Terrestrial accretion rates and the origin of the Moon

Abstract

The former decay of 182Hf to 182W ( T 1/2=9 Myr) has resulted in variations in W isotope composition that reflect early solar system time-integrated Hf/W ratios. The bulk silicate Earth (BSE) has non-chondritic Hf/W because of core formation, yet has a chondritic W isotopic composition. This is inconsistent with models that involve the completion of terrestrial accretion and core formation within the first 10 Myr of solar system history, such as early heterogeneous accretion of silicate and metal from a fractionated partially condensed nebula. Protracted accretion of material that has, on average, chondritic compositions with respect to Hf–W is more in accord with the chondritic W isotopic composition of the BSE. Most early-formed low Hf/W metal and high Hf/W silicate that was added to the Earth during accretion must have largely equilibrated isotopically with the growing BSE, otherwise its W isotopic composition would not be chondritic. Within this framework, both the W and Pb isotope data for the Earth can be modeled with homogeneous accretion and continuous core formation at exponentially decreasing rates. The accretionary mean life would need to be between 25 and 40 Myr assuming the Hf/W ratio of the BSE is ∼15 and 238U/ 204Pb of the total Earth is ∼0.7. Such models do not emulate late stage major impacts such as probably formed the Moon. There is now considerable evidence that the Moon formed no earlier than ∼50 Myr after the start of the solar system. A collision at or before 50 Myr between a near Earth-sized proto-Earth and a Mars-sized impactor, here named Theia, would not yield chondritic W for the present day BSE, unless there was also significant subsequent accretion. The recent suggestion that the proto-Earth to Theia mass ratio was more like 7:3 and that the proto-Earth was <65% formed before the collision is easily reconciled with W isotope data. The Pb isotope data for the average BSE can be modeled with the same accretion parameters provided that the proto-Earth was >50% formed by the time of the impact, Theia adding at least a further 20% of the Earth’s mass. Less than 25% of additional material would be accreted after the collision. If the proposed 238U/ 204Pb of 0.7 for the total Earth is grossly incorrect or if smoothly decreasing rates of accretion before and after the impact are inadequate approximations, these figures would need to be changed. Isotopic equilibration with the W in the silicate portion of the Earth is harder to envisage for a very large impactor with a distinct metal core that immediately coalesces with the Earth’s core, as in Giant Impact simulations. However, the silicate portion of the Earth would not need to isotopically equilibrate with the total mass of Theia during the Moon-forming collision if Theia, like the proto-Earth, had been accreting relatively slowly. The chondritic initial W isotopic composition of the Moon provides supporting evidence that Theia grew slowly. A possible explanation for this slow growth of Theia and the proto-Earth is that they grew in close proximity, competing for, and perturbing the trajectories of accreting material. Close proximity would also increase the probability of a collision between the proto-Earth and Theia and explain why the Earth and Moon share the same O and Cr isotopic compositions.