gas flow, therefore the values of κ should be rather small. The Fig.1 shows that if the ejected dust has a broad range of sizes a_d,min/a_d,max (e.g. 5-6 orders of magnitude) and β>3.5, the maximum possible dust-to-gas loss rate is rather restricted. 

In our presentation, we show an extension of this approach to the more realistic multidimensional case as well. 

Acknowledgments

The work of N.Y.Bykov and A.V.Rodionov was supported by the Russian Science Foundation (grant No. 24-12-00299).

The work of A.Rotundi and V.Della Corte was supported by the Italian Space Agency (ASI) within the ASI-INAF agreements I/032/05/0, I/024/12/0 and 2020-4-HH.0. 

References

1. V.V. Zakharov, S.L. Ivanovski, J.-F. Crifo, V. Della Corte, A. Rotundi, M. Fulle. Asymptotics for spherical particle motion in a spherically expanding flow. Icarus 312 (2018)

How to cite: Zakharov, V., Bykov, N., Rodionov, A., Ivanovski, S., Della Corte, V., and Rotundi, A.: Maximum dust-to-gas mass flux ratio in spherically expanding dusty-gas flow., Europlanet Science Congress 2024, Berlin, Germany, 8–13 Sep 2024, EPSC2024-230, https://doi.org/10.5194/epsc2024-230, 2024.

Introduction:   In-situ measurements of individual dust grain parameters in the immediate vicinity of a cometary nucleus are being carried by the Rosetta spacecraft at comet 67P/Churyumov-Gerasimenko. For interpretation of these observational data, a model of dust grain motion as realistic as possible is requested. In particular, the results of Stardust mission and analysis of samples of interplanetary dust have shown that these particles are highly non-spherical. In many cases precise simulations of non-spherical grain’s dynamics is either impossible or computationally too expensive. In such situation it is proposed to use available experimental or numerical data obtained for other conditions and re-scale them considering similarity of the physical process. Here, we focus on the derivation of scaling laws of rotational motion applicable for any shape of particles. We use a set of universal, dimensionless parameters characterizing the dust motion in the inner cometary coma. The scaling relations for translational and rotational motion of dust grains in a cometary environment are proposed. The scaled values are compared with numerically computed ones in our previous works. This study was published in MNRAS this year.

The scientific objectives:   In the present work we focus on the derivation of scaling laws of rotational motion applicable for any shape of particles. We use a set of universal, dimensionless parameters characterizing the dust motion in the inner cometary coma. This approach was proposed in [1] and successfully applied in [2] to the dynamics of spherical grains. Here we extend this approach on the translational and rotational motion of non-spherical particles. Our approach allows to reduce the number of parameters for analysis, to reveal similarities of the dust flows and to re-scale the available numerical solutions.

The Model:   We assume that the dusty-gas coma is formed by the gas sublimating from the nucleus (from the surface and/or from the interior) and solid particles (mineral or/and icy) released from the nucleus and entrained by the gas flow. It is assumed that the dusty-gas flow is coupled in one way only – the gas drags the dust (i.e. the presence of dust in the coma does not affect the gas motion), and that the dust particles do not collide with each other. The dust particles are assumed to be isothermal, internally homogeneous with invariable size and mass.

Results: We have derived scaling for the terminal dust velocity and rotational frequency, i.e. the velocity and rotational frequency that a dust grain has after decoupling with the gas flow. As was derived from observational, the dust acceleration limited within six nuclear radii for a broad range of particle sizes [3]. The numerical studies (e.g. [1], [2]) also show that gas and dust decoupling occurs within the first ten radii of the nucleus.

To verify the scaling relations, we use the numerically computed data for ellipsoids of revolution with different aspect ratios considered in [4], and for irregularly shaped particles considered in [5]. The gas coma was approximated by a spherically symmetric expanding gas (pure 𝐻₂𝑂) flow. Using the two groups of results, we summarize the corresponding scaling precision ε (the relative difference of scaled and numerically computed values) in Fig. 1. We note that in the cases of prolate spheroids high gas production rate and small particles lead to better precision in scaling for the velocity than for the rotation. Nevertheless, the rotation precision is within maximum 40%. In the cases of oblate spheroid (Fig. 2) an increase in the gas production rate produces better precision in scaling for the velocity than for the rotation. Furthermore, in case of large particles we have an opposite trend, less precision in velocity scaling and better one for rotation. 

Fig. 1. Scaling precision of the velocity and the rotation for the prolate cases in Table 1[6].

Fig. 2. Scaling precision of the velocity and the rotation for the prolate cases in Table 2 [6].

To estimate the precision of the scaling with respect to the shape irregularity we have calculated the dispersion of the moments of inertia of the considered shapes. The dispersion was calculated as a standard deviation of the three moments of inertia of a given shape divided on their mean value. The purpose of this estimation is that the dispersion calculated in this way is dimensionless and can be easily used for comparison in all available cases. The general trend is: the higher the dispersion is, the better the scaling is. The only deviation from this observation is the case of a prolate spheroid the rotational motion is happening only in one plane as discussed in [4]. The scaling works better for more irregular shapes. The shapes with a smaller dispersion can easily and often change their axis of rotation that results in more complex rotational motion, i.e. seems more difficult to be precisely obtained by scaling.

Conclusions: We derived scaling laws of rotational motion applicable for any shape of particles. We use a set of universal, dimensionless parameters characterizing the dust motion in the inner cometary coma. Based on the dimensionless description of the translational and rotational motion of dust particles we derived scaling relations for the terminal velocity and rotational frequency of non-spherical grains. Having one numerically computed “reference case” one can get order of magnitude estimation for other cases via simple scaling. This allows avoiding long time and huge electric power consumption numerical simulations.

Acknowledgements: This research was supported by the Italian Space Agency (ASI) within the ASI-INAF agreements I/032/05/0, I/024/12/0, 2020-4- HH.0 and N. 2023-14-HH.0. The work of N.Y.Bykov and A.V.Rodionov was supported by the Russian Science Foundation (grant No. 24-12-00299). This work was supported by the International Space Science Institute (ISSI) through the ISSI International Team ‘Characterization of cometary activity of 67P/Churyumov–Gerasimenko comet’.

References: [1] Zakharov V. et al. 2018, Icarus; [2] Zakharov V. et al. 2021, Icarus; [3] Gerig, S.-B. et al. 2018, Icarus, [4] Ivanovski S. et al. 2017, Icarus; [5] Moreno F. et al. 2022, MNRAS; [6] Ivanovski et al. 2024, MNRAS;

How to cite: Ivanovski, S. L., Zakharov, V., Moreno, F., Bykov, N., Munoz, O., Fulle, M., Rotundi, A., Della Corte, V., and Rodionov, A.: On the similarity of rotational motion of dust particles in the inner atmosphere of comets , Europlanet Science Congress 2024, Berlin, Germany, 8–13 Sep 2024, EPSC2024-1161, https://doi.org/10.5194/epsc2024-1161, 2024.

Understanding the intricate dynamics of gas-dust interactions within protoplanetary disks is crucial for unraveling the mysteries of planetary system formation. We introduce TEMPus VoLA (Timed Epstien Multi-pressure vessel at Low Accelerations), an experimental setup designed to investigate particle dynamics and rarefied gas behavior in microgravity (Capelo et al. 2022 https://doi.org/10.1063/5.0087030). Figure 1 shows the experimental setup in flight configuration, together with a rendering of the multiple pressure vessels containing low-pressure gas and dust analogue materials.  

Figure 1 (Reproduced from Capelo et al 2022). Left: TEMPusVoLA in flight configuration aboard Air Zero-G. Right: Multiple pressure vessels containing rarified gas and dust particle analog. Each chamber is designated to study a particular process: Shear flow, permeability, and drag forces on aggregates. 

Through multiple dedicated experiments, we explore the effects of collective particle-gas interaction on pressure gradients (permeability), aerodynamic drag coefficients and mechanical properties of dust aggregates, and the onset of turbulence in shear flows. Figure 2 shows an example of a periodic velocity field developing in the shear flow chamber, where dust is injected as a stream in the flow of gas at vaccum pressure. We interpret the velocity field to indicate the onset of a Kelvin-Helmholtz like instability, generated for the first time with dust as the dense phase in pure molecular flow. 

Figure 2 (Reproduced from Capelo et al. 2022). Particle-velocity in the stream-wise direction of the shear flow chamber, derived using particle image velocimetry.  The particle velocities are not constant, but rather oscilate.

Our findings, gleaned from multiple parabolic flight campaigns, support a better understanding of dust transport and dynamics in planet-forming discs and also have implications for understanding phenomena like dust emission from cometary nuclei. The presented framework offers a valuable tool for validating models and numerical simulations of collective dust particle aerodynamics in low-gravity environments. 

How to cite: Capelo, H. L., Bodénan, J.-D., Jutzi, M., Kühn, J., Mayer, L., Schönbächler, M., Thomas, N., and Pommerol, A.: Aerodynamic and Mechanical Properties of Dust Aggregates in Low-Gravity Environments, Europlanet Science Congress 2024, Berlin, Germany, 8–13 Sep 2024, EPSC2024-899, https://doi.org/10.5194/epsc2024-899, 2024.

Abstract

Rosetta/OSIRIS made optical measurements of the intensity of scattered light from the 67P/Churyumov-Gerasimenko coma over a wide range of phase angles. These data have been used to measure the phase angle dependent radiance profile of the dust coma. In order to derive dust properties such as the dust scattering phase function from these measurements, we need to understand the phase angle dependence of the optical thickness of the coma. This can be measured as the column area density, which is the total solid angle fraction covered by all dust particles within a given field of view. We present a simple numerical model that allows us to study the phase angle dependence of the column area density in a cometary coma.

Method

We consider a spherical nucleus with a given initial position and velocity relative to the Sun. From this nucleus we eject a large number of spherical dust particles at random positions and times. The acting forces considered by the model are the gravitational pull and the radiation pressure of the Sun. The neglect of other forces such as gas drag or nucleus gravity is justified for distances greater than about 10 km from the nucleus.

Since our model cannot describe the dust behavior close to the comet, we emit the dust particles from an imaginary sphere with a radius of 10 km around the nucleus. The initial velocity of the dust particles relative to the nucleus points radially away from the nucleus. The magnitude of the initial velocity is determined by the dust radius according to values found in the literature, with larger particles being emitted at lower velocities.

Since the activity of the comet is not constant across its surface, we need to implement a non-uniform dust production rate.We do this by adding a weighting factor to each dust particle released, based on its initial position. The weighting factor is determined by the angle between the particle, the nucleus center, and the subsolar point. We compare several weighting functions, the simplest being a cosine function that has its maximum at the subsolar point and decreases toward the terminator, being zero on the night side of the nucleus. The parameters used in the model correspond roughly to the properties of 67P/Churyumov-Gerasimenko, but the results are expected to be qualitatively valid for other comets as well.

All calculations are performed in an inertial frame of reference. To evaluate the column area density as seen from Rosetta, we then transform back to the spacecraft frame. The column area density is then calculated by summing the solid angle covered by all dust particles within a given field of view as seen from the spacecraft. This allows us to study the phase angle dependence of the column area density in a cometary coma. The model presented here can be easily adapted to parameters of other comets or to more realistic activity distributions.

Results

We find that the observed phase angle dependence of the column area density is largely independent of the position of the spacecraft in the terminator plane. For the case of a cosine activity distribution on the day side of the nucleus, we find that the column area density reaches plateaus at low and high phase angles, with the column area density being about two orders of magnitude larger at high phase angles. The increase occurs between 45° and 135° and appears to be symmetric around the terminator (90°). The dust radius has no effect on the phase angle dependence of the column area density. The activity distribution however proves to have a strong impact on the dust column area phase function. For models with no or almost no activity on the night side of the nucleus, the column area density remains about 2 orders of magnitude lower at low phase angles compared to the high phase angles. Activity distributions with higher night side activity lead to a smaller difference between low and high phase angles as well as deviations from the two plateau structure described above.

Conclusion

The results of this study show that the u-shaped phase function measured by Rosetta/OSIRIS cannot correspond to the single particle scattering phase function of the dust particles in the coma unless the activity distribution is isotropic. Attempts to infer the dust scattering phase function have to debias for the here measured dust column area density.

How to cite: Keiser, F., Markkanen, J., and Agarwal, J.: Phase angle dependency of the dust cross section in a cometary coma, Europlanet Science Congress 2024, Berlin, Germany, 8–13 Sep 2024, EPSC2024-178, https://doi.org/10.5194/epsc2024-178, 2024.

Introduction

Studying the emission of volatiles from planetary surfaces provides fundamental insights concerning the formation and evolution of planetary bodies, as well as their internal structure. A complex interplay occurs between hydrodynamic and thermal processes in several scientific cases, like the plumes outgassing from fractures over the surface of the icy satellites Europa and Enceladus [1-6]. By means of a Smoothed Particle Hydrodynamics (SPH) [9-11] approach, we simulate Enceladus’ plumes, mainly composed of water vapour and icy-grains [7-8]. We show preliminary results stressing the importance of modelling phase transitions, thermal and dynamical interactions with the solid boundaries as well as the solar radiation and the viscosity coupling between gas and grains.

Methods

For our simulations, we use PySPH [12], a Python framework for SPH. It allows us to study the evolution of a multi-component fluid using the Lagrangian approach, following the variation of its physical quantities, even when they rapidly change. We numerically integrate the hydrodynamics equations for the density, velocity and thermo-kinetic energy. We take into account phase transitions from water vapour to icy-grains and their possible sublimation as well, occurring either during flight or solid boundary interactions. Furthermore, we also consider the viscous drag and the solar radiation effect [13-14].

Initial and boundary conditions: we simulate a surface fracture filled with a finite amount of water vapour only, at saturated conditions and at the triple point of water. We mirror particles crossing fracture walls, and we also consider the thermal interaction with the main body surface. Phase transitions can then occur at the surface too. Finally, particles escaping outward the Hill radius are removed.

Results

Our main results concern the effect of the phase transitions, solar radiation, viscous drag and boundary interaction in altering the plume’s spatial, kinematical and thermal structure, its gas/ice fraction and the ice deposition over the surface.

Gas-ice dynamical coupling: when the icy-grains completely follow the gas (for infinitely small grain-sizes), they accelerate due to gas pressure. In the opposite regime of complete decoupling (for very large grain-sizes), ice particles follow ballistic trajectories and are slower than the gas component. The intermediate regime requires the viscous drag acceleration term in the momentum equation. Appropriate modelling is required to convert such microscopic processes into the macroscopic behaviour of each component. Preliminary simulations of Enceladus’ plumes show that a grain-size of ~100 μm gives a small fraction of icy particles coupled with the gas, although the velocity distributions are similar, as shown in Fig. 1. 

Figure 1: Gas and ice velocity distribution in an Enceladus plume, calculated after ~28 s of simulation time. The Sun radiation direction is also shown.

Solar radiation and thermal boundary interactions: the solar radiation adds energy to illuminated particles, preventing very low temperatures that can be obtained from a free expansion in space. However, at Enceladus distance such flux is not high enough to prevent water ice formation, with a consequent predominance of icy-grains with respect to the vapour in the plume composition. The cold surface of Enceladus can efficiently allow phase transitions through heat conduction, causing ice deposition mainly around the emitting fracture, as shown in Figure 2, where we plot the density of deposited ice. Simulating a fixed amount of material naturally brings to an episodic mass loss event, which lasts a few seconds.

Figure 2. Icy-grains deposition near the emitting region after t~28 s. The fracture is a rectangular box with a section of 200 m² and 200 m deep.

Conclusion

Our goal is to provide a flexible code for SPH simulations, that includes the modelling of several important processes altering volatiles emission from planetary surfaces, like the treatment of solid boundary interactions. This could also be achieved by merging other codes previously developed for modelling surface and subsurface physics [15]. A connection between Eulerian and Lagrangian codes can be a strong and useful tool in a wide range of planetary science studies. We plan to further improve the code, by including radiative transfer processes, adding the presence of dust and improving the assumptions mentioned above.  The large applicability of SPH and our modelling offers an important tool for application to different planetary bodies, wherever volatile emissions occur. Among them, we can study post-impact plumes of small objects or the sublimation of ice on cometary surfaces, with the associated release of dust and gas, or sublimation from polar caps (as in the Martian case). It also enables refining models for Europa’s plumes, helping in planning and interpreting future observations of JUICE and Europa Clipper missions. 

References

[1] Schmidt et al. 2008, Nature, 451, 685.

[2] Kempf et al. 2010, Icarus, 206, 446-457. 

[3] Dong et al. 2011, J. Geophys. Res., 116.

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[12] R. Ramachandran et al. 2021, ACM Trans. Math. Softw. 47, 34.

[13] Magni et al. 2024, in preparation.

[14] Teodori et al. 2024, in preparation

[15] Formisano et al. 2018, J. Geophys. Res. 123, 2445.

Acknowledgments: This work was partially supported by INAF-IAPS within the ASI-INAF grant n. 2023.3.HH.0 “Attività Scientifica di preparazione all'esplorazione marziana" and ISSI within the project “Thermophysical Characterization of Ice-Rich Areas on the Surface of Specific Planetary Bodies: Conditions for the Formation of a Transient Exosphere”.

How to cite: Teodori, M., Maggioni, L., Magni, G., Formisano, M., De Sanctis, M. C., Altieri, F., and D'Aversa, E.: Volatiles emissions from surface fractures: Enceladus' plumes through Smoothed Particle Hydrodynamics simulations, Europlanet Science Congress 2024, Berlin, Germany, 8–13 Sep 2024, EPSC2024-55, https://doi.org/10.5194/epsc2024-55, 2024.

Resonances in the main asteroid belt play a significant role in dynamical evolution of small bodies in the Solar system. They are capable of driving objects into near-Earth object (NEO) region as well.

This work re-examines the transportation abilities of 5:2 mean motion resonance (MMR) with Jupiter. We focus on a greater portion of the resonance than in the previous study [1] that used a similar method. Firstly, short-term FLI (fast Lyapunov indicator [2]) maps of 5:2 MMR were computed in order to distinguish between stable and unstable orbits. Then over 10 000 unstable particles were selected and integrated for a longer period of time, up to 10 Myr, to reveal the transportation abilities of the resonance. We are interested in an elimination course along perihelion distance q = 0.26 au that was discovered previously [1]. Moreover, we also search for the orbits of potentially hazardous asteroids (PHAs) and for orbits that correspond to recent L chondrite meteorites with pedigree, because various studies suggest an association of this resonance with some known PHAs and shocked fossil L chondrites [3-7].

Our results in some aspects correspond to the results of [1]. For example, according to our simulation, 99.45% of test particles became NEOs at some point during the integration, which is much more than what was found in the older studies. However, this can be attributed to the method that was used in [1] and this work. Nevertheless, there are also many different results. For example, we obtained considerably smaller amount of particles reaching a < 1 au, although this amount is still considerably greater than in older studies. We also registered very large number (~ 36.19%) of Sun-grazing particles, i.e. particles that reached perihelion distance q < 0.016 au. In our simulation, the vast majority (92.8%) of test particles entered the Hill sphere of the Earth. The amount of particles that got as close to the orbit of Earth as PHAs was, of course, even larger (97.45%). This large amount, in conjunction with the result of [8] that the 5:2 MMR contributes to the NEO population primarily at larger sizes, led us to search for orbits corresponding to the known PHAs. We considered the list of all 2 374 known PHAs. According to our simulation, the orbits of 17 known PHAs were recovered by at least 70% of the test particles at some point. We also searched for heliocentric orbits of recent L chondrite meteorites among test particles in our simulation. Only in the case of the Porangaba and Park Forest meteorites did more than 10% of test particles recover their orbit at some point during the integration. The final distribution of test particles in our simulation revealed that ejections to hyperbolic orbits or to orbits with a > 100 au were predominantly caused by Jupiter, as was expected. Unfortunately, our simulation did not confirm the existence of a removal course along q = 0.26 au. We also tried to repeat the procedures of [1] while using different software, to see if we were able to obtain ejections along q = 0.26 au. However, our attempts were not successful. Our results suggest that there is some kind of discrepancy between using the MERCURIUS integrator (REBOUND package [9]) and the ORBIT9 integrator (OrbFit package [10]). This subject is worth additional examination.

Acknowledgements:

This work was supported by the VEGA - the Slovak Grant Agency for Science, grant No. 2/0009/22.

References:

[1] Todorović N., 2017, MNRAS, 465, 4441

[2] Skokos C., Gottwald G. & Laskar J., 2016, Chaos detection and predictability (Chapter 2)

[3] de León J., Campins H., Tsiganis K., et al., 2010, A&A, 513, A26

[4] Nedelcu D.A., Birlan M., Popescu M., et al., 2014, A&A, 567, L7

[5] Nesvorný D., Vokrouhlický D., Morbidelli A. & Bottke W.F., 2009, Icarus, 200, 698

[6] Simms M., 2021, Geology Today, 37, 225

[7] Todorović N., 2018, MNRAS, 475, 601

[8] Granvik M.,  Morbidelli A., Jedicke R., et al., 2018, Icarus, 312, 181

[9] REBOUND (https://rebound.readthedocs.io/en/latest/)

[10] OrbFit (http://adams.dm.unipi.it/orbfit/)

How to cite: Kováčová, M.: Re-examination of the transportation abilities of the 5:2 MMR with Jupiter, Europlanet Science Congress 2024, Berlin, Germany, 8–13 Sep 2024, EPSC2024-565, https://doi.org/10.5194/epsc2024-565, 2024.

The close approach of the Near-Earth Asteroid 99942 Apophis with Earth in 2029 will shed light on this irregularly shaped object. Since its discovery in 2004, studies, observations, and missions to this object have been performed or planned. Brozović et al. (2018) derived the most recent polyhedron shape model of Apophis. The shape provides an accurate model to study the dynamics around the asteroid. In this work, we aim to study the dynamics around 99942 Apophis. We use the shape model to build a MASCON(mass concentration) model(Geissler et al. 1996) and we use this model to compute the Poincaré Surface of Section(PSS) as proposed by Borderes-Motta & Winter (2017). With this approach, we can map the dynamics around an irregular body, identifying families of periodic and quasi-periodic orbits, and regions of chaos. The stable regions mapped by the PSS indicate where observation missions can seek for structures of meteoroids orbiting the asteroid. Our study can also provide valuable information for space missions to the asteroid, such as safe regions where a spacecraft can pass though to approach to the asteroid. In future works, we will also study the effect of the Earth's gravitational perturbation during the 2029 approach on the families of periodic orbits.

References:

Borderes-Motta, G. & Winter, O. C. 2017, Monthly Notices of the Royal Astronomical Society, 474, 2452 (https://doi.org/10.1093/mnras/stx2958)
Brozović, M., Benner, L. A., McMichael, J. G., et al. 2018, Icarus, 300, 115–128 (https://doi.org/10.1016/j.icarus.2017.08.032)
Geissler, P., Petit, J. M., Durda, D. D., et al. 1996, Icarus, 120, 140 (https://doi.org/10.1006/icar.1996.0042)

How to cite: Borderes Motta, G., Kastinen, D., Kero, J., Valvano, G., Machado-Oliveira, R., Winter, O. C., and Sfair, R.: On the 3-Dimension dynamics in 99942 Apophis vicinity, Europlanet Science Congress 2024, Berlin, Germany, 8–13 Sep 2024, EPSC2024-798, https://doi.org/10.5194/epsc2024-798, 2024.

How to cite: Krüger, H., Strub, P., Sommer, M., Moragas-Klostermeyer, G., Sterken, V., Khawaja, N., Trieloff, M., Kimura, H., Hirai, T., Kobayashi, M., Arai, T., Hillier, J., Simolka, J., and Srama, R.: The interstellar dust detection conditions with the DESTINY+ Dust Analyzer , Europlanet Science Congress 2024, Berlin, Germany, 8–13 Sep 2024, EPSC2024-897, https://doi.org/10.5194/epsc2024-897, 2024.

Observational data have revealed an overwhelming amount of structure in Saturn's rings while indirectly inferring other structures. Most of the finest density variations are likely to have some internal origin. Two mechanisms have been proposed to explain the sub-kilometer scale structures observed in Saturn's inner-A and B rings: viscous overstability manifested as spontaneous growth of axisymmetric oscillations (Schmit & Tscharnuter, 1995) and self-gravity causing the emergence of transient tilted filamentary density-enhancements (Salo, 1992). Numerical experiments have indicated that both structures, overstable oscillations and self-gravity wakes, can coexist for certain ring physical and collisional properties (Salo et al., 2001). In particular, the importance of self-gravity relative to the disrupting tidal force of the planet, characterized by the r_h parameter, requires to be moderately weak for overstability to occur. However, the exact nature of the relationship between these two mechanisms is still poorly understood. Ballouz et al. (2017) have revealed that friction may mediate this interplay and, therefore, play a role in defining the final structure of the ring by allowing overstability to tolerate substantially stronger self-gravity, surviving in simulations with increased r_h.

As a first step towards a better understanding of the interplay between self-gravity and viscous overstability, we have investigated in a recent study the onset of viscous overstability in self-gravitating rings (Mondino-Llermanos & Salo, 2023, hereafter MS2023). The study involved performing an extensive survey of N-body simulations, covering a wide range of dynamical parameters. Dynamical simulations carried out using SoftIS code (Mondino-Llermanos & Salo, 2022) were restricted to the case of identical particles, leaving the cases of particle size distribution unexplored.

Salo et al. (2001) showed that overstability develops in simulations with a broad particle size distribution, albeit under more stringent conditions. Size distribution increases stability, presumably due to the increased velocity dispersion achieved by small particles. However, with an increase in dissipation, overstability is again achieved, even with size distribution. Therefore, we have extended our recent survey by performing particle size distributed simulations.

Figure 1: Examples of highly dissipative (ε=0.1) simulations with different particle size distribution widths. Left frame: Monte Carlo ray tracing image of a typical snapshot, seen from B=90° viewing direction and illuminated from B'=25°. Middle frame: Slice of the same snapshot through the equatorial plane. Label indicates the computed A₄₀ asymmetry amplitude (for definition see French et al., 2007). Right frame: Time-averaged surface density autocorrelation function. Label and red line indicate the effective wake pitch angle calculated from the longitude of minimum I/F brightness. Contour levels correspond to 10-50% overdensities.

We investigate the effect of size distribution on the viscous properties of the ring. The results support that measured total viscosity in Saturn's A-ring with a prominent wake structure should be a proxy for the contribution of gravitational torques. On the other hand, in agreement with results from MS2023, the presence of viscous overstability in the B-ring indicates that the non-local contribution is dominant in this region.

Figure 2: Comparison of the various contributions to total viscosity as a function of size distribution width for weak (left) and strong (right) self-gravity. The quantity R₀ in the normalization corresponds to the identical particle size that yields the same optical depth and surface density. Dashed lines indicate the gravity contribution estimated from Daisaka et al. (2001) viscosity formula. In all simulations, τ=1 and ε=0.1. Surface density is fixed in each frame.

We present the main consequences of incorporating this additional dimension in the parameter space together with a review of the factors determining the threshold density required for triggering viscous overstability and its subsequent suppression.

Figure 3: Examples of how size distribution affects the ring structure (simulations marked in Fig.2). 

Small-scale, systematically oriented density inhomogeneities covering a wide fraction of the ring area lead to a longitude-dependent brightness of the rings. The coexistence of overstable axisymmetric oscillations with inclined wake structures can lead to even more complicated photometric behavior as a function of illumination and viewing geometries.

We then present a detailed survey of the effects of the main dynamical parameters on the expected properties of self-gravitating planetary rings. Such an analysis employs our newly extended set of simulations in combination with the photometric simulation method in French et al. (2007). Figure 4 illustrates the consequences of self-gravity wakes and overstable oscillations on the ring brightness variations as a function of W, the width of the particle size distribution.

Figure 4: Effects of size distribution in the amplitude and longitude of minimum brightness with respect to ring ansa for simulations in Fig.2.

Our models emphasize the importance of size distribution in tandem with the strength of self-gravity. In a weak-gravity regime, increasing W can shift an overstable system to a wake-dominated system due to the increased strength of self-gravity resulting from increased filling factor inside the wakes (Fig.3). In the case of strong-gravity, size distribution reduces the asymmetry amplitude, although wakes remain dynamically strong (Figs. 2 and 4).

Finally, we apply the modeling tool to Saturn's rings to constrain the physical parameters of the ring particles based on the comparison with Hubble Space Telescope observations of the azimuthal asymmetry of the ring brightness. Constraints provided by opacity and viscosity measurements of B and A rings are also analyzed.

The models can match the constraints imposed by the azimuthal asymmetry and reproduce well the A and B ring opacity profiles. Moreover, the inclusion of size distribution significantly improves the match to observations. However, analysis of the HST asymmetry observations suggests very low internal densities ρ∼250kg/m3. Although this is a robust result, to be consistent with the measured A-ring viscosities, the possibility remains that particles are strongly affected by adhesion forces, in which case the particles could have significantly higher densities. This possibility is preliminarily addressed using hybrid models (see MS2023) that mimic these forces by leading to more vertically flattened self-gravitating wake structures.

How to cite: Mondino Llermanos, A. and Salo, H.: Dynamical and photometrical model of Saturn’s A and B ring, Europlanet Science Congress 2024, Berlin, Germany, 8–13 Sep 2024, EPSC2024-993, https://doi.org/10.5194/epsc2024-993, 2024.