WHITE DWARF: CHARACTERISTICS, COMPOSITION, FORMATION, TYPES - ARTE - 2024

A white dwarf is a star in the last stages of its evolution, which has already used up all the hydrogen in its core, as well as the fuel in its inner reactor. Under these circumstances, the star cools down and contracts amazingly due to its own gravity.

It only has the heat stored during its existence, so in a way, a white dwarf is like the ember that remains after putting out a colossal bonfire. It will take millions of years before the last breath of its heat leaves it, turning it into a cold and dark object.

Figure 1. Close-up of the binary system Sirius A (the main star) and Sirius B (white dwarf) in X-rays taken by Chandra. Source: Wikimedia Commons.

Discovery

Although they are now known to be abundant, they were never easy to spot as they are extremely small.

The first white dwarf was discovered by William Herschel in 1783, as part of the Eridani star system 40, in the constellation Eridano, whose brightest star is Achernar, visible to the south (in the northern hemisphere) during winter.

40 Eridani is made up of three stars, one of them, 40 Eridane A. is visible to the naked eye, but 40 Eridani B and 40 Eridani C are much smaller. B is a white dwarf, while C is a red dwarf.

Years later, after the discovery of the 40 Eridani system, the German astronomer Friedrich Bessel discovered in 1840 that Sirius, the brightest star in Canis Major, has a discreet companion.

Bessel observed small sinuosities in the trajectory of Sirius, whose explanation could not be but the proximity of another smaller star. It was called Sirius B, about 10,000 times dimmer than the splendid Sirius A.

It turned out that Sirius B was as small or smaller than Neptune, but with an incredibly high density and a surface temperature of 8000 K. And since Sirius B's radiation corresponds to the white spectrum, it came to be known as a "white dwarf."

And from then on, every star with these characteristics is called that, although white dwarfs can also be red or yellow, as they have a variety of temperatures, white being the most common.

characteristics

To date, some 9000 stars classified as white dwarfs have been documented, according to the Sloan Digital Sky Survey (SDSS), a project dedicated to making detailed three-dimensional maps of the known universe. As we have said, they are not easy to discover due to their weak luminosity.

There are quite a few white dwarfs in the Sun's vicinity, many of them discovered by astronomers G. Kuyper and W. Luyten in the early 1900s. Therefore, its main characteristics have been studied with relative ease, according to the available technology.

The most outstanding are:

- Small size, comparable to a planet.

- High density.

- Low luminosity.

- Temperatures in the range of 100000 and 4000 K.

- They have a magnetic field.

- They have an atmosphere of hydrogen and helium.

- Intense gravitational field.

- Low energy loss due to radiation, which is why they cool very slowly.

Thanks to the temperature and the luminosity, it is known that their radii are very small. A white dwarf whose surface temperature is similar to that of the Sun, barely emits one thousandth of its luminosity. Therefore, the surface of the dwarf has to be very small.

Figure 2. Sirius B and the planet Venus have approximately the same diameter. Tagged

This combination of high temperature and small radius makes the star appear white, as mentioned above.

Regarding their structure, it is speculated that they have a solid nucleus of a crystalline nature, surrounded by matter in the gaseous state.

This is possible due to the successive transformations that take place in a star's nuclear reactor: from hydrogen to helium, from helium to carbon, and from carbon to heavier elements.

It's a real possibility, because the temperature in the dwarf's core is low enough for such a solid core to exist.

In fact, a white dwarf believed to have a 4000 km diameter diamond core was recently discovered, located in the constellation Alpha Centauri, 53 light years from Earth.

The density of white dwarfs

The question of the density of white dwarfs caused great consternation among astronomers in the late 19th and early 20th centuries. The calculations pointed to very high densities.

A white dwarf can have a mass up to 1.4 times that of our Sun, compressed to the size of Earth. In this way, its density is a million times greater than that of water and is precisely what sustains the white dwarf. How is it possible?

Quantum mechanics claims that particles like electrons can only occupy certain energy levels. There is also a principle that limits the arrangement of electrons around the atomic nucleus: the Pauli exclusion principle.

According to this property of matter, it is impossible for two electrons to have the same quantum state within the same system. And furthermore, in ordinary matter not all permitted energy levels are usually occupied, only some are.

This explains why the densities of terrestrial substances are only on the order of a few grams per cubic centimeter.

Degenerate matter

Each energy level occupies a certain volume, so that the region that occupies one level does not overlap with that of another. In this way, two levels with the same energy can coexist without problem, as long as they do not overlap, since there is a force of degeneration that prevents it.

This creates a kind of quantum barrier that limits the contraction of matter in a star, creating a pressure that compensates for the gravitational collapse. This maintains the integrity of the white dwarf.

Meanwhile, the electrons fill all possible energy positions, rapidly filling the lowest ones and only those with the highest energy being available.

Under these circumstances, with all energy states occupied, matter is in a state that in Physics is called a degenerate state. It is the state of maximum possible density, according to the exclusion principle.

But since the uncertainty in the position △ x of the electrons is minimal, due to the high density, by the Heisenberg uncertainty principle, the uncertainty in the linear moment △ p will be very large, to compensate for the smallness of △ x and fulfill So:

△ x △ p ≥ ћ / 2

Where ћ is h / 2π, where h is Planck's constant. Thus, the speed of the electrons approaches the speed of light and the pressure they exert increases, since the collisions increase as well.

This quantum pressure, called the Fermi pressure, is independent of temperature. This is why a white dwarf can have energy at any temperature, including absolute zero.

Evolution

Thanks to astronomical observations and computer simulations, the formation of a typical star like our Sun is carried out as follows:

- First, gas and cosmic dust abundant in hydrogen and helium condense thanks to gravity, to give rise to the protostar, a young stellar object. The protostar is a rapidly contracting sphere, the temperature of which increases gradually over the course of millions of years.

- Once a critical mass is reached and with the temperature increasing, the nuclear reactor is turned on inside the star. When this happens, hydrogen fusion begins and the star joins the so-called main sequence (see figure 3).

- After time, the hydrogen in the nucleus is exhausted and the ignition of hydrogen in the outermost layers of the star begins, as well as that of helium in the nucleus.

- The star expands, increasing in brightness, decreasing its temperature and turning red. This is the red giant phase.

- The outermost layers of the star are detached thanks to the stellar wind and form a planetary nebula, although there are no planets in it. This nebula surrounds the core of the star (much hotter), which, once the hydrogen reserve is exhausted, begins to burn helium to form heavier elements.

- The nebula dissipates, leaving the contracting core of the original star, which becomes a white dwarf.

Although nuclear fusion has ceased despite still having material, the star still has an incredible reserve of heat, which emits very slowly by radiation. This phase lasts for a long time (about 10 ¹⁰ years, estimated age of the universe).

- Once cold, the light it was emitting disappears completely and the white dwarf becomes a black dwarf.

Figure 3. The life cycle of stars. Source: Wikimedia Commons. RN Bailey

The evolution of the Sun

Most likely, our Sun, due to its characteristics, goes through the stages described. Today the Sun is an adult star in the main sequence, but all stars leave it at some point, sooner or later, although most of their lives are spent there.

It will take many millions of years for it to enter the next red giant stage. When that happens, the Earth and the other inner planets will be engulfed by the rising Sun, but before that, the oceans will most likely have evaporated and the Earth will have become a desert.

Not all stars go through these stages. It depends on its mass. Those that are vastly more massive than the Sun have a much more spectacular ending because they end up as supernovae. The remnant in this case can be a peculiar astronomical object, such as a black hole or a neutron star.

The Chandrasekhar limit

In 1930, a 19-year-old Hindu astrophysicist named Subrahmanyan Chandrasekhar determined the existence of a critical mass in stars.

A star whose mass is below this critical value follows the path of a white dwarf. But if her mass is over the top, her days end in a colossal explosion. This is the Chandrasekhar limit and is approximately 1.44 times the mass of our Sun.

It is calculated as follows:

Here N is the number of electrons per unit mass, ћ is Planck's constant divided by 2π, c is the speed of light in vacuum and G is the universal gravitational constant.

This does not mean that stars larger than the Sun cannot become white dwarfs. Throughout its stay in the main sequence, the star continually loses mass. It also does so in its red giant and planetary nebula stage.

On the other hand, once turned into a white dwarf, the star's powerful gravity can attract mass from another nearby star and increase its own. Once the Chandrasekhar limit is exceeded, the end of the dwarf - and the other star - may not be as slow as the one described here.

This proximity can restart the extinct nuclear reactor and lead to a tremendous supernova explosion (supernovae Ia).

Composition

When the hydrogen in the nucleus of a star has been transformed into helium, it begins to fuse carbon and oxygen atoms.

And when the helium reserve is exhausted in turn, the white dwarf is composed mainly of carbon and oxygen, and in some cases neon and magnesium, provided that the nucleus has enough pressure to synthesize these elements.

Figure 4. The star AE Aquarii is a pulsating white dwarf. Source: NASA via Wikimedia commons.

Possibly the dwarf has a thin atmosphere of helium or hydrogen, since as the surface gravity of the star is high, the heavy elements tend to accumulate in the center, leaving the lighter ones on the surface.

In some dwarfs it is even possible to fuse neon atoms and create solid iron nuclei.

Training

As we have said throughout the previous paragraphs, the white dwarf forms after the star depletes its hydrogen reserve. Then it swells and expands and then expels matter in the form of a planetary nebula, leaving the nucleus inside.

This core, made up of degenerate matter, is what is known as a white dwarf star. Once its fusion reactor is turned off, it contracts and cools slowly, losing all its thermal energy and its luminosity.

Types of white dwarfs

To classify stars, including white dwarfs, the spectral type is used, which in turn depends on temperature. To name the dwarf stars, a capital D is used, followed by one of these letters: A, B, C, O, Z, Q, X. These other letters: P, H, E and V denote another series of characteristics, much more particular.

Each of these letters denotes a prominent feature of the spectrum. For example, a DA star is a white dwarf whose spectrum has a hydrogen line. And a DAV dwarf has the hydrogen line and, furthermore, the V indicates that it is a variable or pulsating star.

Finally, a number between 1 and 9 is added to the series of letters to indicate the temperature index n:

n = 50400 / effective T of the star

Another classification of white dwarfs is based on their mass:

- About 0.5 M Sun

- Average mass: between 0.5 and 8 times M Sol

- Between 8 and 10 times the mass of the Sun.

Examples of white dwarfs

- Sirius B in the constellation Can Major, the companion of Sirius A, the brightest star in the night skies. It is the closest white dwarf of all.

- AE Aquarii is a white dwarf that emits X-ray pulses.

- 40 Eridani B, distant 16 light years. It is observable with a telescope

- HL Tau 67 belongs to the constellation of Taurus and is a variable white dwarf, the first of its kind to be discovered.

- DM Lyrae is part of a binary system and is a white dwarf that exploded as a nova in the 20th century.

- WD B1620 is a white dwarf that also belongs to a binary system. The companion star is a pulsating star. In this system there is a planet that orbits them both.

- Procyon B, companion of Procyon A, in the constellation of the Lesser Dog.

Figure 5. The Procyon binary system, the white dwarf is a tiny dot on the right. Source: Giuseppe Donatiello via Flickr.

References

1. Carroll, B. An Introduction to Modern Astrophysics. 2nd. Edition. Pearson.
2. Martínez, D. The stellar evolution. Recovered from: Google Books.
3. Olaizola, I. The white dwarfs. Recovered from: telesforo.aranzadi-zientziak.org.
4. Oster, L. 1984. Modern Astronomy. Editorial Reverté.
5. Wikipedia. White Dwarfs. Recovered from: es. wikipedia.org.
6. Wikipedia. List of White Dwarfs. Recovered from en.wikipedia.org.