Stars and stellar evolution

A star is a self-gravitating ball of plasma in which pressure from nuclear fusion balances gravity. Almost everything about its life is determined at birth by one parameter.

Formation

Star formation begins when a region of a molecular cloud becomes gravitationally unstable. The condition is that self-gravity exceeds thermal pressure support, which happens above a critical Jeans mass that falls with increasing density and rises with temperature.

Collapse is not smooth. The cloud fragments as it contracts, because increasing density lowers the Jeans mass locally, so a single collapsing region breaks into many protostars. This is why stars form in clusters rather than singly.

Angular momentum is the central difficulty. A cloud core with even slight rotation spins up enormously as it contracts, and would fly apart long before reaching stellar density. The excess is shed into a circumstellar disc, which is also where planets form, and removed by magnetically driven bipolar jets. Star formation and planet formation are therefore the same process viewed at different radii.

The distribution of masses that results is the initial mass function, approximately $\mathrm{d}N/\mathrm{d}M \propto M^{-2.35}$ above a solar mass. Low-mass stars vastly outnumber high-mass ones, while high-mass stars dominate the light and the chemical enrichment.

Mass determines everything

Once fusion begins, a star settles onto the main sequence, where hydrogen fuses to helium in the core. Its position there is set almost entirely by mass, through the mass-luminosity relation:

Since the fuel supply is proportional to $M$ and the burn rate to $L$, lifetime scales as

The range is extraordinary. A star sixty times more massive than another lives less than a ten-thousandth as long. Massive stars are rare, brief and disproportionately important: they produce most of the ultraviolet light, most of the heavy elements, and all of the core-collapse supernovae.

Stars below about 0.5 M☉ have main sequence lifetimes longer than the current age of the universe, so no low-mass star has ever died of old age.

The Hertzsprung-Russell diagram

Plotting luminosity against surface temperature produces the single most informative diagram in astronomy. Stars do not scatter across it; they occupy narrow regions.

Because a cluster’s stars all formed at once, the point where its main sequence ends, the turn-off, gives the cluster’s age directly: stars above that mass have already evolved off. This is the primary method for dating stellar populations and hence for establishing that the oldest globular clusters are comparable in age to the universe itself.

After the main sequence

When core hydrogen is exhausted, the core contracts and heats while the envelope expands and cools. The star moves off the main sequence to the red giant branch.

For a solar-mass star, helium ignition occurs in a degenerate core in a runaway helium flash, after which the star settles onto the horizontal branch burning helium to carbon. Later, shell burning on the asymptotic giant branch drives strong mass loss, ejecting the envelope as a planetary nebula and leaving the exposed core as a white dwarf.

Massive stars proceed further, fusing successively heavier elements in onion-like shells: carbon, neon, oxygen, silicon. Each stage releases less energy and runs faster than the last; silicon burning lasts about a day. The sequence stops at iron, because iron has the highest binding energy per nucleon and fusing it consumes energy rather than releasing it.

The endpoints

White dwarfs are supported by electron degeneracy pressure, a quantum effect independent of temperature. Because degenerate matter becomes smaller as mass increases, there is a maximum: the Chandrasekhar limit of about 1.4 M☉. Above it, electron degeneracy cannot hold.

Neutron stars result when core collapse compresses matter past electron degeneracy, forcing protons and electrons together into neutrons. The result is roughly 1.4 M☉ within a radius of 10 to 12 km, at densities exceeding those of an atomic nucleus. Their maximum mass, the Tolman-Oppenheimer-Volkoff limit, is around 2 to 2.3 M☉ and depends on the poorly known equation of state of dense nuclear matter, which gravitational wave observations of merging neutron stars now constrain. See Multi-messenger astronomy.

Black holes form when nothing can halt the collapse. See Black holes.

Supernovae and enrichment

Two physically unrelated processes share the name.

Type Ia consistency is what made the discovery of cosmic acceleration possible, because it allows distances to be measured to billions of light years. See Cosmology.

Both types return processed material to the interstellar medium, and this is how the universe acquires elements heavier than helium. Core-collapse events supply oxygen and the alpha elements; Type Ia supply most of the iron; and the heaviest elements form by rapid neutron capture in neutron star mergers, which gravitational wave and electromagnetic observation of GW170817 confirmed directly.

Every atom heavier than helium in a planet or a person was produced inside a star and released by one of these processes. That statement is now supported by direct observation rather than inference alone.

References

• Prialnik, D. An Introduction to the Theory of Stellar Structure and Evolution, 2nd ed., Cambridge University Press, 2009.
• Carroll, B. W. and Ostlie, D. A. An Introduction to Modern Astrophysics, 2nd ed., Cambridge University Press, 2017.
• Salpeter, E. E. “The Luminosity Function and Stellar Evolution”, The Astrophysical Journal, 121:161, 1955.
• Chandrasekhar, S. “The Maximum Mass of Ideal White Dwarfs”, The Astrophysical Journal, 74:81, 1931.
• Woosley, S. E., Heger, A. and Weaver, T. A. “The evolution and explosion of massive stars”, Reviews of Modern Physics, 74:1015, 2002.