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Justin's Astronomy

White Dwarfs
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A white dwarf is an astronomical object which is produced when a low or medium mass star dies. These stars are not heavy enough to generate the core temperatures required to fuse carbon in nucleosynthesis reactions, and after they have become a red giant during their helium-burning phase, they will shed their outer layers to form a planetary nebula, leaving behind an inert core consisting mostly of carbon and oxygen.

This core has no further source of energy, and so will gradually radiate away its energy and cool down. The core, no longer supported against gravitational collapse by fusion reactions, becomes extremely dense, with a typical mass of about half that of the sun contained in a volume about equal to that of the Earth. The white dwarf is supported only by electron degeneracy pressure. The maximum mass of a white dwarf, beyond which degeneracy pressure can no longer support it, is about 1.4 solar masses. A white dwarf which exceeds this limit (known as the Chandrasekhar limit), typically by mass transfer from a companion star, may explode as a Type Ia supernova via a process known as "carbon detonation".

Eventually, over hundreds of billions and billions of years, white dwarfs cool to temperatures at which they are no longer visible. However, over the universe's lifetime to the present (about 13.7 billion years) even the oldest white dwarfs still radiate temperatures of a few thousand kelvins.

As a class, white dwarfs are fairly common; they comprise roughly 6% of all stars and brown dwarfs within 10 parsecs of the Sun.(estimated from here)

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Formation

Almost all small and medium-size stars will end up as white dwarfs, after all the hydrogen they contain is fused into helium. Near the end of its nuclear burning stage, such a star goes through a red giant phase and then expels most of its outer material (creating a planetary nebula) until only the hot (T > 100,000 K) core remains, which then settles down to become a young white dwarf which shines from residual heat.

A typical white dwarf has half the mass of the Sun yet is only slightly bigger than Earth; this makes white dwarfs one of the densest forms of matter (109 kgm−3), surpassed only by neutron stars and hypothetical quark stars. The higher the mass of the white dwarf, the smaller the size. There is an upper limit to the mass of a white dwarf, the Chandrasekhar limit (about 1.4 times the mass of the Sun). When this limit is exceeded, the pressure exerted by electrons is no longer able to balance the force of gravity, and the star continues to contract, eventually forming a neutron star.

Despite this limit, most stars end their lives as white dwarfs since they tend to eject most of their mass into space before the final collapse (often with spectacular results - see planetary nebula). It is thought that even stars eight times as massive as the Sun will in the end die as white dwarfs, cooling gradually to become black dwarfs.

Characteristics

Many white dwarfs are approximately the size of the Earth, typically 100 times smaller than the Sun; their average mass is about 0.5-0.6 solar masses, though there is quite a bit of variation.(see link for discussion) Their compactness implies that the same amount of matter is packed in a volume that is typically 1003 = 1,000,000 times smaller than the Sun and so the average density of matter in white dwarfs is 1,000,000 times greater than the average density of the Sun. Such matter is called degenerate. Degenerate matter behaves in a seemingly counterintuitive fashion; for instance, white dwarfs grow smaller--and thus their densities increase--with higher mass.(see "further reading") In the 1930's the explanation is given as a quantum mechanical effect: the weight of the white dwarf is supported by the pressure of electrons (electron degeneracy), which only depends on density and not on temperature.

If, for all observed stars, one makes a diagram of (absolute) brightness versus color (Hertzsprung-Russell diagram), not all combinations of brightness and color occur. Few stars are in the low-brightness-hot-color region (the white dwarfs), but most stars follow a strip, called the main sequence. Low mass main sequence stars are small and cool. They look red and are called red dwarfs or (even cooler) brown dwarfs. These form an entirely different class of heavenly bodies than white dwarfs. In red dwarfs, as in all main-sequence stars, the pressure counterbalancing the weight is caused by the thermal motion of the hot gas. The pressure obeys the ideal gas law. Another class of stars is called giants: stars in the high-brightness part of the brightness-color diagram. These are stars blown up by radiation pressure and are very large.

White dwarf stars are extremely hot; hence the bright white light they emit. This heat is a remnant of that generated from the star's collapse, and is not being replenished (unless it accretes matter from other nearby stars). However, since white dwarfs have an extremely small surface area from which to radiate this heat energy, they remain hot for a long period of time. Evidence suggests that their interiors slowly crystallize as they cool and age, ultimately settling into a diamond-like configuration; astronomers know of at least one "diamond white dwarf" already.[1]

Eventually, a white dwarf will cool into a black dwarf. Black dwarfs are ambient temperature entities and radiate weakly in the radio spectrum, according to theory. However, the universe has not existed long enough for any white dwarfs to have cooled down this far yet; no black dwarfs are thought to exist, and the coolest found have surface temperatures around 3900 K.[2](see below) and the cooling is slower as it progresses. A white dwarf may cool from 20,000K to 5,000K in the same amount of time it takes to cool from 5,000K to 4,000K. In all, a 0.5 solar mass white dwarf starting at 20,000K would require approximately twenty five billion years to cool to ambient. Contrast this with the estimated age of the universe, which is thirteen billion years.

Many nearby, young white dwarfs have been detected as sources of soft X-rays (i.e. lower-energy X-rays); soft X-ray and extreme ultraviolet observations enable astronomers to study the composition and structure of the thin atmospheres of these stars.

White dwarfs cannot be over 1.4 solar masses, the Chandrasekhar limit, but there is a working method to get them over this limit. White dwarfs can accrete material from a companion. The material accretes slowly and remains stable. The mass of the white dwarf increases until it hits the 1.4 solar mass limit, at which degeneracy pressure cannot support the star. This creates a type Ia supernova and is the most powerful of all the supernovae. For some white dwarfs the accreted material, which is usually hydrogen rich, will light up in a nuclear explosion and leave the core of the star intact. This phenomenon can be repeated as long as accretion material is available. This weaker kind of cataclysmic (and repetitive) phenomenon is called a nova.

History of discoveries

In 1862 Alvan Graham Clark discovered a dark companion of the brightest star Sirius (Alpha Canis Majoris). The companion, called Sirius B or the Pup, had a surface temperature of about 25,000 K, so it was classified as a hot star. However, Sirius B was about 10,000 times fainter than the primary, Sirius A. Since it was very bright per unit of surface area, the Pup had to be much smaller than Sirius A, with roughly the diameter of the Earth.

Analysis of the orbit of the Sirius star system showed that the mass of the Pup was almost the same as that of our own Sun. This implied that Sirius B was thousands of times more dense than lead. As more white dwarfs were found, astronomers began to discover that white dwarfs are common in our galaxy. In 1917 Adriaan Van Maanen discovered Van Maanen's Star, the second known white dwarf.

After the discovery of quantum mechanics in the 1920's, an explanation for the density of white dwarfs was found in 1926. R.H. Fowler explained the high densities in an article "Dense matter" (Monthly Notices R. Astron. Soc. 87, 114-122) using the electron degenerate pressure a few months after the formulation of the Fermi-Dirac statistics for an electron, on which the electron pressure is based.

S. Chandrasekhar discovered in 1930 (Astroph. J. 1931, vol. 74, p. 81-82) in an article called "The maximum mass of ideal white dwarfs" that no white dwarf can be more massive than about 1.4 solar masses. This is now called the Chandrasekhar limit. Chandrasekhar received the Nobel prize in 1983.

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