---
title: The Evolution of Massive Stars
draft: false
module: Stellar Evolution
moduleNumber: 7
lessonNumber: 3
order: 703
summary: >
  Stars above about eight solar masses burn through hydrogen, helium, carbon,
  neon, oxygen, and silicon in stages that grow shorter as neutrino losses
  accelerate contraction. The interior becomes an onion of concentric burning
  shells around an inert iron core. Radiation pressure near the Eddington limit
  drives fierce winds that can strip the hydrogen envelope entirely, and silicon
  burning builds an iron core toward the threshold of collapse.
topics: [Stellar Evolution]
sources:
  - book: Carroll & Ostlie
    ref: "Ch. 13 §13.3; Ch. 15 — The Fate of Massive Stars; §15.1 Post-Main-Sequence Evolution of Massive Stars"
  - book: Maoz
    ref: "Ch. 4 — Stellar Evolution and Stellar Remnants"
---

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.[^co-mass]

## 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](/astrophysics-cosmology/stellar-evolution/stellar-pulsation-and-the-instability-strip).

$$
% caption: The evolutionary track of a massive star across the top of the H-R
% diagram, from the main sequence rightward to a red supergiant, with a blue loop
% during core helium burning that carries the star back through the instability strip.
\begin{tikzpicture}[scale=1.0, font=\footnotesize]
\definecolor{acc}{HTML}{4A6FA5}
\draw[->, black] (9.2,0) -- (0,0) node[left, black!70] {hotter};
\draw[->, black] (9.2,0) -- (9.2,5.4) node[above, black!70] {luminosity};
% main sequence at upper left
\fill[acc] (7.2,4.2) circle (2pt);
\node[black!70, anchor=south] at (7.4,4.3) {main seq};
% cross to red supergiant (rightward, slight rise)
\draw[acc, very thick] (7.2,4.2) .. controls (5.0,4.3) and (3.0,4.4) .. (1.6,4.6);
\node[black!70, anchor=south] at (2.4,4.6) {red supergiant};
% blue loop back and forth
\draw[acc!60, very thick, densely dashed] (1.6,4.6) .. controls (3.4,4.1) and (5.6,4.05) .. (6.4,4.3)
  .. controls (5.4,4.5) and (3.2,4.7) .. (1.9,4.85);
\node[black!70, anchor=west] at (5.7,3.5) {blue loop};
% instability strip band (vertical dashed region)
\draw[black, densely dotted] (4.4,0) -- (4.4,5.2);
\draw[black, densely dotted] (5.2,0) -- (5.2,5.2);
\node[black, anchor=north, align=center] at (4.8,5.15) {instability\\strip};
\end{tikzpicture}
$$

## 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
$20\,M_\odot$ star the durations collapse from millions of years to days.

| Stage | Fuel | Ignition $T$ | Duration ($20\,M_\odot$) |
| --- | --- | --- | --- |
| Hydrogen | $\text{H}\to\text{He}$ | $4\times 10^7\ \text{K}$ | $\sim 10^7\ \text{yr}$ |
| Helium | $\text{He}\to\text{C, O}$ | $2\times 10^8\ \text{K}$ | $\sim 10^6\ \text{yr}$ |
| Carbon | $\text{C}\to\text{Ne, Mg}$ | $8\times 10^8\ \text{K}$ | $\sim 300\ \text{yr}$ |
| Neon | $\text{Ne}\to\text{O, Mg}$ | $1.5\times 10^9\ \text{K}$ | $\sim 1\ \text{yr}$ |
| Oxygen | $\text{O}\to\text{Si, S}$ | $2\times 10^9\ \text{K}$ | $\sim 6\ \text{months}$ |
| Silicon | $\text{Si}\to\text{Fe}$ | $3\times 10^9\ \text{K}$ | $\sim 1\ \text{day}$ |

$$
% caption: The duration of each burning stage for a twenty-solar-mass star on a
% logarithmic scale; neutrino losses at high temperature shorten each successive
% stage by orders of magnitude, from ten million years for hydrogen to a day for
% silicon.
\begin{tikzpicture}[scale=1.0, font=\footnotesize]
\definecolor{acc}{HTML}{4A6FA5}
\draw[->, black] (0,0) -- (0,5.4) node[above, black!70] {log duration};
\draw[black] (0,0) -- (8.6,0);
% bars decreasing in log height
\foreach \x/\h/\lab in {0.9/5.0/H, 2.2/4.3/He, 3.5/2.6/C, 4.8/1.6/Ne, 6.1/1.1/O, 7.4/0.6/Si}{
  \draw[very thick] (\x-0.4,0) rectangle (\x+0.4,\h);
  \node[black!70, anchor=north] at (\x,-0.05) {\lab};
}
\node[black!70, anchor=west] at (1.4,5.0) {10 million yr};
\node[black!70, anchor=west] at (7.85,0.6) {1 day};
\end{tikzpicture}
$$

## 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
$\epsilon \propto T^\nu$ dependence.

$$
% caption: The onion-shell interior of an evolved massive star just before collapse:
% concentric shells of hydrogen, helium, carbon, oxygen, and silicon burning
% surround a central inert iron core built up by silicon burning.
\begin{tikzpicture}[scale=1.0, font=\footnotesize]
\definecolor{acc}{HTML}{4A6FA5}
\draw[very thick] (4.5,2.6) circle (2.6);
\draw[thick] (4.5,2.6) circle (2.05);
\draw[thick] (4.5,2.6) circle (1.55);
\draw[thick] (4.5,2.6) circle (1.1);
\fill[acc!15] (4.5,2.6) circle (0.65);
\draw[acc, very thick] (4.5,2.6) circle (0.65);
\node[black!80] at (4.5,2.6) {Fe core};
\node[black!70] at (4.5,1.55) {Si};
\node[black!70] at (4.5,3.4) {O};
\node[black!70] at (4.5,3.95) {C};
\node[black!70, anchor=west] at (5.5,1.35) {He};
\node[black!70] at (4.5,4.75) {H};
\end{tikzpicture}
$$

## 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**,

$$
L_{\rm Edd} = \frac{4\pi G M c}{\kappa}
\approx 3.2\times 10^4\,L_\odot\left(\frac{M}{M_\odot}\right)
\quad(\kappa = 0.34\ \text{cm}^2\,\text{g}^{-1}).
$$

At luminosities near $L_{\rm Edd}$ 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 $L_{\rm Edd} \propto M$, the ratio $L/L_{\rm Edd}$ grows
with mass and sets an upper mass limit near $100$–$150\,M_\odot$. The most luminous
stars sit close enough to the limit that instabilities produce episodic eruptions and
heavy, continuous mass loss.

$$
% caption: Force balance in a massive-star envelope; the outward radiation force per
% unit mass equals the opacity times flux over c, and at the Eddington limit it just
% cancels gravity, above which no static envelope exists and a wind is driven.
\begin{tikzpicture}[scale=1.0, font=\footnotesize]
\definecolor{acc}{HTML}{4A6FA5}
% a gas parcel
\draw[very thick] (4.3,2.5) rectangle (5.3,3.3);
\node[black!75] at (4.8,2.9) {gas};
% gravity arrow down
\draw[black, very thick, ->] (4.8,2.4) -- (4.8,0.7);
\node[black!70, anchor=west] at (4.9,1.5) {gravity: G M over r squared};
% radiation arrow up
\draw[acc, very thick, ->] (4.8,3.4) -- (4.8,5.1);
\node[acc, anchor=west] at (4.9,4.3) {radiation: kappa F over c};
% balance note
\node[black!70, anchor=east, align=right] at (3.9,2.9) {balance at\\Eddington limit};
\end{tikzpicture}
$$

## Wolf–Rayet stars and the iron core

Stars above $\sim 25\,M_\odot$ 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.

$$
% caption: A Wolf–Rayet star with its hydrogen envelope stripped by a fast radiation
% driven wind, exposing the helium and CNO-processed layers, with broad emission
% lines formed in the outflow rather than a static photosphere.
\begin{tikzpicture}[scale=1.0, font=\footnotesize]
\definecolor{acc}{HTML}{4A6FA5}
% stripped core
\draw[acc, very thick] (3.0,2.6) circle (1.1);
\fill[acc!14] (3.0,2.6) circle (1.1);
\node[black!75] at (3.0,2.6) {He core};
% wind arrows outward
\foreach \a in {20,70,120,160,200,250,300,340}{
  \draw[black, ->] ({3.0+1.25*cos(\a)},{2.6+1.25*sin(\a)}) -- ({3.0+2.0*cos(\a)},{2.6+2.0*sin(\a)});
}
\node[black!70, anchor=west] at (5.3,3.4) {stripped wind};
\node[black!70, anchor=west] at (5.3,1.8) {H envelope gone};
\end{tikzpicture}
$$

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](/astrophysics-cosmology/nuclear-astrophysics/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](/astrophysics-cosmology/stellar-death-and-compact-remnants/core-collapse-supernovae).

[^co-mass]: Carroll & Ostlie, §15.1 — Post-Main-Sequence Evolution of Massive Stars: crossing the H-R diagram and blue loops, the sequence of nuclear burning stages accelerated by neutrino losses, the onion-shell interior, the Eddington luminosity and radiation-driven mass loss producing Wolf–Rayet stars, and the buildup of an iron core.