Evolution of Low Mass Stars

The evolution of low mass stars is similar to the evolution of high mass stars. The primary difference arises because of the different ways in which the stars generate their internal pressures. This leads to differences in how far an individual star moves along the nuclear burning chain. This then leads to differences in the ways in which the stars end their lives.

• Massive stars ===> explode in Supernova events
• Los Mass stars ===> gently "blow" themselves to death forming planetary nebulae

Representative evolutionary tracks:

• 0.7 M(sun)
• Sun
• Sun and 5 M(sun)

The Sun

• On the Main Sequence, the Sun evolves slowly due to the changing chemical composition of its core. The evolution is in the sense that the Sun gets hotter and increases in luminosity (moving to the left and up in the HR diagram).

• After the hydrogen is used up in the core of the Sun, the helium core contracts, and heats the hydrogen rich layer just outside of the core. The hydrogen ignites in the shell around the core and the Sun moves to the right in the HR diagram.

• When the outer layers of the Sun become convective, the luminosity of the Sun shoots up and the Sun becomes a Red Giant.

• The core continues to contract until it reaches the ignition temperature for helium, roughly 100,000,000 Kelvins.

  At the point of helium ignition, the core of the Sun is supported by the hot (normal) gas of helium nuclei produced by the hydrogen burning and by degenerate electrons; the electrons already occupy many of the available energy levels up to very high energies ====> that it will take a lot of heat in order to increase the energy of even 1 electron. What this means is that the fractional increase in the kinetic energy of the electrons will be very small for a given amount of heat input. So, the pressure due to the electrons does not change very much for a given amount of heat input ===> the core of the Sun will not expand strongly in response to the ignition of the helium.

  The temperature of the core rises (really the temperature of the helium nuclei gas rises) as the reactions turn-on ===> the reaction rate goes up ===> the temperature of the helium nuclei in the core goes up ===> the rate of reactions goes up ===> and so on.... ===> the ignition of helium burning in the Sun will not be gentle; it will lead to what is known as the helium flash.

  The helium flash lasts for a few minutes or less with a peak core luminosity of up to 100,000,000,000 L(sun). This fantastic power is not observable to an outside observer, however! Why?

  The helium flash shuts down because, eventually, as you add enough heat to the gas, you can not heat the gas of helium nuclei, you can also excite most of the electrons to different energy states and you will eventually spread the electrons out over a large enough range of energy states to make the gas become normal (obey the perfect gas law).

  The helium flash occurs in stars less massive than around 2.25 M(sun).

• After the helium flash, the star quiescently burns what is left of the helium in its core (for a time ~ 10 - 20 % as long as its Main Sequence lifetime).

• When the helium is converted into carbon and oxygen, the core again contracts, ignites helium burning in a shell around the core, expands, cools, and moves to the right in the HR diagram.

• When the star becomes convective, it moves up the AGB greatly inrceasing in luminosity at roughly constant temperature. Low mass stars are not, however, massive enough to reach the ignition temperature of carbon before the core becomes completely supported by degenerate electron pressure (which halts the contraction).

The nuclear evolution of the Sun ends at this point and the star is now ready to enter into its final stages of evolution; at this time the star is AGB star characterized by a carbon-oxygen core, surrounded by a helium burning shell and a hydrogen burning shell.

As a final note, what happens to stars whose mass is greater than 2.25 M(sun)? The electrons in their cores are not degenerate at the time of helium ignition and so there is no helium flash and they settle into a stage of quiescent helium burning before they approach the AGB.

Mass Loss

A large uncertainty surrounding the evolution of stars is the question of mass loss (via stellar winds) during the course of their evolution. Low mass stars eventually wind up as white dwarf stars, objects supported by degenerate electron pressure. The maximum mass for a stable white dwarf is around 1.4 M(sun). Since stars of masses up to 8 - 12 M(sun) may form white dwarfs ===> substantial mass loss must occur during the evolution of low mass stars. The rate and timing of the mass loss is not well-known.