Hf-W CHRONOMETRY AND THE TIMING OF THE GIANT MOON-FORMING IMPACT ON EARTH

Introduction: The last major event in Earth’s formation is thought to have been the collision with a Mars-sized differentiated impactor, resulting in the formation of the Earth-Moon system (EMS). The recent discussion of the timing of this event centers on the extent of equilibration of the Hf-W system during this event. While Hf-W equilibration was very effective in small planetesimals [1], its efficiency at the late giant impact stages of planetary accretion is debated [1-4] and remains a source of disagreement in interpretation of 182 Hf182 W chronometry. The key to resolving this disagreement is to obtain experimental data on the scale of physical and chemical mixing and equilibration of metal and silicate in the post-giant impact Earth. Because the extreme conditions that prevailed in the Earth during and shortly after the giant Moon-forming impact [5] are inaccessible for conventional techniques, we use the results of high power laser shockinduced melting of metal-silicate targets at high pressures (100’s GPa) and temperatures (10 4 ’s K). Evaluation of the late Moon formation model: Since planetary accretion is a stochastic process, the last giant impact does not necessarily have to occur on an exponentially decreasing accretion rate curve; it could happen either before or after. It has recently been argued that the Moon formed late at about 70-110 Myr [6]. Because the W isotopic compositions of the modern Earth’s mantle (W(CHUR) (tf) = 1.9) and the bulk impactor (W(CHUR) = 0 by definition) are well known, the recently suggested formation of the Moon by a late impact ~ 70-110 Myr after the Solar System formation places rather tight constraints on the W isotopic composition and the accretion time of the silicate protoEarth, if the mass ratio of the impactor to the total system is known. Simulations of the Moon-forming impact [5] require the mass fraction of the impactor to be ~0.13 of the final Earth-Moon system in order to match its astronomical characteristics. Neglecting the small mass of the Moon, the mass ratio of the pre-impact mantle to the current mantle is 0.87. For this ratio the isotopic composition of the pre-impact Earth’s mantle of W(CHUR) (ti) = 11.6 was calculated from the equation 76 of [1] using the Hf-W fractionation factor f Hf/W = 12 [1]. The time ti when the pre-impact Earth’s mantle reaches the W(CHUR) value of 11.6 can be calculated from the equation 14 of [1] for the two-stage model of core-mantle differentiation. For the mean life of 182 Hf, 182Hf = 13 Myr, ( 182 Hf/ 180 Hf)To = 10 -4 , qW = 1.55x10 4 , and f Hf/W = 12 the pre-impact Earth’s two-stage model age is 6.1 Myr. At this stage the mass of pre-impact proto-Earth is 87% the modern Earth. Then the mean Earth (63.2 % by mass) accretion time of 2 Myr (prior to the giant impact) after the Solar System formation is determined from Figure 12 of [1] and in this case ~90% of Earth accreted in the first 6 Myr of the Solar System.