It is very difficult to make a star out of helium. If Jupiter were composed of pure helium it would be about the same size, but larger masses would actually reach a maximum radius then shrink as the core became more and more compressed as the mass of the overlying layers was increased. Beyond this maximum size the mass increases the compressed density faster than the volume increases and the radius shrinks. This is not a surprise, it is a direct consequence of the equation of state for a perfect gas. You can see this effect happening in Jupiter and Saturn. But surely this cannot be carried to extremes!

Actually it can, but there is one very interesting reprieve. The equation of state for a perfect gas, total pressure P(ion plus electron) equals the total number of particles N(one alpha particle and two electrons per helium atom for a helium body) times Boltzmann's constant k times temperature T, P=NkT, does not apply under conditions of extreme density. Above a tenth(?) of a solar mass the atoms at the center are packed so close that the electrons (which contribute most of the pressure even in an ideal ionized gas) interfere with one another, they get in each other's way. They do not follow the rules for a perfect gas which assumes the particles are all independent points. Rather, the electrons obey an equation of state developed by Fermi, the equation of state of a fermi gas, a quantum theory which embodies the Pauli exclusion principle that applies to electrons, protons, and neutrons. The fermi gas law is the same as the ideal gas law at low density but at the densities encountered here, a million times the density of water (a billion kg/m³), some pretty strange departures from the ordinary occur. The fermi gas pressure can and does in these extreme conditions greatly exceed the ideal law and we often call the difference "degeneracy pressure" or the electron gas a "degenerate gas". If the temperature is too low for a given density the low energy states are all occupied and a "Fermi pressure" must push the gas apart. The gas is really stiff! Nevertheless, even the fermi gas, like the perfect gas, does compress and the more massive the body the smaller it gets. Chandrasekhar was the first to apply the theory to white dwarf stars and found that the theory gave zero radius at about 1.4 solar masses, the Chandrasekhar limit.

This is just a reprieve, but a very interesting one because we actually see this kind of object, we call them helium white dwarf stars. They are most likely low mass stars that have evolved, lost their hydrogen envelopes in the red giant stage of evolution possibly with the formation of a planetary nebula, and are just --cooling. None have masses more than 1.2 times that of the sun.

What about more massive stars? Stars massive enough to actually burn helium might leave behind nitrogen "ash" or even iron ash. Iron is the real end point of nuclear fusion, the (free) iron nucleus being the most tightly bound nucleus possible. Heavier nuclei are at the mercy of the repulsive Coulomb force and actually take energy to make by the fusion process. (You can add neutrons, and this does happen, but under extreme conditions in stellar cores the heavier nuclei would be prone to fission.) If the star can lose its envelope during the red giant phase, we might see a white dwarf composed of anything up to iron.

Calculations show us that if the star is under half a solar mass the helium will not burn so a helium white dwarf remains. Why no hydrogen? If you put hydrogen on the surface of an 0.1 solar mass white dwarf the "fermi zero point temperature" will cause it to burn right away! It will be all helium.

White dwarf (WD) stars that do not show H lines but do show helium are designated DB the D for dwarf or more likely degenerate and the B for spectral type B. Some WD stars do have a thin hydrogen envelope so we see H lines and we designate these stars DA since A stars have the strongest H lines.

Stars in the range 0.5 to 5 Mo burn helium and leave C/N/O ash (which will burn any He or H that lands on them).

Stars in the range 5 to 7 Mo can burn carbon to form Mg/Ne/O ash.

Above 7 Mo another interesting phenomenon occurs. The star may explode, driving the core into a neutron star or even a black hole. How does this happen? And what happens beyond the Chandrasekhar limit?

Now the degenerate electron gas really is stiff but you can still squeeze it. But above a critical density consider what would happen if a neutron were right at the center of the body. A free neutron beta decays with a half life of about twelve minutes and a maximum electron kinetic energy of 782.5 keV. The electrons come out with a range of energies, the "beta ray spectrum", and an antineutrino carries off the balance of the energy. But in a degenerate sea of electrons all the low energy states (up to a limit called the fermi limit) are occupied so only high energy beta decays (low energy antineutrino) are permitted. The neutron lifetime is increased in this situation. As more and more pressure is applied, the central density rises and at some point all available electron states up to 782.5 keV are taken and the neutron just cannot decay. In fact, the neutron is stable. In fact, not only is the neutron stable, but under these circumstances the proton becomes unstable against electron capture, so the electrons at the center disappear into protons forming "neutronium" and the electrons away from the center with no support fall down. Now it gets even worse. The central density rises faster and faster and within seconds the thousand km radius white dwarf becomes a 10 km radius ball of neutronium, a neutron star. A solar mass collapsing from 1000km down to 10km in a few seconds is going to release quite a bit of gravitational energy -- essentially

W(10km) = GM²/R = 6.672×10^-11×(1.99×10³⁰)²/10000=2.642×10⁴⁶J,

the sun's output for two trillion years! This will raise the temperature so raising the fermi limit helping somewhat -- well, the problem is tricky but basically what happens is the star explodes and we have what we will come to know as a supernove (SN Ia).

Does neutronium compress? Yes, it is just like the degenerate electron gas, neutrons are fermions too but now the density is nuclear density and theoretical models now actually have to include the effects of curved spacetime, general relativity. The neutron star radius is not much larger than the schwartzschild radius (R_S=2GM/c²=2.95 km per solar mass) or black hole radius, and above about 2.6 solar masses they merge and I imagine the body just quietly disappears!

By the way, the degenerate gas is an excellent conductor of heat and electricity so the bodies are essentially isothermal and if they spin they make great electromagnets. See PULSAR.