Abstract
The formation of the Inner Oort Cloud (IOC)—a vast halo of icy bodies residing far beyond Neptune’s orbit—is an expected outcome of the solar system’s primordial evolution within a stellar cluster. Recent models have shown that the process of early planetesimal capture within the trans-Neptunian region may have been sufficiently high for the cumulative mass of the Cloud to approach several Earth masses. In light of this, here we examine the dynamical evolution of the IOC, driven by its own self-gravity. We show that the collective gravitational potential of the IOC is adequately approximated by the Miyamoto–Nagai model and use a semi-analytic framework to demonstrate that the resulting secular oscillations are akin to the von Zeipel–Lidov–Kozai resonance. We verify our results with direct N-body calculations and examine the effects of IOC self-gravity on the long-term behavior of the solar system’s minor bodies using a detailed simulation. Cumulatively, we find that while the modulation of perihelion distances and inclinations can occur within an observationally relevant range, the associated timescales vastly surpass the age of the sun, indicating that the influence of IOC self-gravity on the architecture of the solar system is negligible.
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Notes
To ascertain the degree of axial symmetry, we computed the distribution of azimuthal angles of particles across cylinders with a radial thickness of 100 AU at radial intervals of 100 AU, and applied the Kolmogorov–Smirnov test for uniformity. This calculation yielded an average p value of \(\langle p\rangle =0.45\), indicating that axial symmetry is statistically consistent with the simulation data.
References
Adams, F.C., Laughlin, G.: Constraints on the birth aggregate of the solar system. Icarus 150, 151–162 (2001). https://doi.org/10.1006/icar.2000.6567
Adams, F.C.: The birth environment of the solar system. Ann. Rev. Astron. Astrophys. 48, 47–85 (2010). https://doi.org/10.1146/annurev-astro-081309-130830
Arakawa, S., Kokubo, E.: Number of stars in the Sun’s birth cluster revisited. Astron. Astrophys. (2023). https://doi.org/10.1051/0004-6361/202244743
Batygin, K., Brown, M.E.: Evidence for a distant giant planet in the solar system. Astron. J. (2016). https://doi.org/10.3847/0004-6256/151/2/22
Batygin, K., Adams, F.C., Brown, M.E., Becker, J.C.: The planet nine hypothesis. Phys. Rep. 805, 1–53 (2019). https://doi.org/10.1016/j.physrep.2019.01.009
Batygin, K., Adams, F.C., Batygin, Y.K., Petigura, E.A.: Dynamics of planetary systems within star clusters: aspects of the solar system’s early evolution. Astron. J. (2020). https://doi.org/10.3847/1538-3881/ab665d
Batygin, K., Mardling, R.A., Nesvorný, D.: The stability boundary of the distant scattered disk. Astrophys. J. (2021). https://doi.org/10.3847/1538-4357/ac19a4
Brasser, R., Duncan, M.J., Levison, H.F.: Embedded star clusters and the formation of the Oort Cloud. Icarus 184, 59–82 (2006). https://doi.org/10.1016/j.icarus.2006.04.010
Brasser, R., Duncan, M.J., Levison, H.F., Schwamb, M.E., Brown, M.E.: Reassessing the formation of the inner Oort cloud in an embedded star cluster. Icarus 217, 1–19 (2012). https://doi.org/10.1016/j.icarus.2011.10.012
Chambers, J.E.: A hybrid symplectic integrator that permits close encounters between massive bodies. Mon. Not. R. Astron. Soc. 304, 793–799 (1999). https://doi.org/10.1046/j.1365-8711.1999.02379.x
Das, A., Batygin, K.: Suppression of the inclination instability in the trans-Neptunian Solar system. Mon. Not. R. Astron. Soc. 523, 6103–6113 (2023). https://doi.org/10.1093/mnras/stad1687
Fernández, J.A.: The formation of the oort cloud and the primitive galactic environment. Icarus 129, 106–119 (1997). https://doi.org/10.1006/icar.1997.5754
Grimm, S.L., Stadel, J.G., Brasser, R., Meier, M.M.M., Mordasini, C.: GENGA II GPU Planetary N-body simulations with non-newtonian forces and high number of particles. Astrophys. J. (2022). https://doi.org/10.3847/1538-4357/ac6dd2
Hadden, S., Tremaine, S.: Scattered disc dynamics: the mapping approach. Mon. Not. R. Astron. Soc. 527, 3054–3075 (2024). https://doi.org/10.1093/mnras/stad3478
Hills, J.G.: Comet showers and the steady-state infall of comets from the Oort cloudsps. Astron. J. 86, 1730–1740 (1981). https://doi.org/10.1086/113058
Huang, Y., Gladman, B.: Primordial orbital alignment of sednoids. Astrophys. J. (2024). https://doi.org/10.3847/2041-8213/ad2686
Kaib, N.A., Quinn, T.: The formation of the Oort cloud in open cluster environments. Icarus 197, 221–238 (2008). https://doi.org/10.1016/j.icarus.2008.03.020
Madigan, A.-M., McCourt, M.: A new inclination instability reshapes Keplerian discs into cones: application to the outer Solar system. Mon. Not. R. Astron. Soc. 457, L89–L93 (2016). https://doi.org/10.1093/mnrasl/slv203
Miyamoto, M., Nagai, R.: Three-dimensional models for the distribution of mass in galaxiessps. Publ. Astron. Soc. Jpn. 27, 533–543 (1975)
Morbidelli, A.: Modern celestial mechanics : aspects of solar system dynamics. Modern celestial mechanics : aspects of solar system dynamics, by Alessandro Morbidelli. London: Taylor & Francis, 2002, ISBN 0415279399 (2002)
Muñoz-Gutiérrez, M.A., Peimbert, A., Pichardo, B., Lehner, M.J., Wang, S.-Y.: The contribution of dwarf planets to the origin of jupiter family comets. Astron. J. (2019). https://doi.org/10.3847/1538-3881/ab4399
Nesvorný, D., Bernardinelli, P., Vokrouhlický, D., Batygin, K.: Radial distribution of distant trans-Neptunian objects points to Sun’s formation in a stellar cluster. Icarus (2023). https://doi.org/10.1016/j.icarus.2023.115738
Nesvorný, D., Vokrouhlický, D., Dones, L., Levison, H.F., Kaib, N., Morbidelli, A.: Origin and evolution of short-period comets. Astrophys. J. (2017). https://doi.org/10.3847/1538-4357/aa7cf6
Saillenfest, M., Fouchard, M., Ito, T., Higuchi, A.: Chaos in the inert Oort cloud. Astron. Astrophys. (2019). https://doi.org/10.1051/0004-6361/201936298
Sefilian, A.A., Touma, J.R.: Shepherding in a Self-gravitating Disk of Trans-Neptunian Objects. Astron. J. (2019). https://doi.org/10.3847/1538-3881/aaf0fc
Tremaine, S.: The Hamiltonian for von Zeipel-Lidov-Kozai oscillations. Mon. Not. R. Astron. Soc. 522, 937–947 (2023). https://doi.org/10.1093/mnras/stad1029
von Zeipel, H. 1910. Sur l’application des séries de M. Lindstedt à l’étude du mouvement des comètes périodiques. Astronomische Nachrichten 183, 345. https://doi.org/10.1002/asna.19091832202
Wisdom, J., Holman, M.: Symplectic maps for the N-body problemsps. Astron. J. 102, 1528–1538 (1991). https://doi.org/10.1086/115978
Zderic, A., Madigan, A.-M.: Steeper scattered disks buckle faster. Astrophys. J. (2023). https://doi.org/10.3847/2041-8213/accde2
Zink, J.K., Batygin, K., Adams, F.C.: The great inequality and the dynamical disintegration of the outer solar system. Astron. J. (2020). https://doi.org/10.3847/1538-3881/abb8de
Acknowledgements
We are thankful to Fred Adams, Alessandro Morbidelli, Cristian Beauge, and Mike Brown for insightful discussions. We thank the anonymous referees for providing careful and insightful reviews of the manuscript. K.B. is grateful to Caltech, the David and Lucile Packard Foundation, and the National Science Foundation (Grant Number: AST 2109276) for their generous support.
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Batygin, K., Nesvorný, D. Self-gravitational dynamics within the inner Oort cloud. Celest Mech Dyn Astron 136, 24 (2024). https://doi.org/10.1007/s10569-024-10195-2
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DOI: https://doi.org/10.1007/s10569-024-10195-2