1. Generally describe the post main sequence evolution of stars less massive than 4-8 solar masses, and specifically describe the post main sequence evolution of a 1 solar mass star.

2. Describe the evolution to the red giant phase, including the position on the HR diagram, and the properties of a red giant star.

3. Describe the evolution to the helium flash and planetary nebula phases including the position on the HR diagram, and the properties of a planetary nebula.

4. Describe the evolution to the white dwarf phase, including the position on the HR diagram, and the properties of a white dwarf.

5. Discuss the concept of electron degeneracy and how it leads to the Chandrasekhar limit for a white dwarf.

6. Review how the gravitational redshift works in white dwarfs and its role in verifying a prediction of the General Theory of Relativity.

7. Discuss some of the events that can occur when mass is transferred to a white dwarf in a binary system, including the connection to novae.

¶ post main sequence phase

¶ mass loss

¶ 1 solar mass star

¶ red giant phase

¶ helium core

¶ nuclear fusion

¶ shell around the core

¶ gravitational contraction

¶ stellar expansion

¶ helium flash

¶ planetary nebula phase

¶ pulsations

¶ white dwarf phase

¶ electron degeneracy pressure

¶ 1.4 solar masses

¶ Chandrasekhar limit

¶ gravitational redshift

¶ nova

¶ classical nova

¶ dwarf nova

¶ release of gravitational energy

¶ mass transfer between stars

¶ Eventually the hydrogen in the cores of all main sequence stars is converted into helium, and nuclear energy generation in the core cannot proceed at a rate necessary to sustain a stable main sequence star.

¶ The very massive main sequence stars use up their hydrogen quickly, while the lower mass main sequence stars use up their hydrogen slowly.

¶ When the hydrogen becomes depleted, the star enters its post main sequence phases of evolution.

¶ We consider the fate of stars which have masses LESS THAN 4 to 8 solar masses. (Note: The post main sequence evolution of main sequence stars between 4 and 8 solar masses is unclear, because the amount of mass they lose during their post main sequence phase is hard to calculate.

¶ The post main sequence evolution of a 1 solar mass star will be considered. However, any star with mass less than about 4 to 8 solar masses will evolve similarly.

¶ About 10 billion (10¹⁰) years after a 1 solar mass star reaches the main sequence, no hydrogen is left in its core. The core is composed of helium.

¶ Nuclear fusion of hydrogen into helium is still occurring in a shell around the core.

¶ Since the core is no longer being heated by nuclear reactions, the gas pressure in the core drops and gravity makes the core start to contract.

¶ This gravitational contraction makes the core and surrounding shell undergoing hydrogen fusion much hotter than it was before.

¶ This increase in heat makes the outer layers of the star expand and the surface temperature of the star decrease.

¶ The net result is that the small yellow-colored main sequence star (like the Sun) becomes a large red giant star with a diameter over 100 times larger than its main sequence diameter.

¶ Because of its lower surface temperature, less energy is coming out of a square cm of the star’s surface (Stefan-Boltzmann Law), but the star is much more luminous due to its large diameter.

¶ The star resides in the upper part of the HR diagram.

¶ During this evolution, the core of the red giant star will become so hot that the triple alpha process (a nuclear reaction resulting in the fusion of helium into carbon) will occur in the core. This happens suddenly and is called the Helium Flash, causing carbon to form in the star’s core.

¶ During its evolution, the red giant star changes its position in the HR diagram. It is at its largest diameter at the time of the Helium Flash, it then becomes smaller and then larger once again.

¶ The rapid evolution of a star after the red giant phase (it's now a helium-burning star) causes the outer layers of the star to become unstable and pulsate.

¶ Because of these pulsations, during a period estimated to be approximately 1000 years, a star which was originally 1 solar mass on the main sequence will eject about 0.4 solar mass into space.

¶ This ejected mass expands to form a "planetary nebula" around the remaining 0.6 solar mass star.

¶ A planetary nebula has nothing to do with planets. It is simply a cloud of gas that is so large that we can resolve it on images taken with telescopes on Earth. Normally stars are so small that they appear to be unresolved points of light on images taken with telescopes on Earth.

¶ The gas in a planetary nebula emits strong emission lines.

¶ The 0.6 solar mass star in the center of a planetary nebula looks blue because its surface temperature is so hot (up to 100,000 degrees Kelvin).

¶ Once the nuclear energy generation in the star at the center of the planetary nebula stops for good, the star will begin to contract because of the force of gravity.

¶ The star will contract to the point where electrons and protons are next to each other (the normal situation in atoms or ions in a gas has electrons at great distances from protons). The star will contract to about the size of the Earth.

¶ The only force which will support the star from contracting further is something called electron degeneracy pressure. This essentially means that the attractive gravitational forces are not strong enough to push an electron into a proton.

¶ The star is a White Dwarf. It occupies the bottom part of the HR diagram.

¶ Calculations show that the post main sequence evolution of stars less than 4 to 8 solar masses will be similar to what has been considered so far, providing the mass of the star left after the planetary nebula phase is less than 1.4 solar masses.

¶ Note that a 4 solar mass main sequence star will certainly shed enough mass in the planetary nebula phase to leave less than 1.4 solar masses remaining while an 8 solar mass main sequence star will certainly have more than 1.4 solar masses remaining after its planetary nebula phase.

¶ The value of 1.4 solar masses is known as the Chandrasekhar limit.

¶ If 1.4 solar masses is exceeded, the forces due to electron degeneracy pressure are not great enough to overcome the gravitational forces attempting to push electrons into protons.

¶ White dwarfs offer another verification of the predictions of the General Theory of Relativity. In order for light to escape from the surface of a compact star (like a white dwarf) which has a strong gravitational field at its surface, it must lose energy.

¶ This loss of energy causes the light to be redshifted (in the sense that red light is less energetic than blue light). This effect is observed and is called a gravitational redshift.

¶ Novae are newly visible stars but not new stars. They become visible when a white dwarf star brightens by a factor of 100 to 1 million (10⁶). There are two types of novae: classical novae and dwarf novae. Both types occur in binary star systems in which one star is a white dwarf and the other star is in its red giant phase of evolution. These phenomenon may be recurrent in the same binary system.

¶ Observations of novae demonstrate how complicated stellar evolution in binary star systems may be. Complications arise when mass is transferred from one star to the other.

¶ When a star loses mass, it generally evolves slower. When a star gains mass, it generally evolves faster.