Stellar Forge

A star’s life is set almost entirely by its mass at birth. The game places each newborn star on the Hertzsprung-Russell diagram with the fitting formulae of Tout et al. (1996), which reproduce detailed stellar models for 0.1 to 100 solar masses; the surface temperature follows from the Stefan-Boltzmann law. On the main sequence, brightness rises steeply with mass, roughly as mass to the power 3.5 for Sun-like stars, so heavier stars burn their fuel far faster. Lifetimes come from Hurley, Pols and Tout (2000) and fall roughly as mass to the power -2.5. For the smallest red dwarfs, which mix their whole interior and burn almost all their hydrogen, we use the models of Laughlin, Bodenheimer and Adams (1997): about 10 trillion years at the minimum mass.

The fates follow the ranges given by NASA and the Chandra X-ray Center: below 0.08 solar masses a brown dwarf that never fuses hydrogen, white dwarfs below about 8, neutron stars from about 8 to 20, black holes above. Real boundaries are not sharp lines. They shift with a star’s metal content and the mass it loses in winds (Heger et al. 2003), and supernova models find that the stars that explode do not form one simple mass range (Sukhbold et al. 2016). The helium-fusion limit of about half a solar mass is approximate too.

Simplifications: all stars are single, not spinning, and have the Sun’s metal content (Z = 0.02 in the fitting formulae). The main-sequence point is computed; the path after the main sequence is drawn schematically, with the right shape but approximate positions, and the giant stages are given about 10% of the total lifetime. For a star exactly like the Sun the fit gives about 11 billion years on the main sequence, which textbooks round to about 10 billion. Star sizes are drawn on a compressed scale and colors approximate the light of a blackbody at the surface temperature. Red dwarf fates are predictions: none has had time to die yet.