Research ArticleASTRONOMY

Giant convecting mud balls of the early solar system

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Science Advances  14 Jul 2017:
Vol. 3, no. 7, e1602514
DOI: 10.1126/sciadv.1602514

Figures

  • Fig. 1 Particle size distribution in sample model asteroids that accrete a range of chondrule sizes, showing the variety of chondrule sorting [note: if the object accretes a sorted population (the current canonical view), then no additional sorting will occur].

    It is apparent that asteroid radius (lower-gravity objects show less efficient sorting), mud viscosity, and WR ratio (which also influences viscosity) affect sorting. Other factors include chondrule packing density and accretion time (objects that accrete earlier show stronger convection and more efficient sorting). In scenarios where sorting occurs, we typically see an inner core region dominated by 1- and 0.5-mm chondrules, surrounded by 0.1-mm particles, with 50-μm particles concentrated at the edge of the core and 10-μm particles distributed evenly either throughout the object or at the core-mantle boundary. Mud convection complicates this picture, with particles depleted in upwelling regions and concentrated relative to the average in downwelling regions. Particle oscillations reflect a feedback between fluid flow and particle transport. Objects with ×10 higher viscosity show no sorting (although convection still occurs).

  • Fig. 2 Visualizing individual particle trajectories (dimensionless tracer particles scattered throughout the mud) in a 100-km-radius object accreting at CAI + 3 My with WR = 1.0.

    The figure shows the range of tracer particle histories for all latitudinal coordinates at a given level in the model asteroid, for particles beginning at a level of 20 km (A), 50 km (B), and 80 km (C). We see the effect of convection strengthening over time; until by 2 My, mud convection is transporting tracer particles that started at all three levels through the entire object—from the core up to the base of the ice lid.

  • Fig. 3 Temperatures in various model asteroids at a similar stage in their evolution following the onset of convection.

    (A) A 50-km-radius object accreting 3 My after CAI with WR = 0.6 and an f/c ratio of 60:40, 0.9 My after melting. (B) A 100-km-radius object accreting at CAI + 3.5 My with WR = 0.6 and an f/c ratio of 60:40, 2.4 My after melting. (C) A 100-km-radius object accreting at CAI + 3 My with WR = 0.6 and an f/c ratio of 60:40, 1 My after melting. (D) A 100-km-radius object accreting at CAI + 3 My with WR = 1.0 and an f/c ratio of 60:40, 1.3 My after melting. (E) A 100-km-radius object accreting at CAI + 3 My with WR = 0.8, an f/c ratio of 28:72, and ×10 higher viscosity, 2.0 My after melting. (F) A Ceres-class object accreting at CAI + 3 My with WR = 0.6 and an f/c ratio of 60:40, 1.6 My after melting. (G) A Ceres-class object accreting at CAI + 3 My with WR = 1.0 and an f/c ratio of 60:40, 2 My after melting. It is noteworthy that although the model asteroids span a ×1000 range in mass and a large range in viscosity, WR ratio, and f/c ratio, they show a very similar temperature profile: Tpeak < 170°C observed in all the objects, with mud convection minimizing any internal thermal gradient.

  • Fig. 4 Visualizing individual tracer particle histories in a 100-km-radius object accreting at CAI + 3 My with WR = 1.0.

    The figure shows particle histories for all latitudinal coordinates at a given level in the model asteroid over time. There is significant range in particle T-t and WR-t trajectories: Compositional and isotopic heterogeneity over short length scales at the end of convection is expected. (A and B) Range of T-t histories for particles starting at 60 and 90 km (respectively) in our model asteroid. Although mud convection moderates temperature, there are significant excursions, particularly at early times. (C and D) Range of WR histories for particles starting at 70 and 90 km (respectively). The main modification in WR is global serpentinization at 0.9 My. However, as mud convection strengthens, strong upwelling degrades portions of the ice lid, leading to transient spikes in WR at these levels in the model asteroid. The result when convection ceases, and the arrangement of grains is locked in (perhaps approximating what we see in the meteorite), will be a material with significant grain-grain variability over short (100 μm) length scales in grain T-t and WR-t histories. This variability will be increased if secondary mineral growth occurs continually during alteration, while the whole body cools (not accounted for in our model).

Tables

  • Table of symbols in equations
    Table of symbols in equations
    αThermal expansivity of the fluid at a
    reference temperature (dimensionless)
    CMass fraction concentration of solute
    in fluid (kgsolute/kgfluid)
    ciceSpecific heat of ice (J/kg/K)
    crockSpecific heat of mineral phase (J/kg/K)
    DcEffective diffusivity (m/s2)
    EInternal energy (J/kg)
    εPorosity, fraction of volume not occupied
    by rock/mineral phase (unitless)
    ĝGravity vector (m/s2)
    GGravitational constant, 6.67 × 10−11 m3 kg−1 s−2
    hmEnthalpy of mud (J/kg)
    kPermeability (m2)
    KTThermal conductivity (W/m/°C)
    KTiceThermal conductivity of ice (W/m/°C)
    KTwaterThermal conductivity of water (W/m/°C)
    κThermal diffusivity (m2/s)
    LLatent heat of melt, ice (J/kg)
    LopSerpentinization heat of reaction (J/kg)
    λRadionuclide half-life (s−1)
    mSubscript referring to mud
    μViscosity (kg/m/s)
    PPressure (J/m3)
    QHeat source rate (W/m3)
    rRadial position (m)
    ρbBulk density (kg/m3)
    ρiceDensity of ice phase (kg/m3)
    ρrockDensity of rock/mineral phase (kg/m3)
    ρopDensity of olivine/pyroxene (kg/m3)
    ρwDensity of liquid water (kg/m3)
    ρserpDensity of serpentine (kg/m3)
    ρmDensity of mud (kg/m3)
    RLength scale (m)
    RaRayleigh number (dimensionless), ratio
    of buoyant to viscous forces; Ra = ρα gR3ΔT/κμ
    RxFraction of olivine/pyroxene remaining
    (=1 initially)
    SReaction rate (s−1)
    siceFraction of volume occupied by ice
    smFraction of volume occupied by mud
    SradEnergy of decay for a radionuclide (J/kg)
    uVelocity vector (m/s)
    u, v, wVelocity components (m/s)
    tTime (s)
    ΘLatitude (°)
    TTemperature (°C or K), as appropriate
    in different equations
    TpolarTemperature at poles
    TsrfSurface temperature (°C)
    ΔTTemperature difference between core
    and surface (°C)
    XwmVolume water fraction in mud