Physics › Astrophysics › The HR diagram and stellar evolution
The HR diagram and stellar evolution
Plot every star's true brightness against its temperature and the sky sorts itself into bands and clumps: a diagram that doubles as a map of stellar life. Follow a star off the main sequence and the endings get strange, from Earth-sized embers to objects whose escape velocity beats light.
Builds on Black-body radiation and spectral classes and Gravitational potential.
IN THIS TOPIC
- Sketch and read the HR diagram: main sequence, red giants, white dwarfs, and the Sun's place.
- Describe the evolution of a Sun-like star across the diagram, and the type 1a light curve as a standard candle.
- Recall neutron star properties and use the Schwarzschild radius for black holes.
WHAT YOU PROBABLY THINK
The Sun will end its life in a supernova.
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. By convention both axes run backwards: absolute magnitude from +15 at the bottom to −10 at the top, so brighter is higher, and temperature from about 50 000 K down to 2500 K left to right, so hotter is left, often labelled by spectral class OBAFGKM instead.
Stars do not scatter randomly. Most crowd onto the main sequence, the diagonal band from hot-and-bright down to cool-and-dim: these are stars fusing hydrogen in their cores, and 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 white dwarfs sit below and to the left: hot, yet so faint they must be tiny, the Earth-sized object from the last lesson's check question.
The life of a Sun-like star
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; the outer layers swell colossally and their surface cools toward red. On the diagram, the star leaves the main sequence and climbs up and to the right: it has become 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 off into space, and what remains is the exposed core: a white dwarf, no longer fusing, roughly Earth-sized, fantastically dense, and doomed only to cool. 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, and the lie above falls: supernovae are reserved for far heavier stars.
Supernovae and the standard candle
A star several times the Sun's mass dies harder. When its core collapses, the outer layers detonate as a supernova: the star's absolute magnitude increases with astonishing speed, rising within days by ten magnitudes or more, briefly outshining its entire galaxy. Some collapsing giants also fire off gamma-ray bursts, seconds-to-minutes flashes of gamma radiation so intense they are detectable across most of the observable universe.
One breed matters most. A type 1a supernova is a white dwarf pushed over a critical mass by matter stolen from a companion star; because the trigger mass is always the same, the explosion always peaks near absolute magnitude −19.3. An object of known absolute magnitude is a standard candle: measure its apparent magnitude, and the distance modulus hands you its distance. Type 1a supernovae are bright enough to serve as distance markers across billions of light years.
They also started an argument. In the late 1990s, distant type 1a supernovae came out consistently fainter than their red shifts predicted: the expansion of the universe appears to be accelerating, driven by something now labelled dark energy. The claim leans on type 1a explosions behaving identically across cosmic history, and questioning that uniformity is part of the controversy, a live reminder that a standard candle is only as standard as its physics.
WORKED EXAMPLE
The candle as a ruler
A type 1a supernova peaks at apparent magnitude +16.7. Taking its peak absolute magnitude as −19.3, find the distance to its galaxy.
m − M = 16.7 − (−19.3) = 36.0.
5 log(d/10) = 36.0, so log(d/10) = 7.2 and d = 10 × 107.2 = 1.6 × 108 pc.
A hundred and sixty million parsecs from one photometric measurement: this is how the accelerating universe was discovered, one exploding white dwarf at a time.
Neutron stars and black holes
Heavier cores leave heavier corpses. 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: an object of one or two solar masses compressed into a sphere roughly ten kilometres across, made almost entirely of neutrons, with the density of an atomic nucleus.
YOUR TURN
Nuclear matter by the teaspoon
A neutron star has mass 2.8 × 1030 kg, 1.4 solar masses, and radius 10 km. Find its density, and the mass of one teaspoonful, 5.0 × 10−6 m3, before opening the working.
Show the working
ρ = M / (4/3 πr3) = 2.8 × 1030 / (4.19 × 1012) = 6.7 × 1017 kg m−3.
One teaspoon: 6.7 × 1017 × 5.0 × 10−6 ≈ 3 × 1012 kg, three billion tonnes, roughly the mass of every human artefact combined, in a spoon.
Past even that, nothing holds. If the corpse is massive enough, its escape velocity, √2GM/r from the gravitational fields unit, reaches the speed of light at a finite radius, and inside that boundary nothing, light included, can leave: a black hole. The boundary is the event horizon, and its radius, the Schwarzschild radius, follows from setting the escape velocity equal to c:
WORKED EXAMPLE
The Sun, hypothetically crushed
Find the Schwarzschild radius for one solar mass, 1.99 × 1030 kg.
Rs = 2GM/c2 = (2 × 6.67 × 10−11 × 1.99 × 1030) / (3.0 × 108)2 = 3.0 km.
The Sun will never collapse this far, but the number sets the scale: to make any mass a black hole, squeeze it inside its Schwarzschild radius, about three kilometres per solar mass.
TRY IT UNSEEN
The monster at the centre
Observations of stars orbiting the centre of our galaxy reveal a supermassive black hole of about 4 × 106 solar masses. Find its Schwarzschild radius.
Show the working
Rs scales in direct proportion to M, so Rs = 3.0 km × 4 × 106 = 1.2 × 1010 m.
About seventeen times the radius of the Sun, for four million solar masses: supermassive black holes like this one appear to sit at the centre of most large galaxies, ours included.
THE EXAM BIT
- Sketching the HR diagram earns marks for the axes: absolute magnitude +15 to −10 upward, temperature 50 000 K to 2500 K left to right, or OBAFGKM. Both run backwards; label them.
- Place the three populations and the Sun: main sequence diagonal, red giants top right, white dwarfs bottom left, Sun on the main sequence at class G, about +4.8.
- The Sun-like evolution answer is a path: main sequence, then up-right to red giant as shells fuse and the surface cools, then down-left to white dwarf as the layers shed. Narrate it on the diagram.
- Type 1a as standard candle is a three-step argument: fixed trigger mass, so fixed peak absolute magnitude near −19.3, so apparent magnitude plus distance modulus gives distance. All three steps score.
- Rs ≈ 2GM/c2 questions are usually substitution plus commentary: quote the radius, then say what the event horizon means, the boundary from inside which not even light escapes.
CHECK YOURSELF
Describe the future of the Sun as a track on the HR diagram, naming each stage, and explain in one sentence each why the Sun will not become a supernova and why type 1a supernovae can be used to measure distance.
Show a hint
Three stages on the diagram; then mass for the first sentence, fixed peak brightness for the second.
Show the answer
The Sun sits on the main sequence now; when core hydrogen runs low it swells and cools, moving up and to the right as a red giant; after shedding its outer layers the remnant drops down-left as a white dwarf, then cools and fades.
No supernova: the Sun's mass is far below what core collapse requires, so its endpoint is the white dwarf, and the lie of this lesson stays a lie.
Type 1a supernovae all detonate at the same trigger mass and so peak at the same absolute magnitude, about −19.3; comparing that with the measured apparent magnitude gives the distance through the distance modulus.
The HR diagram maps brightness against temperature; the main sequence is where stars live.
Sun-like stars end as white dwarfs; giants die as supernovae, leaving neutron stars or black holes.
WORKBOOK
Printable practice for this topic: original exam-style questions with room to work, and a fully worked answer book. Free to use; please do not redistribute or sell.
CHECK YOUR PROGRESS
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- Sketch and read the HR diagram: main sequence, red giants, white dwarfs, and the Sun's place.
- Describe the evolution of a Sun-like star across the diagram, and the type 1a light curve as a standard candle.
- Recall neutron star properties and use the Schwarzschild radius for black holes.
Open the full revision checklist to track your progress across the whole unit.
No animated video for this topic yet; these notes stand alone. InkPhysics on YouTube.