White Dwarf Stars — An Overview (Part I)
Many fascinating processes work on unimaginable scales of both time and distance to help shape our universe. One such phenomenon is what happens when a star “dies”, and forms into a type of “dead star” called a white dwarf. This is only a brief introduction to the very high level concepts that constitute this very complex and yet not fully resolved topic. The nature of white dwarf stars is one of many areas of active astrophysical research, so our understanding may change drastically as new equipment to study the cosmos and stellar objects become available to us.
Stellar Dynamics
For the purposes of this article, I’ll only be discussing low mass stars. Stellar fates for high mass stars are not white dwarves, but rather neutron stars, or stellar mass black holes, which I won’t be discussing much here.
A normal Main Sequence star, which is essentially a massive natural nuclear fusion reactor, stays burning throughout its lifetime due to the constant combination of lighter elements in its core into heavier elements. The first and most common of these processes, after the star enters its stable phase (post birth) is Hydrogen to Helium fusion. As a star ages, the concentration of helium increases to a point where helium fusion begins to occur. This process cascades through the periodic table all the way up to iron if possible. Energy is released through each of these fusions, and the entire collection of these escalating elemental fusions is called stellar nucleosynthesis.
The reason that a star energy production keeps chugging away and not blowing itself a part from the get-go is due to a balance between its gravity and and the force of fusion. Gravity due to the mass of the star acts to compress the gas within increasing the star’s density. When the gas molecules within the core of the star are compressed enough, the aforementioned nuclear fusion occurs, which pushes radiant energy of the star outwards. This outward-inward force balance is called stellar hydrostatic-equilibrium, and its somewhat similar to the way a balloon stays intact. Except in the case of the balloon, it’s not gravity which is preventing the balloon from popping, but rather the material strength of its expansive rubber surface.
How far a star gets through the nuclear fusion ladder depends on its initial mass, and how much additional mass it accumulates through gravitational entrapment of external matter. Most of the stars in the universe, are heavy enough to fuse elements up to a specific target element — usually up to at least carbon, but fusions only up to neon, or even neutral helium and ionic helium are possible for exceptionally low mass stars. Also, the heaviest possible fusions to occur will be Fe 56 (Iron fusion) after which point, it’s no longer energetically favorable for any kind of nuclear fusion.
Fun Fact: A sort of “fun” comparison to make is comparing the power of a star that’s undergoing “Carbon Burning Fusion” to plain old Hydrogen/Helium fusion in a standard thermonuclear weapon on earth. CBF releases multiple exotons of nuclear energy per second, where as humany’s most powerful H-Bomb, the Soviet Union’s Tzar Bomba released a “mere” 58 Megatons, which is consequently enough power to reach the earth’s stratosphere and destroy an an entire island. This equivalent comparing the power of Nigra Falls to the power of water slowly dripping out of a barely leaky faucet. The order of magnitude difference between such events is unimaginable by human standards.
As the star transitions to heavier and heavier elemental fusions stages, it starts to grow to larger and larger sizes. This larger sized class of star is called a Giant Star (most typically, but not always, a Red Giant). The Red Giant continues fusion until there isn’t enough mass within the star to allow for strong enough gravitation to continue fusing its current heaviest element. At this point, all of the atoms in the star are compressed to a degree where nuclear fusion in the star ceases, causing the shedding off of its outer coronal layer as a planetary nebula. The remnant is the stellar core (the white dwarf). At this new size, the star supports itself not through hydrostatic equilibrium between the balance of gravitation and fusion, but rather through a quantum mechanical phenomenon known as electron degeneracy pressure.
White Dwarves
The white dwarf is white because it’s incredibly hot, which is due to its stellar history and resultant high temperature electrons at its core. The surface temperature of a white dwarf star can reach 25+K. This compares the 6K that of the surface of the sun. However, since there is no nuclear fusion occurring anymore within the stellar remnant, the white dwarf will not generate any new heat. It cools down throughout the course of its existence, where it goes through luminosity reductions and color shifts as the temperature lowers, due to its remaining energy radiating away.
Eventually, a typical white dwarf, after several trillion years (much longer than current age of the universe), will turn into a black dwarf star emanating no energy whats over. If proton decay occurs, it will fuse into a solid iron star and remain that way for eternity. Currently, there seems to be no black dwarves or iron stars in the universe and this is likely because we have quite awhile to go before any white dwarf cools to a complete inert state. So for now, this is only the predicated standard fate of the white dwarf star.
Note: There is also an object called a Red Dwarf, which is NOT a cooling White Dwarf. A Red Dwarf is an actual living star, although an extremely weak one, that will simply burn out without any of the dramatics of Main sequence expansion, and nebular ejection into a white dwarf. Proxima Centauri, the closest star to the earth other than the Sun, is an example of a red dwarf star.
Electron Degeneracy Pressure
The shrunken star, known as a white dwarf, (Carbon Oxygen White Dwarf most commonly) no longer produces solar energy through nuclear fusion, because its constituent elements have gotten as close to each other as possible such that their electrons are forced into their lowest quantum states. Also, the resultant quantum system at this incredibly high pressures is no longer strictly atomic in nature. The resultant electron “lattice” forms a new type of quantum system, where the wave functions of the electron become dependant on gravitational well potential, instead of the Columb potential between the electron and the nucleus of an atom. This is an absolutely bizzare thing to think about.
According to the Pauli Exclusion Principle, since electrons are fermions, no two identically classified electrons (via their spin, angular momentum, position and velocity) can occupy the same quantum mechanical state, and thus resist closer packing. The star essentially becomes a radiant eletrodynamic Carbon-Oxygen crystal with properties of what physicists term an electron gas. The details of the behavior of electron gases are way out of the scope of this article, and the mathematics needed to model such a material state are extremely difficult. But one thing to note about it is that it behaves very differently from molecular gases — which abide by the ideal gas law. It’s interesting to note that even though the internal nuclear dynamics (strong force interaction) of a star are exceedingly complex, the actual molecules still behave like ideal gases. Essentially: Volume and temperature are proportional under steady state isobaric conditions.
Electron gases abide by a much stranger law known as the electron gas law. the properties of which can be found here: https://www.sciencedirect.com/topics/mathematics/electron-gas). We will not be going into it just yet, but just to motivate curiosity (and dread):
A consequence of the above is that an electron gas gets even more dense with higher temperature, which is why more massive white dwarves tend to shrink, as oppose to expand to a greater volume, as would a regular star made up of normal gas. This is of course only a very rough classical description of an electron gas (also known as a fermi gas) behavior, and the complexity and full descriptive behavior lies in the quantum mechanical nature of its structure.
The Chandresekar Limit
A white dwarf star is typically as massive or slightly less massive than the sun, but with a much smaller volume between that of the moon and earth. This makes it super dense. A common comparison is that a teaspoon of white dwarf material can weigh a comically large 10 billion metric tons. Imagine stiring white dwarf material into your coffee instead of stevia.
Super dense objects in the universe are extremely dangerous, as they are typically on the verge of succumbing to gravitational collapse. Due to the large density of the white dwarf, these stars have a tendency to pull matter from the universe such as from other stars or from nebulae, and add to their own mass. You’ve probably seen images of these white dwarves leaching mass via spiraling trail of accretion particles.
As the white dwarf adds to its own mass, it approaches what’s known as the Chandresekar limit. At this point, the force of gravity is so strong that not even electron degeneracy pressure from the star’s constituent elements can hold the star together, causing catastrophic gravitational collapse. This resulting in a super nova, more specifically a type 1A Supernova.
At the subatomic level, electrons essentially have no where to go quantum mechanically speaking, and they get forced to fuse with protons forming neutrons. The number of neutrons accumulate, increasing the density of matter further, forming into the most bizzare states of matter in the entire universe, including neutronium, nuclear pasta, quark-gluon plasma, and the mythical strange matter at the center of the star. These types of matter are far beyond the capability of the laws of modern physics to comprehend and even farther beyond the scope of this article, but suffice to say that the result is a neutron star. There are yet stranger things such as black holes, white holes, and worm holes, but I’ll leave it at that.
Fun fact: Other than being the single most powerful explosion in the universe, The type 1A supernova is an important tool for astronomers to judge astronomical distances that are beyond 50 MegaParsecs. These are called “Standard Explosions”, and their characteristics allow us to locate the distances to objects relative to them and near them all the way up to 1 GigaParsec which is about the size of the observable universe. Why I threw this in here, I’m not sure, but it’s damn useful to astromy geeks!
Most Popular White Dwarf Example: Sirius B
The First White Dwarf discovered is known as Sirius B, a binary stellar remnant coupled in a binary orbit white its much more voluminous partner star Sirius A — popularly known as the Dog Star, residing in the constellation Canis Major. It’s about 8.6 light years away from earth and was postulated to exist in 1844 by astronomer Friedrich Wilhelm Bessel — the same Bessel who the mathematically ubiquitous Bessel functions are named after.
Bessel was observing irregularities in the orbit of Sirus A, and speculated that there must be a hidden mass affecting it somehow. Although he was ridiculed for his proposal, decades later, in 1862 this assertion was proven true when Alvan Graham Clark used a much more sensitive telescope to observe Sirus B. Unfortunately, Bessel had already passed away from an illness in 1946, so he never lived long enough to see his work come to fruitiion.
I’m not going to go too much into depth about the Sirius system because it warrants its own article, as the history of mankind’s observation and estimation of the the Sirius system is rich and storied. However I will mention that if you are new to Astronomy and every want to observe Sirius A, its pretty damn easy, even with low end telescopes. Sirius B is a whole other animal. A clear picture of it wasn’t even obtained until 2003, by the Hubble space telescope and even then, as you can see from the picture below, the size of it is ludicrously small compared to the much larger Sirus A. But despite its volume, keep in mind that Sirius B is able to toss Sirus A around in a celestial dance, lasting billions of years.
This disparity isn’t even due to Stellar Parallax. Sirius B is that small compared to Sirius A, yet Sirius B throws Sirius A around like a ragdoll
Observations of this highly dimension imbalanced binary orbit are a clear demonstration of the gravitational power of Sirius B and of white dwarf stars in general. In a secondary part of this article, I’ll likely go into how we are actually able to determine the mass of the white dwarf Sirus B via the characteristics and trajectory of its binary star orbits. It’s quite wild!
Conclusion
There are approximately 10 Billion white dwarf stars in the Galaxy, which constitutes about 5% of all the stars in the galaxy. They are fascinating objects, not only because of the bizarre physical laws that govern their composition, but also because they represent the history of stars and give us a lot of clues into how stellar evolution works. In the next article I will go more into specifics and discuss in more depth, interesting information about white dwarves and other fascinating stellar phenomena.
