9:45 AM - 10:00 AM
[PPS07-04] Kinematic consideration on the top-shaped figure of asteroid Ryugu
Keywords:asteroid figure, Ryugu, slope stability
The shape of rubble pile asteroids can provide a clue to the transportation mechanism of volatiles inside the snow line. Previously the ellipsoids were regarded as the likely equilibrium figure of rotating self-gravitating aggregates, while in situ observation of Hayabusa2 and OSIRIS-REx have disclosed top-shaped figures of small asteroids. However, the formation process of the top-shaped figure is still under debate, and it is important to clarify whether the mass transfer is constrained in the surficial layer or is involved in internal deformation.
We consider in this study a simple kinematic balance of self-gravity and centrifugal force near the surface of asteroid Ryugu. In soil mechanics, the stability of the slope is evaluated by a ratio of traction along the slope and resistance caused by friction and cohesion, FoS. In this study, we use an inverse of FoS because the traction may become zero depending on the rotation period, P, which has probably changed due to the YORP effect. The local gravitation is calculated assuming the current figure of Ryugu and constant density inside. Also, we take into account cohesion stress among regolith and boulders. Sand or soil cannot withstand for FoS-1 > 1 or < -1 and will collapse. For -1 < FoS-1 < 1, the slope is metastable, meaning the slope can tolerate unless external impetus is excited.
We assume that the current shape of Ryugu was critical in the past fastest rotation. Thus we set FoS-1 = 1 and calculate cohesion stress per unit length as a function of latitude for given P and angle of repose, φ. Considering that the cohesion and φ shall be independent of latitude, plausible sets of P and φ are constrained if the calculated cohesion is constant regardless of latitude. First, we assume the present P of 7.63 hr and φ of 40°, which is often used for terrestrial sand. This set results in a negative, namely, repulsive force of cohesion, meaning slopes are globally metastable at present. Following Watanabe et al. (2019), we also calculate for a set of P of 3.5 hr and φ of 31°. The result seems close to a constant cohesion, at least for a range between 20° and 65°, while there is room for improvement.
We have thoroughly examined ranges of P and φ. A condition for plausible P and φ is arbitrary set such that the standard deviation of cohesion per unit length is less than 5 x 10-6 m s-2. Consequently, P, φ, and cohesion per unit length that match the present top-shaped figure are constrained to be between 3.8 and 4 hr, 20° and 25°, and less than 2.5 x 10-6 m s-2, respectively.
Spectral slopes at the poles and equator of Ryugu show distinctive blue characteristics indicating mass wasting from the equator and poles to mid-latitude. We have examined such spectral slope variation in the view of slope stability with an increase of P. As Ryugu spins down, the critical slope becomes metastable. However, FoS-1 remains positive in most regions suggesting surface rocks tend to move in a direction from the poles to the equator. Only the equatorial region becomes negative.
FoS-1 in the equatorial band can be negative depending on P but is greater than -1 even at present. Thus, spin down solely cannot explain the blue spectrum of the surface of the equatorial bulge, but an additional excitation is required. Probably its source is impact cratering. There are many large craters that postdate the equatorial bulge. The latitudinal width of the blue spectral slope appears ±10°. Therefore the time of large impacts is likely to have occurred when P was 4.5 hr.
This kinematic model is further tested by using slopes of large craters. We take 11 craters from Hirata's list (Hirata et al., 2020) whose topography are retrieved from LIDAR data to produce North-South sections. For example, in case of Urashima crater, P = 4.8 ~ 6.2 hr (solid arrow) for φ of 20° ~ 25°. Considering the large standard deviation of average slope, P at the time of the crater formation is constrained between 4.1 and 7.6 hr.
We consider in this study a simple kinematic balance of self-gravity and centrifugal force near the surface of asteroid Ryugu. In soil mechanics, the stability of the slope is evaluated by a ratio of traction along the slope and resistance caused by friction and cohesion, FoS. In this study, we use an inverse of FoS because the traction may become zero depending on the rotation period, P, which has probably changed due to the YORP effect. The local gravitation is calculated assuming the current figure of Ryugu and constant density inside. Also, we take into account cohesion stress among regolith and boulders. Sand or soil cannot withstand for FoS-1 > 1 or < -1 and will collapse. For -1 < FoS-1 < 1, the slope is metastable, meaning the slope can tolerate unless external impetus is excited.
We assume that the current shape of Ryugu was critical in the past fastest rotation. Thus we set FoS-1 = 1 and calculate cohesion stress per unit length as a function of latitude for given P and angle of repose, φ. Considering that the cohesion and φ shall be independent of latitude, plausible sets of P and φ are constrained if the calculated cohesion is constant regardless of latitude. First, we assume the present P of 7.63 hr and φ of 40°, which is often used for terrestrial sand. This set results in a negative, namely, repulsive force of cohesion, meaning slopes are globally metastable at present. Following Watanabe et al. (2019), we also calculate for a set of P of 3.5 hr and φ of 31°. The result seems close to a constant cohesion, at least for a range between 20° and 65°, while there is room for improvement.
We have thoroughly examined ranges of P and φ. A condition for plausible P and φ is arbitrary set such that the standard deviation of cohesion per unit length is less than 5 x 10-6 m s-2. Consequently, P, φ, and cohesion per unit length that match the present top-shaped figure are constrained to be between 3.8 and 4 hr, 20° and 25°, and less than 2.5 x 10-6 m s-2, respectively.
Spectral slopes at the poles and equator of Ryugu show distinctive blue characteristics indicating mass wasting from the equator and poles to mid-latitude. We have examined such spectral slope variation in the view of slope stability with an increase of P. As Ryugu spins down, the critical slope becomes metastable. However, FoS-1 remains positive in most regions suggesting surface rocks tend to move in a direction from the poles to the equator. Only the equatorial region becomes negative.
FoS-1 in the equatorial band can be negative depending on P but is greater than -1 even at present. Thus, spin down solely cannot explain the blue spectrum of the surface of the equatorial bulge, but an additional excitation is required. Probably its source is impact cratering. There are many large craters that postdate the equatorial bulge. The latitudinal width of the blue spectral slope appears ±10°. Therefore the time of large impacts is likely to have occurred when P was 4.5 hr.
This kinematic model is further tested by using slopes of large craters. We take 11 craters from Hirata's list (Hirata et al., 2020) whose topography are retrieved from LIDAR data to produce North-South sections. For example, in case of Urashima crater, P = 4.8 ~ 6.2 hr (solid arrow) for φ of 20° ~ 25°. Considering the large standard deviation of average slope, P at the time of the crater formation is constrained between 4.1 and 7.6 hr.