Todd Thompson
Department of Astronomy
The Ohio State University

Key Ideas

Low-Mass Star = M < 4 M_sun

Stages of Evolution of a Low-Mass star:

Main Sequence star

Red Giant star

Horizontal Branch star

Asymptotic Giant Branch star

Planetary Nebula phase

White Dwarf star

Key Equations

Main Sequence Phase

What happens to the He created by H fusion? Core is too cool to ignite Helium fusion. The star slowly builds up an inert (not fusing!) He core. Each of the He nuclei produced by the PP chain (star less massive than about 1.2 Msun) or the CNO cycle (stars more massive than about 1.2 Msun) just sits at the center of the star until the end of the main sequence lifetime.

Main-Sequence (H-burning) Lifetime: t = energy reservoir/luminosity ~ M/L ~ 1/M^3:

• ~10 Gyr for a 1 M_sun star (e.g., Sun)
• ~10 Tyr for a 0.1 M_sun star (red dwarf)

Core Hydrogen Exhaustion

• the inert He core collapses & starts to heat up.
• H burning zone moves into a thin shell surrounding the core
• Collapsing core heats the H shell above it, driving the fusion faster.
• More fusion = more heating, so that Pressure > Gravity

Outside the star:

• Envelope expands and cools
• Star gets brighter and redder & climbs up the Giant Branch.

(Graphic by R. Pogge)

Climbing the Red Giant Branch

• He core contracting & heating, but still no fusion
• H burning to He in a shell around the core
• Huge, puffy envelope ~ size of orbit of Venus

• T_core reaches 100 Million K
• Ignites He burning in the core in a flash.

Helium Flash

This is the fusion of three ⁴He nuclei into one ¹²C (carbon) nucleus:

A secondary reaction forms Oxygen from Carbon & Helium:

When this occurs, the star leaves the Giant Branch.

Inside:

• Starts generating primary energy from He burning in the core.
• Gets additional energy from an H burning shell surrounding the core.

Outside:

• Gets hotter and bluer.
• Star shrinks in radius, getting fainter.

The new energy source helps the star begin to regain Hydrostatic and Thermal Equilibrium. As it does so, it moves onto the Horizontal Branch.

(Graphic by R. Pogge)

Horizontal Branch Phase

• He-burning core
• H-burning shell

The Triple-alpha Process is inefficient at producing energy, so it can only last for about 100 Myr. There is less energy for every gram of material fused, partially because of neutrinos being produced, and partly because of the physics of nuclei. You just get less total energy from this process than you do from the PP chain or the CNO cycle.

While it goes on, the star steadily builds up a C-O core, but it is still too cool to ignite Carbon fusion. This phase is analogous to the main sequence phase. The star is burning He into heavier elements (C and O), and while it's doing that it is too cold to ignite CO fusion. So, it builds an inert core of C and O.

Asymptotic Giant Branch Phase

Inside:

• C-O core collapses and heats up (but, no CO fusion!)
• He burning shell outside the C-O core
• H burning shell outside the He burning shell

Outside:

• Star grows rapidly in radius and cools

Climbs the Giant Branch again, but at a higher effective Temperature than the Giant Branch, so it ascends with a bluer color, putting it slightly to the left of the original Giant Branch on the H-R Diagram (the "Asymptotic" Giant Branch:)

The star becomes an Asymptotic Giant Branch Star

The Instabilities of Old Age

Star experiences huge Thermal Pulses that destabilize the outer envelope.

Core-Envelope Separation

Outer envelope gets slowly ejected (fast wind)

C-O core continues to contract:

• With the weight of envelope taken off, the core heats up less
• It never reaches the Carbon fusion ignition temperature of 600 Million K

Core and Envelope separate physically.

Planetary Nebula Phase

• Ionized and heated by the hot central core.
• Expands away to nothing in ~10⁴ years.

The star briefly becomes host to a Planetary Nebula

The hot C-O core is exposed, and moves quickly to the left on the H-R Diagram at nearly constant luminosity and increasing temperature.

Images of Planetary Nebulae

Planetary nebulae are among the most beautiful objects in the sky. Below are links to PNe pretty-picture sites:

• Hubble Space Telescope Gallery of Planetary Nebula Images

• George Jacoby's Planetary Nebula Sampler at NOAO.

Core Collapse to White Dwarf

Degenerate Electron Gas:

• Pressure becomes independent of Temperature
• P grows rapidly & soon counteracts Gravity

Collapse halts when R ~ 0.01 R_sun (~ R_earth)

Degenerate core becomes a White Dwarf

We will learn more about White Dwarfs in Unit 3.