Stellar Evolution - 2D Hertzsprung-Russell Diagram Track

Controls

Live readouts

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Numerical check

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Performance graph

How to use

The Hertzsprung-Russell diagram plots every star by surface temperature (hot on the left) and luminosity. A star spends most of its life on the white main-sequence line; its initial mass then sends it along the orange track: swelling into a giant, then either shedding its envelope to leave a white dwarf (below about 8 solar masses) or collapsing into a neutron star or black hole.

Try: choose the Sun preset and watch it brighten slowly, then jump right and up as a red giant. Switch to the 15 solar-mass preset: it lives only a few tens of millions of years. Drag the progress slider to scrub through time. The dashed blue lines are constant-radius lines: stars on one share the same size.

The science

Mass-luminosity relation (empirical, main sequence):L/Lsun = 0.23 M^2.3 (M<0.43), M^4 (0.43-2), 1.4 M^3.5 (2-55)

Stefan-Boltzmann law links the three observables:L = 4 pi R^2 sigma T^4 => T = 5772 K (L/R^2)^(1/4)

Main-sequence lifetime scales as fuel over burn rate:t_MS ~ 10 Gyr (M/Msun)/(L/Lsun)

White dwarfs are supported by electron degeneracy pressure. The Eggleton fit to the Chandrasekhar mass-radius relation isR = 0.0114 Rsun [ (M/1.44)^(-2/3) - (M/1.44)^(2/3) ]^(1/2)and the initial-final mass relation used here is M_f = 0.109 M_i + 0.394 (capped at 1.38). With constant radius the cooling track follows L ~ T^4; Mestel cooling makes the age since formation grow like T^(-20/7).

What is simplified: real tracks come from stellar-structure codes. The main-sequence brightening, the giant-branch peak luminosity (3000 M^0.7 Lsun), the temperature at the giant tip (3300-3600 K) and the post-giant path are smooth analytic stand-ins that reproduce the shape of real tracks, not their exact values. Mass loss, metallicity, rotation and binary interaction are ignored. The end state for massive stars (neutron star below 20 Msun, black hole above, remnant about 0.3 M) is a typical outcome; it depends on mass loss and explosion physics.

Keyboard, touch and accessibility

Space pauses or resumes the simulation.
R resets it to its initial state.
C re-runs the numerical check.
All sliders are native range inputs and work with arrow keys, Home and End; on touch devices drag on the canvas where the sim supports pointer input.
Rendering is capped at a device pixel ratio of 2 so phones stay smooth; the frame-time graph above shows the cost of the current settings (green line is 16.7 ms, i.e. 60 frames per second).

What is checked and why you can trust it

Every time the page loads, and whenever you press Re-run check, the simulation evaluates its own mathematics against an independent reference, such as a closed-form formula, a finite-difference derivative or an exhaustive count. Each line above reports PASS or FAIL together with the measured numbers, so you can see by how much it agrees. Results are also published on window.__msChecks for automated testing. The check never uses the same code path as the animation it validates, otherwise it would only confirm itself.

How to read a failure: a FAIL line means the measured discrepancy exceeded the stated tolerance for the current slider values. Try Reset, then move the sliders back toward their defaults; if a check still fails at the defaults it is a bug worth reporting. Tolerances are chosen from the numerical method itself, never tuned to make a test pass: round-off level (1e-9) for exact algebra, about 1e-3 for finite differences and Monte Carlo estimates with a few hundred thousand samples, and a documented margin for stochastic learning runs.

Reproducibility: the particle and pen simulations use the browser random generator for initial positions, so exact pixels differ between visits, but the checks depend only on mathematics and not on those positions. Fixed wave tables (curl noise) and fixed grammars (L-system) are deterministic.

This is an educational model. It shows the mechanism clearly, but it is deliberately simplified; the science panel lists what was left out.