SB0
Session assets
The outer Solar System preserves a reservoir of material from the formation of our planetary system and provides evidence of the distant past. Objects in the Trans-Neptunian region have experienced little to no thermal or collisional processing, and objects classified as dynamically cold are expected to still be on primordial orbits. The orbital dynamics and physical structure of the objects found in the Trans-Neptunian region allow us to learn how the Solar System formed and developed. This distant region allows us to study the primordial building blocks of the Solar System that no longer exist in an unmodified form in the inner Solar System.
Objects in Mean Motion Resonance (MMR) with Neptune are one of the more significant populations in the distant solar system (beyond distances of 70 au). Resonant populations have very specific orbital characteristics (angular orbital elements, semi-major axis, etc.) that result in varying but quantifiable detectability for each resonance. We define distant resonances as those beyond, but not including, the 2:1 resonance. We include all resonances at semimajor axes greater than 48 au, and with a sufficient number of detections to be statistically relevant. Using recent improvements in the determination of the size-frequency distribution of the Kuiper belt we provide new estimates of the population sizes of these distant resonant orbits. These population estimates provide a key input into understanding the expectation for the discovery of objects at large heliocentric distances.
Our knowledge of the Trans-Neptunian region is incomplete. As we examine larger heliocentric distances our detection efficiency rapidly decreases. Trans-Neptunian Objects (TNOs) can only be directly observed in reflected sunlight which varies with an r-4 relationship. Due to the extreme faintness of TNOs at large heliocentric distances, an extremely significant population of objects could exist. At distances as close as 90 au [1] populations could rival the size of the known Kuiper belt while still escaping detection, see Figure 1. If every object in the Kuiper belt (Hr < 9) were concentrated into a narrow, low inclination ring, this ring would be on the cusp of detection at 100 au. It is clear that significant populations with novel structure and valuable insights into the Solar System could exist in the regions beyond 70 au where detection rapidly becomes increasingly difficult.
In order to examine this region, it is of vital importance to understand what we already know to exist in this distant region. While probing this region directly is very difficult, the population that resides there is not completely unknown. Known objects with semi major axis beyond ~70 au are usually either very large, on eccentric orbits, or both. Large objects are easier to detect as they reflect more light. Objects with eccentric orbits have perihelia much closer to the sun and therefore become much brighter allowing easier detection near their perihelion passage. The most prominent known populations with these large eccentricities are objects in resonance with Neptune, with many possessing large eccentricities and aphelion distances >70 au. As we probe fainter magnitudes, and therefore greater distances, it is important to be able to disentangle known populations from possible new populations.
The Vera C. Rubin Observatory Legacy Survey of Space and Time will revolutionize our understanding of the Solar System, however this survey will be less sensitive to the most distant Trans-Neptunian regions. LSST will increase the number of known TNOs by an order of magnitude. However, despite massively increased sky coverage, it will have a similar limiting magnitude as the OSSOS survey (~24.5). This results in an effective distance limit of 80-90 au for all but the most massive TNOs. See Figure 2 for a survey simulation of the OSSOS survey (orange points) and note the steep drop off in detections in the 80-90 au range. These results will be analogous to the depth of LSST, except with a much larger sky coverage for LSST. Furthermore, the currently planned LSST Deep fields are not on the ecliptic and will be insensitive to objects on low inclination orbits. This highlights the need for a dedicated deep drilling field on the solar ecliptic to enable the exploration of possible in-situ formed component in the distant Solar System.
The regions of the Solar System beyond 70 au are a fascinating frontier. In the examination of this region it is important to be able to distinguish between known “excited” populations like resonant objects and their large eccentricities and the possible discovery of unknown “cold” populations with low inclination and eccentricity distributions. An entire second cold classical belt could exist at 90 au and it would have escaped detection by modern surveys. As currently planned, LSST, while incredibly powerful, is not the right mechanism to explore this region and dedicated search efforts will be required if we wish to learn more about the distant reaches of our Solar System. Study of objects in resonance with Neptune are the first step toward doing so.
Figure 1 – Graph of the upper limit on the number of objects with Hr < 9 before detection would be likely at increasing heliocentric distance. Each ring represents a simplified orbital toy model. The number of objects was determined by the OSSOS Survey Simulator and characterization data for several modern surveys. Horizontal lines represent the number of objects in the cold Kuiper belt (blue), hot Kuiper belt (orange), and both combined (purple).
Figure 2 – Figure demonstrating oversampled OSSOS Survey Simulator output for several modern surveys and how their detection numbers drop off with distance for a >70 au heliocentric distance ring. Note the (orange) OSSOS++ points that correspond to a detection limit of ~24.5, which is broadly similar to the LSST survey limit. LSST will have greatly increased sky coverage, but it is expected that detection efficiency will drop off in a similar manner to OSSOS in the 80-90 au range. Contrast this with deeper searches like CLASSY (red) that are able to detect more distant objects.
References
1. Gladman & Volk (2021), Transneptunian Space, Annual Review of Astronomy and Astrophysics, Volume 59, pp. 203-246
How to cite: Peltier, L., Kavelaars, J., Petit, J., Gladman, B., Fraser, W., and Lawler, S.: Distant Resonances in the Outer Solar System, EPSC-DPS Joint Meeting 2025, Helsinki, Finland, 7–13 Sep 2025, EPSC-DPS2025-1072, https://doi.org/10.5194/epsc-dps2025-1072, 2025.
The works found in the literature indicate that comet 1P/Halley has chaotic behavior, with some different results about its Lyapunov time. The smallest of them found so far was approximately 70 years by Muñoz-Gutiérrez, Reyes-Ruiz and Pichardo (2015). On the other hand, its orbital evolution for several hundred years does not show any strong radial irregularity, indicating a confined chaotic behavior. However, in the case of Halley, the orbital eccentricity is quite high (> 0.96) in comparison with that of the asteroids and small satellites of Saturn (< 0.1) studied previously.
Applying the approach described above, the results shown in Figure 1 indicate that the radial contribution of the maximum LCE of Halley is not dominant, but it is also not neglegible. The dynamical evolution of Halley is more complicated. Muñoz-Gutiérrez, Reyes-Ruiz and Pichardo (2015) and Boekholt et al. (2016) showed that Jupiter has strong influence on Halley’s chaotic motion. We also found that the close encounters with the planets, mainly Jupiter, play an important role on its chaotic behavior. A more detailed analysis of this dynamics will be presented.
Figure 1. Lyapunov exponent for comet Halley. The yellow points represent Halley's maximum LCE, given by γ, the black points represent the LCE without taking into account the radial contribution (or remainder), given by γ∗, and the red points represent the radial contribution of the LCE, given by γr. The indications of numbers 1 and 2 correspond to close encounters with Jupiter.
Acknowledgements
This study was financed by CAPES – Finance Code 001, CNPq – Proc. 305210/2018-1, and FAPESP – Proc. 2016/24561-0.
References
Benettin, G. et al. Lyapunov Characteristic Exponents for smooth dynamical systems and for hamiltonian systems; a method for computing all of them. Part 1: Theory. Meccanica, 15, 9, 1980
Boekholt, T.C.N. et al. The origin of chaos in the orbit of comet 1P/Halley. MNRAS, 461, 4, 3576–3584, 2016.
Muñoz-Gutiérrez, M.A.; Reyes-Ruiz, M.; Pichardo, B. Chaotic dynamics of comet 1P/Halley: Lyapunov exponent and survival time expectancy. MNRAS, 447, 4, 3775–3784, 2015.
Pereira, L.S.; Mourão, D.C.; Winter, O.C. Confined Chaos and the chaotic angular motion of Atlas, a Saturn's inner satellite. MNRAS, 529, 1012-1018, 2024.
Winter, O.C; Mourão, D.C.; Giuliatti Winter, S.M. , Short Lyapunov time: a method for identifying confined chaos. A&A,523, A67, 2010.
How to cite: Winter, O., Pereira, L., and Mourão, D.: On the Chaotic Dynamics of Comet 1P/Halley, EPSC-DPS Joint Meeting 2025, Helsinki, Finland, 7–13 Sep 2025, EPSC-DPS2025-892, https://doi.org/10.5194/epsc-dps2025-892, 2025.
Introduction: Planets form within protoplanetary disks surrounding protostars. Both the star and the disk originate from the collapse of a dense molecular cloud. The condensation of the earliest solids, Calcium Aluminium-rich Inclusions (CAIs), marks the time zero of the solar system (ss). These refractory minerals are increasingly thought to form contemporaneously with the assembly of the protoplanetary disk, as their existence requires extremely high temperatures and widespread distribution across the disk [1-2].
In contrast to carbonaceous meteorites (non-CI) and Earth, which are enriched in refractory elements as CAIs, non-carbonaceous chondrites (NCC), which should have formed closer to the Sun, exhibit a sub-solar abundance trend of refractory elements such as Al and Mg, both relative to Si. This could be due to the loss of a refractory-rich component from a disc with the original solar composition [3-4].
[5] has proposed an astrophysical scenario for the sequestration of refractory elements from the NCC source region, which suggests that massive olivine condensation increased the dust concentration in the disk as it cooled down, suppressing magneto-rotational instability and prompting the rapid formation of the first planetesimals. This process isolated the condensed solids, preventing their further interaction with gas-solid equilibrium chemistry. Later, as temperatures dropped further, new “residual condensates” could form from the residual gas. Then, NCCs likely formed from a mixture of these residual condensates and solar-composition materials, including local grains non-accreted into the first planetesimals and possibly grains migrating from outer regions to the residual region, without element fractionation.
Whereas there is a general agreement that CAIs may have condensed in high temperature conditions, a major conundrum is how to make Enstatite and Ordinary chondrites with non-solar composition (with lower Al/Si and Mg/Si ratios compared to solar) [5]. So, here, we individually track the different refractory components (Al, Mg, and Si) and investigate their radial distribution along the disk.
Methods: We simulate a 1D protoplanetary disk using a Python-based code DustPy, to evolve systems with gas and dust [7]. We initially distribute the gas surface density radially following [8]. We have also modeled the early infall into the disk by implementing an external source term, Sext, with a flux of mass of 0.5e-5MSun/year falling within 0.2au (Fig. 1).
Our planar disk extends from 0.1 to 100 au with 40 grid cells, from which 16 refined cells around 2 au. To accurately study dust growth evolution, each radial point contains 78 logarithmically spaced mass bins every mass decade, and the growth and fragmentation of dust is calculated using Smoluchowski's equation. We set the standard dust/gas ratio value to 0.01. The newly formed star has radius RStar = 0.1au, mass MStar = 0.3MSun. Dust grain sizes start with minimum radii of 0.5 microns and bulk densities of around 1.25 g cm-3.
Results: Figure 3 showcases the evolution of surface density of refractory elements (Al, Mg, and Si) when we apply the phase equilibrium codeFASTCHEMCOND [10-11] in the post-simulation. The pressure maxima in surface density occurs now near 1au after hundreds of years due to evolution of pressure profile. As the infall material reaches the midplane, it accumulates in the inner disk region, increasing the pressure in it. This material moves outwards due to the viscous spreading, reaching the condensation zone (gray dotted line), when some gas starts to condensate. Figure 4 presents
the average radial velocity of gas and dust. Small dust grains are the most abundant in the first thousand years and they are strongly coupled to the gas flow. Fractionation of the element abundances are observed during all evolution of the disk, especially in the condensation fronts.
Our results show that the dynamical evolution of a viscously evolving protoplanetary disk, when coupled with realistic dust growth and condensation models, naturally leads to the fractionation of refractory elements such as Al, Mg, and Si. The emergence of a pressure bump near the MRI front, as a result of the viscosity transition, prevents the immediate inward drift of solids and promotes a local accumulation of their surface density. This process leads to variations in condensation of the gas, which results in element fractionation over time. These findings support the idea that the observed depletion of refractory elements in non-carbonaceous chondrites is caused by early disc processes.
Our next steps will investigate the relationship between radial mixing and chemical evolution as both the disk becomes accretionary and the global temperature of the disk cools.
References: [1] Drążkowska, J. & Dullemond, C. P. (2018) AAP, 614, A62 [2] Pignatale F. C. et al. (2018) AJL, 867, L23 [3] Larimer J. W. (1979) Icarus, 40, 446-454. [4] Alexander, C.M.O’D. (2019). Geochim. Cosmochim., 254, 246 [5] Morbidelli A. (2020) Earth and Planet. Sci. Letters 538,116220 [7] Charnoz S. et al. (2019), A&A 627, A50 [8] Lynden-Bell & Pringle (1974) MNRAS 168, 603-637 [9] Birnstiel T. et al. (2012) A&A 539, A148 [10] Zhu, Z. et al. (2010) ApJ, 713, 1134 [11] Kitzmann D. et al. (2024) MNRAS 527, 7263–7283 [12] Stock J. W. et al. (2018) MNRAS, 479, 865.
FIGURE 1: Surface density evolution (y-left) of gas (blue line) and 100 x dust (orange line). Dust-to-gas ratio (gray solid line, y-right) as a function of distance r over time. Dotted gray line stands for condensation temperature, Tcond, before which dust is evaporated.
FIGURE 2: The graph shows the temperature (blue line, y-left) and pressure (black line, y-right) profiles evolution as a function of distance r over time. It is possible to note the pressure bump rising around 2au.
FIGURE 3: Surface density profiles of aluminium (Al, orange), magnesium (Mg, red), and silicon (Si, cyan) in both dust and gas phases (solid and dashed lines, respectively). Dotted and dashed black lines stand for condensation and MRI temperatures, respectively.
FIGURE 4. Mean radial velocities of dust (orange line) and gas (blue line). Dotted and dashed gray lines stand for condensation and MRI temperatures, respectively.
How to cite: Franco, P. and Charnoz, S.: Dynamical Evolution of Refractory Elements in an alpha-Protoplanetary Disk, EPSC-DPS Joint Meeting 2025, Helsinki, Finland, 7–13 Sep 2025, EPSC-DPS2025-2091, https://doi.org/10.5194/epsc-dps2025-2091, 2025.