My research focuses on a type of star called a "white dwarf" - the dying ember of a star like our Sun. For most of their lives, Sun-like stars happily convert hydrogen into helium in a runaway nuclear reaction in their central cores. This process creates a huge amount of energy, that we see and feel as light and heat. At some point, however, the hydrogen in the core runs out, and there is nothing left for the star to burn. At this point, the star swells up to a few hundred - few thousand times its original size, to become a red giant. In doing so, it swallows up all of the planets that it touches. In our own Solar System, the Sun is likely to swallow up Mercury, Venus, and possibly Earth, but Mars will probably survive.
The final death throes of the star see its outer layers puffed off into space as a "planetary nebula", leaving the white-hot core of the star exposed. With no ongoing nuclear reactions, this "white dwarf" simply sits and cools for the rest of eternity. The really interesting question, though, is what happens to any planets left around the white dwarf after surviving the red giant phase. At the distances of Neptune and further, it is impossible for us to detect them directly - they are too cool to be seen with our telescopes. Do they stay in orbit around their stars, as we expect, or are they destroyed, or somehow lost as their parent star evolves?
A clue to their fate has been the discovery of dusty rings around some white dwarfs. These rings shouldn't really be there - all of the material that close in to the white dwarf should have been destroyed during the red giant phase. This leads us to believe that it has arrived there *after* the star has become a white dwarf, thrown in from the outer edges of the system. The most likely scenario is that there are a large number of asteroids in the outer reaches of the system, which, under normal circumstances, would happily sit there and orbit around the star at very large distances. This changes, however, if we imagine that there are some big left-over planets out there too. Just as in our Solar System today, big planets disrupt the orbits of smaller asteroids, and can fling them in towards the central star. If one of these asteroids gets too close to the white dwarf, large tidal forces can rip it apart and shred it into dust, which then settles into a ring, or "disk", around the star.
The really cool part about all of this is that it is very difficult to get an asteroid thrown in towards the white dwarf *unless* it has been affected by a large planet. By detecting these dusty disks around white dwarfs, we believe that we are indirectly detecting the presence of large surviving planets that are too cool and too far from their star to be detected by any other method.