Planet formation

Separation of a planet's materials into compositionally different reservoirs, such as metal-rich core, silicate mantle and crust. Melting, gravitational segregation, crystallization and transport can all contribute. The conversion of gravitational energy during segregation is part of an early planet's thermal history.

A concentrated thin layer of solids can become self-gravitating if particle random velocities and stellar shear do not support it. Gas turbulence, drag and settling change both concentration and velocity dispersion. Collapse into solid planetesimals supplies seeds for core accretion and is distinct from direct fragmentation of a gaseous disk patch.

A growing solid protoplanet dynamically important compared with the surrounding smaller planetesimals. The term identifies a formation stage, rather than a single sharply specified mass.

Growth of solid aggregates through collisions and sticking in a protoplanetary disk. Relative motion can arise from Brownian motion, settling, turbulence and differential radial drift. Bouncing and fragmentation can interrupt growth; collision frequency alone does not determine whether an encounter increases aggregate mass.

A regime in which collisions disrupt aggregates faster than sticking can build larger bodies. The outcome depends on collision speed, porosity and material properties; it is distinct from loss of intact aggregates through radial drift of solids in a gas disk.

Core accretion forms a planet by building a solid core through growth and accretion of solid material. A sufficiently massive core can then bind a gaseous envelope. It is distinct from direct fragmentation through gravitational instability of an astrophysical disk.

Gravitational binding is necessary but not sufficient for gas capture. A hydrostatic envelope contracts by losing energy on a Kelvin-Helmholtz scale $t_{\mathrm{KH}}\sim |E|/L$. Solid accretion heats it, while radiative transport depends on opacity and convection carries energy when the radiative gradient is unstable. The disk supply and outer tidal/thermal boundaries also matter.

Rapid envelope growth after cooling and envelope self-gravity allow gas capture to accelerate. It requires an available disk gas supply; eventually disk transport, gap formation or protoplanetary disk dispersal can limit growth. It differs from solid-body runaway planetesimal growth.

The epoch when the gaseous envelope mass becomes comparable with the solid core mass. Envelope self-gravity then changes structure and can accelerate gas capture through cooling and contraction. Crossover is a useful stage in classical models, rather than a universal core mass independent of opacity and accretion history.

A model-dependent threshold beyond which a cooling gaseous envelope cannot remain on a slowly growing low-mass branch around a solid core. Opacity, solid accretion heating, ambient disk conditions and envelope composition affect the threshold. It is not a universal constant assigning one exact mass to every gas-giant progenitor.

A stage in which several neighboring planetary embryos dominate stirring of surrounding planetesimals and grow in a self-regulated manner. Larger embryos heat their feeding populations more strongly, weakening gravitational focusing and preventing unlimited runaway planetesimal growth. A small number of embryos coexist with many much smaller bodies.

The region of a disk from which a planetary embryo can efficiently accrete solids. Its width depends on gravitational encounters and the surrounding orbital population. Approximating that width by a multiple of the Hill radius gives a useful local isolation mass.

The mass reached after consuming an idealized local annulus of solids. With full annular width $\Delta a=Ba[M_{\mathrm{iso}}/(3M_{\star }){]}^{1/3}$ and solid surface density ${\Sigma }_s$, the balance $M_{\mathrm{iso}}=2\pi a\Delta a{\Sigma }_s$ gives the displayed value. Radial replenishment, migration and embryo mergers can overcome local isolation; defining the width with a mutual rather than single-body Hill radius changes the numerical coefficient.

Growth of planetesimal random orbital motions through gravitational encounters. The word viscous does not denote molecular fluid viscosity here. Stirring competes with gas drag, collisions and dynamical friction in setting the encounter speeds that control gravitational focusing.

A growth regime in which larger planetesimals have shorter fractional growth times. In a dispersion-dominated population with nearly mass-independent random speed and strong gravitational focusing, fixed material density gives $\dot{M}\propto M^{4/3}$. The displayed scaling is an illustrative limit, not a universal law once large bodies control the random velocities.

Capture of small drifting solids by a planetary embryo, aided by dissipation through gas drag. Its efficiency depends on the Stokes number, particle-layer thickness, embryo mass and the supply of solids; it is not simply geometric sweeping of every passing particle.

The minimum-mass solar nebula estimates a primordial gas-and-solid protoplanetary disk by spreading planetary material into annuli and restoring a solar mixture. A common idealized surface density is proportional to $r^{-3/2}$. This reconstruction is a model of minimum material requirements, not a unique history of the Solar System. Extrapolating it far beyond the planetary region need not give a physically consistent disk.

Accretion releases gravitational energy. Efficient radiation at an accretion shock leaves a lower-entropy cold start, while greater retained energy gives a higher-entropy hot start; intermediate outcomes are possible. Initial entropy changes a young planet's radius, luminosity and spectrum. Consequently an exoplanet direct imaging luminosity and age need not uniquely fix mass without a formation/evolution model.