Evolution of Low Mass Stars

264-270

In the previous section you began to explore how a star changes or evolves as it consumes its supply of hydrogen in the core. You also began to see the key role that mass plays in determining the fate of a star. In this section you will consider the evolution of low-mass stars.

Red Dwarfs ( M < 0.4 Mo)

In an earlier section you learned that the minimum mass for a main-sequence star is 0.08 Mo. Below this mass the proto-star cannot compress its core to temperatures high enough for nuclear fusion to begin. Stars with mass in the range of 0.08 Mo to 0.4 Mo (the Red Dwarf stars) are able to sustain nuclear burning but their "thermostats" are set so low that they burn fuel at a miserly rate! As well, these stars are fully convective which means that fresh hydrogen fuel is continually being transported (by convection) into the core and the star should be able to consume almost all of its available hydrogen. Red Dwarf stars evolve extremely slowly! Use the applet "starEvolve" to compare the evolution of a low mass Red Dwarf star with higher mass stars.

 
starEvolve allows you to plot evolutionary tracks and explore some of changes that occur in a star over time.

If you inspect the evolutionary track for a 0.5 Mo star you will not see much change over a 20 billion year span!

Example 10.4 Discuss two reasons why astronomers have a hard time testing their theories of evolution of Red Dwarf stars.

Solution: The two most significant reasons are:

  1. Since the rate of evolution of a star depends on mass, there are no highly evolved Red Dwarf stars anywhere in the universe!
  2. Red Dwarf stars are very faint! Although they are numerous they are not easy to study. The Hubble Space Telescope has extended our ability to study these stars and the new generation of giant telescopes will greatly enhance our understanding of these objects.

The Evolution of Medium-Mass Stars (0.4 Mo- 2.5 Mo)

Simply because of mass, medium mass stars have a few more options than their Red Dwarf cousins! In stars similar to our sun core temperatures and densities will eventually lead to helium fusion via the triple-alpha process. These stars are able to undergo dramatic changes in their structure as they evolve. Consider Example 10.5 in which you are asked to predict the "fate of the Earth" as our sun evolves.

Example 10.5 Use the applet starEvolve to prepare a scale diagram that shows how the sun's radius will change as it evolves into the Red Giant region of the HR diagram. Pick at least 5 different epochs over the sun's lifetime. Speculate on the "fate of the Earth".

Solution: Use starEvolve to provide you with relevant information. Some useful data to use in setting the scale:

  • r (earth-sun distance) = 1.49 x 1011 m,
  • Ro (radius of sun) = 6.96 x 108 m so ..
  • r (earth-sun distance) = 214 Ro

Use the interactive figure (Figure 10.12) on the right to assist you.

As the applet starEvolve suggests, the sun will eventually swell to more than 170 times its current size. By that time it will have vapourized Mercury and Venus. Although the sun will not swell to the present size of the Earth's orbit, tidal interaction between the earth and sun may cause the Earth's orbit to decay enough to be engulfed by the sun.
  Figure 10.12 Interactive figure drawn to correct scale depicts current size of sun in relation to the orbits of the terrestrial planets. Adjust both solar radius and surface temperature to see how this will change as the sun evolves.

By the time a medium-mass star has become a Red Giant it has a helium burning core surrounded by a hydrogen burning shell. For a short period of time it will regain a form of stability reminiscent of its life on the main sequence. The star may contract a bit overall and the surface will warm up a bit. On the HR diagram the star will begin to move down and back, horizontally, towards the main-sequence along the Horizontal Branch. Figure 10.13 illustrates this along with a schematic of the shell-structure that is beginning to develop.

The star's life on the Horizontal Branch is short-lived. The helium burning core creates a steadily growing "ash" of carbon and oxygen. Carbon burning requires temperatures on the order of 600 million K - a medium mass star simply lacks the mass to be able to compress itself to these temperatures. The star is now doomed to eventually "go out".

There is however one last and dramatic event or series of events in the star's life. As the carbon-oxygen core develops it collapses a bit and releases energy. This increases the temperature in the helium burning shell.
Figure 10.13 Medium mass star after the Helium Flash developing a carbon-oxygen core surrounded by helium and hydrogen burning shells.  

The triple-alpha process is extremely sensitive to changes in temperature and the star begins to undergo a series of "thermal pulses" or sudden spikes in the energy generated in the helium shell. These produce pulses that travel outward toward the stellar surface. At the same time that this is happening the surface itself is again cooling which causes the gases in the outer envelope to become less transparent to the flood of light coming from below. This causes even more outward pressure on the outer envelope. Eventually the outer envelope of the star drifts outward and gently away from the star.

Figure 10.13 Thermal pulses trigger the eventual ejection of the outer envelope of a medium mass star.

The Planetary Nebula Phase

With its outer envelope gone and a steadily growing core of carbon-oxygen ash the star contracts further. It gets hotter which further accelerates the rate at which it consumes its remaining fuel in the outer shells. The star descends the giant branch for the last time and moves rapidly across the HR diagram. It is during this phase that one of the loveliest of stellar objects is created - the Planetary Nebula. So called because they appear often as small greenish-blue disks in telescopes and thus bear a resemblance to planets like Uranus or Neptune, planetary nebulae are the glowing remains of some of the material of the ejected outer envelope of the star. Figures 10.14 and 10.15 show examples of planetary nebula. At the center of each nebula is a small and intensely hot star. In the case of the planetary nebula NGC 2440 shown in Figure 10.14, the central star has a surface temperature of 400 000 K making it the hottest known star! Although very tiny this star produces a flood of ultraviolet light which causes the ejected gases around the star to glow. Figure 10.15 shows the lovely "Ring Nebula" or M 57.

Figure 10.14 Hubble Space Telescope image of NGC 2440. Figure 10.15 Hubble Space Telescope image of M57.

The formation of planetary nebula is complicated and depends critically on the temperature of the inner star left behind by the ejection of the outer envelope. If too much mass has been ejected or if the rate at which the surface of the inner star heats is not rapid enough the ejected gases may disperse before a nebula forms. At one time it was thought that all medium mass stars form planetary nebula. Research in the past decade suggests that this may not always be the case. Some research suggests that binary star systems have a much greater chance of forming planetary nebulae. One thing that is known, however, is that the planetary nebula phase is brief. Such nebula last for "only" 10 000 to 100 000 years before merging, invisibly and silently into the interstellar medium.

The White Dwarf Phase

The carbon-oxygen core that is left behind as the outer envelope of the medium star expands into interstellar space will continue to contract until electron degeneracy once more sets in. By this time the star will resist any further contraction and have reached a central temperature of several hundred million degrees Kelvin - hot - but still not hot enough to initiate carbon fusion. The star has shrunk down to the size of the earth (or less) and has reached an incredible density of millions of grams per cubic centimeters. The "nuclear fires" have gone out and the star has become a member of the White Dwarf luminosity class. The star has a very tiny surface area at this point and is extremely hot. For this reason it will take an enormous length of time before the star cools off completely to become a "Black Dwarf". In fact, the cooling time for white dwarfs exceeds the present age of the universe - no black dwarfs have yet formed but we know of no way in which the fate of the star can be changed.

The white dwarf is a strange object indeed! The density of a "typical" white dwarf is so great that rather than being a gas the carbon and oxygen atoms are squeezed into a crystalline state. The "atmosphere" surrounding the star would be only tens of meters deep and would consist of a dense mixture of carbon and oxygen with remnants of the hydrogen and helium left over from earlier epochs. It is now believed that all low and medium mass stars will end up as white dwarf objects at the end of their evolution. There is, however, a very distinct upper mass for any White Dwarf. In the early 1930's the brilliant young Indian astrophysicist Subrahmanyan Chandrasekhar showed that if the mass of a white dwarf exceeded 1.4 Mo the degenerate carbon-oxygen core would no longer be able to support the star and it would collapse. This is now called the Chandrasekhar Limit and we will learn more about this in the section 10.3.

So how do we know such objects exist? Surprisingly, astronomers discovered the first white dwarf nearly a century before the prediction of their existence. As early as the 1840's the astronomer Bessel had noted a distinct wobble in the motion of Sirius - the brilliant bluish-white star below and to the left of Orion and concluded that there must be an unseen companion. In 1862, while testing a new telescope, the famed American optician Alvin Clarke discovered the faint companion star - Sirius "B". Subsequent observations showed that Sirius "B" has an apparent magnitude (mV) of 8.3 and a mass of 0.98 Mo. By 1915 spectroscopy had revealed a surface temperature of 25 000 K. Figure 10.16 shows Orion and Sirius, the inset image is a Hubble Space Telescope image showing both Sirius A and B.
  Figure 10.16 (Inset) Hubble image of Sirius A and B with the Orion and Sirius in background.

Example 10.6 Argue that Sirius B cannot be a "normal" star but is, in fact, an excellent candidate for a White Dwarf object.

Solution: The key to this is to recognize that the absolute magnitude of Sirius B is very faint but its surface temperature is very high. This will imply a very tiny size for a star that is roughly the mass of our sun. It must, therefore be much denser than our sun.

First - determine the absolute magnitude by noting that Sirius has a distance of 2.64 pc (Use Stellarium to find this out!). Use distanceModulus to find that the distance modulus is (mV-MV) = -2.93. This means that the absolute magnitude of Sirius B is only (8.3 - MV) = -2.93, so MV= 11.2. SInce our sun has an absolute magnitude of 4.8, Sirius B is 6.4 magnitudes fainter. Using the magnitude-luminosity law you can deduce that the luminosity of Sirius B is only (2.512)-6.4 = 0.0028 Lo

Next, use hrExplorer to find that the radius of the star for surface temperature = 25000K and luminosity is L = 0.0028 Lo is R = 0.0028 Ro!!
Figure 10.17 The location of Sirius B on the HR diagram.

Practice

  1. How do we know that White Dwarf stars exist?
  2. What is the difference between a brown dwarf and a white dwarf?
  3. True or false - a brown dwarf is just a "warmer version" of a black dwarf. Explain.
  4. Why can't white dwarf stars contract and heat up in their cores to stars new fusion reactions?
  5. Explain what happens to the density of the sun's core as it ages. Use one of the applets to assist you in answering this.
  6. Approximately how long will a 0.5 Mo star spend fusing hydrogen in its core? How does this compare to the case of a 5 Mo star? Why are the two so different?

To understand the evolution of low mass main-sequence stars

Chp 13.1

Red Dwarf stars are very low mass stars in the 0.08 Mo to 0.4 Mo range.

 

 

 

 

 

.Red Dwarf stars evolve so slowly that their main-sequence lifetime is greater than the present age of the universe (13.7 billion years). Every Red Dwarf that has ever existed is still shining today!

 

 

 

 

 

 


 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

The Horizontal Branch is the region on the HR diagram in which stars are undergoing "shell burning"

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Planetary Nebulae are one of the remnants of most medium mass stars and are produced by the ejected outer envelopes of these stars. They glow because they are illuminated by ultraviolet radiation from their parent star.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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During the later stages of their evolution medium mass stars lose a considerable amount of mass through a greatly enhanced "stellar wind". This "wind" is enriched with Carbon and Oxygen which had been dredged up from the core through convection and is one of the ways in which stars "seed" the galaxy with heavier elements.

 

 

A White Dwarf is a compact object which represents the endpoint in the evolution of low and medium mass stars. A Black Dwarf is the ultimate end of a White Dwarf as it cools down. The time required for a White Dwarf to cool to be a Black Dwarf exceeds the present age of the universe.

 

 

 

 

 

The Chandrasekhar limit is the maximum mass that a White Dwarf can have

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

For every difference of 1 magnitude there is a factor of 2.512 in brightness or luminosity. If one star is 5 magnitudes fainter than another its luminosity is 1/(2.512)5 or 1/100th the luminosity of the brighter star.