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The astronomical unit is a length scale used for Solar System distances, approximately $1.5\times 10^{13}\mathrm{cm}$. Coarse estimates sometimes round it to $10^{13}\mathrm{cm}$. Numerical coefficients in planet formation estimates depend on which approximation is used.

A protoplanetary disk is a flattened, rotating reservoir of gas and solids around a young star. Its radial gravity is usually dominated by the host, making its rotation close to Keplerian rotation, ${\Omega }_K=(G{M}_{\star }/r^3{)}^{1/2}$. Gas pressure provides vertical support and a small radial correction to the orbital speed; it does not make the disk a nonrotating spherical atmosphere.

At height $|z|\ll r$, vertical hydrostatic equilibrium in the stellar gravitational field givesFor a locally vertically isothermal ideal gas, $P_g={\rho }_g{c}_s^2$ with $c_s^2=k_{B}T/(\mu m_H)$, where $\mu$ is mean molecular weight. Integration givesHere ${\Sigma }_g$ is the vertically integrated gas surface density of a disk, and $H$ is the isothermal disk scale height. The disk aspect ratio $H/r=c_s/v_K$ is small in a geometrically thin disk. For $T\propto r^{-q}$ it scales as $r^{(1-q)/2}$, so $q<1$ produces disk flaring. This illustrative local vertical model does not determine a unique radial surface-density law or temperature normalization from the information given.

The gas is predominantly molecular hydrogen and helium. A much smaller component consists of heavier elements, partitioned between vapor, solid refractory grains and condensed volatile ices. A gas-to-solid mass ratio of order $100$ is a common initial fiducial model, not a universal measurement applying at every disk radius or evolutionary stage. Solids can grow and settle while gas accretes or disperses, changing the local ratio substantially.^[ref]

Thermal structure organizes composition. In the hottest inner region, grains can sublimate and much of their material remains in the gas. Refractory silicate minerals and metallic grains survive at lower temperatures; farther out, water and then other sufficiently volatile species can condense when their local condensation conditions are met. The water snow line can raise the solid inventory available to planet formation. Its location depends on stellar irradiation, accretion heating, opacity and gas pressure, and evolves with time; it is not fixed merely by naming a star or adopting a solar-system distance.

Stellar radiation heats the exposed surface of a passive disk. Beneath it, shielding can leave a cooler, molecule-rich interior with a higher mass density. In the inner actively accreting disk, dissipation can instead make the optically thick midplane the hottest region. These are distinct heating regimes; a vertically isothermal profile is an analytic approximation rather than a claim that every real layer has the same temperature. Dust opacity controls how radiation is absorbed and re-emitted. Infrared and millimetre emission probe solid material, while spectral lines probe gas; neither observable alone supplies a model-free inventory of the whole disk.

Dust settling in an astrophysical disk makes larger, less tightly coupled particles more concentrated toward the midplane, while turbulence and mixing oppose that settling. For an aerodynamic stopping time $t_s$ short compared with ${\Omega }_K^{-1}$, terminal vertical balance gives $v_z\simeq -{\Omega }_K^2{t}_{s}z$. Small grains remain better coupled to the gas. Radial drift also changes the distribution of solids and their access to snow lines and embryos.

The disk evolves through accretion and angular momentum transport, potentially involving turbulent stresses, magnetorotational instability or magnetically driven winds where conditions permit. Protoplanetary disk dispersal eventually removes gas through accretion and mass loss, including photoevaporation. In standard evolutionary pictures this occurs on a scale of a few million years, with substantial system-to-system variation. That finite reservoir lifetime is central to whether an embryo acquires a massive gaseous envelope.^[ref]

The essential structure is a nearly Keplerian gas disk with vertical pressure support, radial and vertical thermal gradients, and an evolving solid population concentrated by settling, growth and drift. Its composition is set jointly by the original elemental inventory, local condensation conditions and transport.

Sub-Keplerian rotation means that the gas rotates more slowly than a pressure-free particle on a circular orbit at the same cylindrical radius. Let $v_K=(G{M}_{\star }/r{)}^{1/2}$. Neglecting radial acceleration, radial force balance in the gas isAn outwardly decreasing pressure, $d{P}_g/dr<0$, supplies part of the inward-gravity balance through an outward pressure force. Less centrifugal support is needed, so $v_{g\varphi }<v_K$. Using $c_s^2=P_g/{\rho }_g$, define the pressure-gradient parameter of a protoplanetary disk byThenFor a thin disk and a smooth radial pressure profile, $\eta$ is small, of order $(H/r{)}^2$. The factor of two is part of this explicit convention; changing the convention for $\eta$ changes the drift formula correspondingly.

A solid particle feels essentially no continuum gas-pressure support. Left alone, it would orbit at $v_K$, so in the gas it feels a headwind. Drag removes angular momentum, causing radial drift of solids in a gas disk. Define Stokes number $\mathrm{St}={\Omega }_K{t}_s$ using the aerodynamic stopping time $t_s$. In a dilute test-particle limit with linear drag, negligible radial gas flow and small departures from a circular Keplerian orbit, let $u_{\varphi }=v_{p\varphi }-v_K$. The steady local radial and azimuthal balances areSolving givesThe sign is inward for the usual negative pressure gradient. Very small particles, $\mathrm{St}\ll 1$, closely follow the gas and have a small relative drift $v_{pr}\simeq -2\eta v_K\mathrm{St}$. Very weakly coupled large bodies, $\mathrm{St}\gg 1$, also drift slowly, with $v_{pr}\simeq -2\eta v_K/\mathrm{St}$. The fastest pressure-driven inward drift occurs at $\mathrm{St}=1$, where $|v_{pr}|=\eta v_K$. The corresponding physical grain or aggregate size depends on gas density, orbital radius and the drag regime; “metre-size barrier” is a conventional description of some disk models, not a universal size.

The drift timescale in this model isIt can be much shorter than the disk gas lifetime, threatening loss of the material needed to make planetesimals. Growth through the vulnerable coupling range must compete with this loss, while differential drift generates collisions that may stick, bounce or fragment. Radial redistribution also changes solid-to-gas ratios and moves material across condensation fronts. These are consequences for planet formation, rather than merely a small correction to an orbital frequency.

The same mechanism can help concentrate solids. At a local radial pressure maximum, $d{P}_g/dr=0$, so this component of drift vanishes. On the inside, a positive pressure gradient gives outward drift; on the outside, a negative gradient gives inward drift. Particles therefore converge toward a dust trap. Turbulent diffusion and inward gas advection can limit retention. With a nonzero radial gas speed $v_{gr}$, the test-particle result generalizes to $v_{pr}=[v_{gr}-2\eta v_K\mathrm{St}]/(1+{\mathrm{St}}^2)$, so gas advection need not vanish even at a pressure maximum.

Finally, if local solid loading becomes large, backreaction on the gas can no longer be neglected. Coupled gas-particle drift can support streaming instability and strong solid concentrations, potentially enabling gravitational collapse into planetesimals. The simple test-particle drift formula is a useful starting point, but not a description of that nonlinear high-loading regime. Pressure support creates both a drift obstacle to growth and opportunities for concentration where the pressure structure changes.

Three research directions natural in the 2017 setting are:

Small-planet atmospheres, formation through composition, and atmospheric dynamics/variability provide three concrete emerging directions. The examples describe research aims as of the paper's date, rather than treating later discoveries or later operating missions as established in 2017.

Three major research directions, appropriate to the scientific questions posed in 2018, are:

These are research goals rather than claims that the relevant mechanisms or habitable atmospheres have already been established.

A protoplanetary disk is a gas-and-solid astrophysical disk around a young star in which planet formation occurs. Its evolution combines accretion, radiation, gas dynamics and the growth of solid material. A minimum-mass solar nebula is one reconstruction of the material needed to form the Solar System.