The crater-induced YORP effect

Wen-Han Zhou,Yun Zhang, Xiao-Ran Yan,Patrick Michel

crossref（2022）

引用 0|浏览0

暂无评分

摘要

1. Introduction The Yarkovsky–O'Keefe–Radzievskii–Paddack effect, or YORP effect, has influence on the rotational state and evolution of asteroids [1]. Depending on several parameters, it can either increase or decrease the spin rate as well as change the spin obliquity of an asteroid, on timescales that also depend on the physical and dynamical properties of the considered asteroid.  The current YORP model reads TYORP = TNYORP + TTYORP, where TNYORP stands for the YORP effect on the whole asteroid and TTYORP stands for the tangential YORP effect, which is related to the presence of boulders and surface roughness.  <img src="" alt="" width="549" height="259" /> Figure 1. The components on asteroids that contribute to the YORP effect. The current model still faces difficulties calculating the YORP torque because of the extreme sensitivity of the YORP effect to the surface topology. Here, we consider the YORP effect of the crater, which has not been considered so far. We show that the crater-induced YORP (called CYORP hereafter) might contribute the total YORP torque as well, which adds a "CYORP" term into the Equation (1): TYORP = TNYORP + TTYORP + TCYORP with TCYORP = ΣiTCYORP,I as a summation for a whole set of craters or concave structures on the asteroid (see Figure 1). The CYORP torque is the difference of the torque caused by the presence of the crater and the torque by the ground before the birth of the crater (dashed curves in Figure 1) TCYORP = Tcrater - Tground. Using these calculations, we find that a single crater with a size equal to one-third of the asteroid size would produce a torque that is comparable to the normal YORP torque. The smaller craters also contribute to the total torque due to their large amount. Therefore, the CYORP should be considered in the future study of the YORP. The derived CYORP torque can be applied both for craters and for any concave structures on the surface of an asteroid, although a modification accounting for the geometry is needed. Since craters arise from collisions, this study builds a link between the rotational evolution and collisional history of asteroids.   2. Heat model As a first step, we simply assume a non-thermal conductivity regime, which leads to a recoil thermal force on the surface element dS f = -(2Φα/3c)dS. where Φ and c are solar flux and light speed, respectively. Here α is the cosine of the angle between the surface normal vector and the light ray.    3. Shape model for the crater <img src="" alt="" width="543" height="251" /> Figure 2. The shape model for the crater. We consider a simple crater shape model, which is represented by a full or a portion of a semi-sphere with crater radius R1 and depth h (see Figure 2). The widely used parameter depth d-diameter D0 ratio expresses: h/D0 = (1-sinγ0)/2. Space mission data from real asteroids show that the average h/D0 for fresh craters covers a range that goes from 0.11 (for Ceres) to 0.19 (for Eros), depending on many parameters and the considered crater diameter range [2].   4. Calculation of the torque For a concave geometry such as a crater, the self-shadowing has a significant influence on the YORP effect. There are two major effects of self-shadowing. (1) During the rotational cycle, only a fraction of the crater is illuminated, depending on where it lies on the asteroid. (2) The effective recoil force is not normal due to the shelter. Considering non-zero thermal inertia and a given asteroid shape requires a numerical model and will be the topic of the next study. The recoil force must be integrated over the whole illuminated area of the crater F = ∫fdS. The total torque of the crater is T = ∫r×fdS ≈r0×F. Here r and r0 are the position vector of the surface element on the crater and the sphere center of the crater, respectively. To understand this effect on the secular spin evolution of the asteroid, we need to average the torque over the orbital and spin motion. In general, TCYORP takes the form of the following scaling rule with the radius of the crater R0 and of the asteroid R: TCYORP = gΦR02 R/c, where g is a function of the properties of the crater and asteroid, Φ is the solar flux and c is light speed.   5. Results and implications We find that a single crater with a size equal to one-third of the asteroid size would produce a torque that is comparable to the normal YORP torque. This torque decreases with the crater as R02. Since the cumulative size distribution of craters typically follows a power law of the form N(R ≥ R0) ∝ R0-b, the larger number of smaller craters contributes also to the total YORP torque, although each of them causes a small torque. Moreover, since an asteroid experiences a lot of impacts leading to a crater during its evolution, the resulting CYORP torques may cause a random walk of the spin rate and obliquity of the asteroid, which may either slow down or even prevent the YORP spin up to occur. This can have strong implications on the formation of top shapes and binary systems based on this process [3], and on the resulting timescale, which will be assessed in future work.   Acknowledgment We acknowledge support from the Universite Cote d'Azur. W.Z. and X.Y. acknowledge funding support from Chinese Scholarship Council. W.Z. acknowledge funding support from Origin Space Company. P.M. acknowledges funding support from the French space agency CNES and from the European Union’s Horizon 2020 research and innovation program under grant agreement No. 870377 (project NEO-MAPP).    [1] Rubincam, D (2000) Icarus 148, 2; [2] Noguchi, R et al (2021) Icarus 354, 114016; [3] Walsh, K and Jacobson, S (2015), in Asteroids IV (Michel et al., eds), UAP, 375.

查看译文

AI 理解论文

溯源树

样例

生成溯源树，研究论文发展脉络

Chat Paper

正在生成论文摘要