First off, there are stars made up mostly of protons. These are just the "usual" luminous stars like our Sun. Our Sun "burns" protons (aka, Hydrogen nuclei) in the process of nuclear fusion, creating heavier nuclei (such as Helium) out of them. It is the heat released by this nuclear burning that prevents the Sun from collapsing under the pull of gravity.
Neutron stars, on the other hand, are very dense collections of neutrons whose weight is supported by so-called "degeneracy pressure" rather than the thermal pressure that supports the Sun. My guess is that you really want to know why there aren't any cold "proton stars" that are supported by proton degeneracy pressure. The short answer is that the proton's electric charge makes this impossible. If one took a whole bunch of cold protons and placed them together in space, their mutual electric repulsion would vastly overwhelm gravity and they would fly apart and not form a compact star.
However, we can go a bit deeper than this and ask what happens when you take equal numbers of protons and electrons. Then the protons still contribute almost all of the gravitational mass, but the collection is electrically neutral as a whole. But this is exactly like a normal star formed from hydrogen clouds that collapse under gravity. Nuclear burning converts the protons (and half the electrons) into Helium nuclei (with two protons and two neutrons). When all the protons are "burned up" into Helium, the star can no longer support its own weight through thermal pressure and we should ask if the there is degeneracy pressure in this case.
The answer is yes, but it turns out not to come from the Helium nuclei or their constituent protons and neutrons. The degeneracy pressure actually comes from the remaining electrons (two per Helium nucleus to keep everything neutral). Such stars are called White Dwarfs. Our Sun will most likely end its days as a white dwarf.
By the way, degeneracy pressure comes from two different aspects of quantum mechanics. The first is the uncertainty principle which says that the smaller the box you put a particle in the faster it will bounce around in that box. The other aspect is the Pauli exclusion principle which says that certain particles called fermions (neutrons, protons, and electrons are all fermions) try to avoid one another, even in the absence of charge based forces. For the white dwarf or neutron star, this means that the large number of fermions present leads to a small available volume for each fermion, and thus a rapid motion for each.
For a short description of degeneracy pressure, try: scienceworld.wolfram.com and the links listed there.
I hope this has answered your questions.
Source: www.fnal.gov
Neutron stars, on the other hand, are very dense collections of neutrons whose weight is supported by so-called "degeneracy pressure" rather than the thermal pressure that supports the Sun. My guess is that you really want to know why there aren't any cold "proton stars" that are supported by proton degeneracy pressure. The short answer is that the proton's electric charge makes this impossible. If one took a whole bunch of cold protons and placed them together in space, their mutual electric repulsion would vastly overwhelm gravity and they would fly apart and not form a compact star.
However, we can go a bit deeper than this and ask what happens when you take equal numbers of protons and electrons. Then the protons still contribute almost all of the gravitational mass, but the collection is electrically neutral as a whole. But this is exactly like a normal star formed from hydrogen clouds that collapse under gravity. Nuclear burning converts the protons (and half the electrons) into Helium nuclei (with two protons and two neutrons). When all the protons are "burned up" into Helium, the star can no longer support its own weight through thermal pressure and we should ask if the there is degeneracy pressure in this case.
The answer is yes, but it turns out not to come from the Helium nuclei or their constituent protons and neutrons. The degeneracy pressure actually comes from the remaining electrons (two per Helium nucleus to keep everything neutral). Such stars are called White Dwarfs. Our Sun will most likely end its days as a white dwarf.
By the way, degeneracy pressure comes from two different aspects of quantum mechanics. The first is the uncertainty principle which says that the smaller the box you put a particle in the faster it will bounce around in that box. The other aspect is the Pauli exclusion principle which says that certain particles called fermions (neutrons, protons, and electrons are all fermions) try to avoid one another, even in the absence of charge based forces. For the white dwarf or neutron star, this means that the large number of fermions present leads to a small available volume for each fermion, and thus a rapid motion for each.
For a short description of degeneracy pressure, try: scienceworld.wolfram.com and the links listed there.
I hope this has answered your questions.
Source: www.fnal.gov