The crater-induced YORP effect

¹ Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS, Laboratoire Lagrange, 96 Bd de l’Observatoire, 06300 Nice, France
e-mail: wenhan.zhou@oca.eu
² Origin Space Co. Ltd., Kechuang Road, Nanjing, 212415 Jiangsu, PR China
³ Department of Aerospace Engineering, University of Maryland, College Park, MD, 20742, USA
⁴ Department of Aerospace Engineering, Tsinghua University, 30 Shuangqing Road, 100190 Beijing, PR China

Received: 30 June 2022
Accepted: 13 October 2022

Abstract

Context. The Yarkovsky–O’Keefe–Radzievskii–Paddack (YORP) effect plays an important role in the rotational properties and evolution of asteroids. While the YORP effect induced by the macroscopic shape of the asteroid and by the presence of surface boulders has been well studied, no investigation has been performed yet regarding how craters with given properties influence this effect.

Aims. We introduce and estimate the crater-induced YORP effect (CYORP), which arises from the concave structure of the crater, to investigate the magnitude of the resulting torques as a function of varying properties of the crater and the asteroid by a semi-analytical method.

Methods. By using a simple spherical shape model of the crater and assuming zero thermal inertia, we calculated the total YORP torque due to the crater, which was averaged over the spin and orbital motions of the asteroid, accounting for self-sheltering and self-sheltering effects.

Results. The general form of the CYORP torque can be expressed in terms of the crater radius R₀ and the asteroid radius R_ast: 〈T_CYORP〉 ~ WR₀²R_astΦ/c, where W is an efficiency factor. We find that the typical values of W are about 0.04 and 0.025 for the spin and obliquity component, respectively, which indicates that the CYORP can be comparable to the normal YORP torque when the size of the crater is about one-tenth of the size of the asteroid, or equivalently when the crater/roughness covers one-tenth of the asteroid surface. Although the torque decreases with the crater size R₀ as ~R₀², the combined contribution of all small craters can become non-negligible due to their large number when the commonly used power-law crater size distribution is considered. The CYORP torque of small concave structures, usually considered as surface roughness, is essential to the accurate calculation of the complete YORP torque. Under the CYORP effect that is produced by collisions, asteroids go through a random walk in spin rate and obliquity, with a YORP reset timescale typically of 0.4 Myr. This has strong implications for the rotational evolution and orbital evolution of asteroids.

Conclusions. Craters and roughness on asteroid surfaces, which correspond to concave structures, can influence the YORP torques and therefore the rotational properties and evolution of asteroids. We suggest that the CYORP effect should be considered in the future investigation of the YORP effect on asteroids.