

Late stages of evolution for low-mass stars

This movie summarizes the evolution of a star like our Sun after it has reached the main sequence.

Today in lecture, I will try to explain what's behind these shifts and countershifts; how the reactions at the center of a star affect its visible outermost layers.

Stars on the main sequence fuse hydrogen to helium in their cores. Since low-mass stars process their hydrogen relatively slowly, they stay on the main sequence for a long time. But what happens when they finally use up all the hydrogen in their cores? The answer turns out to depend on the exact mass of the star: the higher it is, the more violent the end.

Very low mass: gradual decline of hydrogen fusion

Stars which start out with much less mass than the Sun -- around 0.4 solar masses or less -- have a fully convective interior:

Hydrogen fuses to helium only in the central core, but the convective motions mix the helium-rich product throughout the entire interior. At the end of their main-sequence lifetime, they are uniformly helium-rich:

As the star runs lower on hydrogen, the rate at which it generates energy gradually declines. Gravity pulls the outer layers inwards on the core, but the temperatures never rise high enough for any other nuclear reactions to take place. Slowly, gradually, the star becomes fainter, cooler, and smaller. Eventually, it will shrink to a cold ball about the size of the Earth: a black dwarf.

Of course, this is all just speculation. Stars with such small masses take a long, long time to run through all their hydrogen fuel. A star of 0.2 solar masses may take a trillion years to use up all its hydrogen.

 current age of universe:  approx    15,000,000,000  years

 red dwarf lifetime:              1,000,000,000,000  years

There hasn't been time yet for a single very low-mass star to use up all its hydrogen, so we can't check to see if our models are correct!

Sun-like mass: helium burning as a red giant

Stars like our Sun differ from their lower-mass brethren in a crucial way: their central cores transfer heat outwards via radiation, rather than by convection.

The star evolves slightly on the HR diagram, away from the main sequence.

This means that as hydrogen fuses to helium in the core, the resulting helium remains there. As a result, a helium-rich zone builds up in the center of the star, and hydrogen fuses only in a shell around the core:

Material in the hydrogen-burning shell is trapped between the outer layers and the inert helium core. Pressure and temperature rise, greatly increasing the rate at which energy is generated. During the shell-burning phase, the extra energy pushes the outer layers of the star very far outwards, increasing the size of the photosphere. As the photosphere moves away from the hot inner regions, it cools off. The star begins to move to the right in the HR diagram.

Now, as the hydrogen concentration in the core decreases, and the rate of fusion likewise decreases, the outer layers press inwards due to gravity. The temperature and pressure of the gas in the core rises. Because there's so little hydrogen left in the core, ordinary fusion reactions cannot produce enough energy to push the outer layers back, even at higher temperatures. The stellar thermostat is broken, so the force of gravity pulls the star inwards on the core harder and harder.

Eventually, the temperature reaches a critical point of around 130 million Kelvin (!). Helium nuclei in the core move so rapidly that they are able to overcome their electric repulsion for each other and fuse together in the triple alpha process:

Note that the intermediate product produced in step 1, beryllium-8, is VERY unstable: it will radioactively decay back into two helium-4 nuclei within less than 10^(-16) seconds. In order for a third helium-4 nucleus to smash into the beryllium-8 before it decays, the density of the stellar core must be very high: roughly 7700 times that of water.

The rate of energy generated by the triple-alpha process is even more sensitive to temperature than that of the CNO cycle:

      rate of energy production  =  (something) * T

Q:  If the temperature in the core of a star 
    increases by 10%, by how much does the 
    energy generated by helium fusion increase?

The moment at which the inner core begins to fuse helium to carbon is called the helium flash. After it occurs, the star settles down to a new phase of helium burning. Once again, there is a nice thermostat to regulate the internal properties. The star moves onto a place in the HR diagram sometimes called the horizontal branch.

At this point, the star contains





Evolution of the outer envelope: planetary nebulae





We can see these pulsations directly: as a star's photosphere changes in radius and in temperature, the amount of visible light it emits varies. Many red giants are long-term variable stars. Some pulse very regularly:

Thanks to the AAVSO for providing this data.

  Q: How many months does it take for Mira's brightness 
     to go through one complete cycle?

  Q: How much brighter is Mira at maximum than minimum?
       a.  about   7 times brighter
       b.  about  40 times brighter
       c.  about 630 times brighter




Q: Why are they called "planetary" nebulae?




or the Eskimo Nebula:



But that doesn't stop people from doing their best to make models of the procedure. Here are a couple of movies showing simulations of jets coming from an old star blowing bipolar bubbles in its surroundings, created by Vincent Icke.

The bitter end: a white dwarf


Q: At its current size, the Sun has about the same 
   overall density as water.  When it becomes 
   a white dwarf the size of the Earth, 
   how much denser will it be?



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