White Dwarfs and The Heat Death

Nothing is eternal. Not even the universe.

With its young 13.8 billion years, the Cosmos remains active with pulsars, quasars, gravitational interactions, supernovae, nuclear synthesis, among many other processes. As the universe ages, some stars slowly lose their shine while others end their lives as relentless black holes. In addition, the expansion of the universe causes galaxies to distance themselves, which weakens gravitational interactions. This means that the universe will be but an infinite horizon dominated by cold and darkness in the so-called "thermal death" in a future far, far away. But don't be alarmed; we will have plenty of time to enjoy the warmth of the stars, several trillion years.

But what if we want to contextualize ourselves about the scenario in this very distant future? Who will be the "last standing"? When the cosmic lights start to "go out," 97% of all stars in the universe, including what remains of our Sun, will be the last illuminators. The Sun is a relatively small mass star, and, therefore, it will not die in a supernova. Instead, the Sun will become a giant red star, increasing its size very expressively. When the Sun is no longer able to fuse elements (nuclear fusion/stellar nucleosynthesis), it will expel its outermost layers outside. This stellar "dust" is called a planetary nebula, like the magnificent Helix nebula (see photo 2). The Sun's remainings will be its core, composed of heavier materials such as carbon and oxygen. This nucleus will be approximately one million times smaller than the original size of the Sun, but it will retain about half of the original solar mass. This implies a density in the order of 10^(24) kg/m^(3). To illustrate this density, 10^(24) kg/m^(3) would be like having ten quintillions of blue whales compacted in a volume compared to that you are occupying while sitting.

Photo 2

We now have the imagery of a white dwarf star, but what makes them so long living? Despite their small size, such stars are up to 40 times hotter than the Sun. This is because most of the star's heat is confined inside it, unlike active stars (like the Sun today), which violently expel heat in the form of radiation through nuclear fusion reactions. Since white dwarfs have no nuclear activity, heat transfer is minimal, which means that they can shine longer than any other radiating star. When the universe reaches the late elderly (many trillions of years from now), the last cosmic illuminators (white dwarfs) will have already expelled all its heat, becoming black dwarfs (extremely cold and non-radiant nuclei). See photo 3; it shows the evolution of a white dwarf (white dwarf) in an HR diagram. In the end, the universe will be nothing but a sea of ​​black holes and black dwarfs. Again we reinforce: don't worry! On the time-scale mentioned above, the universe is still a newborn baby. An interesting curiosity about the longevity of white dwarfs is that they are one of the main methods for dating star clusters. This is because the presence of white dwarfs implies old stars. When we find the coldest white dwarf in the cluster, we will find the oldest star in the cluster (see the diagram in photo 3 again) and, thus, its age.

Photo 3

We know how white dwarfs "light up" and "light off," but how do they manage to sustain themselves since there is no thermonuclear pressure to counteract the gravitational collapse? The answer lies in a principle of quantum mechanics called the "Pauli exclusion principle." This quantum law governs that a quantum system cannot have two fermions (particles with half spin, like electrons) in the same energetic configuration. The extreme density of the white dwarfs causes the atoms' electrons present in the star to be forced into equivalent energy configurations. Still, due to the exclusion principle, an unprecedented pressure arises to impose a resistance against adhesion to equivalent states. This pressure is called degeneracy pressure. A curious factor is that an increase in the mass of the white dwarf would imply a decrease in its size, not an increase since the gravitational implosion would be reinforced.

Another special feature of white dwarfs occurs at binary systems: stellar systems composed of two stars. Stars in binary systems have a region called "Roche Lobe," which marks the star's gravitational influence regime (see photo 4). Consider a system composed of a yellow dwarf star (same classification as the Sun) and a white dwarf. When the yellow dwarf becomes a red giant, it will expand in size, exceeding its Roche Lobe (see photo 5). When this happens, part of the red giant will enter the gravitational regime of the white dwarf since the gravitational potential of the white dwarf becomes greater than that of the red giant itself (see photo 5). In this way, the red giant begins to have its outer layers sucked, passing through one of the so-called Lagrange points and funneling towards the white dwarf. See photo 6 for the artistic representation of this process. The matter recently acquired by the white dwarf star sits on a disk called an accretion disk, which feeds the white dwarf over time, increasing its mass. However, there is a mass limit for white dwarfs since degeneration's pressure becomes insufficient to sustain the gravitational collapse. The maximum possible mass is around 1.4 solar masses, which is given the name "Chandrasekhar mass." When this limit is exceeded, the white dwarf can become even more dense objects, like a neutron star or a black hole. Finally, the white dwarf heats the light elements that come from the accretion of the neighboring star so that the nuclear fusion process starts on the accretion disk itself. The result of this sudden release of energy is a big explosion called "Nova." Photo 7 presents a real image of a Nova. (P.S: don't confuse it with a supernova!).

Photo 4

Photo 5

Photo 6

Photo 7

When the stars begin ceasing to shine, white dwarfs will be the definitive hope for life in the universe, serving as the last source of heat and energy for possible extraterrestrial civilizations until the last light goes off. But do not worry. Our universe is young and extremely active, and its mortality may remind us to make the best of our brief cosmic contribution.

Photo 2: Helix Nebula

Photo 3: HR diagram (courtesy of Professor S. George Djorgovski, in the course “The Evolving Universe”)

Photo 4: Roche Lobe (courtesy of Professor S. George Djorgovski, in the course “The Evolving Universe”)

Photo 5: Gravitational potential and the Roche lobe

Photo 6: Artistic conception of a white dwarf acquiring its accretion disk

Reference material:

The Evolving Universe (professor S. George Djorgovski) Origin (Neil deGrasse Tyson)

Death in the Black Hole (Neil deGrasse Tyson) https://imagine.gsfc.nasa.gov/science/objects/dwarfs2.html