Research ArticlePLANETARY SCIENCE

Giant impacts stochastically change the internal pressures of terrestrial planets

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Science Advances  04 Sep 2019:
Vol. 5, no. 9, eaav3746
DOI: 10.1126/sciadv.aav3746
  • Fig. 1 Cooling and tidal evolution after the Moon-forming giant impact forced the shape and internal pressures in Earth to change.

    Contours of the internal pressure in Earth at different stages in its evolution after an impact of two 0.52 MEarth bodies with an impact velocity of 9.7 km s−1 and an impact parameter of 0.55 are shown. The post-impact body has a mass of 0.97 MEarth and an AM of 2.16 LEM. In this example, Earth was initially (days after impact) a synestia with modest internal pressures and a large moment of inertia (A). Subsequent cooling led to condensation of the silicate vapor, and the body first fell below the CoRoL (B) and then cooled to become a magma ocean (MO) planet with a volatile-dominated atmosphere (C). The planet was rotating rapidly, and the internal pressures remained modest. Continued cooling solidified the magma ocean but had little effect on the shape of the planet or on the internal pressures. Tidal recession of the Moon to the point that the lunar spin axis underwent the Cassini state transition reduced the AM of Earth, the planet became spherical, and the internal pressures substantially increased (D).

  • Fig. 2 Pressures in the interior of Earth-mass bodies can be substantially lower after giant impacts than those in the modern Earth.

    The pressures in the middle of the mantle by mass (A), at the CMB (B), and at the center (C) of post-impact bodies are presented as a function of the AM of the bound mass (symbols). Symbols indicate structures that are above (∘), below (□), or have an unclear relationship to (Δ) the CoRoL (2). The post-impact bodies plotted are restricted to those with a bound mass between 0.9 and 1.1 MEarth, and colors indicate the geometrically modified specific energy of the impact, QS. In (A) to (C), black bars denote the range of pressures in magma ocean (MO) planets of between 0.9 and 1.1 MEarth and AM equal to that of either the present-day Earth-Moon system (1 LEM) or present-day Earth alone (about 0.18 LEM). The pressures at the same levels are shown for magma ocean planets of the same mass, AM, and core mass fraction as each of the post-impact bodies (symbols) (D to F). The black line describes the pressure in an Earth-like magma ocean planet as a function of AM calculated using the HERCULES planetary structure code. Filled symbols are discussed in the main text.

  • Fig. 3 Contrary to expectations, the pressures in bodies after giant impacts are often lower than those in the larger of the pre-impact bodies.

    Symbols show the pressure differences between the pre-impact target and post-impact body for the impacts in Fig. 2 (A to C). The pressures in the target bodies were calculated using HERCULES, assuming that the body was a magma ocean planet. Panels show the pressure difference at the middle of the mantle by mass (A), at the CMB (B), and at the center (C) of bodies as a function of the AM of the post-impact bound mass. Colors indicate the mass of the target body, and symbols are the same as in Fig. 2. Filled symbols are discussed in the main text.

  • Fig. 4 The moments of inertia of condensed magma ocean planets are lower, and their rotation rates are faster than those of post-impact bodies.

    (A) The moments of inertia of the same post-impact bodies as shown in Fig. 2. (B) Moments of inertia of magma ocean planets with the same mass, composition, and AM. (C) Change in the moments of inertia due to condensation of the silicate vapor. (D) Angular velocity of magma ocean planets with the same mass, composition, and AM. Colors and symbols are the same as in Fig. 2. Black lines show the moment of inertia (A and B) or angular velocity (D) of an Earth-like, magma ocean planet as a function of AM. Note the large change in vertical scale between (A) and (B).

  • Fig. 5 Pressures in the interior of Earth-mass bodies change substantially during cooling and tidal evolution.

    The change upon condensation of the post-impact vapor, i.e., the difference in pressure between the post-impact state (Fig. 2, A to C) and the magma ocean planet (Fig. 2, D to F), varies substantially between different impacts (A to C). The decrease in the AM of Earth during lunar tidal recession could have substantially increased the internal pressures in the planet. (D to F) Demonstration of the increase in internal pressures upon tidal recession of the Moon to the Cassini state transition for a body with a given initial AM. Assuming that the AM of the Earth-Moon system had reached its present-day value, the AM of Earth at the Cassini state transition (a lunar semi-major axis of about 30 Earth radii) was 0.417 LEM. The black line shows the pressure increase for an Earth-like body. Symbols and colors are the same as in Fig. 2. Paths and points in (E) are discussed in the main text.

  • Fig. 6 The rotation rates expected during the giant impact stage of planet formation could substantially reduce the internal pressures in bodies of a wide range of masses.

    (A) The angular velocity of different mass bodies at the end of accretion as calculated in (3) (gray points and bars). The bars are the 1σ standard deviation in the rotation rates found in their simulations. The gray line gives the critical angular velocity for breakup of a rigid, spherical body of bulk density 3000 kg m−3 as used in (3). The black and red lines give the CoRoL calculated using HERCULES for magma ocean planets and substantially vaporized, thermally stratified bodies, respectively. (B) AM of different mass bodies as calculated in (3) (gray points and bars). Notations and lines are the same as in (A) but in AM space. (C) Pressure at the CMB for Earth-like, magma ocean planets of different masses and AM in increments of 1 LEM (colors) calculated using HERCULES. The black line gives the pressure at the CoRoL for a magma ocean planet.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/5/9/eaav3746/DC1

    Fig. S1. Pressure change in cooling from the CoRoL to a magma ocean planet.

    Fig. S2. Effect of forming the Moon on internal pressures.

    Fig. S3. Isentropes for the M-ANEOS–derived forsterite equation of state in pressure-temperature space.

    Fig. S4. Effect of thermal state on the pressure in condensed bodies.

    Fig. S5. Sensitivity to the number of concentric layers used in HERCULES.

    Fig. S6. Sensitivity to the number of points used to describe each surface in HERCULES.

    Fig. S7. Sensitivity to the maximum spherical harmonic degree used in HERCULES.

    Fig. S8. Comparison of pressures calculated using SPH and HERCULES.

    Table S1. Impact parameters and properties of resulting bodies at different stages in evolution.

  • Supplementary Materials

    The PDF file includes:

    • Fig. S1. Pressure change in cooling from the CoRoL to a magma ocean planet.
    • Fig. S2. Effect of forming the Moon on internal pressures.
    • Fig. S3. Isentropes for the M-ANEOS–derived forsterite equation of state in pressure-temperature space.
    • Fig. S4. Effect of thermal state on the pressure in condensed bodies.
    • Fig. S5. Sensitivity to the number of concentric layers used in HERCULES.
    • Fig. S6. Sensitivity to the number of points used to describe each surface in HERCULES.
    • Fig. S7. Sensitivity to the maximum spherical harmonic degree used in HERCULES.
    • Fig. S8. Comparison of pressures calculated using SPH and HERCULES.
    • Legend for table S1

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    Other Supplementary Material for this manuscript includes the following:

    • Table S1 (.csv format). Impact parameters and properties of resulting bodies at different stages in evolution.

    Files in this Data Supplement:

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