The Hertzsprung-Russell Diagram and Variable Stars
A Map of the Stars
In the early twentieth century, Ejnar Hertzsprung and Henry Norris Russell independently discovered that stars are not randomly scattered in terms of their temperature and luminosity — they fall into distinct groups. The Hertzsprung-Russell diagram (H-R diagram) plots luminosity against surface temperature and is one of the most powerful tools in astronomy. Understanding how to read and sketch it is essential.
The H-R diagram has two unusual axis conventions: the y-axis runs from low luminosity at the bottom to high luminosity at the top; the x-axis runs from high temperature on the left to low temperature on the right (opposite to most graphs). The Sun sits near the middle of the main sequence at spectral type G, with luminosity 1 solar luminosity.
Regions of the H-R Diagram
Most stars (about 90%) fall along a diagonal band from the upper-left to the lower-right, called the main sequence. The Sun sits in the middle of the main sequence. Stars spend the bulk of their lives here, steadily fusing hydrogen into helium in their cores. Upper-left main-sequence stars are hot, blue, and far more luminous than the Sun; lower-right stars are cool, red, and dim.
Other regions house stars at later evolutionary stages:
- Red giants — upper-right of the diagram: cool (red) but very luminous because they are enormously large. A Sun-like star expands into this region after leaving the main sequence.
- Supergiants — above the red giants, extending across the top of the diagram: these are the most luminous stars, both red supergiants (cool, enormous) and blue supergiants (hot, extremely luminous).
- White dwarfs — lower-left: hot but very dim, because they are small — roughly Earth-sized. Despite their high surface temperature, their tiny surface area means they radiate little total energy.
Luminosity depends on both temperature and surface area. A white dwarf’s surface temperature can be 20,000 K or more (hotter than the Sun), but its radius is only about 1% of the Sun’s — roughly the size of Earth. Total energy output (luminosity) scales as the surface area times the temperature to the fourth power. Despite high temperature, the tiny area makes white dwarfs very dim. This is why they plot in the lower-left of the H-R diagram: hot, but low luminosity. This is also why the H-R diagram position of a star does NOT represent its location in space — it plots properties, not position.
Stellar Evolution Tracks on the H-R Diagram
A star’s position on the H-R diagram changes as it evolves. The diagram does not show stars moving in space; it shows their changing temperature and luminosity over millions or billions of years. A Sun-like star spends about 10 billion years on the main sequence. As its core hydrogen is exhausted, it begins to expand: its outer layers cool (moving rightward) while luminosity increases (moving upward), eventually becoming a red giant. The star then sheds its outer layers as a planetary nebula and the hot remnant core cools slowly as a white dwarf, moving leftward then downward in the H-R diagram.
High-mass stars follow a different track. They are born as blue supergiants (upper-left), then expand rapidly into red supergiants (upper-right), and end in a supernova explosion. The remnant becomes a neutron star or black hole, which are too small and dim to appear on the conventional H-R diagram.
Star Clusters and the H-R Diagram
All stars in an open cluster formed at the same time from the same gas cloud, so they all began at the same point on the main sequence. Over time, the most massive (upper-left) stars evolve off the main sequence first. By plotting a cluster’s H-R diagram, astronomers can estimate its age from the “main-sequence turn-off point” — the luminosity level at which stars are just starting to leave. Older clusters have lower turn-off points. Globular clusters, found in the galactic halo, are ancient (often 10-13 Gyr old) and have very low turn-off points.
More massive main-sequence stars are far more luminous and burn their hydrogen fuel much faster despite having more of it. A star 10 times the Sun’s mass may last only tens of millions of years on the main sequence; the Sun will last about 10 billion years; a very low-mass red dwarf may last hundreds of billions of years.
Variable Stars
Some stars change in brightness regularly. Variable stars can be intrinsic (the star itself changes) or extrinsic (something blocks the light). On a light curve — a graph of brightness (or magnitude) against time — variable stars show repeated cycles of brightening and dimming.
Cepheid variables are yellow supergiants that pulsate with periods of 1-70 days. Henrietta Swan Leavitt published her period-luminosity law in 1912 (building on observations she had begun in 1908). She found that the pulsation period is directly related to the star’s luminosity (the period-luminosity relation): longer period = higher luminosity. This makes Cepheids exceptional standard candles — by measuring the period, astronomers know the true luminosity, and combining this with the apparent brightness gives the distance via the distance modulus. Cepheids were used by Edwin Hubble to measure the distance to the Andromeda Galaxy, proving it lies far beyond the Milky Way.
Eclipsing binaries are two stars orbiting each other in a plane nearly edge-on to us. When one star passes in front of the other, it blocks some light — producing a dip in the light curve. Two dips per orbit occur: a deeper one when the brighter star is eclipsed, and a shallower one when the dimmer star is eclipsed. The orbital period and relative sizes and temperatures of both stars can be extracted from the light curve shape.
Novae occur in binary systems where a white dwarf accretes hydrogen from a companion star. Accumulated hydrogen eventually undergoes runaway nuclear fusion on the white dwarf’s surface, producing a sudden dramatic brightening (the nova) before fading over weeks or months. A nova does not destroy the white dwarf; it may recur.