Glossary

asymptotic giant branch

(AGB) The region of the Hertzsprung–Russell diagram occupied by stars that are powered by a mixture of shell-hydrogen burning and shell-helium-burning, with a carbon and oxygen core. Shell-helium burning causes the outer envelope of the star to expand and cool further, so that stars lie above and to the right of the red giant stars in the Hertzsprung–Russell diagram in this phase.

black hole

In the general theory of relativity, an object whose density is so high that nothing that comes within a certain distance of it, crossing a boundary called the event horizon, can subsequently emerge. This includes light (photons) and other massless particles, giving the black hole its name.

brown dwarf

Objects similar to stars, but with a temperature too low for hydrogen burning to begin. Brown dwarfs contract from protostars in the same way as stars, but their low mass means that electron degeneracy sets in before the temperature required for thermonuclear reactions is attained.

Chandrasekhar limit

The theoretical upper limit to the mass of a white dwarf, about , also called the Chandrasekhar mass. Contrast with Tolman–Oppenheimer–Volkoff (TOV) limit.

Chandrasekhar mass

The maximum stellar mass that can be supported by electron degeneracy pressure: hence an upper limit on the mass of a white dwarf. The limit arises when the electrons at the centre of the star become fully relativistic. The value of the Chandrasekhar mass depends on the model used for the internal structure of the white dwarf and on its composition, but is around .

chemical potential

A quantity used to describe the energy that each particle in an ensemble brings to the total.

CO white dwarf

A white dwarf composed chiefly of carbon and oxygen, formed from the core of a star whose initial mass was between about and . They will have masses from to .

de Broglie wavelength

According to quantum mechanics, any force-free particle can be described by a sinusoidal de Broglie wave. The wavelength of the wave is known as the de Broglie wavelength and is related to the particle’s momentum by where is the Planck constant.

degeneracy

The phenomenon whereby more than one quantum state is associated with a particular energy level in a given system. Any energy level that corresponds to more than one quantum state is said to be degenerate.

degeneracy pressure

A pressure that arises in degenerate matter as a result of the Pauli exclusion principle, which forbids two fermions in a system from occupying the same quantum state. This means that a degenerate system always has a non-zero kinetic energy density and therefore a non-zero pressure, independent of its temperature.

degenerate matter

Matter that is so dense that the laws of quantum mechanics must be used to describe the behaviour of the particles that it consists of. The critical density for degeneracy is the quantum concentration: if the density exceeds this value then the system will be degenerate.

electron

A type of elementary particle with charge , mass (or about ) and spin . The electron is a stable lepton. As far as is known, it has no internal structure, and is therefore regarded as a truly fundamental particle. Electrons are constituents of all atoms.

electron capture

A form of beta decay in which a nucleus absorbs one of its own electrons, causing a proton to become a neutron and a neutrino to be emitted.

electron degeneracy

A condition in which the quantum nature of electrons cannot be ignored. If electrons are packed so densely that their separations are comparable to their de Broglie wavelength, then the Pauli exclusion principle prohibits the overlapping of electrons with the same energy.

electron degeneracy pressure

Pressure due to degenerate electrons.

equation of state

An equation that relates the variables of pressure, volume and temperature for a macroscopic system in an equilibrium state. (1) For an ideal gas, the equation of state is or , where is the Boltzmann constant. (2) For non-relativistic degenerate electrons, where . (3) For ultra-relativistic degenerate electrons, where .

Fermi energy

The energy of the highest occupied state is called the Fermi energy, . A degenerate gas may be regarded as very cold, the available energy levels being much higher than those corresponding to the temperature of the material. For this reason, the Fermi energy is useful in considering the state of degenerate matter in the cores of low-mass giant stars or in compact stellar remnants.

Fermi kinetic energy

The kinetic energy (in the non-relativistic case) of a particle whose momentum is the Fermi momentum .

Fermi momentum

The momentum magnitude of a particle whose energy is the Fermi energy where (in the non-relativistic case).

fermion

A subatomic particle with spin . Electrons, protons and neutrons are all fermions.

free-fall time

The time it would take for a body to collapse under the influence of gravity alone.

gravitational potential energy

The potential energy of a particle or body that arises from its interaction with other particles or bodies via the (conservative) gravitational force. The gravitational potential energy of a test mass , placed at a point with gravitational potential due to a central body of mass , is given by , where is the mass of the central body.

helium burning

A nuclear fusion process in which helium nuclei react with one another to produce carbon, via the triple-alpha process. The process is initiated at temperatures of around , and can, for a time, be the dominant means of energy production in the cores of post-main-sequence stars.

helium flash

A runaway thermonuclear reaction that takes place in the centres of low-mass () stars when they initiate helium burning. Because the electrons in the centres of these stars are degenerate when helium burning starts, and because the electron pressure in the centre is dominant, the cores do not respond to the increased energy supply by expanding.

Hertzsprung–Russell diagram

(H-R diagram) A graph showing the relationship between temperature and luminosity for a group of stars.

He white dwarf

A helium white dwarf would form from a main-sequence star whose mass is less than . Such a star will have a main-sequence lifetime of order 100 billion years, hence no such stars have yet evolved to become white dwarfs.

hydrogen burning

A nuclear fusion process in which hydrogen nuclei react with one another (possibly with the involvement of other nuclei) to produce helium. The process occurs in the cores of main-sequence stars, where it is the dominant form of energy production. It can also be responsible for shell burning in post-main-sequence stars.

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.

main sequence

A well-defined region in the Hertzsprung–Russell diagram, showing a positive correlation between temperature and luminosity, in which stars in their (core) hydrogen-burning phase can be found. Protostars evolve onto the main sequence and spend most of their lifetime as stars there until core hydrogen burning ceases and they evolve towards the red giant branch.

mass fraction

The number fraction weighted by the mass of each type of particle. The mass fraction of a particular type of particle in a sample may be expressed as , where is the mass per particle, is the number density, and is the overall mass density of the sample.

mass gap

The apparent absence of compact objects between the upper mass limit for neutron stars and the observed lower mass limit for black holes.

neutrino

A spin uncharged lepton of very small mass. Three different types of neutrino are known: electron neutrino, muon neutrino and tau neutrino.

neutron

An uncharged elementary particle with mass (about 0.1% greater than that of the proton), and spin . Neutrons are baryons, composed of up and down quarks, and (when free) are unstable, with a mean lifetime of about 15 minutes.

neutron degeneracy

A condition in which the quantum nature of neutrons cannot be ignored. If neutrons are packed so densely that their separations are comparable to their de Broglie wavelength, then the Pauli exclusion principle prohibits the overlapping of neutrons with the same energy.

neutron degeneracy pressure

Pressure due to degenerate neutrons.

neutron drip

Under conditions of extremely high density (), the most stable nuclei are those with large neutron excesses compared to normal. At still higher densities, (), free neutrons ‘drip’ from the nuclei, giving rise to a sea of nuclei, electrons and free neutrons.

neutronisation

The fusion of an electron with a proton in a nucleus to produce a neutron, thus reducing the atomic number of the nucleus by 1 and increasing the neutron number by 1. Neutronisation occurs in the high density of compact stellar remnants, and produces neutron-rich isotopes prior to neutron drip occurring.

neutron star

A stellar-mass object supported against gravitational collapse by the degeneracy pressure of neutrons. A neutron star is expected to form in the final stages of the life of a massive star; at extremely high densities and pressures it becomes energetically favourable for protons and electrons to merge (inverse beta decay).

nucleon

A term used to mean either a proton or a neutron.

number density

The number of particles per unit volume, usually represented by the symbol . The SI unit of number density is .

number of electrons per nucleon

The quantity used to define the electron number density as . For pure hydrogen it is equal to 1, whereas for helium-4, carbon-12 and oxygen-16 it is equal to 0.5.

ONeMg white dwarf

A white dwarf composed chiefly of oxygen, neon and magnesium, formed from the core of a star whose initial mass was between about and . ONeMg white dwarfs will have masses in the range about .

Pauli exclusion principle

A principle asserting that no two fermions can occupy the same quantum state.

photodisintegration

The breakup of a nucleus into small parts due to the absorption of a photon – typically a gamma ray – whose energy exceeds the binding energy of the compound nucleus.

planetary nebula

A shell of material with a mass of a few tenths of a solar mass that has been ejected from a star in the late red giant phase of its evolution. The gas is photoionised by the remaining hot material of the star (possibly by now a white dwarf). The majority of planetary nebulae are asymmetric, with a small fraction being largely spherical or elliptical.

polytropic stellar model

A model for the structure of a star in which the pressure and density are related by everywhere in the star, where is the adiabatic index.

proton

A type of elementary particle found in the nucleus of every atom. Protons carry a positive charge and have a mass of . The mass of a proton is about less than the mass of a neutron and the two particles have similar sizes (about ).

quantum concentration

The maximum number density of particles in some material if it is to remain non-degenerate. That is, if the actual number density , degeneracy will have set in. Quantum concentration is defined as for non-relativistic particles, and for ultra-relativistic particles.

red giant

A star which has ceased to burn hydrogen in its core and started shell hydrogen burning. Shell hydrogen burning causes the outer layers of the star to expand, making the star more luminous but reducing its surface temperature. Consequently, red giants occupy a region of the Hertzsprung–Russell diagram above and to the right of their original position on the main sequence.

red giant branch

(RGB) The region of the Hertzsprung–Russell diagram in which red giant stars are found.

Schwarzschild radius

The characteristic radius () in the general relativistic treatment of an isolated non-rotating spherically symmetric body of mass . It is about . A body all of whose mass lies within its Schwarzschild radius is a black hole.

spin

An intrinsic form of angular momentum carried by elementary particles and also by composite particles such as hadrons, nuclei and atoms. Electrons, protons and neutrons are fermions and each have spin of either +1/2 or -1/2.

supergiant star

An evolved massive star that has left the main sequence. Supergiants have a high luminosity and a range of temperatures, appearing as cool red supergiants and hot blue supergiants.

supergiant branch

The region of the Hertzsprung–Russell diagram in which supergiant stars are found.

supernova

A star whose luminosity temporarily increases to very high values before fading rapidly on a timescale of weeks to months. Energy is emitted in the form of light but also as a burst of neutrinos and as kinetic energy of ejected material. There are several ways in which this can happen.

Tolman–Oppenheimer–Volkoff (TOV) limit

The theoretical upper limit to the mass of a neutron star, about . Contrast with Chandrasekhar limit.

white dwarf

A stellar-mass compact object, with a mass below the Chandrasekhar mass () supported against gravitational collapse by the degeneracy pressure of electrons. White dwarfs are the final products of the evolution of low-mass stars, after thermonuclear reactions have ceased and the outer regions of the star have been lost in stellar winds or as a planetary nebula.