Evolution of Low and Intermediate Mass Stars

Protostar-->Main Sequence-->Subgiant-->Red Giant--> Horizontal Branch-->AGB-->Planetary Nebula-->White Dwarf-->Black Dwarf

The evolution of low and intermediate mass stars is similar to the evolution of high mass stars. The primary difference is 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 process up to iron ===> explode in Supernova events

Low and Intermediate Mass stars stop before iron ===> gently "puff" themselves to death, throwing off their outer layers forming planetary nebulas

The Sun: The Paradigm for Low and Intermediate Mass Stars

(1)-(2). On the Main Sequence, the Sun converts hydrogen to helium in its core through the proton-proton chain. Hydrogen is first scoured out of the center of the Sun where it is hottest and densest. The helium center then constracts slowly in response causing the helium center to get hotter and denser. This heats the overlying layers of hydrogen to higher temperatures and the rate of nuclear fusion increases. The increased rate of energy production causes the overall Sun to get hotter and brighter. This process continues as the Sun enjoys life on the Main Sequence. This slow evolution causes the Sun to move to the left and up in the HR diagram over its Main Sequence lifetime.
(2)-(3). After the hydrogen is completely used up in the Sun's core, the helium core contracts, again heating the hydrogen rich layer just outside of the core. The heated hydrogen ignites in the shell around the core and the Sun moves to the right in the HR diagram.
(3)-(4). After the outer layers become convective, the luminosity shoots up and the Sun becomes a Red Giant.
The helium core continues to contract and heat until it reaches the ignition temperature for helium, roughly 100,000,000 K. Once this temperature is reached, 3 helium nuclei will fuse to form a carbon nucleus in what is called the Triple Alpha Process. After a carbon nucleus is formed, the carbon may capture another helium nucleus to form oxygen. At helium ignition (4), 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 pressure due to the electrons does not change very much when the helium ignites ===> the core of the Sun does 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 is not gentle; it leads to the helium flash.
The helium flash lasts for a few minutes or less with a peak core luminosity of up to 100 billion 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 excite electrons to higher energy states and make the electron gas normal so that the helium burning core expands and so becomes less dense and cooler, thus ending the helium flash.
The helium flash occurs in stars less massive than around 2.25 MSun.
(5). After the helium flash, the star settles into Region (5) where it quiescently burns what is left of the helium into carbon and oxygen (for a time ~ 10 % as long as its Main Sequence lifetime).
(5)-(7). After the helium in the Sun's core is converted to carbon and oxygen, the nuclear reactions again shut down. This causes the core to contract and heat which also heats the regions adjacent to the core igniting nuclear burning in two shells, one where helium is converted into carbon and oxygen , and another one where hydrogen is converted into helium. At this time, the Sun expands and cools, moving to the right in the HR diagram.
When the Sun becomes convective, it moves up the Asymptotic Giant Branch (AGB) greatly increasing in luminosity at roughly constant temperature. During this time the Sun's core continues to contract trying to reach temperatures high enough to ignite the carbon and oxygen. Low mass stars like the Sun, however, are not massive enough to reach the ignition temperature for such burning before the core becomes completely supported by degenerate electron pressure (which halts the contraction just as in the protostar case).

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.
(7)-(8). At this point, the evolution becomes controversial but current wisdom suggests that the shell burning becomes unstable and a series of nuclear burning pulses can occur. This coupled with the fact that as the outer layers of the star cools, the protons and electrons combine to form neutral hydrogen which produces photons and heats the envelope of the star. These effects combine to eject the outer tens of percents of the envelope of the star at a speed of a few tens of kilometers per second in a few million years.

In the left panel, we see a plot showing the shell luminosity of typical thermal pulses in an AGB star. The shell luminosity more than doubles with outburst intervals of a few hundred thousand years. The pulsing leads to the evolution shown in the right panel. This leads to the formation of Planetary Nebulas, e.g., the Cat's Eye Nebula.

Planetary nebula are emission nebulas which consist of a glowing shell of gas (the outer envelope of the star which has been ionized and energized by the hot central star). They were given their name because they resembled planets when viewed through small telescopes. They are short-lived lasting only tens of thousands of years. There are around 3,000 planetary nebulas known in our Galaxy. Planetary Nebulas are important because they return chemically enriched matter from low-mass stars to the Interstellar Medium, material to be used in the next generations of stars.
Why do the Planetary Nebulas to the left appear nearly circular (ring-like)? Are they like smoke rings ejected by the dying stars?

(8)-(9) The hot central core which has just been laid bare becomes a white dwarf star.

What Happens to the Earth as the Sun Evolves?
The Sun slowly heats and increases in luminosity while it is on the Main Sequence. When it was born, the Sun was 70 % of its current luminosity. Since then, it has been slowly increasing in brightness. In around 1.1 billion years, the luminosity of the Sun will be 10 % higher than today and our atmosphere will lose it moisture (become drier) and large forms of land-life will likely disappear. The Earth will still be habitable, however, because ocean-life will extract CO₂ from the atmosphere and weaken the Greenhouse Effect. In 3.5 billion years, the Sun will be 40 % brighter than today. This increase cannot be dealt with, even if we completely eliminate the Greenhouse Effect. This causes the oceans to evaporate which leads to a Runaway Greenhouse Effect as occurred on Venus.
After the hydrogen in the core is used up, the core contracts, and shell burning starts and the Sun cools at nearly constant luminosity. When the Sun becomes convective, it rapidly increases in luminosity at nearly constant temperature and becomes a Red Giant reaching a radius 20 % larger than the Earth's current orbit (1 Astronomical Unit).
During this phase, strong stellar winds cause the Sun to lose ~ 30 % of its mass. Consequently, as the Sun expands, the size of the orbit of the Earth also grows as it spirals out to an orbit of size 1.4 Astronomical Units. Although the Earth may outrace the expanding Sun in this manner, recent work suggests that a tidal interaction between the Earth and the Sun will cause the size of the Earth's orbit to shrink and the Earth to be engulfed by the Sun even when including mass loss.
Without mass loss, the Sun easily expands beyond the orbit of the Earth and the Earth is engulfed. With mass loss, it is closer as noted above, but the Earth will be engulfed during the Red Giant phase.
If the current orbit of the Earth was > 1.15 A.U., we would survive the expansion of the Sun; Mars will survive. After the Helium Flash, the Sun settles in steady helium burning and the Sun shrinks well inside the orbit of the Earth. After helium burning concludes, the core shrinks and the Sun ignites nuclear burning in two shells and the Sun evolves into an AGB star. At the tip ofthe AGB branch, the Sun does not become as large as the Red Giant because it loses more mass to an enhanced stellar wind; 0.4-0.5 of the mass of the Sun is lost by the top of the AGB.

Instability Strip and Pulsating Stars

As stars evolve (change their position on the H-R Diagram) they may pass through a region known as the Instability Strip. Here the stars are not in strict hydrostatic and thermal equilibrium. If they remain there long enough, they are observable as pulsating stars. Stars whose masses are larger than 3 to 5 times the mass of the Sun, spend time in the Instability Strip and so become variable stars. The most important types of variable stars are the Cepheid Variables and RR Lyrae stars.

Instability Strip

Stars in the Instability Strip have structures that are unstable to pulsations. Stars in the Instability Strip go through cycles where they expand and contract periodically with accompanying changes in luminosity. It is found that there is a well-defined relationship between the period of pulsation and the average luminosity of the stars, the Period-Luminosity relation. This is a very useful property as it means that the luminosity of a star can be found by simply measuring how long are the periods of pulsation. Measuring these sorts of periods is easy. This feature of Cepheids makes them what are referred to as Standard Candles.

Henrietta Leavitt, working at the Harvard College Observatory, studied 1,777 stars in our nearest neighbor large galaxies, the Small Magellanic and Large Magellanic Clouds. Henrietta Leavitt found that the Cepheid variables, variable stars showed a well-defined relationship between the period of their pulsation and average luminosity publishing a paper on a couple dozen variables in the Small Magellanic Cloud. Over her career she discovered more than 2,400 Cepheids.

Schematic Cepheid Pulsation

Cepheid Period-Luminosity Relation

The Period-Luminosity relationship meant that simply through measurement of the pulsation period of a Cepheid variable, we could infer its average luminosity and so from measurement of its apparent brightness, we could infer the star's distance:

Cepheid variables in M31, Andromeda

Cepheid variables in M100

RR Lyrae in NGC 3201

This distance measurement tool laid one of the basic foundations for determinations by finding distances to nearby galaxies and so to the initial discovery of the expansion of the Universe and the Hubble constant in the 1920s by Vesto Slipher and Edwin Hubble.

The distances to nearby galaxies also led to the determination (calibration) of the luminosities of Type Ia Supernovae. Such studies showed that Type Ia Supernovae are standardizable candles. Because the large intrinsic brightnesses of Type Ia Supernovae, they can be used to determine cosmological distances. This led to re-determinations of the expansion rate of the Universe in the 1990s through measurement of the important cosmological parameter, the Hubble Constant, and to the first creditable demonstration that the expansion rate of the Universe is increasing with time.

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.