Compact star
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In astronomy, a compact star (sometimes called a compact object) is a star that is a white dwarf, a neutron star, a strange star, or a black hole. "Compact star" is often used when the exact nature of the star is not known, but evidence suggests it is very massive and has small radius, thus leaving the above-mentioned possibilities.
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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 (by nuclear fusion) in the interior of the star. When a star has exhausted all its energy (stellar death) the gas pressure of the hot interior cannot support anymore the weight of the star (the gravitational pull) and the star collapses to a denser state: a compact star. It is analogous to the difference between gases and solids. On the hard surface one could land with a rocket, if one waited long enough for the object to cool and if the rocket could survive the enormous gravitational forces (particulary the tide). Note that typical cooling times are much longer than the present age of the universe.
Compact stars last forever
The structure of compact stars is independent of temperature. They could just sit there forever, shining and cooling (hence terminology such as "the endpoints of stellar evolution"). The pressure is supplied by other means, which (as long as the hydrogen atom remains stable) does not change over time.
Eventually, given enough time (when we enter the so called degenerate era of the universe), all stars will stop shining and evolve into compact stars.
One sometimes defines a somewhat wider class of compact objects as compact stars plus 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 matter in the universe must eventually end in one of only five classes of compact objects.
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 doing so, we find the five possible objects: planet-like, white dwarf, neutron star, strange star, and black hole.
Planets
At low density (planets and the like) the object is held up by electromagnetic forces (chemical bonds between electrons) which allow stiff objects such as rocks. The objects are so stiff that they can deal easily with the increased gravity from the added mass. So adding more (cold) mass means making larger objects (radius increases with mass). This corresponds with our intuitive thinking.
Eventually a point is reached where all matter is (pressure) ionized, the electrons are stripped from the nuclei and are free. No chemical bonds can hold up the object. This point is reached at the center of the planet Jupiter. Add more mass to Jupiter and the pressure increase is smaller than the increase of gravity, so the radius will decrease with increasing mass. The object will shrink!
The largest cold mass in the universe
A planet such as Jupiter is about the largest cold mass that can exist. Add mass to Jupiter and the planet, somewhat counter-intuitively, becomes smaller. The central density now is large enough that the free electrons become degenerate. Quantum mechanical forces hold the center of the planet apart, the ions hardly contributing at all. The matter has become "soft", in that adding more mass will result in a still smaller object. As an increasing part of the interior contains degenerate electrons, such objects are called white dwarfs. Massive white dwarfs are smaller than less massive ones.
White dwarfs
In continuing our thought-experiment we keep adding mass to what is now a white dwarf, the star shrinks and the central density becomes even larger, with higher degenerate-electron energies. A point is reached where the electrons have sufficient energy to react with the protons in the nuclei (inverse-beta decay). The effect is that neutrons are formed and electrons disappear. Odd neutron-rich nuclei become possible, which would not exist at lower density. Such nuclei are less well-bound and at a certain density, called the neutron drip point, the atomic nucleus falls apart into many neutrons and as many protons as there are electrons. This stage is reached at a mass slightly below the theoretical upper limit of the mass of a white dwarf, the Chandrasekhar limit, about 1.4 times the mass of the Sun.
Neutron stars
We have reached a point where nature takes over our thought experiment: 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. Most electrons disappear and cannot supply the necessary pressure to resist gravity. The star will collapse. It is thought that such a gravitational collapse is observed as a Type Ia supernova. 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 at a radius which is of order 1000 times smaller than a white dwarf, at around 10 km. It is a neutron star.
Strange stars
Neutron stars also have a maximum mass, called the Tolman-Oppenheimer-Volkoff limit. It is currently thought to be about 3 times the mass of the Sun. The exact value depends on the forces between neutrons at high density that in addition to the degenerate neutron-pressure could add to the overall pressure. If more mass accretes onto a neutron star, eventually this mass limit is reached. It is possible that yet another equilibrium will be found as the neutrons decompose into their constituent quarks. The star will shrink further, but it may survive in this new state indefinitely if no extra mass is added. It has become the largest nucleon in the universe.
Black holes
Continuing our experiment, added mass pushes equilibrium to 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 (but see Hawking radiation). It is presumed that the collapse will continue, forming a gravitational singularity occupying no more than a point. One expects a new "halt" of the catastrophic gravitational collapse at a size according to the Planck length, but at present there is no theory of gravity at such densities to predict that.