Sublimation as an effective mechanism for flattened lobes of (486958) Arrokoth

Abstract

The New Horizons spacecraft’s flyby of Kuiper belt object (486958) Arrokoth revealed a bilobed shape with highly flattened lobes both aligned to its equatorial plane, and a rotational axis almost aligned to the orbital plane (obliquity ~99°)1,2,3,4. Arrokoth belongs to the cold classical Kuiper belt object population that occupies dynamically undisturbed orbits around the Sun, and as such is a primitive object that formed in situ. Therefore, whether its shape is primordial or evolutionary carries important implications for understanding the evolution of both Kuiper belt objects and potentially their dynamically derived objects, Centaurs and Jupiter-family comets5,6. Applying our mass-loss-driven shape evolution model (MONET)7, here we suggest that the current shape of Arrokoth could be of evolutionary origin due to volatile outgassing in a timescale of about 1–100 Myr, while its spin state would not be dramatically affected. We further argue that such a process may be ubiquitous in the evolution of the shape of Kuiper belt objects shortly after their formation. This shape-changing process could also be reactivated when Kuiper belt objects dynamically evolve to become Centaurs and then Jupiter-family comets5,6 and receive markedly increased solar heating.

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Fig. 1: Shape models of the Arrokoth KBO as observed today and the analogues of a parent body derived from our modelling.
Fig. 2: CH4 mass-loss rate of different dust-layer models.
Fig. 3: Final shapes of Arrokoth analogues simulating mass-loss evolution with different dust-layer properties.
Fig. 4: Shape evolution results taking into account gravity, and tensile stress effects on the mass loss distribution.

Data availability

Source data are provided with this paper. The data that support other plots within this work and other findings of this study are available from Y.Z. and L.R. upon reasonable request.

Code availability

MONET is not yet ready for public release—its details and validation have been presented in our previous study as mentioned in this Letter and are available from the corresponding authors upon reasonable request.

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Acknowledgements

We acknowledge that NSFC–DFG joint funding allows this collaboration and study to happen. We thank H. U. Keller and X. Shi for their encouragement and helpful discussions. Y.Z. and S.C.H. are supported by the National Natural Science Foundation of China (grants 11761131008, 11673072, 11873098, 11633009), the Strategic Priority Research Program on Space Science (CAS) (grant XDA15017600) and the Foundation of Minor Planets of Purple Mountain Observatory. L.R. was supported by project DFG-392267849. J.-Y.L. acknowledges support from the Solar System Exploration Research Virtual Institute 2016 (SSERVI16) Cooperative Agreement (grant NNH16ZDA001N), SSERVI-TREX, to the Planetary Science Institute.

Author information

Affiliations

Authors

Contributions

Y.Z. initiated and led this study, constructed the numerical modelling tool, performed the simulations, analysed the numerical results and drafted the manuscript. L.R. contributed to the design of the work, constructed the numerical modelling tool, performed the simulations, analysed the numerical results and drafted the manuscript. Y.S. contributed to the thermal modelling and interpretations of the numerical results. S.C.H. performed simulations of low-speed merger of two round bodies. N.S. carried out analytical justification of the numerical results regarding spin-state evolution. J.-Y.L. participated in early discussions and data interpretation and helped to improve the manuscript.

Corresponding authors

Correspondence to Y. Zhao or L. Rezac.

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The authors declare no competing interests.

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Peer review information Nature Astronomy thanks John Spencer and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data

Extended Data Fig. 1 Shape configuration produced by a low-speed collision of a spherical and an oblate body.

The soft-sphere discrete element method implemented by N-body code pkdgrav is used to simulate the merging process of two planetesimals that formed the precursor body of Arrokoth3,37. The primary and secondary bodies in the upper panels (oblate and spherical shape, respectively) are of the same scale as the lobes of SHAPE-SYN. The two lobes are constructed with 40,000 and 25,775 spherical particles with a power-law distribution of radii ranging from 309 m to 927 m using a -3 index, and an inter-particle cohesion of 27500 Pa is assumed1. A set of material parameters are selected to obtain a friction angle of 40° and the bulk density3 is set to be 0.47 g/cm−3. The resulting contact binary shown in the lower panels is obtained with impact speed v = 5 m/s and impact angle α = 45° (measured with respect to the vertical at the impact point), which is close to the SHAPE-SYN. The upper panels show the two original objects from -y axis and +z axis viewpoints, in which blue and red particles belong to the spherical and oblate body, respectively. The bottom panel shows the resulting contact binary for the same viewing geometry, and the wireframe in yellow outlines the SHAPE-SYN we build from the inverse evolution result. This simulation result shows a good agreement and indicates that our idealized bilobed body is consistent with physics of slow collisions, and, as already noted, it is taken as our starting shape in our evolution model.

Extended Data Fig. 2 Results illustrating the time evolution of Arrokoth analogues for different dust layer properties at a fixed point in time.

For easier visual comparison we plot only extracted cross sections aligned at the body axes. The blue outline belongs to Arrokoth (SHAPE-ORIG), shown for a reference. The other colored outlines [red, green, magenta, gray] are for cases with different dust layers, each 5 cm in thickness but varying monomer particle sizes, Ra, from 10−6 to 10−3 meters (as labeled in the figure). The curves show results extracted at the same time instant of about 3.1 Myr, which is when the scenario Ra = 10−6 m (red curve) reaches the approximate volume of Arrokoth. On the other hand, the layer constructed from the largest monomers (grey curve) conducts little heat to the ice and provides the weakest mass loss. Under these conditions, it would take another 4.4~Myr to reach the same volume as SHAPE-ORIG.

Extended Data Fig. 3 Simulations of obliquity and orientation evolution taking into account sublimation torques.

These simulations are performed with reduced assumption of pure CH4 icy bodies in order to get the upper limit of the sublimation torques. This reduces the time to reach the volume of the SHAPE-ORIG from the initial states (SHAPE-SYN and SHAPE-REV) to about 1 Myr. Due to the computationally intensive integral needed to solve the Euler equation, we present a tendency of the simulated spin state evolution for around 0.05 to 0.1 Myr. In panel A we show the obliquity change for both initial shapes as a function of time (for approx. 320 orbits or 0.1 Myr), starting with the current obliquity of Arrokoth. The relevant movement of the spin axis’ orientation in the space is shown in panel B in terms of right ascension and declination (Ra, Dec). The initial (Ra, Dec) state is in the lower right corner of the plot. These simulations show that obliquity, Ra. and Dec. changes are within 0.4, 0.3 and 0.5 deg respectively. The spin axis has a tendency to stay near the orbital plane, which is demonstrated in panels C and D, for two cases of obliquity close to 90° (89.99° and 90.002°) starting with SHAPE-SYN. The orientation changes of the spin axis are presented again in Ra. Dec. space for a simulation time of 200 orbits (about 0.06 Myr), during which the variation is less than 10−3 deg for both angles. A strong stability of orientation is preserved when the spin axis lies closely to the orbital plane and perihelion because the net torque in the inertial frame is minimized32,33.

Extended Data Fig. 4 Simulation results estimating the magnitude of spin period change.

(Left) Time evolution of rotational period change for SHAPE-SYN and SHAPE-REV assuming current Arrokoth obliquity. The SHAPE-REV body experiences stronger changes in spin period by about two orders of magnitude during simulation because it’s more asymmetrical compared to the SHAPE-SYN (see also Supplementary Fig. 5). (Right) simulations done for SHAPE-REV for two cases of obliquity close to 90° in which case the spin period does change considerably slower, at change of ~10−5 hrs after 0.6 Myr. Here, combined with the result shown in Supplementary Fig. 5, we can conclude that if the external gravitational torque from planet encounters could be ignored1,3, then the spin state of Arrokoth didn’t change appreciably during its evolution history even when taking sublimation torques into consideration (under the assumptions of homogeneity).

Extended Data Fig. 5 Torque efficiency of SHAPE-SYN (upper panels) and SHAPE-REV (lower panels).

Here we provide additional information on surface torque efficiency \(-{\mathbf{r}}_i \times \hat n_{vi}\) in x, y and z direction for both initial shapes to assess whether to expect pronounced sublimation driven torques on the body. Here, ri and \(\hat n_{vi}\) are the radius and the unit vector in the direction of gas ejection of i-th facet. The distribution of positive (red) and negative (blue) values of torque efficiency indicating increasing or decreasing of the spin rate along the corresponding spin axis, are perfectly ‘symmetric’ on the surface of SHAPE-SYN. When the body is in a circular orbit with an obliquity of 90° (or 0°), the orbital averaged solar flux distribution on its surface is even between ‘red’ and ‘blue’ regions, resulting in a balance between the torques induced by mass loss in both regions This balance could not be perfectly achieved for SHAPE-REV since it exhibits a small degree of asymmetry, but the resulted non-zero torque is also of small absolute value in the case of circular orbit and an obliquity of 90°. Since Arrokoth has an obliquity close to 99° and small orbital eccentricity, the illumination distribution on its surface is evenly distributed in positive and negative regions and, hence, leads to a low magnitude of the sublimation induced torques. The red, green and blue arrows point in the direction of +x, +y and +z respectively, as labeled in the plots.

Extended Data Fig. 6 Comparison of evolution simulations for two different ices.

The red outline belongs to the CO ice sublimation case, while the blue one is for CH4. In both cases the properties of the dust layer are the same with a thickness of 5 cm and Ra = 10−6 m. It takes about 0.9 Myr to reach the volume of SHAPE-ORIG when CO is the major volatile species, while about 3.1 Myr for CH4 ice sublimation. In the left panel the results are shown as cross-sections through equatorial and polar regions. In the right panel we show the final 3D body with color scale denoting radial differences between facet centers of the two cases (CH4 minus CO case). From the point of view of the flattening process of the two lobes we conclude that the results are nearly identical, hence, independent of the type of ice in question. However, a faster volume loss due to higher CO volatility produces less erosion in the polar regions but higher at the equatorial areas in the time it takes to reach the SHAPE-ORIG volume. The principle of this effect follows from the fact that the CO to CH4 volatility in the less illuminated equatorial region is higher than the time ratio needed to reach the final shape, which is not the case for areas under nearly constant illumination.

Supplementary information

Supplementary Video 1

Merger process of a low-speed collision between a spherical and an oblate body modeled by the N-body code pkdgrav.

Supplementary Video 2

Shape evolution process modelled by MONET starting with SHAPE-SYN. This simulation case assumes CH4 as the dominant sublimating volatiles below a dust layer with a thickness of 5 cm and Ra = 10−6 m. The color bar indicates surface radius distance in meters.

Source data

Source Data Fig. 1

Digital shape model of bodies shown in Fig. 1.

Source Data Fig. 4

Digital shape model of bodies shown in Fig. 4.

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Zhao, Y., Rezac, L., Skorov, Y. et al. Sublimation as an effective mechanism for flattened lobes of (486958) Arrokoth. Nat Astron (2020). https://doi.org/10.1038/s41550-020-01218-7

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