Stars on the main sequence burn Hydrogen in their cores into Helium. This week we will look at what happens to stars after the Hydrogen runs out.
The process of change in stars from birth to death is called stellar ``evolution''. This may be an unfortunate name, since evolution in biology is concerned with changes that take place over many generations in a species, rather than in individual members of the species during their lifetime. The latter is what is meant by stellar evolution!
The key observations which lead to the discovery of the processes which take place within the stars during their lives, were of the open and globular clusters. We saw the colour magnitude of examples of these in lecture 2, and it would be worth reviewing that material.
There are quite a number of phases which a star can pass through after it has used up its core Hydrogen. These phases are termed post main sequence evolution. The time spent in this phase and the changes that take place are very dependent on the mass of the star and properties of the core.
Consider the core of a star which is burning Hydrogen into Helium. Because of the temperature and density gradient in the core, Hydrogen will be converted more rapidly in the center of the core than at its edge. Eventually the Hydrogen at the center will run out. Further out, there may still be burning of Hydrogen in a shell around the core (see figure 10.1).
The luminosity of the core has dropped because it is no longer burning, but it can still release energy through gravitational collapse. Since the temperature gradient in a star is proportional to the luminosity
this means that the core temperature becomes almost isothermal, i.e. close to constant.
The evolution of the star can be followed as the core releases energy gravitationally and Hydrogen is burnt in the shell. It turns out that when the isothermal, non-burning core mass is 10 to 15% of the total mass of the star, the first big changes take place. At this point the internal pressure in the core is no longer able to support the outer layers, and the core collapses rapidly. This point is called the Schönberg-Chandrasekhar limit. This releases gravitational energy, and the core heats up. Surprisingly, the outer layers of the star expand at this stage, although this seems counter-intuitive. One explanation of this is that the Hydrogen burning shell luminosity increases and that in order for the energy to escape the outer layers of the star must have lower opacity, which it achieves by expanding and becoming less dense.
What stops the core continuing to collapse? Eventually the density in the core can reach a high enough temperature that Helium burning begins. Furthermore the core may reach sufficient densities that the effect of degeneracy pressure comes into play. Up to now we have considered the gas in the stars to be ideal, so that its pressure and density obey the perfect gas law. However, at high enough density Pauli's exclusion principle provides a new source of pressure support in the star. This states that no more than one electron can occupy a bound energy level state in an atom (in fact, two electrons can occupy the state but must have opposite spin). Free electrons which are tightly packed together must satisfy the Heisenberg uncertainty principle
where x is the position and p the momentum. In order to satisfy this relation, at very high density, the electrons must have a greater momentum (and hence pressure) than would be predicted by the perfect gas law. The free electrons in the plasma at the stellar core eventually reach densities that allow the core to be supported by this degenerate pressure.
One further factor plays an important role in the development of the core. If the core is radiative (i.e. energy is transported out of the core by radiation), then as the core Hydrogen is burnt, the chemical composition of the core will change, with more Helium in the core center than at the surface. On the other hand, if the core is convective (i.e. energy transport by bulk motion), the rate at which Hydrogen can be moved from the surface of the core to the center, where it can be burnt, will control the core evolution.
Stars more massive than the sun can have convective cores, and this allows a lot of Hydrogen to be transported to the central regions where it can be burnt into Helium. A considerable fraction of the Hydrogen can be processed before the core reaches the Schönberg-Chandrasekhar limit, and the gravitational collapse phase which follows may be relatively short, before the star begins Helium burning. High mass stars spend only a short time between the points marked B and C in figure 10.2. In an open cluster for example, where there are a range of stars with different masses but the same age and composition, only a few of the stars will be in this region. The region is called the Hertzsprung gap and it lies between the main sequence and the giant branch.
The evolution of three stars, with masses of 60, 5 and 1 MO is shown in figure 10.3. The track of the 5 MO star well illustrates the Hertzsprung gap. The points along the track in the gap are at approximately equal time intervals of 100,000 years, in order to see the track more clearly, whereas points in the slower evolution regions are at intervals of order 106 years.
We will now consider in detail the evolution of a 5 MO star of solar metallicity (Z = 0.02). The evolutionary track is shown in figure 10.4, with the following points marked.
Stars with low masses have radiative cores, so that the surrounding Hydrogen cannot be transported into the core where it can be burnt. Instead, the Hydrogen initially in the inner core, where the temperature is high enough to burn it, is the only Hydrogen which is converted to Helium. Another factor is that burning takes place by the p-p chain rather than by the CNO cycle. This is less sensitive to temperature, and burning can take place in a wider region than would be the case for a high mass star. In any case, when the Hydrogen is used up, the core mass is well below the Schönberg-Chandrasekhar limit, and the gravitational contraction phase is much longer than for a high mass star. In fact, this phase is so long that many stars in a cluster can find themselves in the subgiant phase and the Hertzsprung gap effectively dissapears. This is what we see in older clusters, in which the stars leaving the main sequence have lower masses than for young clusters. Core contraction is halted by the onset of degeneracy. Eventually, the core will heat up until Helium can be ignited and while this occurs the star is in a giant phase. Helium ignition takes place under special circumstances; because the core is degenerate, Helium burning begins but takes place explosively. Helium burning in a non-degenerate core is like a controlled nuclear reaction, where as in a degenerate core it is like a nuclear explosion. This is called the Helium Flash. Changes take place very rapidly in the core (few 100 seconds!) and the physics becomes very difficult to compute and the results of such computations are still uncertain.
Let's look at the evolution of a 1 MO star of solar metallicity (i.e. the Sun). The evolutionary track is shown in figure 10.5, with the following points marked.
Below about 0.4 MO, stellar evolution is much less complicated. We can start by considering stars below about 0.08 MO. These objects, which have only been found directly in the last few years (although their existance has been suspected for any decades) are called brown dwarfs. They are not true stars because they never develop a central temperature which is high enough to ignite Hydrogen burning. Instead, they release energy by gravitational contraction. They radiate this energy away and get slowly fainter and more difficult to find, and do not stop for a long time on the main sequence as stars do. Above the limit for brown dwarfs, between about 0.4 and 0.1 MO, we find red dwarfs or M dwarfs. These are real stars and burn Hydrogen so slowly in their cores that they will stay on the main sequence for a very long time, much longer than the Sun. Once the Hydrogen is burnt, the core collapses but never reaches high enough temperatures for Helium burning to commence. Such stars may not become bright giants but instead evolve directly to white dwarfs without the complications that arise for stars near 1 MO. However, the Universe is still so young that no very low mass stars have had time to evolve off the main sequence, so this prediction is not really testable!
On the course website I have placed a link to series of models computed by Schaller et al, 1992, like the ones shown in the lecture. The models are
In the files, each line gives physical parameters for the star. The interesting columns are as follows: the second column is the age, the third the mass relative to the Sun, the 4th is the luminosity log(L/LO) relative to the Sun and the 5th the effective temperature at the surface log(T eff) in K.
Consider stars of different mass but with the same age. For an age of 1 Gyr make a plot of log(L/LO) versus log(T eff for stars of different mass. Try the same for 5 Gyr. The result is an isochrone and should look like the colour magnitude diagram of a star cluster. Note that if there is no entry in the table for a certain mass star, this is because it has already evolved off the end of the giant branch.