5:15 PM - 7:15 PM
[PPS03-P04] Numerical simulations of impact craters on a rapidly rotating top-shaped asteroid
The near-Earth asteroid (162173) Ryugu has a characteristic top-shape, which is thought to have formed as a result of past rapid rotation (Watanabe et al., 2019). However, the process of spin-down to its current state remains unclear. On the other hand, craters formed by celestial impacts on an asteroid rotating rapidly near the critical speed (ωc, where the centrifugal force equals the gravitational force at the equator) are believed to exhibit east-west asymmetries due to the bending of ejecta trajectories by the Coriolis force (Hirata et al., 2021) and north-south asymmetries caused by landslides under effective gravity (the net force of gravitational attraction and centrifugal force).
The objective of this research is to calculate crater topography formed on a rapidly rotating asteroid using numerical simulations and to estimate Ryugu's rotation rates during the formation of its observed craters.
For craters of various sizes and central latitudes formed at different rotational velocities on an axisymmetric top-shaped body based on a Ryugu shape model, we calculated the excavation topography using two methods: simple spherical excavation (spherical excavation relative to the body) and isopotential excavation (excavation in isopotential coordinates under the effective gravity field).We also determined the trajectories and landing sites of ejecta produced during crater excavation and simulated landslides of the accumulating transient rims under effective gravity. Furthermore, we calculated the final crater topographies, accounting for landslides caused by changes in effective gravity during the gradual spin-down of the body after crater formation.
In the case of simple spherical excavation, the final topography of craters is elongated in the east-west direction compared to the north-south direction at the equator, regardless of rotational velocity. In the case of isopotential excavation, however, the north-south axis tends to be longer than the east-west axis at the equator and at 5°N, particularly at higher rotational velocities. In both cases, craters formed at the equator with rotational angular velocities greater than 0.85 times the critical value (ω/ωc≧0.85) exhibited a noticeable east-west asymmetry (Fig.1(a)). However, crater formation at latitudes of 5°–10° exhibits a significant reduction in east-west asymmetry, while a north-south asymmetry dominated the rim height due to landslides. This asymmetry arose from the differing tilt of the inner slopes of the north and south rims relative to the effective gravity (Fig.1(b)). Consequently, for ω/ωc>0.85, the north side of the rim is higher than the south side, whereas for ω/ωc>0.85, the south side become higher than the north side (Fig.1(b)).
Based on an analysis of the rim shapes of 12 craters with distinct topography located within ±45° latitude on Ryugu, many of the low-latitude craters exhibit a slightly elongated shape in the north-south direction, which is consistent with crater shapes formed during rapid rotation under isopotential excavation conditions.
Further, we compared Ryugu's crater #16 (Hirata et al., 2020) with a radius of 43 m and a central latitude of 5.5°N with numerical simulations based on isopotential excavation. The rim shape of crater #16 is elongated in the north-south direction and closely resembles the rim shape formed during rapid rotation at ω/ωc=0.9 and 0.92 in our simulations. Additionally, a Fourier series expansion of the azimuthal variation in rim height for crater #16 revealed a similar trend in rim height with the numerical results for ω/ωc=0.9 and 0.92, further supporting the hypothesis that the Ryugu crater formed under past rapid rotation. Based on the rim shape and height asymmetry of various craters on Ryugu, we will explore its rotational evolution by estimating the rotational speed at the time of each crater's formation.
The objective of this research is to calculate crater topography formed on a rapidly rotating asteroid using numerical simulations and to estimate Ryugu's rotation rates during the formation of its observed craters.
For craters of various sizes and central latitudes formed at different rotational velocities on an axisymmetric top-shaped body based on a Ryugu shape model, we calculated the excavation topography using two methods: simple spherical excavation (spherical excavation relative to the body) and isopotential excavation (excavation in isopotential coordinates under the effective gravity field).We also determined the trajectories and landing sites of ejecta produced during crater excavation and simulated landslides of the accumulating transient rims under effective gravity. Furthermore, we calculated the final crater topographies, accounting for landslides caused by changes in effective gravity during the gradual spin-down of the body after crater formation.
In the case of simple spherical excavation, the final topography of craters is elongated in the east-west direction compared to the north-south direction at the equator, regardless of rotational velocity. In the case of isopotential excavation, however, the north-south axis tends to be longer than the east-west axis at the equator and at 5°N, particularly at higher rotational velocities. In both cases, craters formed at the equator with rotational angular velocities greater than 0.85 times the critical value (ω/ωc≧0.85) exhibited a noticeable east-west asymmetry (Fig.1(a)). However, crater formation at latitudes of 5°–10° exhibits a significant reduction in east-west asymmetry, while a north-south asymmetry dominated the rim height due to landslides. This asymmetry arose from the differing tilt of the inner slopes of the north and south rims relative to the effective gravity (Fig.1(b)). Consequently, for ω/ωc>0.85, the north side of the rim is higher than the south side, whereas for ω/ωc>0.85, the south side become higher than the north side (Fig.1(b)).
Based on an analysis of the rim shapes of 12 craters with distinct topography located within ±45° latitude on Ryugu, many of the low-latitude craters exhibit a slightly elongated shape in the north-south direction, which is consistent with crater shapes formed during rapid rotation under isopotential excavation conditions.
Further, we compared Ryugu's crater #16 (Hirata et al., 2020) with a radius of 43 m and a central latitude of 5.5°N with numerical simulations based on isopotential excavation. The rim shape of crater #16 is elongated in the north-south direction and closely resembles the rim shape formed during rapid rotation at ω/ωc=0.9 and 0.92 in our simulations. Additionally, a Fourier series expansion of the azimuthal variation in rim height for crater #16 revealed a similar trend in rim height with the numerical results for ω/ωc=0.9 and 0.92, further supporting the hypothesis that the Ryugu crater formed under past rapid rotation. Based on the rim shape and height asymmetry of various craters on Ryugu, we will explore its rotational evolution by estimating the rotational speed at the time of each crater's formation.