Astronomy 162:
Introduction to Stars, Galaxies, & the Universe
Prof. Richard Pogge, MTWThF 9:30

Lecture 16: The Evolution of Low-Mass Stars

Readings: Ch 21, sections 21-1 & 21-2, and Ch 22, sections 22-1 to 22-4

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

Main Sequence Phase

Energy Source: Hydrogen fusion in the core

What happens to the He created by H fusion?

Core is too cool to ignite He fusion
Slowly builds up an inert He core

Main-Sequence (H-burning) Lifetime:

~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

Inside:

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:

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

Climbing the Red Giant Branch

It takes a star about 1 Gyr to climb the Red Giant Branch

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

At the Tip of the Red Giant Branch:

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

Helium Flash

At 100 Million K, a new fusion source ignites: the Triple-alpha Process.

This is the fusion of three ⁴He nuclei into one ¹²C (carbon) nucleus through a multi-step nuclear reaction chain that involves the momentary formation of ⁸Be:

Once Carbon is formed, a secondary reaction forms Oxygen from the fusion of Carbon & Helium:

When this occurs, the star once again has a nuclear power source in its core and 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.

He Flash to Horizontal Branch on the H-R Diagram

Horizontal Branch Phase

Structure:

He-burning core
H-burning shell

The Triple-alpha Process is very inefficient at producing energy, so it can only last for about 100 Myr.

While it goes on, the star steadily builds up a C-O core, but it is still too cool to ignite Carbon fusion

Asymptotic Giant Branch Phase

After 100 Myr, the core runs out of Helium for Triple-Alpha fusion.

Inside:

C-O core collapses and heats up
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:

Asymptotic Giant Branch on the H-R diagram

The star becomes an Asymptotic Giant Branch Star

The Instabilities of Old Age

He burning is very temperature sensitive: Triple-alpha fusion rate ~ T⁴⁰!

Consequences:

Small changes in T lead to
Large changes in fusion energy output

Star experiences huge Thermal Pulses that destabilize the outer envelope.

Core-Envelope Separation

Rapid Process: takes ~10⁵ years

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

Expanding envelope forms a nebula around the contracting C-O core:

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.

Final Stages: Envelope Ejection to White Dwarf

Images of Planetary Nebulae

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

Enough, already, back to the story...

Core Collapse to White Dwarf

The contracting C-O core becomes so dense that a new gas law takes over...

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.

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