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The formation of exoplanets
The formation of exoplanets

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Glossary

angular momentum
The momentum associated with the rotational motion of a body.
aspect ratio
The ratio of the height cap h to the radius r for a two-dimensional structure such as a protoplanetary disc or an accretion disc. Typically cap h solidus r equals c sub s solidus v sub cap k where c sub s is the sound speed and v sub cap k 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 tau sub cool less than or equivalent to one solidus left parenthesis three times omega sub cap k right parenthesis where omega sub cap k 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 cap h equals c sub s divided by omega sub cap k where c sub s is the sound speed and omega sub cap k 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 v sub esc equals left parenthesis two times cap g times cap m solidus r right parenthesis super one solidus two where cap g is the universal gravitational constant, cap m is the mass of the gravitating body and r 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 normal cap delta times a either side of the core from within which further planetesimals are accreted during the growth of planetary cores in a protoplanetary disc. Typically normal cap delta times a equals cap c times cap r sub Hill where cap c is a small constant and cap r sub Hill 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 cap f sub g equals one plus v sub esc squared divided by v sub rel squared where v sub esc is the escape velocity and v sub rel is the relative velocity between the two impacting bodies.
Hill radius
The radius of the Hill sphere defined by cap r sub Hill equals a times left parenthesis cap m sub p divided by three times cap m sub asterisk operator right parenthesis super one solidus three where a is the semimajor axis of the planet’s orbit around a star, cap m sub p is the mass of the planet and cap m sub asterisk operator 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 cap m sub Jeans equals one divided by cap sigma times left parenthesis two times k sub cap b times cap t divided by cap g times m macron right parenthesis squared where cap sigma 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 cap p sub orb squared proportional to a cubed . More generally: a cubed divided by cap p sub orb squared equals cap g times cap m divided by four times pi squared where cap m 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. omega sub cap k equals left parenthesis cap g times cap m solidus cap r cubed right parenthesis super one solidus two where cap m is the mass of the central body and cap r 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. v sub cap k equals left parenthesis cap g times cap m solidus cap r right parenthesis super one solidus two where cap m is the mass of the central body and cap r is the orbital radius.
Keplerian speed
The tangential speed of a body in a Keplerian orbit, i.e. v sub cap k equals left parenthesis cap g times cap m solidus cap r right parenthesis super one solidus two where cap m is the mass of the central body and cap r 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 ( cap h sub two ), together with dust. Molecular clouds are generally detected through emission lines of molecular species at radio frequencies; important species include CO , OH and CN . 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 tau sub cap s typically according to v sub rad equals negative v sub cap k times eta divided by tau sub cap s plus tau sub cap s super negative one where v sub cap k is the Keplerian speed and eta equals n times left parenthesis cap h solidus r right parenthesis squared where n is a dimensionless constant and cap h solidus r 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 one ), 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 c sub s is given by left parenthesis cap p solidus rho right parenthesis super one solidus two where cap p is the gas pressure and rho is its density, or equivalently by left parenthesis k sub cap b times cap t solidus m macron right parenthesis super one solidus two where cap t is the temperature, k sub cap b is the Boltzmann constant and m macron 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 tau sub cap s equals tau sub stop times omega sub cap k where tau sub stop is the stopping time and omega sub cap k is the Keplerian angular speed. Large particles will generally have large Stokes numbers ( tau sub cap s much greater than one ) and will detach from the flow when it changes velocity abruptly. Small particles will generally have small Stokes numbers ( tau sub cap s much less than one ) and will closely follow fluid streamlines at all times.
stopping time
A characteristic timescale that describes how a particle of mass m interacts with gas surrounding it. It is defined as tau sub stop equals m times normal cap delta times v solidus cap f sub drag where cap f sub drag is the magnitude of the drag force that acts in the opposite direction to normal cap delta times v , 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 cap q parameter must satisfy cap q less than one where cap q equals omega sub cap k times c sub s divided by pi times cap g times cap sigma where omega sub cap k is the Keplerian angular speed, c sub s is the sound speed, and cap sigma is the disc surface density.
velocity dispersion
The spread of velocities present in a given population of objects.