The Evolution of Massive Stars

Massive stars, above roughly eight solar masses, follow a different path from their low-mass counterparts. Their cores never become degenerate before igniting the next fuel, so burning proceeds continuously through carbon and beyond. Each successive stage is hotter, less energetic per gram, and increasingly drained by neutrino losses, so the stages telescope from millions of years down to days. The star ends with an inert iron core that cannot yield fusion energy, poised for collapse.¹

Crossing the diagram and blue loops

After core hydrogen exhaustion a massive star's envelope expands while the luminosity stays nearly constant, and it moves rapidly to the right across the Hertzsprung gap to become a red supergiant of hundreds of solar radii. The crossing is fast because it happens on the thermal timescale of the envelope, not the nuclear timescale, so few stars are caught in the gap.

During core helium burning the track can reverse. As the internal structure adjusts, the envelope contracts and the surface heats, carrying the star back toward the blue in a blue loop before it returns redward. A star executing a blue loop crosses the instability strip, where the envelope becomes pulsationally unstable, and appears as a Cepheid variable. The Cepheid period–luminosity relation that anchors the distance ladder comes from stars in exactly this phase, developed in stellar pulsation and the instability strip.

Successive burning stages

A massive core contracts and heats until each new fuel ignites. Hydrogen burns to helium, helium to carbon and oxygen, and then the heavier ashes ignite in turn: carbon burning near $8\times 10^8\text{K}$, neon burning by photodisintegration near $1.5\times 10^9\text{K}$, oxygen burning near $2\times 10^9\text{K}$, and silicon burning near $3\times 10^9\text{K}$. Each stage releases less energy per unit mass than the last, because the reacting nuclei climb toward the maximum of the binding energy per nucleon.

Above $\sim 10^9\text{K}$ the interior loses energy directly to neutrinos, produced by pair annihilation and other thermal processes, which stream out unimpeded and carry away energy far faster than photons can diffuse. The core must contract faster to replace this drain, so the advanced stages run at breakneck speed. For a $20M_{\odot }$ star the durations collapse from millions of years to days.

The onion-shell interior

Because each fuel ignites first at the center and then in a shell around the growing ash core, the star develops a set of concentric burning shells, an onion-shell structure. At the surface lies unprocessed hydrogen; moving inward, shells of helium, carbon, neon, oxygen, and silicon burning surround an inert iron core. Each shell burns the ash of the shell outside it and feeds the ash inside it. The layers are separated sharply because the temperature rises steeply inward and each reaction switches on over a narrow temperature range, a consequence of the steep $ϵ\propto T^{\nu }$ dependence.

The Eddington limit and mass loss

The luminosity of a massive star approaches the maximum that a static envelope can sustain. Radiation pushes outward on the gas with an acceleration $\kappa F/c$, where $F=L/4\pi r^2$ is the flux and $\kappa$ the opacity, dominated by electron scattering in a hot envelope. Balancing this against gravity $GM/r^2$ defines the Eddington luminosity,

At luminosities near $L_{\mathrm{Edd}}$ the envelope can no longer be held in hydrostatic equilibrium, and radiation pressure drives a strong wind. Because $L\propto M^3$ on the upper main sequence while $L_{\mathrm{Edd}}\propto M$, the ratio $L/L_{\mathrm{Edd}}$ grows with mass and sets an upper mass limit near $100$–$150M_{\odot }$. The most luminous stars sit close enough to the limit that instabilities produce episodic eruptions and heavy, continuous mass loss.

Wolf–Rayet stars and the iron core

Stars above $\sim 25M_{\odot }$ lose mass fast enough to strip the hydrogen envelope entirely, exposing the products of core burning. The bare, hot, helium-rich or carbon-rich surface, embedded in a dense outflowing wind at $\sim 10^{-5}{M}_{\odot }{\text{yr}}^{-1}$ and thousands of kilometers per second, defines a Wolf–Rayet star. Its spectrum shows broad emission lines of helium, nitrogen, or carbon formed in the wind rather than the absorption lines of a normal photosphere. Mass loss of this severity changes the final mass of the core and helps decide whether the star ends as a neutron star or a black hole.

Silicon burning is the last stage. It proceeds by photodisintegration and rapid capture reactions that drive the composition toward nuclear statistical equilibrium, in which forward and reverse reactions balance and the abundances settle at the most tightly bound nuclei, the iron peak. The binding energy per nucleon reaches its maximum at ${}^{56}\text{Fe}$ and ${}^{56}\text{Ni}$, so fusing iron absorbs energy rather than releasing it. The iron core grows toward the Chandrasekhar mass with no further nuclear energy to support it. The physics of the iron peak and the end of energy-yielding fusion is worked out in advanced burning and neutron-capture nucleosynthesis. What happens when the core exceeds its supportable mass, collapse and the supernova, is the subject of core-collapse supernovae.