Astronomy 1101 --- Planets to Cosmos

Todd Thompson
Department of Astronomy
The Ohio State University

Low-Mass Stars

Key Ideas

Low-Mass Star = M < 4 Msun

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

During the main sequence phase, the energy source is Hydrogen fusion in the core.

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:

Core Hydrogen Exhaustion

Inside the star:
Red Giant Star Interior
(Graphic by R. Pogge)

Outside the star:

Red Giant Branch on H-R Diagram

(Graphic by R. Pogge)

Climbing the Red Giant Branch

It takes a 1 solar mass star about 1 Gyr (about 1/10th of its main sequence lifetime) to climb the Red Giant Branch At the Tip of the Red Giant Branch the core is compressed enough that it finally reaches the critical temperature to burn He:

Helium Flash

At 100 Million K, a new fusion source ignites: the Triple-alpha Process (just 3 He nuclei getting together: an "alpha" particle is just a He nucleus (2 protons and 2 neutrons)).

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

Triple-Alpha Process

A secondary reaction forms Oxygen from Carbon & Helium:

C12-Alpha-Gamma Reaction
(Graphic by R. Pogge)

When this occurs, the star leaves the Giant Branch.



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 (Graphic by R. Pogge)

Horizontal Branch Phase

Horizontal Branch Star Interior
(Graphic by R. Pogge)

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

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


Asymptotic Giant Branch Star Interior
(Graphic by R. Pogge)


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:)

Asymptotic Giant Branch on the H-R diagram
(Graphic by R. Pogge)

The star becomes an Asymptotic Giant Branch Star

The Instabilities of Old Age

He burning is very temperature sensitive: Triple-alpha fusion rate is proportional to T40, so very tiny changes in temperature lead to big changes in the fusion rate. This can destabilize the outer layers of the star: 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:

Core and Envelope separate physically.

Planetary Nebula Phase

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

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
(Graphic by R. Pogge)

Images of Planetary Nebulae

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

Core Collapse to White Dwarf

The contracting C-O core becomes so dense that a new gas law takes over. It turns out that this new gas law is NOT the ideal gas law of P = n k T.

Degenerate Electron Gas:

Collapse halts when R ~ 0.01 Rsun (~ Rearth)

Degenerate core becomes a White Dwarf

We will learn more about White Dwarfs in Unit 3.

Updated/modified Sept 2014, Todd Thompson
Copyright Richard W. Pogge, All Rights Reserved.