Number of words: 688
What the calculation shows is that if you take a star of mass greater than one and a half times the solar mass and if the process of collapse occurs, the process of collapse could not be arrested at a stage with mean densities of the order of million gm/cc. Or, to put it in another way, suppose I take a star less than this critical value – say one solar mass like the sun – then it will lose its source of energy and it will collapse, and the collapse will continue to a stage where the mean density becomes million gm/cc. At this point it will stop collapsing further and it will stay there indefinitely.
On the other hand, if you take a star with mass which is 2 to 3 times the solar mass, then it radiates energy at a much faster rate and it will evolve. It will exhaust its energy sooner, but as it collapses its contraction will not be arrested at a stage where the mean density is of the order of a million gm/cc. Then the question is: what will it do? If it cannot be arrested, it can do one of two things. It can eject all the excess mass and become a white dwarf. That does not seem to be reasonable because if you take a star of 5 solar masses, then it must eject 3.6 solar masses. If you take 10 solar masses, then it must eject 8.6 solar masses. It seems unreasonable that there is a law of nature which tells you that every star must, when it loses its energy, collapse in such a way that it must always eject the mass so that you have a residue less than 1.4 solar masses. In fact it is very unlikely to happen.
Consequently, such stars must collapse still further and the next question is: What is the next possible stage where the collapse could be arrested? It is, clearly, when the density becomes comparable to nuclear density. At this stage a transformation occurs: the neutrons which under normal laboratory conditions are radioactive, become a stable species. That is, in the environment of high densities, the protons capture the electrons which are there and become neutrons, which are now a stable species. The result is a neutron star. Of course we know now that neutron stars exist in nature. They are the so-called pulsating-stars or pulsars. So the fact that a massive star can collapse into a neutron star is a well-established fact.
Now the question arises: Can every star find a stable state of equilibrium as a neutron star? The answer is no. And the reason why neutron stars of every possible mass cannot exist comes from general relativity theory. This is something which I cannot explain to you in detail. But let me say that here we have to study in detail the stability of a star against radial oscillations. The result is that if you construct a stable neutron star, then depending on what its ratio of specific heats is, it will become unstable before it reaches some value, and therefore there exists a certain maximum mass for neutron stars. The actual calculation for this may appear complicated but the most general principles of relativity tell you that there must be a maximum mass for stable neutron. stars, and when you compute it you find that it may be 2 or 2.5 times the solar mass. Consequently, the picture of evolution is the following: You take a star with mass less than one solar mass. It will become a white dwarf. You take a star with, say, three solar masses. Then it could collapse, and during the process of collapse it may shed enough matter (about one half solar mass) and you will be left with a core which is a stable neutron star – the so-called pulsar. When it fails to eject sufficient matter, no stable states are possible; it contracts and contracts and ultimately becomes a black hole!
Excerpted from page 46-47 of S. Chandrasekhar ‘Man of Science ’ by A.P.J. Abdul Kalam