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Investigation of the initial state of the Moon-forming disk: Bridging SPH simulations and hydrostatic models

Nakajima, Miki and Stevenson, David J. (2014) Investigation of the initial state of the Moon-forming disk: Bridging SPH simulations and hydrostatic models. Icarus, 233 . pp. 259-267. ISSN 0019-1035. https://resolver.caltech.edu/CaltechAUTHORS:20140501-132540904

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Abstract

According to the standard giant impact hypothesis, the Moon formed from a partially vaporized disk generated by a collision between the proto-Earth and a Mars-sized impactor. The initial structure of the disk significantly affects the Moon-forming process, including the Moon’s mass, its accretion time scale, and its isotopic similarity to Earth. The dynamics of the impact event determines the initial structure of a nearly hydrostatic Moon-forming disk. However, the hydrostatic and hydrodynamic models have been studied separately and their connection has not previously been well quantified. Here, we show the extent to which the properties of the disk can be inferred from Smoothed Particle Hydrodynamic (SPH) simulations. By using entropy, angular momentum and mass distributions of the SPH outputs as approximately conserved quantities, we compute the two-dimensional disk structure. We investigate four different models: (a) standard, the canonical giant impact model, (b) fast-spinning Earth, a collision between a fast-spinning Earth and a small impactor, (c) sub-Earths, a collision between two objects with half Earth’s mass, and (d) intermediate, a collision of two bodies whose mass ratio is 7:3. Our SPH calculations show that the initial disk has approximately uniform entropy. This is because the materials of different angular momenta are shocked to similar extents. The disks of the fast-spinning Earth and sub-Earths cases are hotter and more vaporized (∼80–90% vapor) than the standard case (∼20%). The intermediate case falls between these values. In the highly vaporized cases, our procedure fails to establish a unique surface density profile of the disk because the disk is unstable according to the Rayleigh criterion (the need for a monotonically increasing specific angular momentum with radius). In these cases, we estimate non-unique disk models by conserving global quantities (mass and total angular momentum). We also develop a semi-analytic model for the thermal structure of the disk, including the radial temperature structure and the vapor mass fraction. The model requires only two inputs: the average entropy and the surface density of the disk.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1016/j.icarus.2014.01.008DOIArticle
http://www.sciencedirect.com/science/article/pii/S001910351400030XPublisherArticle
https://arxiv.org/abs/1401.3036arXivDiscussion Paper
ORCID:
AuthorORCID
Stevenson, David J.0000-0001-9432-7159
Additional Information:© 2014 Elsevier Inc. Received 20 September 2013; Revised 30 December 2013; Accepted 9 January 2014; Available online 14 February 2014. We would like to thank Hidenori Genda for the helpful discussions about inherent problems of SPH, Kaveh Pahlevan, Aaron Wolf, Sarah Stewart, Robin Canup and anonymous reviewers for the insightful comments, Jay Melosh for sharing ANEOS data, and Takaaki Takeda for providing a visualization software, Zindaiji 3. Numerical computations were carried out on GRAPE system at Center for Computational Astrophysics, National Astronomical Observatory of Japan.
Subject Keywords:Moon; Satellites, formation; Thermal histories; Disks
Record Number:CaltechAUTHORS:20140501-132540904
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20140501-132540904
Official Citation:Nakajima, M. and D. J. Stevenson (2014). "Investigation of the initial state of the Moon-forming disk: Bridging SPH simulations and hydrostatic models." Icarus 233(0): 259-267.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:45431
Collection:CaltechAUTHORS
Deposited By: David McCaslin
Deposited On:01 May 2014 20:44
Last Modified:03 Oct 2019 06:30

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