Abstract
Hafnium and tungsten are both highly refractory elements, and hafnium is a lithophile element whereas tungsten is a moderately siderophile element that should strongly partitioned into metal phases during metal/silicate segregation. The Moon may have formed from debris created by a giant impactor that hit the Earth with a glancing blow, after terrestrial core formation. The decay of now extinct 182Hf (half-life, 9Myr) to 182W is an ideal chronometer for tracing this process, because Hf is retained in the silicate mantle while W is largely partitioned into the core during core segregation (Halliday et al. 1996; Lee et al. 1997).It has been argued that the age of terrestrial core formation was limited by accretion time, that it started very early, and that it was largely completed within the first 10-20 Myr or less of Earth history (Jacobsen & Harper 1996; Lee & Halliday 1995, 1996). And recently, according to the new results of measurements of W isotope compositions and Hf/W ratios of several meteorites, it shows that the main growth stage for the Earth is largely completed in 10 Myr, and the Moon-forming giant impact is dated at 29 Myr (Kleine et al. 2002; Yin et al. 2002). However, they applied only magma ocean model and two-stage model. Magma ocean model considers exponentially decreasing rates of accretion and the rate of core formation limited by the accretion rate, and two-stage model has strict time significance only in the case where there is complete equilibration between the core and the silicate mantle at a single point in time, with no subsequent additions of material to the Earth (Harper & Jacobsen 1996; Jacobsen 1998). They assumed that a single giant impact could give rise to this perfect resetting on Hf-W chronometer.In this study, we consider the effect of partial resetting on Hf-W system by multiple giant impacts. We show limit of the age estimation by Hf-W chronometry, and on the other hand, possibility to constrain the required resetting ratio by giant impacts or other equilibrating events.Recent works on planetary formation show that several tens of Mars-sized protoplanets are formed through a successive accretion of planetesimals in the terrestrial planet region (Kokubo & Ida 1998; Wetherill & Stewart 1989). Then we consider two different stages: (1) protoplanets formation stage and (2) giant impacts stage. Primarily, in the stage of planetary accretion, metal of impactor and silicate of target are equilibrated each other, then Hf-W chronometer of this equilibrated region is reset. This resetting continues during the metal sink in the silicate to reach the core of target body. We assume metal of impactor split into lots of metal sphere grains sinking in a silicate melt at a velocity following from Stokes sedimentation equation and reset its chronometer. Achieved resetting ratio is estimated through the volume of target add the volume of impactor divided by the volume reset its chronometer.As the result of these considerations, we show this chronometer cannot determine the age of melt-silicate separation precisely and achieving large resetting ratio is not so easy by giant impact or other. To determine the age of core formation of Earth by Hf-W chronometry, we should determine the number and the resetting ratio of each giant impacts, and to achieve the high resetting ratio of Mars (= 0.6), we should reexamine the theory of planetary formation or introduce certain drastic events for Mars.
