Hot Stars - White Dwarfs

We have just looked at a group of stars called Red Giants. These are stars which have lived out their lives on the main sequence and later expanded into their giant size with cool surface temperatures placing them in the very luminous but low spectral class of M8III, with the M meaning low temperature and complex absorption spectrum, the 8 refers to the subclass of M, that in this case tells us that it is really cool, and the II represents the luminosity class that is a giant. These Red Giants are very large, and thus very luminous. Their luminosity per unit area is quite low due to the low surface temperature, but the sheer size of these giant stars make them among the brightest objects in our visible sky. The next question that needs to be asked by you it, "what happens as these stars ascend the HR Diagram giant branch the second time?"

The images above are examples of the objects we will be studying next. To the far right is a cluster of stars that orbit our galaxy. Within that cluster are countless tiny, white dwarf stars, barely visible when compared to the brighter main sequence dwarf stars nearby. To the left is the Eskimo Nebula with its white dwarf star in the center of the dust and gas cloud. These images are just so incredibly beautiful, but I have more to come in this unit, and because of their unusual beauty, these stars have become a personal favorite of mine now. So, just what does happen when the Red Giant stars continue their ascent to the right of the giant branch?

In the case of stars like our own Sun, and those with perhaps up to 10 solar masses, the star has been fusing Helium into a mixture of Carbon and Oxygen. It is possible for gravity to crush the C/O cores of these to greater densities and increased temperatures such that the Carbon and Oxygen are fused into Neon, Magnesium, and more Oxygen. However, the temperature for this reaction needs to be 600 million K, and in stars like our Sun or those with a few more solar masses, the loss of mass from the shockwave winds will deplete the star to such an extent that insufficient mass exists to generate those extreme densities and temperatures. Instead, the Carbon/Oxygen mixture in the cores of these dying stars is destined to just sit there forever in an exposed state. Remember, the repeated shockwaves from internal compression and ignition has blown away the outer envelopes and left behind the tiny core. The core can become no hotter during its prolonged death, and because it has such a small size, it is very difficult to visually see. However, these small objects are extremely hot at their surfaces. Only neutron stars have higher surface temperatures, but they are so unusual that we will look at them later as a separate category. These dead Red Giant cores may be tiny and dim, but they are perhaps the hottest and also prettiest stars in the Universe.

The images above are Hubble Space Telescope images of various Red Giant cores. These objects are called "planetary nebulae," because they look like planets from a basic large telescope. The HST has revealed much greater detail than had previously been thought to exist in these objects. What is common to all of these objects is a tiny, white-hot stellar remnant in the center, and a huge cloud of gas and dust surrounding it. The core remnant from the Red Giant is called a White Dwarf, and the cloud is the old Red Giant envelope that has been blown out from the star's shockwave events over time, such that the huge and very beautiful nebula is seen and lit up by the central White Dwarf. The upper left image is the Ring Nebula (M57) and can be found in the constellation Lyra with my telescope. The upper right image is the Dumbbell Nebula (M27) and is found in Vulpecula. The Cat's Eye Nebula (NGC 6543) is the lower left image, and this object is found in Draco. The lower right image is the Blinking Eye Nebula (NGC 6826) is found in Cygnus. The image at the top right of this page is the Eskimo Nebula (NGC 2392) and if found in Gemini. All five of these images are classic examples of planetary nebulae, and are the subjects of this page ... the hottest stars.

Some representative planetary nebulae are listed in the chart below. In each case, the distance to the object is an estimate. The apparent magnitude and temperature refer to the central star in the nebula.

Nebula

Common Name

Constellation

Distance (ly)

Radius (ly)

Apparent Magnitude

Temperature K

Comments

NGC 40

 

Cepheus

3500

0.30

10.65

32,000

very low excitation

NGC 650-1

 

Perseus

2400

0.80

16.30

135,000

M76; large outer shell

NGC 2392

Eskimo

Gemini

4000

0.45

10.53

80,000

double shell

NGC 2440

 

Puppis

3600

0.30

17.66

220,000

hottest confirmed

NGC 6543

 

Draco

3200

0.15

11.31

47,000

AGB halo visible

NGC 6572

 

Serpens

1800

0.06

12.86

60,000

very bright

NGC 6720

Ring

Lyra

2500

0.40

15.00

145,000

M57; large outer halo

NGC 6826

 

Cygnus

5000

0.30

10.69

47,000

AGB halo visible

NGC 6853

Dumbbell

Vulpecula

900

0.75

13.82

160,000

M27

NGC 7009

Saturn

Aquarius

2900

0.20

11.30

80,000

first discovered

NGC 7027

 

Cygnus

3000

0.10

16.26

174,000

big molecular cloud

NGC 7293

Helix

Aquarius

500

1.0

13.43

120,000

closest planetary

NGC 7662

Ring

Andromeda

3500

0.25

13.20

100,000

double shell

Planetary Nebulae Definition and Discovery

None of the M Class Red Dwarfs are visible with the naked eye. On the other hand, the M Class Red Giant stars are easy to find. As we move down the HR Diagram and to the lower left, we find ourselves in the realm of the planetary nebulae. These tiny stars are dim in apparent magnitude owing to their small size, but enough are relatively easy to find with even a small telescope. The first astronomer to really study these objects was William Herschel, and he announced this particular class of stars as planetary nebulae in 1785. Herschel was of German descent and raised in the arts as a musician. He put his love of music aside when he became enamored with the stars, and never went back. His discoveries make him of legendary status, having discovered: planet Uranus, double stars, infrared radiation, a sense of the shape of the Galaxy, planetary nebulae, a large number of star clusters, other forms of nebulae, and more. Herschel was the first to notice a central "condensation" that appeared in NGC 6543, which turned out to be a central star. We now know that all planetary nebulae have them, even if they are sometimes hard to see.

Their names are given for their appearance, but you will notice that other forms of designations exist beyond a common name. Charles Messier was a famous astronomer and comet hunter who would occasionally be confused by the presence of a fuzzy patch in the sky. After noticing that a fuzzy patch was not moving as a comet, but staying put in its celestial position, Messier decided to catalogue these objects and locations so future comet hunters would not be confused by them. He made a list of 103 Messier Objects (M27, M57) and the list is a great goal for amateur astronomers to locate. Some even schedule Messier Marathons in late March in an attempt to locate all 103 (now a total of 110) in one evening run. I have seen all 110 objects, but not in one night :) When other deep sky objects were discovered, a new designation method was devised ... the "New General Catalogue." This NGC list was compiled in 1888 by J.L.E. Dreyer. Therefore, the Ring Nebula in Lyra and the Dumbbell Nebula in Vulpecula have designations M57 & NGC 6720, and M27 & NGC 6853 respectively.

The Hottest Stars Have Emission Spectra

Each planetary nebula has a central star that is the collapsed Carbon/Oxygen remnant from the Red Giant AGB star. These tiny objects are in the last stages of dying. They are extremely hot, and it is the little star that makes the surrounding nebula glow. In 1864, William Huggins turned his spectroscope onto the Cat's Eye Nebula (NGC 6543) and saw three emission lines instead of the usual absorption spectrum. He realized immediately that he was looking at an object made of heated gas. One of the bright emission lines was that of Hydrogen, so the planetary nebula was a least composed of a bunch of hot Hydrogen gas. There are other bright lines of Hydrogen emission as well as Helium, Carbon, Oxygen, and others.

To your left is a reminder of what an emission spectrum looks like. They result from spectral lines being generated by a hot gas, and are the opposite of an absorption spectrum that results from light shining through the gas. By looking at the bright lines of an emission spectrum, astronomers can determine which elements are in the heated gas.

These bright lines confirmed that the planetary nebula is made of material ejected from the parent star. Furthermore, a finely-tuned instrument can discern a subtle difference in the spectral signature from the gas in front of the star and behind it. The evidence of red and blue shifting demonstrates that the gas is expanding away from the central star in all directions. When all of the evidence was pieced together with our knowledge of the final stages of an AGB star, is was concluded that a planetary nebula is the remains of a Red Giant which has blown its outer envelope away with its strong stellar winds. Since we can even measure the speed of the nebular expansion, we can determine that these objects are young, having pushed out their envelopes within the past few thousand years. This makes sense, since the expanding shell of gas would dissipate into space and become invisible in only a few tens of thousands of years. The planetary nebula that we can see is therefore a relatively new object compared to time measured on a universal basis.

To me, this next part is pretty cool, if not a bit technical for a high school Astronomy course. I will try to keep it simple for my sake as well as yours because it is pretty confusing. An atom of Hydrogen has one electron. When that electron absorbs a photon of energy, it is jumped to a higher orbital. If the energy of the incoming photon is sufficiently high, the electron will absorb it and be knocked away from the Hydrogen proton nucleus, creating a Hydrogen ion. There is a "Lyman limit" of 912 Angstroms (91.2 nm), which is the wavelength or energy of a photon sufficient to move a Hydrogen electron up to a higher orbital and then completely away, and also the wavelength that would result in deadly radiation to an exposed human. This wavelength is equivalent to far Ultraviolet radiation. If enough Far UV light is emitting from the central star, the entire nebula cloud may become ionized. The result is a vast sea of particles called "plasma" ... free electrons and ionized nuclei.

These electrons of high energy, due to their capture of the high energy photon are "swimming" about in the nebular cloud and when they pass by an ionized nucleus, the nucleus may capture the electron. The electron will seek the lowest possible energy orbital, and thus rid itself of the absorbed photon. As we learned earlier, these orbitals are of a fixed nature, and the drop in energy is a distinct quanta of energy. Sometimes, the Helium or Hydrogen nucleus that captures the electron will have different orbital levels available for the incoming electron, and different photon wavelengths are emitted, corresponding to different colors of the visible spectrum. Some nebulae will have a reddish hue, and others a distinctly green hue. Early on, the spectrum of these nebulae showed these bright lines in areas unknown to chemists. A new element was named "Nebulinium" to describe the spectral signature of the new elements found in the nebulae. Later it was demonstrated that these spectral lines were equivalent to energy orbital levels in Hydrogen, Helium, and other elements.

For a planetary nebula to have its Hydrogen gas all be ionized, the central star that is emitting the radiation must have a surface temperature in excess of 25,000 K. There is even a theoretical connection between the particular ionized gases found in the nebulae and the initial mass of the star, but this relationship is not well understood. It appears that these hot stars can result from G,F, and A class stars, but a B class star seems to be destined to a different fate.

Finally, these little central stars all look alike to the undiscerning eye. They are small and white. To follow Wein's Law that relates temperature to emitted wavelength, all the central stars would have the same wavelengths of radiation and therefore the same surface temperature. To really tell one apart from the other, you need a telescope attuned to the ultraviolet end of the spectrum. By looking at the bright line spectra we can determine the temperature. To ionize Hydrogen requires an energy of 912 Angstroms. Using Wein's Law where Wavelength = 3,000,000/T, if we see ionized Hydrogen in the nebula, the central star must have a surface temperature greater than 32,000 K. But, we also see Helium ions in the cloud, and to ionize the first electron away from a Helium nucleus requires wavelengths shorter than 512 Angstroms. To ionize both electrons away requires an energy of 228 Angstroms, corresponding to temperatures of 58,000 K and 131,000 K respectively. By looking at the emission spectra of the central stars and their ionized nebulae, we can figure out how hot the central star is.

There is an interesting pattern between the energy of the central star and the nebula. As the surface temperature increases, the visibility of the star goes down because more energy is being released in the shorter wavelengths that are hard for us to see. The opposite is happening to the nebular gas that is being brightened greatly by the ionizing power of the short waves. The central star gets more dim and the nebula gets more bright the hotter the central star. The central star of William Huggins's favorite planetary nebula, NGC 6543, has a temperature of 47,000 K, which is at the highest limit of the hottest main sequence dwarf O class star. The star in the center of NHC 7009 has a temperature of 80,000 K. The stars in the Ring Nebula of Lyra and the Helix are at 130,000 K. These stars are exceedingly hot, and produce more ultraviolet radiation than visible light, so they are also very dim. There are some planetaries with central stars whose presence has eluded astronomers for decade, but with better telescopic optics are now popping into view. The use of ultraviolet telescopes has revealed the "star" in the center of NGC 7027 in Cygnus (below and left) to have a temperature at a whopping 175,000 K. Finally, there is a star in NGC 2440 in Puppis (below and right) whose surface comes in at 220,000 K. These are absurdly hot temperatures, and the HR Diagram does not even have a place for them, because the spectral class O only goes to the left to about 25,000-50,000 K. Astronomers are finding stars today with unconfirmed temperatures over 300,000 K. What can we construct in terms of a graph to represent these unusual objects with such a huge spread of temperatures?

 

I cannot believe the struggle I had trying to generate this HR Diagram of white dwarf stars with my power point. So, after wasting over 90 minutes in vain, I just scanned an image in from Kaler's book, "Extreme Stars" Cambridge University Press, 2001. Then, I triumphed in my efforts and constructed my own, using Kahler as a reference. The diagram shows a region not even on the typical HR Diagram because the temperatures of the central stars of planetary nebula are off that chart to the right. This modified version shows two tracks of planetary stars based on their masses of 0.8 (top track) and 0.6 Suns (lower track). What the chart of planetary central stars reveals is the the older the nebula, the greater the dispersal of dust and gas, and thus the larger size of the cloud. Also, these central stars compress with time and get smaller and smaller in size, which also results in hotter and hotter temperatures. Since these stars evolved from cool Red Giant stars, it is amazing to note that the coolest stars now become the hottest.

Here is the simple version of interpretation of the graph above. A star begins its life, similar to our own Sun, fusing Hydrogen in the core into Helium. Eventually, the core runs out of fuel, and collapses. The shrinking core heats up neighboring Hydrogen in a shell surrounding the core, inflating the star to the Red Giant stage. Later, Helium ash rekindles the fusion process in the core, fusing it into Carbon and Oxygen, and perhaps these products into Neon. Surrounding this new igniting core are layers of Hydrogen and Helium that are fusing as well. The star reswells into the classic Asymptotic Giant Branch star. As shell fuel supplies dwindle, they collapse under gravitational pressure toward the hotter core, and may either reignite into heavier elements, or cause a nearby of lighter elements such as Hydrogen and Helium to ignite fusion . This inward collapse, and reignition results in tremendous outward pressure, blowing strong winds of stellar material out into space. The star is essentially blowing itself out, by pushing its own material away from the star's gravitational in fluence. As a star nears the top of the AGB giant branch, its winds blow ever more fiercely. The core is stripped down to a ball of nuclear burning Helium into Carbon and Oxygen, plus a thin envelope of Hydrogen. The shrinking core gets hotter and hotter and more luminous. The hotter star now releases great amounts of energy in the form of far ultraviolet, and the gas in the expanding shells are ionized and "lit" up for our telescopes to see.

The Egg Nebula (left) in Cygnus, consists of dozens of expanding dusty shells. Light from a warm star hidden in the thick dust illuminates the surroundings through the disk's poles. Eventually, the star's wind will compress its surroundings to a shell that will be ionized as the star heats to 25,000 K. This object is a planetary nebula in the making.

Eventually, the electrons have their dramatic effect. The higher the temperature, the greater the kinetic energy of the electrons that are "swimming" free from their nuclei in the core. The higher kinetic energies results in these electrons acting like light waves, and moving at high speeds, the electrons cannot interact with each other or resume a location within the orbital of any nucleus. Unable to come any closer than their energies permit, the electrons become "degenerate." The core cannot be compressed any further even though gravity would attempt to crush it ever smaller. The outward pressure of degenerate electrons is balanced by the inward pressure of gravity, but at a much smaller diameter and higher density. The star stabilizes and cannot get any brighter.

 

This "electron degeneracy" was a force that Subrahmanyan Chandrasekhar proposed in the 1960's to explain the unusual properties of a white dwarf star ... research that earned him a Nobel Prize. And to think that this famous Indian physicist never looked through a telescope, saying "it simply wasn't necessary." His theory holds that a white dwarf will form as the result of gravitational collapse on a star whose mass is 1.4 Suns. If a star has a mass greater than 1.4 Suns, gravity will be able to crush it past the outward pressure of those degenerate electrons, and we will look at the results of such a collapse later in this unit. For now, back to the collapsing white dwarf.

As the collapses core of the former AGB Red Giant blows its outer envelope of Hydrogen away while fusing helium into Carbon and Oxygen in the core, the surface heats past 25,000 K and ionizes the Hydrogen in the expanding cloud, thus illuminating it. While the central star does not get more luminous, it does smaller under the inward force of gravity, and gets progressively hotter. The star stays at the same luminosity level, but the surface temperature of the shrinking objects surpasses 100,000 K. The smaller it gets, the hotter the star becomes, and the more elements and multiple electrons are ionized. At a temperature of about 100,000 K, the nuclear burning in the thinning shell of Hydrogen begins to slow down. The star reverses direction, cooling and dimming on the descending track.

The larger the stellar mass, the greater its brightness. But, the larger mass also lets gravity collapse the core to a smaller object, thus causing the star to get more dim due to the smaller surface area. By the time the star cools to 75,000 K, the nebula has expanded to the point where it can no longer be seen. All that remains is the cooling Carbon/Oxygen core, becoming a White Dwarf.

The White Dwarf is the hottest star we have encountered, but because it is so small, they are hard to find. If our Sun were to collapse someday into a White Dwarf, it would be no larger than the Earth. This is a decrease in volume of a million fold! The density of this object would cause tea spoons to weigh many, many tons. Eventually, nuclear burning in the white dwarf ceases ... after hundreds of thousands or even millions of years, and the star cools down to a black stellar corpse. The blown-out envelope dissipates into space, and there is nothing visibly remaining to tell of its former presence in the night sky.

If you want click on more images of planetary nebulae, and enjoy some of the sights, and sounds since this site has music playing. Man, I wish I knew how to put music into my course. No that would be so cool. If you think there are a lot of pictures about Astronomy, there is a lot of space music too. There are over 1000 planetaries described, and as many as 10,000 may reside in our Galaxy.

There are stars smaller and hotter than White Dwarfs ... the Neutron Star and Black Hole about which most students drool with anticipation. But, before we look at the supersmall and infinitely hot, we will first look at the counterpart to these small white stars. We need to look at the most luminous stars on the upper left of the HR Diagram, and what they give rise to ... the supergiants!

But, before I encourage you to move to the Brightest Stars, please move to the second page on these amazing planetary nebulae, for there is a new surprise awaiting you, and the result of a meeting I attended October 1, 2002. The page is entitled, the rest of the planetary nebulae story.

Or return to Star Introduction, Stellar Spectra, or regettably to the Syllabus.


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