Compact star
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In astronomy, the term compact star (sometimes compact object) is used to refer collectively to white dwarfs, neutron stars, other exotic dense stars, and black holes. These objects are all small for their mass. The term compact star is often used when the exact nature of the star is not known, but evidence suggests that it is very massive and has small radius, thus implying one of the above-mentioned possibilities. A compact star which is not a black hole may be called a degenerate star.
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[edit] Compact stars as the endpoint of stellar evolution
Compact stars form the endpoint of stellar evolution. A star shines and thus loses energy. The loss from the radiating surface is compensated by the production of energy from nuclear fusion in the interior of the star. When a star has exhausted all its energy and undergoes stellar death, the gas pressure of the hot interior can no longer support the weight of the star and the star collapses to a denser state: a compact star. The difference between a white dwarf or neutron star and an ordinary star is analogous to the difference between gases and solids. If you waited until a white dwarf or neutron star was sufficiently cold, and if you had a rocket which could survive the enormous gravitational and tidal forces, you could land on the surface of the star. Typical cooling times for white dwarfs, however, are much larger than the present age of the Universe.
[edit] Compact stars last forever
Although compact stars may radiate, and thus cool off and lose energy, they do not depend on high temperatures to maintain their pressure. Barring external perturbation or baryon decay, they will persist forever. Eventually, given enough time (when we enter the so-called degenerate era of the universe)[1], all stars will have evolved into dark, compact stars.
One sometimes defines a somewhat wider class of compact objects to contain, as well as compact stars, smaller solid objects such as planets, asteroids, and comets. These compact objects are the only objects in the universe that could exist at low temperatures. There is a remarkable variety of stars and other clumps of matter, but all dense matter in the universe must eventually end in one of only five classes of compact objects.
[edit] Thought experiment in building compact objects
Suppose we do a thought experiment and build a cold object by adding mass and ignoring thermal pressure. How will it stand the gravitational pull? In this experiment, we will find the five possible types of object: planet-like, white dwarf, neutron star, exotic star, and black hole.
[edit] Planets
At low density (planets and the like) the object is held up by electromagnetic forces. These forces constrain electrons to occupy orbitals around nuclei, which give rise to chemical bonds and thus allow stiff objects such as rocks to exist. These objects are so stiff that they do not compress very much when mass is added. Adding more (cold) mass therefore makes the object larger: radius increases with mass. This agrees with our intuitions.
Eventually a point is reached where the central pressure is so large that all matter is ionized so that the electrons are stripped from the nuclei and move freely. No chemical bonds now exist to hold up the object. This point is reached at the center of the planet Jupiter. Add more mass to Jupiter and the increase of pressure is smaller than the increase of gravity, so the radius will decrease with increasing mass. The object will shrink!
[edit] The largest cold mass in the universe
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A planet such as Jupiter has about the largest volume possible for a cold mass. Add mass to Jupiter and the planet's volume, somewhat counter-intuitively, becomes smaller. The central density now is large enough that the free electrons become degenerate. This term means that the electrons have fallen into the lowest-energy states available. Since electrons are fermions, they obey the Pauli exclusion principle, and no two electrons can occupy the same state. The electrons thus occupy a wide band of low-energy states. Compressing the mass forces this band to widen, creating the quantum-mechanical force of electron degeneracy pressure which now holds the center of the planet apart. (The ions present contribute almost no force.)
[edit] White dwarfs
If we continue to add mass in our thought-experiment, we will find that more and more of our object becomes degenerate. The stars called degenerate dwarfs, or, more usually, white dwarfs are made up mainly of degenerate matter—typically, carbon and oxygen nuclei in a sea of degenerate electrons. White dwarfs arise from the cores of main-sequence stars and are therefore very hot when they are formed. As they cool they will redden and dim until they eventually become dark black dwarfs. White dwarfs were observed in the 19th century, but the extremely high densities and pressures they contain were not explained until the 1920s.
The equation of state for degenerate matter is "soft", meaning that adding more mass will result in a smaller object. If in our thought experiment we keep adding mass to what is now a white dwarf, the object therefore shrinks and the central density becomes even larger, with higher degenerate-electron energies. The star's radius has now shrunk to only a few thousand kilometers[2], and the mass is approaching the theoretical upper limit of the mass of a white dwarf, the Chandrasekhar limit, about 1.4 times the mass of the Sun.
If we were to take matter from the center of our white dwarf and slowly start to compress it, we would first see electrons forced to combine with nuclei, changing their protons to neutrons by inverse beta decay. The equilibrium would shift towards heavier, more neutron-rich nuclei which are not stable at everyday densities. As the density increases, these nuclei become still larger and less well-bound. At a critical density of about 4·1011 g/cm³, called the neutron drip line, the atomic nucleus would tend to fall apart into protons and neutrons. Eventually we would reach a point where the matter is on the order of the density (~2·1014 g/cm³) of an atomic nucleus. At this point, the matter is chiefly free neutrons, with a sprinkling of protons and electrons. Objects with these central densities will be formed if in our thought experiment we continue to add mass to a white dwarf until the Chandrasekhar limit is exceeded. They form our third class of compact objects.
[edit] Neutron stars
We have reached a point where nature takes over from our thought experiment, as addition of matter to a white dwarf actually happens in nature. In certain binary stars containing a white dwarf, mass is transferred from the companion star onto the white dwarf, eventually pushing it over the Chandrasekhar limit. Electrons react with protons to form neutrons, and thus no longer supply the necessary pressure to resist gravity. The star will collapse. If the center of the star is composed mostly of carbon and oxygen, such a gravitational collapse will ignite runaway fusion of the carbon and oxygen, resulting in a Type Ia supernova which entirely blows apart the star before the collapse can become irreversible. If the center is composed mostly of magnesium or heavier elements, the collapse continues.[3],[4],[5] As the density further increases, the remaining electrons react with the protons to form more neutrons. The collapse continues until (at higher density) the neutrons become degenerate. A new equilibrium is possible after the star shrinks by three orders of magnitude, to a radius between 10 and 20 km. This is a neutron star.
Although the first neutron star was not observed until 1967 when the first radio pulsar was discovered, neutron stars were proposed by Baade and Zwicky in 1933, only one year after the neutron was discovered in 1932. They realized that because neutron stars are so dense, the collapse of an ordinary star to a neutron star would liberate a large amount of gravitational potential energy, providing a possible explanation for supernovae.[6][7][8] This is the explanation for supernovae of types Ib, Ic, and II. Such supernovae occur when the iron core of a massive star exceeds the Chandrasekhar limit and collapses to a neutron star.
Like electrons, neutrons are fermions. They therefore provide neutron degeneracy pressure to support a neutron star against collapse. In addition, repulsive neutron-neutron interactions provide additional pressure. Like the Chandrasekhar limit for white dwarfs, there is a limiting mass for neutron stars, the Tolman-Oppenheimer-Volkoff limit, where these forces are no longer sufficient to hold up the star. As the forces in dense hadronic matter are not well understood, this limit is not known exactly, but is thought to be between 2 and 3 times the mass of the Sun. If more mass accretes onto a neutron star, eventually this mass limit will be reached. What happens next is not completely clear.
[edit] Exotic stars
[edit] Strange stars
It is possible that the neutrons will decompose into their component quarks. In this case, the star will shrink further and become more dense, but it may survive in this new state indefinitely if no extra mass is added. It has become a very large nucleon. A star in this hypothetical state is called a quark star or strange star. The pulsars RX J1856.5-3754 and 3C58 have been suggested as possible quark stars.
[edit] Preon stars
If we go beyond the standard model of particle physics and assume that quarks and leptons are not the fundamental elementary particles but are themselves composed of preons, then even denser objects, preon stars, would not be unthinkable. A star may collapse to one ten-thousandth of its size, bringing its radius to one metre or less. It would be a sort of giant quark whose density might exceed 1020 g/cm³, and might even approach 1030 g/cm³.
The stellar-mass objects we have seen so far, white dwarfs, neutron stars, and, presumably, the more exotic possibilities of quark and preon stars, have all been held up wholly or partially by degeneracy pressure. Collectively, we may therefore call them degenerate stars. We now come to a different possibility.
[edit] Black holes
As we add more mass, equilibrium against gravitational collapse reaches its breaking point. The star's pressure is insufficient to counterbalance gravity, and a catastrophic gravitational collapse occurs in milliseconds. The escape velocity at the surface, already at least 1/3 light speed, quickly reaches the velocity of light. No energy or matter can escape: a black hole has been created. All light will be trapped within an event horizon, and so a black hole appears truly black, except for the possibility of Hawking radiation. It is presumed that the collapse will continue. In the classical theory of general relativity, a gravitational singularity will be created, occupying no more than a point. There may be a new halt of the catastrophic gravitational collapse at a size comparable to the Planck length, but at these lengths there is no known theory of gravity to predict what will happen.
[edit] References
- D. Blaschke, S. Fredriksson, H. Grigorian, A. M.Oztas, and F. Sandin, The phase diagram of three-flavor quark matter under compact star constraints. (arXiv:hep-ph/0503194)
- Johan Hansson and Fredrik Sandin, Preon stars: a new class of cosmic compact objects. Phys. Lett. B 616, 1, 2005. (arXiv:astro-ph/0410417)
- Fredrik Sandin, Compact stars in the standard model - and beyond, Eur. Phys. J. C.
- Fredrik Sandin, Exotic Phases of Matter in Compact Stars. (May 8, 2005)
