# Glossary

angular momentum
  The momentum associated with the rotational motion of a body.

aspect ratio
  The ratio of the height to the radius for a two-dimensional structure such as a protoplanetary disc or an accretion disc. Typically where is the sound speed and is the Keplerian speed.

coagulation
  The process by which small (micron-sized) particles in a protoplanetary disc collide with each other gently enough that they stick together to form millimetre-sized aggregates.

cooling criterion
  The condition necessary for a protoplanetary disc to undergo self-regulation when forming planets via the disc-instability scenario. It is satisfied if the cooling time obeys where is the Keplerian angular speed.

cooling time
  The characteristic timescale for a system to reduce its temperature to some previous level.

core-accretion scenario
  A model for planet formation in which planets form by accumulation of solids into a core, on which an atmosphere is accreted once a critical value of the core mass is achieved. Initially, micron-sized dust grains in a protoplanetary disc coagulate to form metre-sized rocks, then kilometre-sized planetesimals, Mercury-sized planetary embryos and eventually planetary cores. Contrast with disc-instability scenario.

critical mass
  In relation to planet formation, the limiting mass of a planetary core above which the gas surrounding it cannot maintain hydrostatic equilibrium and starts contracting. Exceeding the critical mass triggers a phase of rapid accretion onto the core until the gas in the protoplanetary disc is dispersed.

disc-instability scenario
  A model for planet formation in which planets form directly from gravitational instabilities within a protoplanetary disc. It may be responsible for the formation of massive planets that lie at large distances from their star. Contrast with core-accretion scenario.

disc scale height
  The scale height of an accretion disc or protoplanetary disc. It is generally given by where is the sound speed and is the Keplerian angular speed.

escape velocity
  A quantity that gives the minimum speed required for an object to escape the gravitational influence of a massive body. In Newtonian gravity, the magnitude of the escape velocity is given by where is the universal gravitational constant, is the mass of the gravitating body and is the initial distance from its centre.

exoplanet
  A planet orbiting a star other than the Sun. According to the International Astronomical Union (IAU), an exoplanet has a mass that is below the limiting mass for nuclear fusion of deuterium (currently calculated to be 13 times the mass of Jupiter for objects with the same isotopic abundance as the Sun) and orbits a star or stellar remnant. This definition takes no account of how the object formed, so it is possible that the definition may include objects that would otherwise be classified as brown dwarfs.

feeding zone
  The distance either side of the core from within which further planetesimals are accreted during the growth of planetary cores in a protoplanetary disc. Typically where is a small constant and is the Hill radius.

fragmentation
  The process by which a contracting interstellar cloud breaks up into a number of separate cloudlets as energy is radiated from the cloud and the Jeans mass decreases.

gravitational focusing
  A dimensionless parameter that describes how the gravitational attraction between two bodies increases their collision probability. It is expressed as where is the escape velocity and is the relative velocity between the two impacting bodies.

Hill radius
  The radius of the Hill sphere defined by where is the semimajor axis of the planet’s orbit around a star, is the mass of the planet and is the mass of the star.

hot Jupiter
  A giant exoplanet in an extremely close orbit around a star.

hydrostatic equilibrium
  A situation in which the forces acting on a fluid (normally gravitational forces) are balanced by the internal pressure of the fluid (including thermal, degeneracy and radiation pressure), so that the fluid neither collapses nor expands.

isolation mass
  During the growth of a planetary core, this is the total mass of planetesimals within the feeding zone.

Jeans mass
  In a disc geometry (such as a protoplanetary disc undergoing planet formation via the disc-instability scenario), the Jeans mass is where is the surface density of the disc.

Kepler’s first law
  One of three laws of planetary motion stated by Johannes Kepler. The first law states that planets orbit stars in elliptical orbits with the star at one focus of the ellipse.

Kepler’s laws
  Three laws summarising the nature of planetary motion.

Kepler’s second law
  One of three laws of planetary motion stated by Johannes Kepler. The second law states that a line joining a planet and its star sweeps out equal areas in equal times. The consequence of this is that planets move fastest when they are closest to their star.

Kepler’s third law
  One of three laws of planetary motion stated by Johannes Kepler. The third law states that the square of a planet’s orbital period is proportional to the cube of the semimajor axis of its orbit . More generally: where is the total mass of the star and planet.

Keplerian
  A term used to denote quantities that relate to properties of a (circular) Keplerian orbit, e.g. Keplerian speed, Keplerian angular speed.

Keplerian angular speed
  The angular speed of a body in a Keplerian orbit, i.e. where is the mass of the central body and is the orbital radius.

Keplerian orbit
  The orbit a point mass executes if it is subject only to the gravitational force from another point-like mass. Quite often this term is used in a stricter sense to denote a circular orbit with constant angular speed that obeys Kepler’s third law.

Keplerian orbital speed
  The tangential speed of a body in a Keplerian orbit, i.e. where is the mass of the central body and is the orbital radius.

Keplerian speed
  The tangential speed of a body in a Keplerian orbit, i.e. where is the mass of the central body and is the orbital radius. Contrast with Keplerian angular speed.

Kozai-Lidov effect
  Synchronised changes in the eccentricity and inclination of an orbit such that one increases while the other decreases, in a cyclic manner, caused by the presence of a third, more distant companion.

migration
  The process by which protoplanets move away from their place of formation in a protoplanetary disc.

minimum-mass solar nebula
  A hypothetical protoplanetary disc with a surface density profile defined as the minimum value of the surface density that a protoplanetary disc would need to have to form our Solar System.

molecular cloud
  A cloud of dense cold gas containing molecules, principally molecular hydrogen (), together with dust. Molecular clouds are generally detected through emission lines of molecular species at radio frequencies; important species include , and . Because molecular clouds are cold and dense, they are important sites for star formation.

oligarchic growth
  In planetary formation, this describes the situation where the largest planetary embryos grow quickly while the smallest grow slowly.

planetary core
  A solid body resulting from a planetary embryo that will accumulate further material to form the core of a planet.

planetary embryo
  An object that will likely grow into a planet. Planetary embryos comprise roughly Mercury-sized bodies formed from planetesimals and may grow into planetary cores.

planetesimal
  Solid, roughly kilometre-sized bodies that are intermediate in size between rocks and planetary embryos during the growth of planets in protoplanetary discs.

protoplanet
  A planet growing by a process of accretion in the protoplanetary disc of a young star or protostar. Small inhomogeneities in the disc are thought to lead to the growth of protoplanets.

protoplanetary disc
  A protoplanetary disc consists of cold gas and dust, and is left over from the material that formed the central protostar. Small inhomogeneities in the disc are thought to lead to the growth of protoplanets. Radiation pressure and the solar wind compete against the gravity of the protoplanets and eventually drive off the remaining material of the protoplanetary disc.

radial drift speed
  The speed with which particles in a disc move radially through it. It depends on the Stokes number typically according to where is the Keplerian speed and where is a dimensionless constant and is the aspect ratio of the disc.

runaway growth
  An accelerated phase in the growth of planetesimals.

self-regulation
  In relation to the disc-instability scenario for planet formation, the situation where, as a protoplanetary disc becomes unstable (due to the Toomre Q parameter falling below ), shock waves are generated in the disc. These heat up the disc, so increasing 𝑄, and the disc stabilises. A disc will undergo self-regulation if the cooling criterion is met.

sound speed
  The speed at which the wavefronts of a sound wave propagate. In an ideal gas, the sound speed is given by where is the gas pressure and is its density, or equivalently by where is the temperature, is the Boltzmann constant and is the mean mass of the particles involved.

Stokes number
  A dimensionless parameter which characterises how well particles embedded in a fluid flow follow streamlines. It is given by where is the stopping time and is the Keplerian angular speed. Large particles will generally have large Stokes numbers () and will detach from the flow when it changes velocity abruptly. Small particles will generally have small Stokes numbers () and will closely follow fluid streamlines at all times.

stopping time
  A characteristic timescale that describes how a particle of mass interacts with gas surrounding it. It is defined as where is the magnitude of the drag force that acts in the opposite direction to , which is the speed of the particle with respect to the gas.

streaming instabilities
  A mechanism for the formation of planetesimals in which the drag felt by solid particles orbiting in a gas disk leads to their spontaneous concentration into clumps which can gravitationally collapse.

surface density
  The density, in units of mass per unit area, of an (essentially) two-dimensional structure such as a protoplanetary disc or accretion disc.

Toomre criterion
  The necessary condition that must be satisfied for a protoplanetary disc to undergo planet formation via the disc-instability scenario. For fragmentation to occur the local surface density of the disc needs to be high enough that the self-gravity of the gas and its differential rotation are higher than the thermal pressure.

Toomre Q parameter
  For a protoplanetary disc to fragment, and for planets to form via the disc-instability scenario, the disc must satisfy the Toomre criterion. For this to happen, the Toomre parameter must satisfy where where is the Keplerian angular speed, is the sound speed, and is the disc surface density.

velocity dispersion
  The spread of velocities present in a given population of objects.

OpenLearn - The formation of exoplanets
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