White Dwarf Stars

If you will take a close look at this HR Diagram, you will see a thin line of stars 10 to 15 orders of magnitude below the main sequence, and well to the left of the temperature baseline. These White Dwarfs are the ultimate descendants of stars like our Sun. Previously thought to be rare, we are now finding them everywhere within our Galaxy. These stars are evolved from the terminal life stages of B,A,F,G main sequence dwarfs, and are the same stars that formerly existed as Red Giants, Asymptotic Giants, and blew our spectacular planetary nebulae.

The first White Dwarfs were discovered in the 1800's. Friedrich Bessell noticed, in 1844, that neither Sirius (an A1 dwarf in Canis Major) nor Procyon (an F5 dwarf-subgiant in Canis Minor) moved through space in a straight line. He reasoned that some massive object was gravitationally influencing the motion of these two stars. Alvan Clark was testing a new 18-inch lens at Northwestern University's Dearborn Observatory in 1862 when he discovered the 8th magnitude companion to Sirius, named Sirius B. Since it is 10 orders of magnitude more dim than Sirius and also so close to its companion, it is exceedingly difficult to see. Procyon B was discovered at magnitude 11 in 1895 at the Lick Observatory in California.

A quick analysis of the orbit of Siruis B gave us information about its mass (about 1.0 solar masses), but knowing what kind of star Sirius B was proved longer in discerning. Doing a direct analysis of the spectrum of Sirius B proved to be difficult owing to its close proximity to Sirius. Then astronomers got a break. A binary star system, 40 Eridani is made of 9.6 magnitude star, 40 Eridani B, and a fainter 11th magnitude red dwarf of spectral class M4V. They orbit each other every 250 years, and because they are so widely separated, and because the red dwarf star is so dim, a spectrum of 40 Eridani B could be obtained. Initially thought to be a simply cool and dim star, astronomers were surprised to find 40 Eridani B to be an A class star. Clearly it must be hot, evidenced by its strong Hydrogen absorption lines. For the visual magnitude to be so low for a star that was so close to Earth meant that its surface area and radius must be very small. 40 Eridani B became the first officially-designated White Dwarf.

Shortly after the announcement about the status of 40 Eridani B, W.S. Adams at Mt. Wilson Observatory in California discovered that Sirius B was also an A star. With a visual magnitude 10 orders below Sirius A, Sirius B must be 1/100th of the size of Sirius A. Since Sirius A is a known A1 dwarf, radiating at 9000K, and an absolute visual magnitude of 1.4, it must have a diameter twice that of the Sun. Sirius B was estimated to have a diameter of only two Earths. With its established mass of 1.0 solar masses, Sirius B must have a density 100,000 times that of water, or 10,000 times that of lead. With the advent of better instrumentation today, we now know that Sirius B has a radius of only three-quarters of the Earth, and a density over 1 million times that of water! The conditions on a White Dwarf must be truly exotic.

White Dwarf Conditions

Once again, we turn to a spectral analysis of the star to reveal its personality and characteristics. Like all stars, the White Dwarf will have its highest densities in the center and progressively lower densities as you move farther out toward the surface, where in a thin atmosphere the absorption lines are formed. Even though the atmosphere is thin in terms of thickness, it is thick in terms of density. A Hydrogen absorption line formed in a low-density atmosphere will be narrow because the atoms are farther apart from each other and there is minimal electrical effect upon the energies of individual atoms by their neighbors. The more dense the atmosphere, the more energy interactions between close proximity atoms and the wider the Hydrogen lines. Therefore, the Hydrogen absorption lines of a Class A Red Supergiant will be more thin than those of a Class A Red Giant, which in turn will be more thin than a Class A Main Sequence Dwarf.

White Dwarfs carry this widening of Hydrogen absorption lines to an extreme. These lines are amazingly wide and indicate an almost unbelievable density. I say "almost unbelievable," because the evidence is clear, and even greater extremes than this are found in space. How can these densities be achieved? A Hydrogen atom is about a hundred-millionth of a centimeter across, but the nucleus - which is just a single proton - is 100,000 smaller. This means that only one single part of one thousand trillion parts of the space of a Hydrogen atom is filled, while the rest is empty. Picture a grain of rice representing the nucleus of a Hydrogen atom, and placed gently on the 50 yard marker of Lambeau Stadium. The electron, whose diameter cannot even be measured, would be someplace out in the skyboxes at the very edge of the stadium.

Sir Arthur Eddington, a Cambridge astrophysicist, realized that all of the Hydrogen atoms must be completely ionized for a White Dwarf to exist. This ionization can come if enough energy from the core excites the electrons completely away from their nuclei. With no occupied orbitals, the ionized Hydrogen atoms can now be greatly compressed. A problem with the theories presented itself when one considers that the dead White Dwarf should be slowly cooling. Under the lower temperatures, the electrons should recombine with their nuclei and the star should then physically swell. However, the intense gravities (10,000 times solar) within the collapsed White Dwarf prevent such expansion.

For your pleasure here, I will just tell you that R. H. Fowler, Linus Pauling, and Walter Heisenberg offered a series of theoretical explanations in an area of physics known as Quantum Mechanics. I have limited understanding of this subject, but will try to explain Quantum Mechanics, the Pauli Exclusion Principle, and the Heisenberg Uncertainty Principle as they relate to a White Dwarf.

In an ordinary gas, atomic particles are free to take on any value of velocity or momentum (mass times velocity), But at the extremely high densities these same particles are limited in their freedom. The Heisenberg Uncertainty Principle states that an atomic particle's momentum and its position cannot be simultaneously known. The uncertainty of a particle's momentum multiplied by the uncertainty of its location roughly equals Planck's constant h, a tiny number that relates the energy of a photon to its frequency (E = h X frequency). In units of centimeters, seconds, and grams, h is around 10^-27, so this Principle only takes effect in the exceedingly small world of the atom.

Next, we define a six-dimensional "volume" that consists of the three dimensions of real space and three more of momentum whose axes are directed along the real coordinates of ordinary space. This strange six-sided volume is derived by multiplying all six directions together. The Pauli Exclusion Principle states that in a minimum six-sided volume of size h^3, no two particles with identical properties can exist; only one can be there at a given time. As a result, there can be at most two electrons within this minimum box, and they are required to spin in opposite directions. I think the reason you can have two electrons in the same box is because one electron can occupy the h^3 volume box spinning on one direction, and the one spinning in the opposite direction can be in the same h^3 volume box because there are 6 dimensions ... (h^3)^2. The practical result of the Pauli Exclusion Principle for free electrons is that at any given small volume of space can contain only a certain number of particles moving at a particular momentum or speed. We can add particles to the small volume, but only if they are moving at faster speeds. This means that more than two electrons can occupy the same physical volume of h^3, but only because the newly incoming electrons must be of faster velocity or momentum than the two oppositely spinning electrons already there. As more faster and faster free electrons are added to the small volume of h^3, the actual physical space becomes so crowded that the electrons begin to produce an outward pressure against new electrons invading the space. This electron pressure now defines the gas as "degenerate," and the "degeneracy pressure" is sufficient to hold up a White Dwarf against the inward pressure of gravity and keep the White Dwarf from collapsing forever!

In an ordinary gas, pressure and temperature are directly proportional to each other, and inversely proportional to the volume or density (pv=nrT). Degenerate gas does not obey the ideal gas law entirely, because under extreme densities, pressure is dependent only on that density and not at all on temperature. As the White Dwarf and its degenerate gas cools, the electrons are packed at low velocities as tightly as possible and they cannot slow down, and except at the stellar surface (which is not degenerate), recombination of electrons and protons into atoms cannot take place. The star maintains a constant internal pressure dependent upon its mass, and as time goes by, the White Dwarf will cool with a constant radius.

Most White Dwarf stars have masses that are roughly half that of our Sun. The higher the mass of the White Dwarf star, the greater the gravitational compression and the smaller the radius, causing the star to be less luminous than its lower-mass companion. Here is where it gets really weird, for as the mass increases, even the conditions of the degenerate gas are no longer ordinary. The velocities of the highest speed electrons attempting to fill the already crowded six-dimensional volume must approach the speed of light, and thus these electrons fall under rules no longer pertaining to degenerate gas, but to "relativistic gas." Subrahmanyan Chandrasekhar discovered in 1930 that if the mass of the White Dwarf exceeds 1.4 solar masses, electron degeneracy can no longer hold off the crushing force of gravity, and indeed, there are no White Dwarfs ever discovered with a mass greater than 1.4 solar masses. The White Dwarf star that exceeds this Chandrasekhar Limit will either be crushed into a Neutron Star, Black Hole, or explode into nothing at all.

Star Life Reminder

Once again, we see that the mass of the star is the all-important factor that determines its fate. Stars that begin their lives with 1 to 10 solar masses will burn Hydrogen into Helium on the Main Sequence line of the HR Diagram, followed by core collapse and star expansion to a giant star. Helium ignition into Carbon and Oxygen halts the expansion and converts the star into the Asymptotic Giant Branch star. When the core Helium is gone, the star will evolve into a Planetary Nebula with a White Dwarf remnant. Calculations show that stars below 0.8 solar masses have not had enough time to evolve off the Main Sequence. When they do, they will probably develop into a White Dwarf with about half the mass of the Sun. An A0 Dwarf will begin with an initial mass of 2.8 solar masses, and die as a 0.8 solar mass White Dwarf. A B7 Dwarf will begin with 4.5 solar masses and terminate at a 1 solar mass White Dwarf. Finally, around 10 solar masses starting point (typically a B2 Dwarf), the endpoint will be a 1.4 solar mass White Dwarf at the Chandrasekhar Limit.

Variable White Dwarfs

As I attended the HEA Symposium and the AAVSO Workshop in July, 2002, I was amazed to learn that some White Dwarfs are variable in their brightness, pulsating in a rhythmic fashion. Some White Dwarfs in the B Class spectral group change their brightness by 0.01 - 0.3 magnitudes, with periods of 3 to 20 minutes. These are similar to the regular pulsations of the larger Cepheids, whose magnitude change may be of several orders, and over periods of days. Unlike the Cepheids that pulsate as an entire star, the variable White Dwarf stars pulsate in one area outward, and contract inward in another area.

Even more strange are Dwarf Novae and Novae that we have begun to unravel the mystery surrounding their patterns of extreme brightening. If the White Dwarf is close enough to its companion, the less-evolved star in the pair will begin to lose mass to the White Dwarf. As this mass falls toward the White Dwarf, it spins around the smaller star before finally falling onto its surface. This spinning gas is called an "Accretion Disk," and is a rather common phenomenon among binary systems. The intense gravity of the White Dwarf star causes the infalling Hydrogen gas to heat up to nuclear burning when sufficient gas has collected on the surface, and a tremendous explosion of this new gas ensues. The explosion generates great energy, raising the apparent visual magnitude of the White Dwarf by perhaps 10 orders of magnitude. Later, the erupting gas has become so powerful in its outward pressure that it escapes from the star itself, and is quickly ionized and lit up by the White Dwarf inside the shell of expanding gas. The sudden brightening of the star is called a "Nova," and we can witness one within our galaxy about once per generation. The accretion disk and then an explanation are both shown below.

After the surface of the White Dwarf has been blasted away by the nova, the phenomenon can repeat itself. Under some binary system configurations, the repeated event might happen every 100,000 years or so. If conditions are just right, then the recurrent nova might explode every few decades ... like the star RS Ophiuchi. In between major events, minor instabilities within the accretion disk might cause sudden brightening, but on a far less expansive scale, and without such a tremendous nuclear blast. These minor events are called "Dwarf Novae," and are common to two stars U Geminorum and SS Cygni, that brighten by a few magnitudes irregularly every several months.

Indeed, the star SS Cygni appeared to be brightening a little bit in 1996. A call from the AAVSO Headquarters to my Uncle Bill requested his confirmation of the earliest stages of brightening before three satellites were slewed to that location. When Bill Albrecht reported to Janet Mattei that SS Cygni was brightening, the satellites were pointed at the star just as the dwarf nova event was beginning, and from that event, a great deal of information was derived about the cause. As theorized, instabilities in the accreting Hydrogen from the larger companion star was causing clumps of gas to suddenly fall onto the star's surface and be greatly heated, brightening the star by several orders of magnitude. The light curve for this famous star, SS Cygni is found below, and shows the repeated pattern of dwarf novae events. I selected the data from the AAVSO website and what is below contains come 9000+ observations over a period of 700 days. The reason the data is unvalidated is that not every plotted point has received confirmation from the AAVSO headquarters yet. Notice that the star changes in magnitude by over 4 orders of magnitude, very quickly, but not in perfect regularity.

What happens if the White Dwarf exceeds the Chandrasekhar Limit?

The variable White Dwarf stars brighten and dim due to pulsations and accretion of mass. Typically, the accreted mass is ejected into space during nova events. But, if the accreted material accumulates so rapidly that the star cannot eject it, then the White Dwarf might exceed the Chandrasekhar Limit of 1.4 solar masses. Gravity suddenly has enough mass to continue contraction past electron degeneracy. The core suddenly collapses and intense nuclear burning brings about a sudden explosion of the White Dwarf. This explosion is the most grand of all supernova events, and are termed Type Ia Supernovae. These explosions do not show Hydrogen lines, can occur anywhere, even in galactic halo globular clusters where no massive stars exist. The detonations ALWAYS produce absolute visual magnitudes of -19, and exceed even the massive star Type II supernova events. Such an event was witnessed in 1994 in the galaxy NGC 4526, and the bright star is seen in the image below. The sheer enormity of a Type Ia Supernova boggles, as astronomers estimate an energy output in excess of 10^48 ergs. This total exceeds the energy output of the ENTIRE Universe during the monumental eruption of a collapsing White Dwarf. There is plenty of speculation of what would happen if such an explosion were to occur nearby, but the opinions all agree that life would certainly be extincted on Earth if a Type Ia Supernova were to occur within a few tens to hundreds of light years of Earth. Is it possible that such events happened in coincidence with major extinction level moments in Earth's past geologic history? Is it possible that such an event triggered an inward rush of comets from the Oort Cloud, sending some directly into Earth's orbital path?

Ideal Distance Indicators

Since these Type Ia Supernova all come from the same beginning (a White Dwarf at the Chandrasekhar Limit), and follow the same pattern of explosion, then the absolute visual magnitude is always -19. This makes these superbright events the ideal distance indicators. If you can see the spectral pattern of a Type Ia Supernova in a distant galaxy, or even follow the amazingly consistent brightening and dimming curve over time, then you can apply the Magnitude-Distance Formula to the object and determine how distant the host galaxy is. It is the search for and study of Type Ia Supernovae that consumes Saul Perlmutter, and gives him an opportunity to measure the expansion of the Universe, which might yield a value for the amount of material in the Universe, which can then be used to help determine its ultimate fate.

What if the White Dwarf collides with another star ... say like our Sun?

The November, 2002 issue of Scientific American Magazine has a cover article that addresses this very question, and I have included the article within this course for your reading pleasure. See White Dwarf collision.

The final demise of a White Dwarf

In the end, the White Dwarf is destined to cool down and become a black stellar corpse. Although it takes an exceedingly long time, these objects will change in form from a gas to a crystal ball when the surface temperature finally cools under 7000K. By now, the absolute visual magnitude is decreased to a very dim 17, and such stars are almost impossible to find. In addition, not a single White Dwarf has been able to move off the HR Diagram toward that Black Dwarf stage. The Galaxy, and the Universe for that matter, simply are not old enough for these stars to have cooled down yet. If it were possible to find one, we could then determine the age of the area in which the star was formed, and get a better idea of just how old parts of our Galaxy are. It is pretty amazing that such tiny objects can make such big explosions, and also yield such important information.

Tom's comments from being tired at this point in course-writing

At this point, the sheer breadth of this course has made it impossible for me to finish writing it within the allocated two weeks remaining in the quarter. I have probably lost most of my students in the technical aspects of Astronomy, but I could not help myself as I was preparing this material. I have always wanted to know more of the details of stellar evolution, and finally took the time to synthesize that material in a such a way that I can understand just a little bit of it. I beg you to have in there for the discussion in the next two pages on Neutron Stars and Black Holes. I am going to put by "Extreme Stars" book away for the rest of this course and teach the final two star categories from material I have already digested, but without the technical jargon. Then we can move on to Galaxies and Cosmology in the final few days of the quarter.

Please move now to Neutron Stars, or return to the Star Introduction or go to the Syllabus .

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