Evolutionary Tracks

A star spends most of its life on the main sequence, slowly turning hydrogen into helium in its core. In Red Giants and White Dwarfs you saw what comes next. Here we follow the path, or evolutionary track, a star traces on the H–R diagram, and connect each turn to what is happening in its core. The tool is the one from effective temperature and radius: $L = 4\pi R^2\sigma T^4$, so a move to the right at the same luminosity means the star is swelling.

Why it works

The core drives everything. While hydrogen burns in the core, a star changes slowly: helium builds up, the core contracts a little and heats, and the luminosity creeps up (the young Sun gave out only about 70% of its present power). When core hydrogen runs out, nothing balances the core's energy loss, so it contracts and heats, as the virial theorem requires. Hydrogen keeps burning in a shell around it, and the extra energy from the shell inflates the envelope, which cools. The star moves right, then up the red-giant branch. When the core reaches about 100 million K, helium fuses to carbon and oxygen, the star settles down for a while, and the cycle repeats with the next fuel.

Key idea

Stars do not move along the main sequence as they age; they sit near one point on it and then leave it. A Sun-like star goes: main sequence → subgiant → red giant → helium burning (horizontal branch or red clump) → asymptotic giant branch → planetary nebula → white dwarf. Massive stars cross the diagram almost horizontally, at nearly constant luminosity, becoming red supergiants.

Evolutionary tracks for stars of 1, 5 and 15 solar masses. Each starts on the main sequence and leaves it to the upper right; the massive ones cross nearly horizontally.

Worked examples

Worked example: How much does a red giant swell?

A star leaves the main sequence at $L = 1.0\,L_\odot$, $T = 5800$ K and later sits at $L = 100\,L_\odot$, $T = 4200$ K. By what factor has its radius grown?

$R \propto \sqrt{L}/T^2$, so $R_2/R_1 = \sqrt{100/1.0}\,(5800/4200)^2$.
$= 10 \times 1.91$.

Answer: About 19 times larger.

Worked example: The Sun at the tip of the red-giant branch

Near the top of its red-giant branch the Sun will reach about $2500\,L_\odot$ at about 3000 K. What will its radius be, in AU?

$R/R_\odot = \sqrt{2500}\,(5772/3000)^2 = 50 \times 3.70 = 185$.
$185 \times 6.96 \times 10^{8}$ m $= 1.29 \times 10^{11}$ m.

Answer: About 0.86 AU, past the orbits of Mercury and Venus. (Whether it reaches Earth depends on how much mass the Sun loses first.)

Worked example: Dating a cluster from its turnoff

The brightest main-sequence stars left in a cluster have about $100\,L_\odot$. Using $L \propto M^{3.5}$ and a lifetime of $10\text{ Gyr} \times M^{-2.5}$, how old is the cluster?

Turnoff mass: $M = 100^{1/3.5} = 3.7\,M_\odot$.
Lifetime: $10 \times 3.73^{-2.5} = 0.37$ Gyr.

Answer: About 400 million years. All stars in a cluster formed together, so the stars just leaving the main sequence tell its age.

Common mistake

Thinking stars move along the main sequence as they age, sliding from hot to cool. The main sequence is a sequence of mass: each star lands at the point set by its mass and stays near it for 90% of its life, brightening slowly. When it ages it leaves the main sequence for the giant region. Check: a 1 $M_\odot$ star never becomes a red dwarf, and a cluster's main sequence gets shorter from the top as it ages, it does not shift.

When the core of a Sun-like star starts burning helium, its electrons are degenerate (see the next topic), so the ignition runs away almost at once: the helium flash. Stars above about 2 solar masses ignite helium gently.

Evolutionary Tracks

Worked examples

Practice

Builds on

Leads to

Sources and further reading