Lecture 16: Evolution of Low-Mass Stars

Readings: 21-1, 21-2, 22-1, 22-3 and 22-4

 

For the protostar and pre-main-sequence phases, the process was the same for the high and low mass stars, and the main difference was the speed with which they went through the various stages.

 

On the main sequence, high and low mass stars are again quite similar. They fuse H to He in their cores, have cooler envelopes, and are in hydrostatic and thermal equilibrium. There are some differences: energy transport, CNO vs. proton-proton and lifetime on the main-sequence, but both high and low mass stars pass through this phase.

 

However, once stars leave the main-sequence, high and low mass stars have very different paths. And the key difference is whether they end their lives as white dwarfs or as neutron stars/black holes.

 

We look first at the evolution of low-mass stars after the main-sequence

 

Key Ideas

 

Low Mass Star = M < 8 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

 

Please note that after the Red Giant phase, the names of the phases are exceedingly unhelpful and the result of history. But youÕll need to learn them nonetheless.

 

Main Sequence Phase

Energy Source: H fusion in the core

What happens to the He from H fusion?

Too cool to ignite He fusion

         Slowly build up an inert He core

 

M-S Lifetime

~10 Gyr for a 1 MSun

~10 Tyr for a 0.1 MSun (red dwarf or M dwarf)

 

Hydrogen Exhaustion

 

Inside:

         Loss of pressure=end of hydrostatic equilibrium

         He core collapses & heats up

         H burning zone shoved out into a shell

         Collapsing He core heats the H shell above it, driving the fusion faster

 

Outside

         Envelope expands and cools

         Star gets brighter and redder

         Becomes a Red Giant Star

 

AppleMark

 

Climbing the Red Giant Branch

 

See the path of the star as it moves up the red giant branch

Figure 22-1 (a)

 

Takes ~1 Gyr (= 1 billion years) to climb the Red Giant Branch

         He core contract & heats, but no fusion

         H burning to He in a shell around the core

         Huge, puffy envelope ~ 0.7 AU in radius

 

Top of the Red Giant Branch

         Tcore reaches 100 Million K

         Ignites core He burning in a Helium Flash

 

The Sun as a Red Giant

 

When the Sun becomes a Red Giant, Mercury and Venus will be vaporized, the Earth burned to a crisp. Long before the Sun reaches the tip of the red giant branch, the oceans will be boiled away and most life will be gone.

 

The most ÒEarthlikeÓ environment at this point will be Titan, a moon of Saturn.

 

Helium Flash-Pt 1

Triple-alpha Process

 

Fusion of 3 4He nuclei into 1 12C nucleus (carbon)

 

 

Secondary reaction with 12C makes 16O

 

 

So why donÕt we talk about He fusing into 8Be? Why is there so little Be in the Universe?

 

8Be is unstable to radioactive decay. With a half life of 7x10-17 seconds, it decays back to 2 4He nuclei (9Be is the only stable isotope).  So unless during that fraction of a second, the 8Be nucleus can fuse with a 4He nucleus, it will disassemble into He nuclei again and we will be back to where we started.

 

Degeneracy Pressure

Degeneracy pressure is important at high densities.

Degeneracy pressure depends only on the density. It is independent of the temperature.

Maximum pressure that electrons can exert.

 

Helium Flash – Pt 2.

 

When the core of stars with M < 4Msun reach temperatures hot enough to fuse He into C, O, degeneracy pressure is important in the cores of the stars. Therefore, when the He ignites, there is no thermostat because the pressure in the core does not depend on the temperature. So the core does not expand and the temperature does not drop.

 

T rises -> rate of nuclear fusion increases -> T rises -> rate of nuclear fusion increases.

 

Runaway nuclear reaction releases 1011 LSun. This provides enough energy to finally expand the core and reduce the density enough that degeneracy pressure is not important. The ideal gas law now provides the pressure and the thermostat is back in action. The energy created in the helium flash takes millions of years to leak out of the star, so this very interesting phenomenon in the center of the star does not lead to an optical flash for observers outside the star.

 

Leaving the Giant Branch

 

Inside

         Primary energy: He burning core

         Additional energy: H burning shell

         Inert envelope

 

Outside

         Gets hotter and bluer

         Star shrinks in radius, getting fainter

 

Moves onto the Horizontal Branch

 

AppleMark     

 

Path on the HR diagram after the helium flash to the horizontal branch

Figure 22-1 (b)

 

Horizontal Branch Phase

Structure:

         He-burning core

         H-burning shell

Triple-alpha Process is inefficient (mass of 12C only slightly less than mass of 3 4He nuclei)

         Only lasts for ~100 Myr

 

Build up a massive C-O core, but itÕs too cool to ignite Carbon fusion

 

 

 

Asymptotic Giant Branch

 

After 100 Myr, core runs out of He

         C-O core collapses & heats up

         He burning shell

         H burning shell

 

Star swells and cools

         Climbs the Giant Branch again, but at higher temperature

 

 

AppleMark

 

Path of the Asymptotic Giant Branch star on the HR diagram

Figure 22-1  (c)

 

Higher Mass Lower Mass Stars

 

For stars that start with M>4 MSun, (but < 8MSun), it gets hot enough in the cores to avoid the He flash and start C fusion. They still end their lives as white dwarfs, but they are made up of O, Ne and Mg (the products of C fusion) rather than C and O. Degeneracy pressure still supports them.

 

The Instabilities of Old Age

 

He burning is very temperature sensitive

         Triple-alpha fusion rate

 

Consequences:

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

 

Huge Thermal Pulses destabilize the outer envelope.

 

Core-Envelope Separation

 

Rapid Process: ~105 years

Outer envelope ejected in a fast wind

C-O Core continues to contract

With less envelope weight above, gravity is not compressing the core and the C-O core does not heat up as much

         Never reaches the 600 million K Carbon Ignition temperature

 

Core and Envelope Separate

 

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

 

Planetary Nebula—has nothing to do with planets, but looked like a planet when observed through early telescopes because they are not points.

 

Hot C-O core is exposed, moves to the left on the H-R Diagram

 

Figure 22-10

 

Planetary Nebula are

         Pretty

         Emission Line objects

They carry the elements produced in low mass stars back into space. ½ of the carbon in the solar system came from lower mass stars.

 

Core Collapse to White Dwarf

 

Contracting C-O core becomes so dense that it becomes degenerate again.

 

Reaches hydrostatic equilibrium when Degeneracy Pressure balances Gravity.

 

Collapse halts at R~0.01 Rsun (~Rearth)

 

At this stage, the star is called a white dwarf star.

SUMMARY

 

Stage                            Energy Source

Main Sequence                        H burning Core

Red Giant                               H burning Shell

Horizontal Branch                   He Core + H Shell

Asymptotic Giant                    He Shell + H Shell

White Dwarf                           None!

 

 

The Seven Ages of the Sun

Main Sequence Star: 11 Gyr

Red Giant Star: 1.3 Gyr

Horizontal Branch Star: 100 Myr

Asymptotic Giant Branch Star: 20 Myr

Thermal Pulsation Phase: 400,00 yr

Planetary Nebula Phase: ~10,000 yr

0.54 Msu  White Dwarf: final stateÉ..