What happens when you change the mass of a White Dwarf or Neutron Star?
I was wondering about the sizes of white dwarf and neutron stars. The problem is not their size per se, but what happens when you add matter to them.
For example, if a white dwarf star is in a binary system with a red giant that is loosing matter which is added to the white dwarf, how does the size of the white dwarf change over time. Does the added matter make it larger until there is so much mass that it collapses into a neutron star or does the added mass make it shrink even more since there is now more mass to hold up? I think the same analogy can be used with a neutron star getting mass, eventually turning into a black hole. How does it's size change as mass is added? I also thought that the size remains the same but I have no idea how. My question would be, What happens to the size of these type of stars when matter is added?
These are very interesting questions, and the answer is a little complicated and differs whether you're talking about something happening "in principle," or in "the real world." White dwarfs (WDs) and neutron stars (NSs) are two of a class of objects, the "inert self-gravitators," which support themselves against gravitational collapse by force of gas pressure alone. In this context, "gas" can mean either the kind of gas we're used to, or the degenerate matter found in WDs and NSs. Other objects in this class include brown dwarfs and giant planets. In fact, if you disregard chemical composition and think only about the gravity and pressure, giant planets can be considered to be very low-mass white dwarfs. The physics is very similar.
So let's consider a small giant planet, like Neptune. That planet is supported entirely by gas and degeneracy pressure. If we were to slowly add mass to Neptune, the planet would begin to grow in radius. The gravity and pressure would increase as well, of course, but not enough to offset the increase in volume. This will keep occurring until our planet is a few tens or hundreds the size of Jupiter. At that point, the increase in gravity and pressure overcomes the extra volume of mass we add, and the object begins getting smaller. (Remember that we're adding inert mass here--- if we were to add fusionable hydrogen, we'd have a fusing star; a totally different story!) Eventually, when you have added a solar mass or so, you end up with an object about the size of the Earth: a white dwarf.
So the answer to your question is that for objects less massive than Jupiter, adding mass increases their size. For objects more massive than Jupiter, adding even more mass decreases their size due to increased gravity and pressure. Since WDs and NSs are much more massive than Jupiter, their sizes decrease with increasing mass.
In practice, when a binary dumps material onto a white dwarf, a nova will occur, sending most of the added material back out into space. If a white dwarf does, however, gain enough mass through this process, it will collapse in a supernova type I. The supernova is probably too powerful to leave a neutron star behind; the white dwarf is blown apart. On the other hand, a neutron star which accretes too much mass will indeed collapse into a black hole.
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