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Andrew D
2010-Dec-02, 02:09 PM
Hello all.

I was chatting with a graduate student at my school who is currently in the final stages of his masters thesis. He studies the mineral composition of asteroids. We were talking (or rather, he was telling me) about the difference between the composition of the material at the core-mantle boundary vs. the proper mantle and the mantle crust boundary. Then I did the thing graduate students love most, and asked him a question he didn't know the answer to:

What is the minimum (radius/mass) necessary for an early solar system object to undergo differentiation?

AndreasJ
2010-Dec-02, 03:18 PM
I's not immediately obvuous to me there will be a well defined minimum mass. Wouldn't, frex, one expect rapidly accreting bodies to melt (and therefore differentiate) at lower mass than slowly accreting ones of the same composition?

HypersonicMan
2010-Dec-02, 04:41 PM
The minimum size depends mostly on the timing of formation. During planet formation, the solar nebula was full of short-lived radioactive isotopes (like 26Al) that provided abundant heat, provided that rocky bodies formed while they were still around. A body with a diameter of 10 km that formed within the first 1 million years after the condensation of the first solid materials (the CAIs) would have had enough 26Al for its silicate to melt and differentiate an iron core, but a 1000 km body that formed 4 million years after CAIs would not, and so would not completely differentiate. Cooling rates for iron meteorites suggest that many of them formed from bodies as small as 20 km within about 1-2 million years after CAIs. For this reason, we see a wide variety of differentiation states for small to moderate-sized bodies.

For instance, the asteroid Vesta with a diameter of only 530 km is completely differentiated, whereas the Galilean satellite Callisto with a diameter of 4800 km is only partially differentiated (and if new work on the matter is correct, the partial differentiation of Callisto only happened due to the Late Heavy Bombardment, and would have remained undifferentiated had it not been pummeled by impacts).

For larger bodies, heat due to the accretion process itself as well as long-lived radioactive isotopes become more important.

Andrew D
2010-Dec-02, 05:12 PM
Not necessarily; it depends on the mechanism for heat loss between impacts. That said, we should assume uniform accretion: some amount of energy per unit surface area per time, along with some amount of additional mass. Logically, more massive bodies to attract more (and more energetic) matter than smaller ones. So, it seems to me there should be a minimum mass limit for 1) bodies to acquire enough energy to liquefy sufficiently to allow differentiation, 2) bodies to have a gravitational field strong enough to cause component materials to stratify before cooling.

Andrew D
2010-Dec-02, 05:14 PM
The minimum size depends mostly on the timing of formation. During planet formation, the solar nebula was full of short-lived radioactive isotopes (like 26Al) that provided abundant heat, provided that rocky bodies formed while they were still around. A body with a diameter of 10 km that formed within the first 1 million years after the condensation of the first solid materials (the CAIs) would have had enough 26Al for its silicate to melt and differentiate an iron core, but a 1000 km body that formed 4 million years after CAIs would not, and so would not completely differentiate. Cooling rates for iron meteorites suggest that many of them formed from bodies as small as 20 km within about 1-2 million years after CAIs. For this reason, we see a wide variety of differentiation states for small to moderate-sized bodies.

For instance, the asteroid Vesta with a diameter of only 530 km is completely differentiated, whereas the Galilean satellite Callisto with a diameter of 4800 km is only partially differentiated (and if new work on the matter is correct, the partial differentiation of Callisto only happened due to the Late Heavy Bombardment, and would have remained undifferentiated had it not been pummeled by impacts).

For larger bodies, heat due to the accretion process itself as well as long-lived radioactive isotopes become more important.

very informative, thanks!