HR Diagram Simulator: Explore Stellar Luminosity, Temperature & Evolution

simulator intermediate ~10 min
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L = 1.0 L☉, T = 5778 K — a solar-type G2V star

A 1 solar-mass star has luminosity 1 L☉ and surface temperature 5778 K, placing it in the middle of the main sequence as a G-type yellow dwarf with a lifetime of about 10 billion years.

Formula

L = L☉ × (M/M☉)^3.5
T_eff = 5778 × (M/M☉)^0.505 K
τ_MS ≈ 10 × (M/M☉)^(−2.5) Gyr

Mapping the Stars

In 1911, Ejnar Hertzsprung and Henry Norris Russell independently discovered that plotting stellar luminosity against surface temperature reveals striking order: most stars fall along a diagonal band called the main sequence. This HR diagram remains the most powerful tool in stellar astrophysics, encoding mass, age, composition, and evolutionary state in a single plot. This simulation lets you place stars on the diagram and watch how mass and age determine their position.

The Mass-Luminosity Relation

On the main sequence, a star's luminosity scales roughly as L ∝ M^3.5, meaning a star twice the Sun's mass is about 11 times more luminous. This steep dependence arises because more massive stars have higher core temperatures, accelerating nuclear fusion rates exponentially. The trade-off is lifetime: a 10 M☉ star exhausts its hydrogen in just 30 million years, while a 0.3 M☉ red dwarf can shine for over a trillion years.

Beyond the Main Sequence

When core hydrogen is exhausted, stars leave the main sequence. Low-mass stars expand into red giants as hydrogen shell burning inflates the envelope, eventually shedding outer layers as planetary nebulae and leaving behind white dwarfs. Massive stars undergo successive fusion stages — helium, carbon, oxygen, silicon — before iron core collapse triggers a supernova. The HR diagram captures these dramatic transitions as evolutionary tracks.

Observational Frontiers

Modern surveys like Gaia have measured precise parallaxes for over a billion stars, producing the most detailed HR diagrams ever constructed. These reveal fine structure: the red clump of helium-burning giants, the instability strip of pulsating variables, and the white dwarf cooling sequence. By comparing observed diagrams of star clusters with theoretical isochrones, astronomers determine cluster ages, distances, and chemical histories.

FAQ

What is the Hertzsprung-Russell diagram?

The HR diagram plots stellar luminosity against surface temperature (or spectral class). Most stars fall on the main sequence — a diagonal band from hot, luminous O-stars to cool, dim M-dwarfs. Giants, supergiants, and white dwarfs occupy distinct regions, revealing stellar evolutionary stages.

Why does the main sequence exist?

Stars on the main sequence are fusing hydrogen to helium in their cores. The mass-luminosity relation (L ∝ M^3.5) creates the tight diagonal band: more massive stars are hotter and more luminous. Once hydrogen is exhausted, stars leave the main sequence.

How does mass determine a star's fate?

Low-mass stars (< 8 M☉) become red giants then white dwarfs. High-mass stars (> 8 M☉) undergo supernova explosions, leaving neutron stars or black holes. The most massive stars (> 25 M☉) may collapse directly to black holes.

What is metallicity in stellar astrophysics?

Metallicity (Z) is the fraction of elements heavier than helium. Higher metallicity increases opacity, affecting a star's structure, temperature, and evolutionary track. Population II stars (low Z) are hotter and bluer than Population I stars at the same mass.

Sources

Embed

<iframe src="https://homo-deus.com/lab/stellar-evolution/hr-diagram/embed" width="100%" height="400" frameborder="0"></iframe>
View source on GitHub