A Shock-Wave Heating Model for Chondrule Formation: Maximal Size of Chondrules

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Several models of heating events, which formed chondrules, have been proposed to date, though a consensus has not been reached yet. Shock-wave heating model is one of the possible models. In the model, dust particles are heated by the drag heating in the post shock flow. The maximum temperature and the cooling rates of chondrules that are estimated from laboratory experiments can be obtained in the model. Here we show that two other features of chondrules, characteristic size and rotation rates, may also be explained naturally in the framework of the shock-wave heating model. In the model, the sizes of chondrules are bounded by the balance between the surface tension and the ram pressure on a molten droplet. As the size of a molten particle increases, the surface tension descreses. So a large droplet whose radius exceeds a critical value is expected to fragment into small droplets. The acceptable upper bound is around 1 mm, which is consistent with characteristic sizes of chondrules. The upper bound does not depend on the shock flow conditions significantly, i.e., almost all the shocks which heat the dust particles up to the melting point provide similar maximal sizes of chondrules. Moreover, when a chondrule forms through the distribution of a larger droplet, it acquires a spin of the order of 1 x 103 rad s-1. It is also consistent with observations.

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