The HR diagram and stellar evolution

One diagram, every star

Take a large sample of stars, work out each one's absolute magnitude and temperature using the tools of the last two lessons, and plot one against the other. The result, the Hertzsprung-Russell diagram, is the most information-dense picture in astronomy. Two axis conventions want keeping apart. The temperature axis genuinely runs backwards: from about 50 000 K on the left down to 2500 K on the right, so hotter is left, and it is often labelled by spectral class OBAFGKM instead. The vertical axis is only backwards when it carries absolute magnitude, whose scale was born reversed: it runs from +15 at the bottom to −10 at the top, so brighter is still higher.

The vertical axis carries the star's own output, and the boards differ only in what they print on it. Some draw the same diagram with luminosity up the side, the total power radiated, given as a multiple of the Sun's and on a logarithmic scale from about 10⁻⁴ to 10⁶, increasing upward like any ordinary log axis. That is not a different diagram. Absolute magnitude is itself a logarithmic measure of the same power, running the opposite way, which is exactly why the magnitude axis is drawn upside down: brighter is higher whichever label is printed. Read either as a luminosity against temperature plot and the picture is the same.

Stars do not scatter randomly. Most crowd onto the main sequence, the diagonal band running from hot-and-bright down to cool-and-dim, and every star on it is fusing hydrogen in its core. The Sun sits partway down, class G, absolute magnitude +4.8. The red giants sit above and to the right, cool at the surface yet hugely luminous, which by Stefan's law forces them to be enormous.

The extremes sit further out again. Higher still, in a band stretched right across the top of the diagram, are the supergiants, and the cool right-hand end of that band is the red supergiants, the swollen late stage of a heavy star: tens of thousands of times the Sun's luminosity at a surface no hotter than a red giant's, which by the same argument makes them hundreds of times the Sun's radius. Betelgeuse is the one everybody knows. Below and to the left are the white dwarfs, hot yet so faint they must be tiny. That is the Earth-sized object from the last lesson's check question.

The life of a Sun-like star

Every star begins as a nebula, a cloud of gas and dust collapsing under its own gravity. The collapse heats the core, now a protostar, until hydrogen fusion lights. The star then settles where the outward push of radiation and gas pressure balances gravity, and that equilibrium is what the main sequence is.

A star spends most of its life parked at one spot on the main sequence, fusing core hydrogen. When the core hydrogen runs low, the balance breaks. The core contracts and heats, fusion moves outward into a shell, and the outer layers swell colossally while their surface cools towards red. On the diagram the star leaves the main sequence and climbs up and to the right, becoming a red giant. The Sun will do this in about five billion years, swelling past the orbits of the inner planets.

A star of the Sun's modest mass cannot ignite much beyond helium. The bloated outer layers drift away as a glowing shell called a planetary nebula, lit by the hot core it has just uncovered. The name is a two-hundred-year-old misunderstanding, kept out of habit: in a small telescope those shells looked like the discs of planets, and there are no planets involved. What the shell leaves behind is the exposed core, a white dwarf, no longer fusing, roughly Earth-sized and doomed only to cool.

With fusion gone, what holds it up is electron degeneracy pressure, a quantum refusal of electrons to be squeezed into the same state. That support has a ceiling, the Chandrasekhar limit of about 1.4 solar masses, and a core heavier than that cannot end as a white dwarf. On the diagram the star drops down and to the left into the white dwarf region and fades. That is the Sun's whole future. Supernovae are reserved for far heavier stars.

Supernovae and the standard candle

A star several times the Sun's mass dies harder, and it takes a different road to get there. Leaving the main sequence it swells past the red giant stage into a red supergiant, out at the cool end of that band across the top of the diagram, while its core fuses on through carbon, oxygen and silicon as far as iron, where fusion stops releasing energy and the support fails. The core collapses, and the energy that collapse releases blasts the outer layers away as a core-collapse supernova, leaving a neutron star, or a black hole if the surviving core is heavy enough.

The explosion is what an observer actually sees of all that. The star brightens with astonishing speed, its absolute magnitude dropping by ten or more on the backwards scale within weeks, and for a while it outshines its entire galaxy. Keep the core-collapse label attached, because the breed that matters for distances comes from something else entirely.

Some collapsing giants also fire off gamma-ray bursts, flashes of gamma radiation lasting seconds to minutes and detectable across most of the observable universe. The spec asks you to set that output beside the Sun's, so carry the two numbers. A burst radiates of order 10⁴⁵ J in a few seconds, quoting the isotropic-equivalent energy, the figure computed as if the burst shone equally in every direction when in reality it is beamed. The Sun pours out 3.9 × 10²⁶ W, so across its whole ten-billion-year life it will manage roughly 10⁴⁴ J. One burst, in seconds, beats the Sun's entire career.

A type Ia supernova is a different animal. No massive star is involved at all. A white dwarf in a binary system detonates as a runaway thermonuclear explosion, and the fuel is broadly similar every time, a carbon-oxygen dwarf igniting through a limited set of routes, more than one of which is still argued over. That is why the peaks come out alike, near absolute magnitude −19.3, without being identical. Any object of known absolute magnitude is a standard candle. Measure its apparent magnitude, run the distance modulus, and out comes the distance.

Two qualifications belong with that. The trigger is not a single settled story. A dwarf may pull matter from an ordinary companion until it approaches the limit, or two white dwarfs may spiral together and merge, or a dwarf below the limit may be set off by a detonating skin of helium, and which route dominates is still argued over. Nor are the peaks identical. They scatter by a few tenths of a magnitude, and the fix comes from the light curve itself, since the brighter explosions fade the more slowly.

Measure the decline rate over the first fortnight or so after the peak and it tells you how bright that particular explosion really was, which is how astronomers pull the scatter down to around a tenth of a magnitude. Type Ia supernovae are therefore standardisable candles rather than perfectly identical ones, and they are bright enough to serve as distance markers across billions of light years.

They also started an argument. In the late 1990s distant type Ia supernovae came out consistently fainter than their red shifts predicted, and within the standard cosmological model that means the expansion of the universe is accelerating, driven by something now labelled dark energy. The claim leans on type Ia explosions behaving the same way across cosmic history, once corrected, and questioning that uniformity is the heart of the controversy. A standard candle is only as standard as its physics.

Neutron stars and black holes

Heavier cores leave heavier corpses. Stars born with more than roughly eight solar masses, a model-dependent boundary rather than a sharp line, are the ones whose cores collapse this way. If the collapsing core is too massive to settle as a white dwarf, gravity crushes its protons and electrons together into neutrons, leaving a neutron star. Picture one or two solar masses compressed into a sphere roughly ten kilometres in radius, made almost entirely of neutrons, at the density of an atomic nucleus.

Past even that, nothing holds. If the corpse is massive enough, its escape velocity, √2GM/r$\sqrt{2GM/r}$√(2GM/r) from the gravitational fields unit, reaches the speed of light at a finite radius. Inside that boundary nothing, light included, can leave, and the object is a black hole. The boundary is the event horizon, and its radius, the Schwarzschild radius, follows from a Newtonian shortcut, setting the escape velocity equal to c, a heuristic that happens to land on the answer general relativity gives:

Naming the furniture, an OCR definition set

OCR opens its astrophysics with six terms and asks for each one defined by name. No other board examines the list, so read this section only if OCR A is your specification. The six climb in scale, and defining them in that order is the easiest way to keep them apart.

A planet is a body in orbit around a star, massive enough that its own gravity has pulled it into a nearly spherical shape and massive enough to have swept its orbital neighbourhood clear of other bodies. In visible light it shines chiefly by reflection, though like any warm body it also emits its own thermal radiation, mostly infrared; nothing fuses inside it. A planetary satellite is a body in orbit around a planet rather than around the star directly, which covers natural moons and the artificial satellites of the gravitational fields unit alike.

A comet is a small body of ice, dust and rock orbiting a star on a highly elliptical path. Far out it is inert. Close in, the Sun's heat drives the ice straight to vapour, and radiation pressure and the solar wind blow the released gas and dust into a tail that always points away from the Sun, whichever way the comet happens to be travelling.

A solar system is a star together with everything gravitationally bound to it, meaning its planets, their satellites, and the asteroids, comets and dust between them. Ours takes the capital letters. A galaxy is a gravitationally bound collection of stars, gas, dust and dark matter, anything from millions to hundreds of billions of stars, usually with a supermassive black hole at its centre. The universe is everything that exists: all matter and radiation, and the space and time they occupy. The ladder runs satellite, planet, solar system, galaxy, universe, with each rung bound to the one above it by gravity.