White dwarf

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. After such a star has become a red giant during its helium-burning phase, it will shed its 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 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 approaches 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 of years, white dwarfs will 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 at temperatures of a few thousand kelvins.

As a class, white dwarfs are fairly common; they comprise roughly 6% of all stars.(RECONS estimate)

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 kg·m⁻³), surpassed only by neutron stars, black holes 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). If this limit was exceeded, the pressure exerted by electrons would no longer able to balance the force of gravity. In the absence of any ability to generate further energy, the star would collapse, eventually forming a neutron star. Carbon-oxygen white dwarfs avoid this fate by undergoing a runaway nuclear fusion reaction (leading to a Type Ia supernova explosion) prior to reaching the limiting mass.

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 in diameter 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 1930s this was explained 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. Very useful in understanding this effect is the Fermi gas model.

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.

Most 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 white dwarfs 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 25 billion years to cool to ambient. Contrast this with the estimated age of the universe, which is 13 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 independently exceed 1.4 solar masses (the Chandrasekhar limit). Most white dwarfs form with a mass close to 0.6 solar masses, but there is a working method to get them close to this limit. White dwarfs in binary systems can steadily accrete material from a companion star. If the accreted material were to push the mass of the white dwarf beyond the 1.4 solar mass limit, degeneracy pressure would no longer support the star, and collapse would ensue. This mechanism was once thought to be the trigger for Type Ia supernovae, the brightest of all supernovae types. Since the 1960s, however, the prevailing view has been that increasing density in the star's interior triggers carbon fusion at a mass slightly below the Chandrasekhar limit, leading to a runaway nuclear fusion reaction in which some of the oxygen is also consumed. The fusion reaction is unregulated because the white dwarf is supported against gravity by quantum degeneracy pressure, not by thermal pressure. Initiation of fusion thus increases the temperature of the star's interior without increasing the pressure, so the white dwarf does not expand and cool in response. However, the increased temperature increases the rate of the fusion reaction, in a process that feeds on itself. This leads to an explosion that obliterates the white dwarf.

When accretion does not push the white dwarf close to the Chandrasekhar limit, hydrogen-rich accretion material on the surface may still light up in a thermonuclear explosion. Since the white dwarf's core remains intact, these surface explosions can be repeated as long as accretion continues. This weaker kind of repetitive cataclysmic phenomenon is called a nova. In general, binary systems with a white dwarf accreting matter from a companion are called cataclysmic variables.

Mass and radius relationship

To find a relationship between the mass of a white dwarf and its radius, one can start from the hydrostatic equilibrium condition:

$\frac{dP}{dr} = - \frac{GM(r)}{r^2} \rho(r) \,$

where

$\frac{dP}{dr}$ is the rate of change in pressure as a function of radius

G is the gravitational constant

M is the mass inside a specific radius, r

$\rho$ is the density as a function of radius

This derivation will show that higher-mass white dwarfs will have a smaller radius. First, one makes the very rough estimation of an average constant density, given by the mass of the white dwarf divided by its volume:

$\rho = \frac{M}{\frac{4}{3} \pi R^3} \,$

Putting that into the hydrostatic equilibrium equation and then integrating, one obtains an equation for pressure inside the center of the star to be:

$P \approx \frac{GM^2}{R^4} \,$

Now, for a degenerate gas (which is what makes up a white dwarf), pressure is also proportional to density by:

$P \sim \rho^{5/3} \,$

So setting these two equations of pressure proportional:

$\frac{GM^2}{R^4} \sim \left(\frac{M}{\frac{4}{3} \pi R^3} \right)^{5/3} \,$

Now this is a relationship between mass of a white dwarf to its radius. So, drop all the constants to see it more clearly:

$R \sim \frac{1}{M^{1/3}}$

After this rough derivation, what has been shown is that as mass of a white dwarf increases, its radius decreases.

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. Fowlerexplained 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 (along with Fowler) in 1983.

NASA's Spitzer Space Telescope has recently spotted what may be comet dust sprinkled around the white dwarf star G29-38, which died approximately 500 million years ago. The findings suggest the dead star, which most likely consumed its inner planets, is still orbited by a ring of surviving comets and possibly outer planets. This is the first observational evidence that comets can outlive their stars.

Helium White Dwarf

A helium white dwarf is a white dwarf star that is made out of helium. They are thought to be formed when a very low mass red dwarf dies. Other theories suggest they form as a result of mass lass in binary systems.

External links

• Gates et al., "Discovery of New Ultracool Dwarfs in the Sloan Digital Sky Survey"
• Gibson et al., "White Dwarfs and Dark Matter"
• Provencal et al., "Testing The White Dwarf Mass-Radius Relation With Hipparcos"
• "White Dwarf Stars and the Chandrasekhar Limit"
• Estimating the M(R) relationship and the Chandrasekhar Limit using simple energy arguments

See also

• Degenerate dwarf
• Black dwarf
• electron-degenerate matter - degenerate matter - white dwarf matter
• Brown dwarf
• Red dwarf
• Stellar classification
• Timeline of white dwarfs, neutron stars, and supernovae
• Supernova