Planetary Formation I: Core Accretion and Migration

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Core Idea

Core accretion is the dominant theory of planetary formation, in which kilometer-sized planetesimals accumulate through collisions to form planetary cores. Planets migrate inward and outward through gravitational interactions with the protoplanetary disk, explaining why giant planets are found at various orbital distances rather than being segregated by their formation distance from the star.

Explainer

You already know that protoplanetary disks are rotating structures of gas and dust surrounding young stars, with temperature and composition varying by distance from the star. The core accretion model explains how the raw material in these disks assembles into planets through a sequence of stages that span millions of years, starting from microscopic dust grains and ending with worlds the size of Jupiter.

The process begins with dust coagulation: micron-sized grains of silicate and ice collide gently in the disk and stick together through electrostatic and surface forces, growing into millimeter- and centimeter-sized aggregates. This early phase is straightforward, but a major theoretical challenge arises at the meter scale — the so-called meter-size barrier. Objects around a meter across experience strong aerodynamic drag from the surrounding gas, causing them to spiral inward toward the star on timescales of only a few hundred years, faster than they can grow by further collisions. The leading solution involves streaming instabilities, where particles concentrate into dense clumps through collective interactions with the gas, bypassing the problematic size range and jumping directly to kilometer-scale planetesimals.

Once planetesimals reach roughly a kilometer across, gravity takes over as the dominant growth mechanism. Larger bodies have stronger gravitational fields, so they sweep up more material than smaller ones — a process called runaway accretion. The biggest planetesimals grow fastest, quickly outpacing their neighbors. Eventually, a few dominant bodies — planetary embryos — have consumed or scattered most of the nearby material, and growth transitions to oligarchic accretion, where a handful of similarly sized embryos compete for the remaining planetesimals in their feeding zones. For rocky planets like Earth, this oligarchic stage produces Mars-sized embryos that later undergo giant impacts over tens of millions of years, gradually assembling into the final terrestrial planets.

Gas giants require an additional step. Beyond the snow line — the distance from the star where water ice condenses, roughly 3 AU in our solar system — solid cores can grow larger because ice adds to the available solid material. When a core reaches approximately 10 Earth masses (the critical core mass), its gravity becomes strong enough to capture and retain hydrogen and helium gas from the surrounding disk. Gas accretion begins slowly but accelerates dramatically in a process called runaway gas accretion, allowing a planet to balloon from a rocky core to a gas giant of hundreds of Earth masses in as little as a hundred thousand years. This must happen before the disk dissipates — typically within 3–10 million years — which sets a tight deadline for giant planet formation.

Planetary migration resolves a puzzle that the basic core accretion model cannot: why hot Jupiters orbit closer to their stars than Mercury orbits the Sun, far inside the snow line where they could not have formed. A forming planet exchanges angular momentum with the gas disk through gravitational torques. Type I migration affects lower-mass planets embedded in the disk and can move them inward (or occasionally outward) over millions of years. Type II migration occurs when a planet grows massive enough to open a gap in the disk; it then migrates locked to the disk's own viscous evolution. Migration explains the wide diversity of observed exoplanet architectures — from hot Jupiters to compact multi-planet systems — as outcomes of the same physical process operating under different disk conditions and timescales.

Practice Questions 5 questions

Prerequisite Chain

Counting to 10Counting to 20Understanding ZeroThe Number ZeroCounting to FiveOne-to-One CorrespondenceCombining Small Groups Within 5Addition Within 10Addition Within 20Two-Digit Addition Without RegroupingTwo-Digit Addition with RegroupingAddition Within 100Repeated Addition as MultiplicationMultiplication Facts Within 100Division as Equal SharingDivision as Grouping (Measurement Division)Division: Grouping (Repeated Subtraction) ModelDivision: Fair Sharing ModelDivision as Equal SharingDivision as GroupingBasic Division FactsDivision Facts Within 100Two-Digit by One-Digit DivisionDivision with RemaindersRemainders and Quotients in DivisionDivision Word ProblemsIntroduction to Long DivisionFactors and MultiplesPrime and Composite NumbersEquivalent FractionsRelating Fractions and DecimalsDecimal Place ValueReading and Writing DecimalsComparing and Ordering DecimalsAdding and Subtracting DecimalsMultiplying DecimalsDividing DecimalsDividing FractionsMixed Number ArithmeticOrder of OperationsInteger Order of OperationsVariable ExpressionsCombining Like TermsOne-Step EquationsTwo-Step EquationsSolving Multi-Step EquationsEquations with Variables on Both SidesAngle Pairs: Complementary, Supplementary, and VerticalParallel Lines and TransversalsCorresponding AnglesAlternate Interior AnglesTriangle Angle Sum TheoremExterior Angle TheoremTriangle Inequality TheoremSimilar Triangles: AA SimilaritySimilar Triangles: SSS and SAS SimilarityProportions in Similar TrianglesRight Triangle Trigonometry IntroductionTrigonometric Ratios ReviewRadian MeasureConverting Between Degrees and RadiansThe Unit CircleGraphing Sine and CosineGraphing Tangent and Reciprocal Trigonometric FunctionsDerivatives of Trigonometric FunctionsAntiderivativesIterated Integrals and Fubini's TheoremDouble Integrals in Cartesian CoordinatesDouble Integrals over Rectangular RegionsDouble Integrals in Polar CoordinatesDouble Integrals: Definition and SetupIterated Integrals and Fubini's TheoremDouble Integrals over Rectangular RegionsDouble Integrals over General RegionsApplications of Double Integrals: Area, Mass, and MomentsTriple Integrals in Cartesian CoordinatesTriple Integrals in Cylindrical and Spherical CoordinatesChange of Variables and the Jacobian DeterminantApplications of Triple Integrals: Volume and MassVector Fields and Their RepresentationsLine Integrals of Vector FieldsGreen's TheoremSurface Integrals and Flux of Vector FieldsSurface Integrals and Flux of Vector FieldsDivergence Theorem: Flux and OutflowDivergence TheoremElectric FluxGauss's LawConductors in Electrostatic EquilibriumCapacitance and CapacitorsDielectricsDielectric Constant and Relative PermittivityElectric Field Inside Dielectric MaterialsDielectric Materials and PolarizationDielectric Susceptibility and PermittivityEnergy Density in Electric FieldsElectric Current and Current DensityElectrical Resistance and ResistivityOhm's Law and Circuit ElementsElectromotive Force (EMF) and BatteriesKirchhoff's Circuit Laws: Voltage and CurrentDC Circuit Network Analysis MethodsTransient Response in RC CircuitsRC CircuitsLC and RLC CircuitsAC Circuits: FundamentalsImpedance and ReactanceAC Power and ResonanceElectromagnetic WavesThe Electromagnetic SpectrumBlackbody Radiation and Planck's LawMulti-Wavelength AstronomyPlanetary Formation: The Nebular HypothesisProtoplanetary Disk Structure and EvolutionPlanetary Formation I: Core Accretion and Migration

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