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2 Compact stars last forever 3 Thought-experiment in building compact objects |
Compact stars form the endpoint of stellar evolution. A star shines and thus looses 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: the compact stars.
One could see the compact stars, such as the white dwarf and the neutron star, as a solid state as opposed to the gasseous interior of all other stars.
On the hard surface one could land with a rocket, if one waits long enough for the object to cool and if the rocket can stand the enormous gravitational forces. Note that typical cooling times are much longer than the present age of the universe.
The structure of compact stars is independent of temperature.
They could just sit there forever, shine and cool (hence the 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 a compact star.
One sometimes defines compact objects somewhat wider as compact stars plus the smaller solid objects such as planets and asteroids.
These compact objects are the only objects in the universe that could exist at low temperature. There is a remarkable variety of stars and other clumps of matter, but all matter in the universe must eventually end in only one of only four compact objects.
Suppose we do a thought-eperiment and build such cold objects by adding mass and ignoring thermal pressure. How will it stand the gravitational pull?
In doing so, we will zoom through the four possible "cold" objects: planetslike, white dwarf, neutron star and black hole.
At low density (planets and the like) the object is held up by electromagnetic forces (chemical bonds between electrons) which allows 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. Adding 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 thrink!
The largest cold mass in the universe.
Jupiter is about the largest cold mass to exist in the universe.
Adding mass to Jupiter and the planet will become smaller, a bit counter intuitive. The central density now is large enough such that the free electrons
become degenerate, see degenerate matter. Quantum mechanical forces now
hold the center of the planet apart, the ions hardly contribute at all. Matter, however, now is soft, and adding more mass will result in still smaller objects. As an increasing part of the interior contains degenerate electrons,
such objects are called white dwarfs. The massive white dwarfs are smaller than the less massive ones.
In continuing our thought-experiment we keep adding mass to what is now a white dwarf, the star thrinks 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 are now 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 in 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.
We have now reached a point where nature takes over our thought experiment. Adding 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 have disappeared and cannot supply the pressure against gravity. The star will collapse. It is thought that such a gravitational collapse is observed as a type Ia supernova. 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 the neutron star. Also neutron stars are "soft" (in fact all
degenerate matter is "soft") in the sense that adding more mass will thrink the star, like in white dwarfs, but unlike planets.
Also neutron stars have a maximum mass, called the Tollman-Oppenheimer-Volkoff limit.
It is most likely is around 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 we let nature accrete more mass onto a neutron star, eventually this mass limit is reached. No further equilibrium is possible, the pressure is insufficient to counterbalance gravity and a now catastrophic gravitational collapse sets in, further increasing the gravity on a time scale of milleseconds. The escape velocity at the surface, which was already 1/3 of the speed of light for a neutron star, quickly reaches the velocity of light.
A stage is reached where nothing, light nor matter, can escape.
A black hole is formed. We won't be able to see the final state, it is hided behind an event horizon,
nor do theoreticians at present know how such a final state inside a black hole would look like.
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.Compact stars as the endpoint of stellar evolution
Compact stars last forever
Thought-experiment in building compact objects
Planet-stage and the largest cold mass in the universe
The white dwarf stage
The neutron star stage
The black hole stage