Will Our Sun Expand and Go Nova or Shrink into a Black Hole?

[Anomalocaris]

What conditions cause a star to do one or the other?

There are several ways a star can go nova.   One common way is for the star to be massive enough so that its interior temperature and pressure will cause nuclear fusion in its core to progressively fuse heavier and heavier elements until eventually iron is produced.  When a star's core is mostly iron, further energy production through fusion at the core becomes impossible, and the balance between inward gravitational pull and outward radiation pressure is broken, and the core will collapse.   If the collapsing core is not quite massive enough for its gravity to overcome structural strength of neutrons, then the core collapse will stop before it becomes a black hole, supported solely by the strength of neutrons.  When the core collapse stops, all the outer layers of the star falling in after the collapsing core hits the now rigid core and converts the kenetic energy of the fall into heat.   This is a supernova.   The supernova blows away all the infalling outer layers of the star, leaving a naked collapsed core consisting mostly of tightly packed neutrons, with a thin layer of iron near the surface.   This is a neutron star.    A neutron star packs about twice the mass of the sun into a ball about the size of a largish city.

The sun is nowhere massive enough for its core to experience fusion progression much beyond carbon, far short of iron.  So the sun will not go supernova, nor will its core collapse into a neutron star.

There are more exotic ways for even more massive stars to go supernova, but obviously the sun's mass is even more inadequate for that.

But if the core of the star is sufficiently massive, even neutrons won't have the structural strength to resist gravitational collapse. In this case the collapse will not stop and the star will collapse into a black hole. Under some circumstances, the collapse of the core into a black hole can be accompanied by a supernova like explosion of material in the outer layers. In other circumstances a massive star can collapse completely into a black hole, with no accompanying explosive out burst. The star will just wink out.

All of the above only happen to stars much more massive than the sun.

But There is one way for a star like the sun to go nova.   Here is how:

When a star like the sun exhausts its hydrogen supply at its core, the core will progress some way up the fusion ladder and fuse at least helium.  During this process the star will puff up, and photo pressure will eventually blow away most of its outer layers in a gradual fashion.   But eventually the fusion reaction in its core stops because all available fusion fuel is used up and the star core is not massive enough to further fuse the products of previous fusion reactions.   When this happens the balance between gravity and photo pressure is also broken, but lacking enough mass, the core will only collapse to the point where repulsion between electrons stops the collapse.   When this happens the naked core is about the size of the earth, but contain roughly the mass of the sun.  This is a white dwarf.    Where is the nova, you ask.

Well, white dwarve is not as exotic as neutron star but it is still a pretty extreme object.   The gravity on its surface is hundreds of thousands of times stronger than on earth.   The surface temperature is tens of millions of degrees.

If the white dwarf is in close orbit around another star, it is possible, if the orbit and stellar evolution occurs in the right combination, for the white dwarf to pull hydrogen off the surface of its companion star.  This hydrogen will fall onto the white dwarf and accumulate on its surface.   Under the intense gravity and temperature on the surface of a white dwarf, as hydrogen continue to accumulates, it adds more pressure to the hydrogen already there.   Eventually enough hydrogen can accumulate to exceed some critical threshold, and a good portion of hydrogen accummulated on the surface suddenly flash in a giant fusion explosion like a single gigantic hydrogen bomb.  This is an ordinary nova.   The flash is the outer layer of accumulated hydrogen on the surface of a white dwarf in a binary system exploding.   Some nova can undergo nova dozens of times as the white dwarve pull material off its companion, go nova, pull more material off its companion, go nova again, etc.   If this happens for long enough, the white dwarf can undergo many individual nova events but eventually be destroyed in one final supernova explosion.   Unlike the supernova described in the first paragraph, this type of supernova that follows a series of nova will utterly destroy the star, blowing it completely apart leaving no collapsed ramnant.

Notice I said a star like the sun can go nova, not the sun can go nova.   Why not?  Because the sun doesn't have a close companion star in orbit around it.