Magnetized models for the formation of the moon

Mullen, Patrick Dean

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https://hdl.handle.net/2142/113014 Copy

Description

Title

Magnetized models for the formation of the moon

Author(s)

Mullen, Patrick Dean

Issue Date

2021-07-12

Director of Research (if dissertation) or Advisor (if thesis)

Gammie, Charles F

Doctoral Committee Chair(s)

Gammie, Charles F

Committee Member(s)

• Ricker, Paul M
• Fields, Brian D
• Looney, Leslie W

Department of Study

Astronomy

Discipline

Astronomy

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• Moon
• magnetohydrodynamics

Abstract

The leading theory for the origin of the Moon suggests that a planetary impactor struck the proto-Earth in an oblique collision shortly after the formation of the solar system. The giant impact produces liquid and vapor debris, drawn from the proto-Earth and impactor. The debris either escapes the system, falls back to Earth, or enters circumterrestrial orbits forming a “protolunar disk.” The Moon is thought to have formed from this disk. Any Moon formation theory must explain three observables: (1) Earth and lunar masses, (2) the angular momentum of the Earth--Moon system, and (3) Earth and lunar isotopic ratios. Geochemical analyses of lunar samples reveal that the Earth and Moon are surprisingly similar in isotopic ratios, e.g., the lunar oxygen isotope ratio \delta17O/\delta18O falls atop the terrestrial fractionation line (the “isotope crisis;” see Melosh, 2014). Unless the proto-Earth and impactor were isotopically identical, the giant impact hypothesis requires vigorous mixing between impactor- and Earth-derived material to erase the isotopic signature of an impactor. It is plausible that the proto-Earth and impactor hosted a magnetic field. Even if they did not, remnant magnetization in meteorites provides evidence for a ~0.05-0.5 G background solar magnetic field in the terrestrial planet-forming region (Fu et al., 2014). Any magnetic field well-coupled to hot debris from the impact will be amplified by a number of processes. Turbulent amplification of the field occurs during the collision phase as the planets shear against one another. In the post-impact, differentially rotating debris disk, magnetic winding grows field strengths linearly in time. Turbulence driven by the magnetorotational instability (MRI) is capable of growing field strengths exponentially in time (Balbus & Hawley, 1998). In this dissertation, we assess the potential role of magnetic fields in the Moon-forming giant impact hypothesis using numerical simulations. To evolve a magnetized, Moon-forming giant impact scenario, we must integrate the equations of magnetohydrodynamics subject to a planetary equation of state with self-gravity. Herein, we have implemented various extensions to the Athena++ framework (Stone et al., 2020) that enable (1) fully conservative self-gravitating (magneto)hydrodynamics (Mullen et al., 2021), (2) super-time-stepping algorithms for diffusive (parabolic) physics, and (3) the ability to interface with planetary equations of state. Our magnetized, giant impact simulations (Mullen & Gammie, 2020a) investigate the amplification of magnetic fields via turbulence, magnetic winding, and the onset of the MRI. Our models demonstrate that vigorous magnetized turbulence in the protolunar disk leads to growth of vorticity and angular momentum transport. Magnetic fields potentially make Moon formation less efficient: hot vapor in the debris disk will be accreted onto Earth due to magnetically driven angular momentum transport, thereby depleting the mass available to form the Moon. Magnetic fields also speed the evolution of the vapor component of the debris disk: the disk spreading timescale associated with the MRI is much shorter than the spreading timescale associated with gravitational instabilities (as in the classical picture for the evolution of the protolunar disk, Thompson & Stevenson, 1988). Looking to the future, this dissertation presents preliminary results from a numerical model of an unmagnetized Earth--protolunar disk boundary layer (i.e., the transition region from the solid body rotation profile of Earth to the centrifugally supported protolunar disk). We find that the Earth--disk boundary layer is unstable to supersonic shear instabilities (Belyaev & Rafikov, 2012; Belyaev et al., 2012) that promote weak angular momentum transport at inner radii of the disk, while inefficiently mixing material between Earth and the disk. Our results motivate global simulations of the Earth--disk boundary layer with magnetic fields to investigate how the MRI works in tandem with supersonic shear instabilities to mix material and govern the early evolution of the protolunar disk.

Graduation Semester

2021-08

Type of Resource

Thesis

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http://hdl.handle.net/2142/113014

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Copyright 2021 by Patrick Dean Mullen. All rights reserved.

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