Thermal consequences of impact bombardments to silicate crusts of terrestrial-type exoplanets

<p><strong>Introduction. </strong>Post-accretionary impact bombardment is part of planet formation and leads to localized, regional [e.g., 1-3], or even wholesale global melting of silicate crust [e.g., 4]; less intense bombardment can also create hydrothermal oases favorable for life [e.g, 5]. Here, we generalize the effects of late accretion bombardments to extrasolar planets of different masses (0.1-10M<sub>⊕</sub>). One example is Proxima Centauri b, estimated at ~2× M<sub>⊕</sub> [6]. We model a 0.1M<sub>⊕ </sub>“mini-Earth”<sub></sub>and “super-Earth” at 10M<sub>⊕</sub>, the approximate upper limit for a “mini-Neptune” [7]. Output predicts lithospheric melting and subsurface habitable volumes.</p><p><strong>Methods. </strong>The model [1,2] consists of (i) stochastic cratering; (ii) analytical thermal expressions for each crater [e.g., 8,9]; and (iii) a 3-D thermal model of the lithosphere, where craters cool by conduction and radiation.</p><p>We analyze impact bombardments using our solar system’s mass production functions for the first 500 Myr [10]. Surface temperatures and geothermal gradients are set to 20 °C and 70 °C/km [2]. Total delivered mass for Earth is 7.8 × 10<sup>21</sup> kg, and scaled to other planets based on cross-sectional areas, with 1.7 × 10<sup>21</sup> kg for mini-Earth, 1.2 × 10<sup>22</sup> kg for Proxima Centauri b, and 3.6 × 10<sup>22</sup> kg for super-Earth. The impactors' SFD is based on our main asteroid belt [11]. Impactor and target densities are set to 3000 kg m<sup>-3</sup> and planetary bulk densities are assumed to be 5510 kg m<sup>-3</sup>, omitting gravitational compression [7]. Impactor velocity was estimated at 1.5 × v<sub>esc</sub> for each planet, with 7.8 km s<sup>-1</sup> for mini-Earth,  16.8 km s<sup>-1</sup> for the Earth, 21.1 km s<sup>-1</sup> for Proxima Centauri b, and 36.1 km s<sup>-1</sup> for super-Earth.</p><p><strong>Results. </strong>We assume fully formed crusts, so melt volume immediately increases due to impacts. Super-Earth reaches a maximum of ~45% of the lithosphere in molten state, whereas mini-Earth reaches a maximum of only ~5%.  This is due to much higher impact velocities and cratering densities on the super-Earth compared to mini-Earth. We also show the geophysical habitable volumes within the upper 4 km of a planet’s crust as the bombardment progresses. Impacts sterilize the majority of the habitable volume on super-Earth; however, due to its large total volume, the total habitable volume is still higher than on other planets despite the more intense bombardment in terms of energy delivered per unit area.</p><p><strong>References:</strong> [1] Abramov, O., and S.J. Mojzsis (2009) Nature, 459, 419-422. [2] Abramov et al. (2013) Chemie der Erde, 73, 227-248. [3] Abramov, O., and S. J. Mojzsis (2016) Earth Planet Sci. Lett., 442, 108-120. [4] Canup, R. M. (2004) Icarus, 168, 433-456. [5] Abramov, O., and D. A. Kring (2004) J. Geophys. Res., 109(E10). [6] Tasker, E. J. et al. (2020). Astronom. J., 159(2), 41. [7] Marcy, G. W. et al. (2014). PNAS, 111(35), 12655-12660. [8] Kieffer S. W. and Simonds C. H. (1980) Rev. Geophys. Space Phys., 18, 143-181. [9] Pierazzo E., and H.J. Melosh (2000). Icarus, 145, 252-261. [10] Mojzsis, S. J. et al. (2019). Astrophys. J., 881(1), 44. [11] Bottke, W. F. et al. (2010) Science, 330, 1527-1530.</p>

Особенности ускорения тел миллиграммовой массы в рельсовых электромагнитных ускорителях с внешним импульсным магнитным полем

Solid polycarbonate impactors were accelerated in a channel of electromagnetic railgun to which an external pulsed magnetic field was applied. The channel was filled with air at atmospheric pressure. The dynamics of impactor acceleration in the railgun was calculated. The impactor velocities in the railgun muzzle were measured in two cases. In the first case the railgun and external field system were powered from independent energy sources (scheme 1) and in the second case the railgun and external field circuits were connected in series to a common energy source (scheme 2). It was established that the effective coefficient of rail erosion in a 2-mm caliber channel that takes into account only the eroded mass captured by the plasma piston was 1.5–1.7 mg/C, and the eroded mass involved in the motion was comparable with the impactor mass. It was shown that in scheme 1, when the external field system was switched earlier, the impactor was accelerated at a maximum magnetic induction, and the impactor velocity in the channel muzzle exceeded 6 km/s.

Measuring Behavior of Impactor Penetrating through Polymer Sheet Based on Electromagnetic Induction

In the paper, the behavior of an impactor penetrating through a polymer sheet was measured using electromagnetic induction phenomena. First, electromotive forces generated in a coil were measured to decide the relation between the impactor velocity and the electromotive force when the impactor with an embedded neodymium magnet passed through a coil at several constant velocities. The intensity of the electromotive force was found to be proportional to the impactor velocity at each impactor position. The relation was used as the calibration data to calculate the velocity and position of the impactor. Next, penetration tests of polyvinyl chloride sheets were conducted with the coil set at the front of the sheet. The electromotive force generated in the coil was measured when the impactor penetrated through the sheet. The impactor velocity and position were calculated from the electromotive force with the calibration data. The validity of the measuring method was confirmed because the calculated results from the measured electromotive force agreed with the observed results by using a high speed video camera.

Failure Prediction of Fiber Reinforced Laminated Composite Plates Under Low Velocity Impact

The low velocity impact on composites has been studied as it leads to serious damage. The damage initiates as an intra ply matrix crack due to shear or bending which propagates further into the interface causing de-lamination between dissimilar plies and fiber breakage. This damage evolves with time and adversely affects the mechanical properties and strength of the composite. Since, multiple cracks in the ply are difficult to track, a progressive damage mechanics approach is used to model this failure. The inter ply failure is modeled using cohesive surfaces between the plies. The low velocity impact on composite plate is studied using finite element method. Impact parameters like velocity of impactor, the mass of the impactor and elastic properties of the material etc. are considered. An explicit central difference integration scheme is used to solve for displacements and impact forces. Progressive damage and failure in composites is modeled; an efficient algorithm has been developed and implemented in the FE code ABAQUS through a user-defined subroutine (VUMAT). Reduced integration yields satisfactory results for the impactor velocity less than or equal to 3 m/s for larger mass impact. However, full integration is recommended to obtain the satisfactory results for the (impactor velocity beyond 3 m/s), high velocity impact involving small masses. For the low velocity impact, the peak contact force and displacement are linear functions of impactor velocity for a constant mass. However, a nonlinear behavior is observed for the variation of mass with a constant striking velocity.