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Large main belt asteroids deviation from homogeneous hydrostatic equilibrium

Presentation #503.03D in the session Asteroids: Main Belt (Oral Presentation)

Published onOct 23, 2023
Large main belt asteroids deviation from homogeneous hydrostatic equilibrium

1. Introduction

Asteroids are among the oldest remnants of the building blocks that led to the formation of the planets. As valuable tracers of the early time of the Solar System, the study of their physical properties is key to understanding the formation and evolution of planetary systems. A recent high-angular resolution imaging survey of 42 large main belt asteroids (LMBA) with the VLT/SPHERE (Vernazza et al. 2021) provided shape models of these bodies with an unprecedented accuracy. The adaptive-optics images reveal that most asteroids, with diameters larger than 100 km, present irregular shapes with important topographic features.

2. Deviation to hydrostatic equilibriums

Whereas asteroids are mainly understood as homogeneous fractured self gravitating pile of rocks, their structure is still debated. By comparing the semi-major axis ratios and rotation rates of the 42 LMBA observed with those of homogeneous hydrostatic equilibrium figures, a significant difference appears. Their high polar flattenings and low rotation rates globally prevent them from matching the Maclaurin and Jacobi equilibrium solutions (Chambat et al. 2023). Moreover, their equatorial axes present a large deviation from axial symmetry, required for the Maclaurin figures. Only the few largest water-rich asteroids (<10) remain compatible with hydrostatic equilibriums.

3. Non hydrostatic equilibriums

The assumption of fluid bodies with zero interior shear stress seems inappropriate to describe the LMBA. However, their modelling as solid elastic-plastic materials with cohesive and shear strength (Holsapple 2004, Sharma 2009), in addition to a weak gravity, provides an other limit on equilibrium shapes. The elastic-plastic theory allows to derive the maximum surface load that can be withstood before failure occurs. This constrains a spin-shape space where ellipsoids could exist in equilibrium depending on their cohesion strength and friction angle. The few compatible asteroids with the hydrostatic solutions present angles of friction lower than 1°, while smaller asteroids with less water can reach friction angle of tens of degrees, as measured for Earth soil rocks.

4. Error discussion

With the VLT observations, we conducted a statistical geophysical study of LMBA, sampling every major objects compositional classes in the Solar System. However, to assess their distance to equilibrium states, uncertainty calculations are crucial. Therefore, errors on shape models coming from SPHERE had been estimated by comparing observed limbs profiles with models from the Dawn mission (NASA) for the two asteroids Ceres and Vesta.

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