The Lucy spacecraft encountered the Main Belt asteroid (152830) Dinkinesh on 01 November 2023 revealing it to be a binary system with a first-of-its-kind contact binary secondary, now named Selam. However, despite the novelty of Selam’s structure, most aspects of the Dinkinesh system can be considered typical in the broader context of similar Main Belt (MB) and Near-Earth Asteroid (NEA) binary systems.

Groundbased lightcurve photometry and imaging by Lucy throughout its encounter were employed to constrain Dinkinesh’s spin state. Ground-based lightcurves obtained from November 2022 to February 2023 showed a lightcurve with an amplitude of 0.39 magnitudes and a period of T = 52.67±0.04 hrs [1]. Lucy’s L’LORRI instrument imaged the system during the encounter. Most relevant for understanding the spin state are resolved images obtained during the short period around close approach and a series of unresolved images obtained hourly from +4 hours to +95 hours after close approach at a phase angle of approximately 60°. The Lucy data have the advantage of a known configuration for the components that can be used to interpret the lightcurve.

Imaging during close approach was able to identify retrograde rotation of the primary, Dinkinesh, ruling out a doubly synchronous system. No indication of rotation was observed for the secondary, Selam.  Thus, interpretation of the combined lightcurve data requires separating the lightcurves of the two components. Using an iterative process, it was possible to identify a period for the primary of 3.7387 ± 0.0013 hr [2,3] with a relatively low amplitude as seen in Figure 1a. After subtracting this from the combined lightcurve, Selam’s period is determined as 52.04±0.14 hrs with almost a factor of two amplitude (figure 1b). This is consistent with the period found from the longer time-baseline, lower-uncertainty ground-based observations and indicates a singly synchronous system. Furthermore, eclipse mutual events are observed spaced half a rotation apart, shown by the red data points. The timing of these eclipses indicates that the satellite orbit is retrograde and nearly in the plane of Dinkinesh's heliocentric orbit.

Tidal forces, YORP, and BYORP, play a role in shaping the dynamics of the system. Tidal alignment of the long axis of a satellite radial to the primary occurs rapidly, typically t_sync < 10⁵ yr [4,5]. Spin-pole and orbit-pole reorientation by YORP has a timescale of less than 1 Myr for the spin-pole to approach 0/180° [5,6]. A more comprehensive simulation [7] finds the current spin state and semimajor axis is consistent with tidal and radiative forces operating on 1-10 Myr timescales. These times are consistent with the ~few Myr age of the surfaces as estimated from crater counts [8].

With a period of 52.67±0.04 hrs and a semimajor axis of 3.11±0.05 km, as measured from flyby imaging, the system mass is found to be M_sys = 4.95 ± 0.25 × 10¹¹ kg [4]. Assuming the components have equal densities and using volumes derived from imaging and shape models [9], the system angular momentum can then be derived. This can be compared to the angular momentum of an object with the system mass spinning at maximum frequency corresponding to a period of ~2.13 hours [10]. The ratio of the current angular momentum to the maximum possible is written as a_L. When this ratio has a value near one, it points to formation from a spin-up fission event [11]. For Dinkinesh we find a_L = 0.88±0.2.

Figure 1. The separate lightcurves of Dinkinesh (panel a) and Selam (panel b) are shown plotted as flux vs. rotational phase. In this figure, reproduced from [4], the period for Dinkinesh is 3.7387±0.0013 hrs and that for Selam is 52.04±0.14 hrs. Red data points indicate observed mutual events. The Sun symbol icon with arrows shows where mutual eclipse events should be seen, yellow for a retrograde orbit and green for prograde. Only a retrograde orbit is consistent with the lightcurve. Mutual events as seen from Lucy are also indicated. None were seen indicating that the inclination of Selam's orbit must be less than ~4° based on the geometry of Lucy's trajectory relative to that of Dinkinesh.

Taken altogether, the dynamical state of the Dinkinesh–Selam binary is fully consistent with formation via YORP spin up triggering a mass-shedding event and formation of a debris ring that later evolves to form both the observed equatorial ridge and the satellite. Dinkinesh shares properties with many similar systems [12,13,14] that, it can be assumed, have followed a similar evolutionary path. However, as only the second such system to be studied at close range by spacecraft, Dinkinesh shows that additional levels of previously unnoticed complexity may be common features in this class of object.

Acknowledgements: The Lucy mission is funded through the NASA Discovery program on contract No. NNM16AA08C. The authors thank the entire Lucy mission team for their hard work and dedication.

References:  [1] Mottola, S. et al. (2023) MNRAS, 524, L1-L4. [2] Buie, M. et al. (2024), LPSC 2024. [3] Levison, H. et al. (2024), Nature, in press. [4] Jacobson, S. A. and Scheeres, D. J. (2011) Icarus, 214, 161. [5] Pravec, P. et al. (2012) Icarus, 218, 125. [6] Statler, T. (2015) Icarus, 248, 313. [7] Merrill C. C., et al. (2024) A&Ap 684, L20.  [8] Marchi et al. (2024), LPSC 2024. [9] Preusker, F. et al. (2024) LPSC 2024. [10] Pravec, P., and Harris, A. W. (2000) Icarus 148, 1, 12-20. [11] Pravec, P. and Harris, A. W. (2007) Icarus, 190, 250. [12] Pravec, P. et al. (2016) Icarus 267, 267-295. [13] Pravec, P. et al. (2012) Icarus, 218, 125. [14] Johnston, W. R. (2019) NASA Planetary Data System.

How to cite: Noll, K., Spencer, J., Buie, M., Levison, H., and Marchi, S. and the Lucy Team: The Dynamical State of the Dinkinesh - Selam Binary, Europlanet Science Congress 2024, Berlin, Germany, 8–13 Sep 2024, EPSC2024-463, https://doi.org/10.5194/epsc2024-463, 2024.

ABSTRACT

Planetary surfaces present binary craters that can be associated with the synchronous impact of binary asteroids. In this work, we identify binary craters on asteroids (1) Ceres and (4) Vesta, and aim to characterize the properties (size ratio and orbital plane) of the binary asteroids that might have formed them. We used global crater databases developed in previous studies and mosaics of images from the NASA DAWN mission. We established selection criteria to identify craters that were most likely a product of the impact of a binary asteroid. We find geomorphological evidence of synchronous impacts on the surfaces of Ceres and Vesta. The associated binary asteroids are widely separated and similar in diameter in contrast to the current census of binary asteroids. The distributions of the orientation of these binary craters on both bodies are statistically different from numerical impact simulations that assume binary asteroids with coplanar mutual and heliocentric orbits. These findings agree with a population of well-separated and similarly sized binary asteroids with non-zero obliquity that remains to be observed.

INTRODUCTION

Planetary surfaces present binary craters that are associated with the synchronous impact of binary asteroids. The detection and characterization of satellites of small asteroids rely on observations by radar echoes for near-Earth asteroids (NEAs) [1] and optical light curves for both NEAs and main belt asteroids (MBAs) [2]. Although these observations are efficient and precise, they are biased by a limited range from the Earth for radar observation and a strong preference for compact and low-obliquity systems for light curves.

To have a better understanding of the distribution of the binary asteroid population in the Solar System, we created a catalog of binary craters for Ceres and Vesta that are associated to binary asteroids that might have formed them, focusing on the size ratio and orbital plane of the binary system. Out catalog was based on the global crater databases of Ceres [3] and Vesta [4], combined with high altitude mapping orbit (HAMO) and low altitude mapping orbit (LAMO) images for each body from the NASA’s DAWN mission [5].

METHODS

Airless planetary objects have their surfaces covered by craters but proximity between two of them is not enough to determine if they are product of the impact of binary asteroids. We created a criterion of classification for binary craters on Ceres and Vesta which main aspects are that:

• The pairs of craters must be in contact and show a septum. We cannot label objects separated as synchronous because there is no ejecta blanket surrounding them since their surfaces are not hydrated enough.
• These craters should not exhibit poligonality, which has been observed on Ceres [6], since this feature can be confused with a pair having a septum and be misidentified as synchronous.
• An inspection on the surroundings is critical to avoid identifying possible secondary craters from previous impacts as a binary asteroid.
• Each pair of craters must have a similar degradation state, and similar depth when they have a similar size.

We established a level of confidence in our catalog and distinct between likely and very likely pairs of craters. We compared our results according to their main-to-secondary diameter ratio, the separation between the craters, the morphological classification of the binary system [7] and the orientation of the line that connects the center of both craters. We also found ranges for the sizes of the impactors which formed the binary craters.

RESULTS

We identified 39 and 18 synchronous impacts on the surfaces of Ceres and Vesta, respectively. Some examples are shown in Fig. 1, in which the contact between all rim pairs is characterized by a continuous septum without any visible stratigraphic relationship, as well as a similar preservation state, thus indicating a very likely synchronous formation. We note that in the case of the pairs on Vesta presented here, an excess of ejecta material is visible in the direction of the septum, which is expected in the case of a binary asteroid impact [7].

Fig. 1. Examples of binary craters identified on the surface of Ceres (top) and Vesta (bottom). Background imagery: LAMO mosaic

We compared the orientation of the binary crater with the numerical simulations considering a population of binary asteroids with zero obliquity impacting a surface. We performed a two-sample Kolmogorov-Smirnov test [8] to determine if the distribution of the observed and simulated orientation is similar (null hypothesis). We found that for values of significance level between 0.01 and 0.2, the D-statistic resulting from the tests on both Ceres and Vesta is always higher than the significance level. Hence, there is a significant difference between the distributions of the simulations and the observations. These results support what was found by a previous study on Mars [8]: binary craters on planetary surfaces cannot be explained by a population of binary asteroids with zero obliquity.

SUMMARY AND OUTLOOK

Our findings are consistent with well-separated and similarly-sized binary asteroids. Additionally, comparing our catalogs with numerical simulations indicates a non-zero obliquity. A population with these characteristics remains to be observed, as suggested by a previous study of binary craters identified on Mars.

Considering the recent discoveries of unexpected satellites (e.g., around Dinkinesh and Arecibo, during Lucy flyby and using Gaia astrometry [9]), the current census of binary asteroid systems is likely biased. Future observations using for instance astrometry or stellar occultations may reveal satellites that have so far remained beyond the reach of direct imaging, light curves, and radar echoes [10,11].

REFERENCES

[1] Benner et al., 2015; [2] Pravec et al., 2006; [3] Zeilnhofer & Barlow, 2021a; [4] Liu et al., 2018; [5] Russell et al., 2015; [6] Zeilnhofer & Barlow, 2021b; [7] Miljkovic et al., 2013; [8] Vavilov et al., 2022; [9] Tanga et al., 2023; [10] Pravec & Scheirich, 2012; [11] Segev et al., 2023.

How to cite: Herrera, C., Carry, B., Lagain, A., and Vavilov, D.: Binary craters on Ceres and Vesta and implications for binary asteroids , Europlanet Science Congress 2024, Berlin, Germany, 8–13 Sep 2024, EPSC2024-1009, https://doi.org/10.5194/epsc2024-1009, 2024.

1. Introduction

Binary asteroids are found throughout the Solar System at a wide range of size scales. Their formation mechanisms are also diverse. Km-sized systems are generally thought to form by rotational disruption of the primary resulting from radiative torque, large main-belt systems are thought to form by collisions, while binaries in the Kuiper Belt are thought to be primordial, forming directly from the streaming instability. This study primarily focuses on ~ km-sized binaries found among both the near-Earth asteroids (NEAs) and main-belt asteroids (MBAs). These systems are small and close enough to the Sun that radiation forces play an important role in their long-term evolution. Understanding their long-term dynamics is crucial to trace back their evolution and estimate their lifetime, which also provides information on physical properties and geologic structures of asteroids.

It is widely accepted that the long-term dynamics of binaries are dominated by tides and the Binary YORP (BYORP) effect, which is a radiative torque that modifies the orbit of the secondary asteroid (Cuk & Burns, 2005). Tidal dissipation can either drive the secondary outward or inward, depending on whether the secondary's mean motion is slower or faster than the primary's spin (Murray & Dermott, 1999).

In this work, we investigate the Yarkovsky effect that has been largely overlooked in the context of the long-term evolution of binary asteroids. The Yarkovsky effect, which is the radiation force raised on the afternoon side of a rotating object, has been well studied for single asteroids (Vokrouhlicky, 1999). However, its impact on binary asteroids remains less explored.

2. Results

The Yarkovsky effect on a binary consists of two components: the Yarkovsky-Schach (YS) effect and the planetary Yarkovsky effect. The YS effect is caused by: (1) elimination of the satellite irradiation by sunlight when it is located in the primary shadow; and (2) the related asymmetric thermal cooling and heating of the secondary after it enters and exits the shadow  (in fact, there is also a similar effect on the primary related by the shadow of the secondary, but this produces smaller dynamical perturbation). This effect was noticed for binary asteroids too, but not studied in detail yet (Vokrouhlicky et al, 2005). The planetary Yarkovsky effect is simply the Yarkovsky effect caused by the primary's radiation instead of the Sun. 

We find that for prograde secondaries (ε < 90^o), the Yarkovsky effect tends to drive the secondary towards the synchronous orbit a_syn determined by n = ω, while for retrograde secondaries (ε > 90^o), the Yarkovsky effect always drives the secondary outward until it leaves the system. The timescale for the orbital migration of the Yarkovsky effect is roughly 0.1 Myrs, depending on the physical properties of the binary. This brings us new insights about the mechanism of the synchronization of binary asteroids and the underlying reason why the majority of binary asteroids are found to be in synchronous states. Our calculations also predict that the secondary asteroids with spin periods shorter than 4.3 hours (the orbital period around the Roche limit) will fall into the Roche limit quickly driven by the Yarkovsky effect and then get tidally disrupted, reshaped or accreted on the primary. In addition, some asynchronous binaries might be in the Yarkovsky-tide equilibrium state where the orbit does not drift, but such a state may be quickly broken by the YORP effect or tides. For retrograde secondaries, the Yarkovsky effect would drive them outward until they leave the binary system due to planetary perturbations or collisions, producing asteroid pairs. In this scenario, the two components of the asteroid pair would exhibit opposite spin directions. 

We found that the synchronization of the Dinkinesh-Selam system discovered by the Lucy spacecraft could be due to the Yarkovsky effect, considering that tides are weak for such a distant secondary. In addition, we calculated the possible Yarkovsky effect on Didymos-Dimorphos system in its state following the impact of the NASA DART mission, which might have perturbed it into an asynchronous state. The Yarkovsky-induced semimajor axis drift rate is ~7.6 cm/yr. This could be examined by in-situ observation conducted by the space mission ESA Hera during its rendezvous with Didymos in late 2026.

References

Ćuk, M., & Burns, J. A. (2005). Effects of thermal radiation on the dynamics of binary NEAs. Icarus, 176(2), 418-431.

Murray, C. D., & Dermott, S. F. (2000). Solar system dynamics. Cambridge university press.

Vokrouhlický, D. (1999). A complete linear model for the Yarkovsky thermal force on spherical asteroid fragments. Astronomy and Astrophysics, v. 344, p. 362-366 (1999), 344, 362-366.

Vokrouhlický, D., Čapek, D., Chesley, S. R., & Ostro, S. J. (2005). Yarkovsky detection opportunities: II. Binary systems. Icarus, 179(1), 128-138.

How to cite: Zhou, W.-H.: The Binary Yarkovsky Effect: A New Mechanism for Changing the Mutual Orbits of Asynchronous Binary Asteroids. , Europlanet Science Congress 2024, Berlin, Germany, 8–13 Sep 2024, EPSC2024-157, https://doi.org/10.5194/epsc2024-157, 2024.

Many binary asteroid systems (‘Binary systems’) are believed to originate from Yarkovsky–O’Keefe–Radzievskii–Paddack (YORP) deformation; that is, the YORP spin-up of an asteroid triggers the rotational failure, and the material shed from the main body finally reaccumulates and forms its satellite(s). A binary system can form from a single YORP shedding event (‘SSh’), or from a sequence of such events (‘MultiSh’). In the latter one, a satellite formed in the first shedding event, thereby in the subsequent shedding events the evolution of shed material is influenced by the presence of this first-generation satellite. These different scenarios can result in various final configurations of binary systems. We aim to systematically investigate this relevance, and thereby obtain a ‘map’ of the various formation paths of binary systems.

Our work primarily focuses on the MultiSh scenario, which is rarely concerned in previous works. We use 2 dimensionless parameters to characterize the perturbation effects of a satellite to the shed material. With semi-analytical investigation and discrete element method (DEM) simulations, we reconstructed the links between the character of an already-existed satellite and the final dynamical configuration of the binary system. Special attention is also paid to binary systems whose satellite itself is a contact-binary, such as the Dinkinesh system. We propose that this kind of binary systems can only form through some specific and interesting formation paths.

This work has been supported by the National Natural Science Foundation of China grant No. 12372047.

How to cite: Dai, W.-Y., Cheng, B., Yu, Y., Baoyin, H., and Li, J.-F.: Formation paths of binary asteroid systems born from YORP deformation, Europlanet Science Congress 2024, Berlin, Germany, 8–13 Sep 2024, EPSC2024-679, https://doi.org/10.5194/epsc2024-679, 2024.

Abstract

One of the most important observables to characterize the packing behaviour and flowability of sand, dust and regolith over the terrestrial bodies of our Solar System is their granular angle of repose — the angle that the sloping side of a heap of particles makes with the horizontal. This angle depends, for instance, on particle size, because the smaller the grain diameter is, the more significant attractive forces between atoms and molecules on the surface of the grains be- come relative to particle weight. However, the dependence of the angle of repose on particle size and gravity has remained elusive. Here we elucidate this dependence by means of direct (particle-based) numerical simulations of granular heaps. We obtain a simple mathematical expression that reproduces a comprehensive set of experimental observations on the angle of repose as a function of particle size, as well as results from our simulations under gravity values from 0.06 to 100 times Earth’s gravity. Our model could find, thus, application to infer on particle size from extra-terrestrial granular slopes, for instance of impact craters and extra-terrestrial dunes. Moreover, our model suggests that the angle of repose on Mars or Pluto may be studied experimentally without any need of adjusting gravity, and by tuning, instead, particle size according to our mathematical expression.

Numerical Experiments

We investigate the particle dynamics using the Discrete-Element-Method [1], which consists of solving Newton’s equations for all particles in the system. We consider contact forces, sliding and rolling friction, as well as non-bonded attractive particle interaction (van der Waals) forces. Our reproduces the packing fraction and packing structure of fine polydisperse powders of different materials [2, 3]. Here we assume spherical SiO2 particles owing the broad range of experimental data available for validation.

To form the heaps, we pour the particles onto a frictional square horizontal plate of sides 40 d. The particles are inserted within a square cross-section of side length 4.4 d, which is cocentric with and extends from a height of 20 − 30 d above the plate. We pour in total 25, 000 particles and apply open boundaries (no vertical walls). Therefore, some particles abandon the simulation domain through its lateral borders and are not replaced by new ones. The final heaps are contain between 5, 000 and 14, 000 particles.

Results and Discussion

First we elucidate the dependence on the particle size by considering terrestrial gravity (Fig. 1). We find that our simulation results can be fitted well by the equation [4]

θ = tan^-1[μ · (1+D/d)]   (1),

with the effective friction coefficience μ≈0.45 and the characteristic length-scale D≈87 µm. We find that the term D/d encodes the effect of attractive van der Waals forces. Indeed, our results from numerical simulations without these forces can be described by the model θ = tan^-1[μ] [4].

Next, we vary the gravity level g̃ ≡ g/g_Earth from 0.06 to 100. We find that Eq. (1) fits our simulation results well over this entire broad range of g̃, provided D is adjusted according to D ≈ D_E ·g̃^-1/2, where D_E = 87 μm is the terrestrial value for D in Eq. (1). Therefore, if, for a granular material of given type, the values of D_E and μ are known (by fitting Eq. (1) to experiments on Earth), then, with our model, it is possible to estimate the particle-size-dependence of the angle of repose for this material under extra-terrestrial gravity. Our model is consistent with experimental observations in the Bremer drop tower and in parabolic flights, that granular materials behave more cohesively under lower gravity [5, 6]. For instance, we find that dry sand-sized (∼ 200 μm) SiO2 particles on Pluto would have angle of repose comparable to powdered sugar particles (∼ 50 μm) on Earth. Moreover,  due to the scaling of van der Waals forces and particle weight with d and d^-3g^-1, respectively, Eq. (1) leads to

θ = tan^-1[μ · (1+ β · Bo^1/2)]   (2),

where Bo is the Bond number, i.e., the ratio of attractive interaction forces to particle weight, and β ≈0.014. Figure 2 shows that Eq. (2) describes very well the results from our numerical simulations for all values of gravity. Currently, we are modelling the angle of repose with other types of particle-particle interactions. We also find that particle shape exert a crucial role and is indispensable to understand, for instance, the angles of repose of sand dunes on Earth and Mars.

Acknowledgements

We thank the German Research Foundation (DFG) for funding through the Heisenberg Programme and grant 348617785.

References

[1] Cundall, P. A. and Strack, O. D. L. A discrete numerical model for granular assemblies. Geotechnique 29, 47-65 (1979).

[2] Parteli, E. J. R., Schmidt, J., Blümel, C., Wirth, K.-E., Peukert, W. and Pöschel, T. Attractive particle interaction forces and packing density of fine glass powders. Scientific Reports 4, 6227 (2014).

[3] Schmidt, J., Parteli, E. J. R., Uhlmann, N., Wörlein, N., Wirth, K.-E., Pöschel, T. and Peukert, W. Packings of micron-sized spherical particles ? insights from bulk density determination, x-ray microtomography and discrete element simulations. Advanced Powder Technology, 31:2293?2304 (2020).

[4] Elekes, F. and Parteli, E. J. R. An expression for the angle of repose of dry cohesive granular materials on Earth and in planetary environments. Proceedings of the National Academy of Sciences of the USA, 118, e2107965118 (2021).

[5] Hofmeister, P. G., Blum, J. and Heisselmann, D. Flows of dense granular media. Annual Review of Fluid Mechanics 40, 1-24 (2008).

[6] Kleinhans, M. G., Markies, H., de Vet, S. J., in’t Veld, A. C. and Postema, F. N. Static and dynamic angles of repose in loose granular materials under reduced gravity. Journal of Geophysical Research 116, E11004 (2011).

Figure 1: Angle of repose under Earth’s gravity [4]: Blue squares denote our simulation results, the other symbols denote experimental observations, while the continuous line is the best fit using Eq. (1).

Figure 2: Angle of respose as a function of the Bond number, which scales with 1/(d² g) [4]: Symbols denote our simulation results, the continuous line denotes the best fit using Eq. (2).

How to cite: Parteli, E. and Elekes, F.: A model for the angle of repose of granular matter in extra-terrestrial environments, Europlanet Science Congress 2024, Berlin, Germany, 8–13 Sep 2024, EPSC2024-643, https://doi.org/10.5194/epsc2024-643, 2024.

Recent observations of asteroid satellites with unexpected shapes, such as the spherically oblate Dimorphos observed by NASA’s DART mission [1] or the bilobate contact binary satellite Selam imaged by the Lucy spacecraft [2], have highlighted the complexity of binary asteroid formation. Previous theories focused on long-term spin-up of rubble pile asteroids leading to slow, continuous mass-shedding [3] or rotational fission [4] can account for the predominantly prolate population given their shape due to tidal forces, keeping the satellite's shape intact and often putting it in a synchronous orbit but struggle to explain the existence of Dimorphos and Selam [5,6]. Scenarios where the spinning asteroid has increased structural integrity due to e.g. a small amount of cohesion [7] lead to debris disks that extend to the fluid Roche limit of the primary, generated from a rotational failure that results in an instantaneous, chaotic mass-shedding [5,6]. In our work, we have investigated and identified the dynamical mechanisms that determine the shape of satellites in such disks using a combination of three-dimensional smoothed-particle hydrodynamics (SPH) and non-spherical N-body codes [6].

In our method, we performed two series of spin-up simulations of a Ryugu-like and a Didymos-like primary body with the Bern SPH code [8]. Then, we used the initial conditions generated from the resulting debris disks post rotational failure to study satellite formation with the N-body code GRAINS [9]. To transition between the two different codes, we perform a hand-off. This is necessary due to SPH needing a large number of particles (around 10⁶) to improve realism which would significantly slow down an N-body simulation. Moreover, SPH particles are constituents of a smoothed continuum and will as a result often overlap physically which causes numerical issues for N-body codes. The interface detects clusters of SPH particles and generates single, angular bodies based on the physical properties of the group. Due to the resolution of the SPH simulations where we used 50,000 particles, the minimum diameter of each N-body particle post hand-off (determined by the mass of single SPH particles) is 20 m, which is significantly larger than the diameters of boulders observed on the surface of e.g. Dimorphos which range between 1 m and 16 m [10].

For the rotational failure scenario of the Ryugu-like primary, the debris disks radially extended for 2 primary radii, had a thickness of 0.4 primary radii and masses of on average 4.5% of the primary mass. Snapshots from an example simulation where for a debris disk mass of 5.5% primary mass can be found in Figure 1. The formation process in this type of disks that extend beyond the fluid Roche limit is rapid and largely hierarchical, where the largest remnant will contain most of the mass as it accretes smaller aggregates and single particles and reaches masses of 1% of the primary in a matter of days. However, due to the width of the disk, additional aggregates can form and survive without getting tidally disrupted. This proves to be a key dynamical mechanism, as these surviving satellites can merge with the largest remnant, reshaping it and breaking its often synchronous orbit. The chaotic and unpredictable nature of the formation process also leads to significant perturbation of satellite orbits and they sometimes undergo close encounters with the primary, which leads to tidal disruption events.

Figure 1: Snapshots for a hand-off simulation. The merger occurring during the period between the two final images determines the shape of the satellite as the two prolate satellites merge side-to-side, forming a more oblate body [6].

Due to the hierarchical nature of the process, the mass ratio between the impactor and the largest remnant during a shape-defining satellite merger usually satisfies 0.5. Moreover, the impact velocities for the mergers in our simulations are below one mutual escape velocity, which leads to a soft impact which pads the shape of the largest remnant rather than compacting it. If the merger occurs side-to-side, the resulting shape of the satellite is more oblate, while edge-to-edge mergers generate bilobate objects. Our results further indicate that only systems where the largest remnant has undergone a significant tidal disruption event before the shape-defining merger can form satellites as oblate as Dimorphos. This is due to the mass-shedding that occurs during these tidal events, which makes the aggregate less prolate and easier to deform into an oblate shape with mergers. With upcoming space missions such as ESA’s Hera [11] which will return to Dimorphos in 2027, the shape and structure of oblate spheroids can be further constrained which will help us improve our model and understanding of the underlying formation process.

References
[1] Daly et al. Nature, 616(7957):443–447, 2023.
[2] Levison et al. Nature, submitted, 2024.
[3] Walsh et al. Nature, 454(7201):188–191, 2008.
[4] Jacobson and Scheeres. Icarus, 214(1):161–178, 2011.
[5] Agrusa et al. PSJ, 5(2):54, 2024.
[6] Wimarsson et al. Icarus, submitted, 2024.
[7] Hirabayashi et al. ApJ, 808(1):63, 2015.
[8] Benz and Asphaug. Icarus, 107(1):98–116, 1994.
[9] Ferrari et al. Multibody System Dynamics, 39:3–20, 2017.
[10] Pajola et al. Nature Communications, submitted, 2023.
[11] Michel et al. PSJ, 3(7):160, 2022

How to cite: Wimarsson, J., Xiang, Z., Ferrari, F., Jutzi, M., Madeira, G., Raducan, S. D., and Sanchez, P.: Rapid formation of binary asteroid systems post rotational failure: a recipe for making atypically shaped satellites, Europlanet Science Congress 2024, Berlin, Germany, 8–13 Sep 2024, EPSC2024-264, https://doi.org/10.5194/epsc2024-264, 2024.

Introduction:

The evolution of rotation rates of small asteroids is subjected to mechanisms including (1) The Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) effect [1]: a thermophysical process that arises from the anisotropic thermal re-radiation of absorbed sunlight from a non-axially symmetric surface, resulting in a net torque that can secularly modify the bulk rotation rate. (2) Off-spin-axis collisions by a small projectile [2]: such collisions can change the spin state of an asteroid through the exchange between the projectile orbital angular momentum and the impacted body rotational angular momentum. (3) Planet/star close encounters: asteroids may experience close encounters with planets or their parent star, resulting in tidal forces that change their rotation state [3]. The relative significance of each mechanism depends on the interplay between the sizes, shapes, compositions, structures, and geometries of the interactions.
It has been proposed that the YORP effect may gently spin up small asteroids close to or beyond their breakup limit, assuming the effect is constant and unaltered with time by bulk deformation or spin orientation changes. This will cause gradual mass shedding from their surface, which leads to the formation of satellites [4, 5]. Alternatively, a single strong collisional event or strong tidal encounter may abruptly spin up the body well beyond the breakup limit, causing sudden fission. The significant amount of mass detached from the original body can be efficient at forming satellites. This process has not been thoroughly investigated with realistic asteroid structures, prompting the present numerical study of sudden spin-up events as a mechanism for forming binary asteroids.

Method:

Many studies usually use spherical components to simulate rubble-pile asteroids, in mono- or poly-dispersed distribution. The possible drawbacks are, for example, it prevents a suitable packing fraction in a real aggregate and overlooks the fact that real angular particles have larger friction forces than rounded particles. Therefore, we developed a pipeline called “SHattering EXperiments to Synthetic Shapes through PhotogrammetrY” (hereafter SHEXSSPY) to better reproduce the realistic shapes and mass distribution of internal components using real fragments from shattering experiments [6] (see Fig. 1 for the illustration of the pipeline). Using SHEXSSPY, asteroids are modelled as gravitational aggregates with realistic components. The sudden spin-up events can then be simulated with an updated SSDEM implementation of the PKDGRAV N-body gravity code for the handling of non-spherical components [7, 8, 9, 10].

Fig. 1. Illustration of the SHEXSSPY pipeline.

Results:

We find that relatively large fragments and clumps can detach from the original body and potentially evolve into a binary system (Fig. 2), asteroid pair, contact binary, or simply be disrupted, depending on the spin-up conditions. A significant proportion of the internal structure of the satellite formed through the fission event may come from material well beneath the surface of the primary. This may be different from the YORP-induced binary formation mechanism, where the satellites are mainly formed by material from the surface of the primary [4].

Fig. 2. Satellites formed in this study. The mass ratio between each satellite and the primary, the semimajor axis, and eccentricity of the satellite’s orbit are shown in the plot.

Acknowledgments:

P-YL, ACB, and PGB acknowledge funding by the NEO-MAPP project through grant agreement 870377, in the frame of the EC H2020-SPACE-2018-2020 / H2020-SPACE-2019. ACB and PBL acknowledge funding by the Ministerio de Ciencia e Innovación (PGC 2018) RTI2018-099464-B-I00. P-YL acknowledges funding from the ESA OSIP programme (4000136043/21/NL/GLC/my). LMP acknowledges the CIAPOS/2022/066 postdoctoral grant Generalitat Valenciana (European Social Fund). PB acknowledges the María Zambrano 2021-2023 retraining plan (ZAMBRANO22-04). JCM acknowledges the NASA FINESST grant No. 80NSSC20K1392. JVD acknowledges the NASA FINESST Award No. 80NSSC21K1531.

References:

[1] Rubincam, D., 2000, Icarus 148, 2–11.

[2] Marzari, F., Rossi, A., Scheeres, D. J., 2011, Icarus 214, 622–631.

[3] Scheeres, D. J., Marzari, F., Rossi, A., 2004, Icarus 170, 312.

[4] Walsh, K.J., Richardson, D.C., Michel, P., 2008. Nature 454, 188–191.

[5] Walsh, K.J., Richardson, D.C., Michel, P., 2012. Icarus 220, 514–529.

[6] Durda, D. D. et al., 2015. Planetary and Space Science 107, 77-83.  

[7] Richardson, D. C. et al., 2000, Icarus 143, 45–59.

[8] Stadel, J. G. 2001, Ph.D. Thesis, 3657.

[9] Schwartz, S. R. et al. 2012, Granular Matter 14, 363–380.

[10] Marohnic J. C., et al. 2023, PSJ 4, 245.

How to cite: Liu, P.-Y., Campo Bagatin, A., Schwartz, S. R., M. Parro, L., Bartczak, P., Benavidez, P. G., DeMartini, J. V., Marohnic, J. C., and Richardson, D. C.: Formation of binary asteroids via abrupt spin-up events., Europlanet Science Congress 2024, Berlin, Germany, 8–13 Sep 2024, EPSC2024-110, https://doi.org/10.5194/epsc2024-110, 2024.

Introduction

Rubble-pile asteroids, which are defined to be bodies consisting of loosely consolidated material that is mainly held together by gravity, are currently believed to be a significant part of the asteroid population. The origin and evolution of these types of bodies are governed by granular mechanics and are highly dependent on external excitations like meteoritic impacts, the YORP effect, and planetary encounters[1]. Universal modelling of granular systems is one of the major unsolved topics in physics, as these systems are chaotic, multi-scale, and highly dependent on the non-linear interactions between their constituent particles. Most analytical models are derived on the basis of continuity of the body and omit their complex granular nature [2]. These models can explain some observations, but are not capable of fully modelling their complex dynamics. On the other hand, numerical simulations implementing different contact models and particle properties have shown a great potential to predict the evolution of these systems. However, their long computation times and sensitivity to initial conditions make it harder to generalize their results. This work tries to bridge the gap between numerical and analytical modelling of rubble pile asteroids, by using the data produced by numerical simulations to derive a set of analytical equations of motion that can be generalized to systems outside the generated simulation dataset.

GRAINS

In this work the GRAINS N-body code is used [3] to obtain high-fidelity simulation data for the shape dynamics inference. GRAINS models both the gravitational attraction between different particles in the simulation, together with the interaction upon contact between two complex shaped particles.  The inclusion of the shape of individual particles increases the fidelity of particle-particle interactions compared to the spherically shaped particles that are mostly used in other N-body simulation. The state of each particle is saved over time and converted to some macroscopic state variable. These state variables can be physical variables like energy, the moments of inertia, or some angular momentum components. Besides the state variables, other environment, i.e. static, variables like the spin-up rate and bulk density are considered as well. Then, multiple simulations can be run with different values for the environment variables to obtain a large dataset containing different dynamical regimes, see Figure 1.

Figure 1 Three different GRAINS simulations at different time snapshots.

Sparse Symbolic Regression

Symbolic regression techniques aim to identify functional relationships present in large datasets. Machine learning based methods like genetic programming or neural networks have been shown to work well in predicting complex non-linear dynamical systems from data. However, key properties of good analytical models, like interpretability and generalizability, are often neglected by these methods. For this reason, the sparse identification of non-linear dynamics (SINDy) method was developed in [4]. The SINDy method avoids this problem by applying a sequential thresholding least-squares algorithm to the problem to promote sparsity in the final equations of motion. This research takes the data produced by GRAINS and uses the SINDy method to identify the analytical governing dynamical equations. Allowing for more in-depth analysis of the data produced by these simulations.

Results

Some first results were produced by taking a set of 110 simulations from GRAINS with each simulation consisting of a different combination of initial spin rate, and bulk density. Each simulation consists of 800 particles and runs for 5 hours in simulation time. As is common for regression problems, to avoid overfitting only 80 percent of simulations were given to SINDy to generate a model, and the other 20 percent were used as a validation test set. A relatively simple SINDy model was created using a 3rd degree monomial function library, tuning the thresholding value to obtain a satisfactory result. A comparison between the time evolution of the rubble pile’s moment of inertia ratio for one of the validation simulations and the produced SINDy model is given in Figure 2. The arrows represent the dynamics of the system, and the solid line is the result from GRAINS. Qualitatively, the simulation follows the arrows from the analytical model, which shows a spiralling structure towards an equilibrium point. Other coherent structures can be observed as well, which separate the flow into different regions

Figure 2 The flow field of the SINDy model (light color) compared to a GRAINS simulation.

Conclusion

The high reconstruction accuracy and the potential information that can be inferred from these models presented here show the promise of the SINDy method for modelling the granular mechanics of rubble-pile asteroid. These simulations only considered single initial shapes for each density and rotational rate setup, thus increasing the amount of data can improve the reliability of the analytical model. Furthermore, other simulation setups with more particles, large inner cores, or other external excitations that mimic the actual evolution of a rubble-pile asteroid will be included as well.

Acknowledgements

Funded by the European Union (ERC, TRACES, 101077758). Views and opinions expressed are however those of the authors only and do not necessarily reflect those of the European Union or the European Research Council. Neither the European Union nor the granting authority can be held responsible for them.

References

[1] Hestroffer D, Sánchez P, Staron L, et al (2019) Small Solar System Bodies as granular media. The Astronomy and Astrophysics Review 2019 27:1 27:1–64. https://doi.org/10.1007/S00159-019-0117-5

[2] Holsapple KA, Michel P (2006) Tidal disruptions: A continuum theory for solid bodies. Icarus 183:331–348. https://doi.org/10.1016/J.ICARUS.2006.03.013

[3] Ferrari F, Tanga P (2020) The role of fragment shapes in the simulations of asteroids as gravitational aggregates. Icarus 350:113871. https://doi.org/10.1016/J.ICARUS.2020.113871

[4] Brunton SL, Proctor JL, Kutz JN (2016) Discovering governing equations from data by sparse identification of nonlinear dynamical systems. Proc Natl Acad Sci U S A 113:3932–3937. https://doi.org/10.1073/PNAS.1517384113/SUPPL_FILE/PNAS.1517384113.SAPP.PDF

How to cite: Fodde, I. and Ferrari, F.: Data-driven Estimation of Rubble-pile Asteroid Granular Dynamics, Europlanet Science Congress 2024, Berlin, Germany, 8–13 Sep 2024, EPSC2024-1036, https://doi.org/10.5194/epsc2024-1036, 2024.