Target Weakening and Temporary Fluidization in Large Impact Events

Introduction: A predictive, quantitative model for complex crater collapse remains elusive [1]. Theoretical work [2, 3, 4] suggests that complex crater formation requires a prodigious change in target rheology to facilitate collapse. It would appear that, from a macroscopic point of view, the target must adopt a fluid-like rheology for the few minutes during which collapse occurs. The rheologic model that best represents the apparent behaviour of the target following a large impact event is the Bingham model. In this model the target behaves as a solid for stresses below a finite yield value. For stresses in excess of this value, the Bingham substance behaves as a fluid with a constant viscosity. Recent numerical modeling [1, 5, 6, 7] has constrained further the requirements for complex crater collapse. Such studies indicate that: (1) the yield strength of the Bingham substance must be at least an order of magnitude lower than the yield strength of standard broken-rock material; (2) that the effective viscosity of the fluidized region must be an order of magnitude or more below the critical viscosity that precludes overshoot of the collapsing central uplift (given approximately by crit 0:14 gD 3=2 t , where g is gravity, is the density of the target material and Dt is the diameter of the transient crater); and (3) that the volume of rock involved in the collapse must be on the order of the volume of the transient crater. Here we compare the merits of several weakening mechanisms, postulated in the literature to explain complex crater collapse, in the context of the three requirements discussed above. Impact melt production: Perhaps the most intuitive explanation for the change in rheology of the target is heat. Molten rock possesses the correct material properties; it is a Bingham fluid with a yield strength lower than that of standard rock debris by more than an order of magnitude. The viscosities of most magmas are sufficiently low to permit flow in the required time-scale. Moreover, there is direct geologic evidence for melting of the target in terrestrial complex craters; and the collapse time-scale appears to be limited by the cooling of a clast-rich impact melt [8]. However, scaling laws relating transient crater dimension to melt production, which have been derived from numerical modeling [9, 10], suggest that the volume of melt produced is comparable to the transient crater volume only in extremely large impact events (Dt > 200 km for terrestrial impacts). Melt production, therefore, cannot be the sole fluidizing agent facilitating the collapse of most complex craters. Thermal softening: [11] propose a weakening mechanism that relies on temperature, without necessitating the melting of large volumes of the sub-crater region. This process of "thermal softening" is analogous to the effect the ductile behaviour of metals at high temperatures. [5] successfully simulate complex crater collapse using a thermal softening model where strength linearly approaches zero for temperatures in excess of 80% of the melt temperature Tm. However, work by [12] suggests that even for a Chicxulub-scale event, temperatures within the target are not extreme enough over a large enough volume for thermal softening to be the dominant collapse mechanism. In the thermal softening model, strength degradation of an order of magnitude or more requires the local temperature to be greater than 0:98Tm; we suggest that thermal softening, like melt production, becomes relevant to crater collapse only in the formation of very large complex craters. More work on the effect of thermal softening is required.