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Register a new userScaling laws for the oblique impact cratering on an inclined granular surface
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Although a large number of astronomical craters are actually produced by the oblique impacts onto inclined surfaces, most of the laboratory experiments mimicking the impact cratering have been performed by the vertical impact onto a horizontal target surface. In previous studies on the effects of oblique impact and inclined terrain, only one of the impact angle $varphi$ or target inclination angle $theta$ has been varied in the experiments. Therefore, we perform impact-cratering experiments by systematically varying both $varphi$ and $theta$. A solid projectile of diameter $D_{rm i}=6$~mm is impacted onto a sand surface with the range of impact velocity $v_{rm i}=7$--$97$~m~s$^{-1}$. From the experimental result, we develop scaling laws for the crater dimensions on the basis of $Pi$-group scaling. As a result, the crater dimensions such as cavity volume, diameter, aspect ratio, and depth-diameter ratio can be scaled by the factors $sin varphi$ and $cos theta$ as well as the usual impact parameters ($v_{rm i}$, $D_{rm i}$, density of projectile, and surface gravity). Finally, we consider the possible application of the obtained scaling laws to the estimate of impact conditions (e.g., impact speed and impact angle) in natural crater records.
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We develop an original apparatus of the granular impact experiment by which the incident angle of the solid projectile and inclination angle of the target granular layer can be systematically varied. Whereas most of the natural cratering events occur on inclined surfaces with various incident angles, there have not been any experiments on oblique impacts on an inclined target surface. To perform systematic impact experiments, a novel experimental apparatus has to be developed. Therefore, we build an apparatus for impact experiments where both the incident angle and the inclination angle can be independently varied. The projectile-injection unit accelerates a plastic ball (6~mm in diameter) up to $v_isimeq 100$~m~s$^{-1}$ impact velocity. The barrel of the injection unit is made with a three-dimensional printer. The impact dynamics is captured by high-speed cameras to directly measure the impact velocity and incident angle. The rebound dynamics of the projectile (restitution coefficient and rebound angle) is also measured. The final crater shapes are measured using a line-laser profiler mounted on the electric stages. By scanning the surface using this system, a three-dimensional crater shape (height map) can be constructed. From the measured result, we can define and measure the characteristic quantities of the crater. The analyzed result on the restitution dynamics is presented as an example of systematic experiments using the developed system.
Here, we develop scaling laws for (1) the distribution of impact-induced heat within the mantle and (2) shape of the impact-induced melt based on more than 100 smoothed particle hydrodynamic (SPH) simulations. We use Legendre polynomials to describe these scaling laws and determine their coefficients by linear regression, minimizing the error between our model and SPH simulations. The input parameters are the impact angle $theta$ ($0^{circ}, 30^{circ}, 60^{circ}$, and $90^{circ}$), total mass $M_T$ ($1M_{rm Mars}-53M_{rm Mars}$, where $M_{rm Mars}$ is the mass of Mars), impact velocity $v_{rm imp}$ ($v_{rm esc} - 2v_{rm esc}$, where $v_{rm esc}$ is the mutual escape velocity), and impactor-to-total mass ratio $gamma$ ($0.03-0.5$). We find that the equilibrium pressure at the base of a melt pool can be higher (up to $approx 80 %$) than those of radially-uniform global magma ocean models. This could have a significant impact on element partitioning. These melt scaling laws are publicly available on GitHub ($href{https://github.com/mikinakajima/MeltScalingLaw}{https://github.com/mikinakajima/MeltScalingLaw}$).
The collapse of an inclined cohesive granular layer triggered by a certain perturbation can be a model for not only landslides on Earth but also relaxations of asteroidal surface terrains. To understand such terrain dynamics, we conduct a series of experiments of a solid-projectile impact onto an inclined wet granular layer with various water contents and inclination angles. As a result, we find two types of outcomes: crater formation and collapse. The collapse phase is observed when the inclination angle is close to the maximum stable angle and the impact-induced vibration at the bottom of wet granular layer is sufficiently strong. To explain the collapse condition, we propose a simple block model considering the maximum stable angle, inclination angle, and impact-induced vibrational acceleration. Additionally, the attenuating propagation of the impact-induced vibrational acceleration is estimated on the basis of three-dimensional numerical simulations with discrete element method using dry particles. By combining wet-granular experiments and dry-granular simulations, we find that the impact-induced acceleration attenuates anisotropically in space. With a help of this attenuation form, the physical conditions to induce the collapse can be estimated using the block model.
Galaxy scaling laws, such as the Tully-Fisher, mass-size and Fall relations, can provide extremely useful clues on our understanding of galaxy formation in a cosmological context. Some of these relations are extremely tight and well described by one single parameter (mass), despite the theoretical existence of secondary parameters such as spin and concentration, which are believed to impact these relations. In fact, the residuals of these scaling laws appear to be almost uncorrelated with each other, posing significant constraints on models where secondary parameters play an important role. Here, we show that a possible solution is that such secondary parameters are correlated amongst themselves, in a way that removes correlations in observable space. In particular, we focus on how the existence of an anti-correlation between the dark matter halo spin and its concentration -- which is still debated in simulations -- can weaken the correlation of the residuals of the Tully-Fisher and mass-size relations. Interestingly, using simple analytic galaxy formation models, we find that this happens only for a relatively small portion of the parameter space that we explored, which suggests that this idea could be used to derive constraints to galaxy formation models that are still unexplored.
For a fundamental understanding of terrain relaxation occurring on sloped surfaces of terrestrial bodies, we analyze the crater shape produced by an impact on an inclined granular (dry-sand) layer. Owing to asymmetric ejecta deposition followed by landsliding, the slope of the impacted inclined surface can be relaxed. Using the experimental results of a solid projectile impact on an inclined dry-sand layer, we measure the distance of centroid migration induced by asymmetric cratering. We find that the centroid migration distance $x_mathrm{mig}$ normalized to the crater minor-axis diameter $D_mathrm{cy}$ can be expressed as a function of the initial inclination of the target $tantheta$, the effective friction coefficient $mu$, and two parameters $K$ and $c$ that characterize the asymmetric ejecta deposition and oblique impact effect: $x_mathrm{mig}/D_mathrm{cy}=K tantheta/(1-(tantheta/mu)^2)+c$, where $K=0.6$, $mu=0.8$, and $c=-0.1$ to $0.3$. This result is consistent with a previous study that considered the effect of asymmetric ejecta deposition. The obtained results provide fundamental information for analyzing the degradation of sloped terrain on planetary surfaces, such as crater-shape degradation due to the accumulation of micro-impacts.
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