Research ArticleASTRONOMY

Origin of Phobos and Deimos by the impact of a Vesta-to-Ceres sized body with Mars

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Science Advances  18 Apr 2018:
Vol. 4, no. 4, eaar6887
DOI: 10.1126/sciadv.aar6887
  • Fig. 1 Accretion of a Phobos-Deimos type system from an impact-generated disk with initial mass Mdisk = 10−5 MM.

    The Roche interior disk’s mass and radial extent are indicated by thick horizontal bar; black circles show masses and semi-major axes of simulated moons, with horizontal lines indicating radial variation due to orbital eccentricity. (A) The initial outer disk is described by 1500 particles with a size frequency distribution ∝ d−3 (d is particle diameter) and a surface density profile ∝ r−5, as suggested by SPH simulation results (see the Supplementary Materials). (B and C) Moons with up to ~10 times the mass of Phobos and Deimos accrete in the mid-region of the outer disk, but strong tidal interaction with Mars causes them to spiral inward and be lost. (D) After 107 years, two small moons with similar properties to those inferred for Phobos and Deimos (red circles) remain on orbits straddling async.

  • Fig. 2 Results of disk accretion simulations.

    Left axis and symbols: Total mass of final moons orbiting beyond the synchronous orbit across ~90 accretion simulations as a function of initial disk mass and assumed martian tidal parameters. Survival of small moons (defined as having a total mass < 10−7 MM, which is ~5 MPD, represented by dashed line) requires Mdisk ≤ 3 × 10−5 MM and (Q/k2) <80. Right axis and solid curve: Percentage of all accretion simulations with final moons orbiting beyond async as a function of the initial disk mass. For cases with Mdisk ≥ 5 × 10−5 MM, either no moons survive beyond async or those that do survive are more massive than Phobos-Deimos by a factor of 10 or more (see also the Supplementary Materials). The latter are moons that initially accreted interior to async but were subsequently driven outward beyond async by mutual interactions and disk torques.

  • Fig. 3 Simulations of the impact of a Vesta-mass body with Mars, with Mimp = 0.5 × 10−3 MM, vimp = 1.5 vesc (7 km s−1), and a 45° impact angle.

    Color scales with temperature in kelvin; distances shown in units of 103 km. Top row: 106-particle simulation with standard SPH. Bottom row: Same impact modeled with SPH + particle splitting and an order-of-magnitude higher resolution of the ejected material. After 10 hours, the disk mass is 8.5 × 10−6 MM, with ~2 MPD having equivalent circular orbits at and beyond ~5 RM, consistent with subsequent accumulation of Phobos and Deimos in the 5- to 7-RM region. Disk material orbiting beyond the Roche limit is 85% martian in origin and 12% vapor by mass, with temperatures between 1800 and 2000 K.

  • Fig. 4 Properties of disks simulated with SPH + particle splitting of the ejected material.

    Shape indicates impactor mass, with (Mimp/MM) = 3 × 10−3 (circles), 10−3 (triangles), and 0.5 × 10−3 (squares). Color scales with impact velocity, with blue, yellow, orange, and red corresponding to (vimp/vesc) = 1.1, 1.5, 2, and 3, respectively. Dashed lines indicate upper limit on disk mass needed to preserve small moons near async based on our accretion simulations. Plots show disk mass versus (A) scaled impact parameter (equal to the sin of the impact angle, with a 90° angle corresponding to a grazing impact), (B) percentage of Roche-exterior disk originating from Mars, and (C) aeq,max. The cumulative radial disk mass profiles for disks with masses <3 × 10−5 MM are shown in (D).

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/4/4/eaar6887/DC1

    Supplementary Methods and Data

    fig. S1. Disk masses produced by N = 5 × 105-particle SPH impact simulations with differentiated impactors having masses Mimp = 0.03 MM (circles) and 0.003 MM (triangles), shown as a function of the scaled impact parameter, equal to the sin of the impact angle where 90° is a grazing impact.

    fig. S2. Properties of disks produced by N = 1.4 × 106-particle SPH impact simulations with undifferentiated impactors having masses Mimp = 3 × 10−3 MM (circles), 10−3 MM (triangles), and 0.5 × 10−3 MM (squares).

    fig. S3. Schematic of particle splitting.

    fig. S4. Instantaneous disk mass calculated at various times in three SPH simulations of the same impact but performed with 105 equal-mass SPH particles (blue curve), 105 particles plus particle splitting of the impactor and ejected material (gray curve), and 106 equal-mass particles (orange curve).

    fig. S5. Orbital elements of disk particles from the three SPH simulations shown in fig. S4, which model the same impact with 105 particles (top, blue points), 105 particles + particle splitting of the ejected material (middle, gray points), and 106 particles (bottom, orange points).

    fig. S6. Fate of material in Fig. 2 simulation.

    fig. S7. Snapshots of the evolution of the initial disk from Run 73 (table S1).

    fig. S8. Snapshots of the evolution of the initial disk from Run 86 (table S1).

    table S1. Accretion simulation data.

    References (3638)

  • Supplementary Materials

    This PDF file includes:

    • Supplementary Methods and Data
    • fig. S1. Disk masses produced by N = 5 × 105-particle SPH impact simulations with differentiated impactors having masses Mimp = 0.03 MM (circles) and 0.003 MM (triangles), shown as a function of the scaled impact parameter, equal to the sin of the impact angle where 90° is a grazing impact.
    • fig. S2. Properties of disks produced by N = 1.4 × 106-particle SPH impact simulations with undifferentiated impactors having masses Mimp = 3 × 10−3 MM (circles), 10−3 MM (triangles), and 0.5 × 10−3 MM (squares).
    • fig. S3. Schematic of particle splitting.
    • fig. S4. Instantaneous disk mass calculated at various times in three SPH simulations of the same impact but performed with 105 equal-mass SPH particles (blue curve), 105 particles plus particle splitting of the impactor and ejected material (gray curve), and 106 equal-mass particles (orange curve).
    • fig. S5. Orbital elements of disk particles from the three SPH simulations shown in fig. S4, which model the same impact with 105 particles (top, blue points), 105 particles + particle splitting of the ejected material (middle, gray points), and 106 particles (bottom, orange points).
    • fig. S6. Fate of material in Fig. 2 simulation.
    • fig. S7. Snapshots of the evolution of the initial disk from Run 73 (table S1).
    • fig. S8. Snapshots of the evolution of the initial disk from Run 86 (table S1).
    • table S1. Accretion simulation data.
    • References (36–38)

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