Analytical thermochronometric models of Earth&#8217;s crust during the late accretionary bombardment epoch (4.5-3.5 Ga)
Authors: Mojzsis Stephen J. , Abramov Oleg 
Published: March 2020

&lt;p&gt;Late accretionary bombardments in the first billion years of solar system history strongly affected the initial physical and chemical states of the Earth. Evidence of ancient impacts can be preserved in the oldest known terrestrial zircons with ages up to ca. 4.4 Ga. Here, we use the Hadean zircon record to directly assess the thermal effects of impact bombardment on the early Earth&amp;#8217;s crust, couple the results to models of closure temperature-dependent diffusive loss and U-Pb age-resetting in zircon, derive zircon ages, and compare them to published ages.&lt;/p&gt;&lt;p&gt;The impact bombardment model consists of (i) a stochastic cratering model which populates the surface with craters within constraints derived from the lunar cratering record, the size/frequency distribution of the asteroid belt, and dynamical models; (ii) analytical expressions that calculate a temperature field for each crater; and (iii) a three-dimensional thermal model of the terrestrial lithosphere, where craters are allowed to cool by conduction and radiation. Equations for diffusion in zircon are coupled to these thermal models to estimate the amount of age-resetting.&lt;/p&gt;&lt;p&gt;We present modeling results for the Earth between 4.5 Ga and 3.5 Ga based new mass-production functions. Mean surface temperatures and geothermal gradients were assumed as 20 &amp;#176;C and 70 &amp;#176;C/km. Total delivered mass was estimated at 0.0013(M&lt;sub&gt;planet&lt;/sub&gt;), or 7.8 &amp;#215; 10&lt;sup&gt;21&lt;/sup&gt; kg. The size-frequency distributions of the impacts were derived from dynamical modeling. We begin model runs with a global magma ocean, which would have been formed by the Moon-forming impact. Mean impactor density of 3000 kg/m&lt;sup&gt;3&lt;/sup&gt; and impactor velocity distribution from [1,2] was used, and impact angle of each impactor was stochastically generated from a gaussian centered at 45 degrees. The typical impact velocity of the Earth is ~21 km s&lt;sup&gt;-1&lt;/sup&gt;.&lt;/p&gt;&lt;p&gt;It is important to note that the model age outputs we report omit normal processes of generation of zircon-saturated magmas that were operative in the Hadean. We find that as the impact flux decreases with time and becomes negligible for the purposes of thermal modeling by ca. 3.5 Ga. We find that the probability of randomly selecting a zircon of a given age increases with increasing age, predicting a large number of very old zircons. This contrasts with the actual age distribution of Hadean zircons, which, for &gt;4 Ga, indicates the opposite case: the probability of selecting a zircon of a given age decreases with increasing age. We interpret this discrepancy to mean that impacts were not the dominant process in determining the ages of Hadean zircons. This is consistent with observations that the majority of Hadean zircons had formation temperature significantly lower than those expected for melt sheets and thermobarometry measurements suggesting formation of some Hadean zircons in a plate boundary environment.&lt;/p&gt;&lt;p&gt;[1] Mojzsis, S.J. et al. (2019). Astrophys. J., 881, 44. [2] Brasser, R. et al. (2020) Icarus 338, 113514.&amp;#160;&lt;/p&gt;