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

Introduction. 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_⊕). One example is Proxima Centauri b, estimated at ~2× M_⊕ [6]. We model a 0.1M_⊕ “mini-Earth”and “super-Earth” at 10M_⊕, the approximate upper limit for a “mini-Neptune” [7]. Output predicts lithospheric melting and subsurface habitable volumes.

Methods. 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.

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 × 10²¹ kg, and scaled to other planets based on cross-sectional areas, with 1.7 × 10²¹ kg for mini-Earth, 1.2 × 10²² kg for Proxima Centauri b, and 3.6 × 10²² 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^-3 and planetary bulk densities are assumed to be 5510 kg m^-3, omitting gravitational compression [7]. Impactor velocity was estimated at 1.5 × v_esc for each planet, with 7.8 km s^-1 for mini-Earth,  16.8 km s^-1 for the Earth, 21.1 km s^-1 for Proxima Centauri b, and 36.1 km s^-1 for super-Earth.

Results. 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.

References: [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.