A circumstellar disk is a byproduct of star formation. At the earliest stages, a disk is most likely full of gas and dust that will eventually accumulate into planets or exit the system. This is the protoplanetary disk stage. As the disk ages and planets form, the leftover gas dissipates and the remaining debris has either settled or been confined by the most massive planets in the system. This is the debris disk stage.
Debris disks are not expected to last very long (more than 10 million years), so the fact that we see them around stars that are ~30-40 million years old tells us that the debris is replenished--most likely through collisions within the disk or erosion. An example of a debris disk is shown below.
Astronomers study these disks by looking for re-emitted heat from the astronomical version of a grains of sand. On Earth, sand forms from the erosion of rocks and it also absorbs light from the sun, re-emitting it at longer wavelengths. Walking on a beach, you would feel this as heat on the soles of your feet. The debris produced in a disk around a star does the same thing. Yes, space dust is "cold," but it is not at absolute zero, so we can see the heat it emits if we look at the right wavelength! This is similar to looking at a human at infrared wavelengths (a heat map). To study these debris disks we go to radio wavelengths.
Debris disks around Sun-like Stars
While at Wesleyan University being advised by A. Meredith Hughes, I used data from the Submillimeter Array in Hawaii to analyze a sample of 5 debris disks from the "Formation and Evolution of Planetary Systems" Spitzer Legacy Survey. In a broad sense, the goal of this work was to see how common Kuiper belts are around Sun-like stars. False color radio images of the disks are shown below. Check out the paper here on ArXiv!
Polluted white dwarf stars
Currently I'm working with John Debes (Space Telescope Science Institute) studying white dwarf stars that show signs of heavy element accretion. These polluted white dwarfs can help inform cosmochemistry of stellar systems since any elements heavier than helium should not be there! Additionally, any metals that do make it to the white dwarf surface should sink rapidly. As an example, see this Nature paper on the white dwarf, WD 1145+017, which has a trasiting, disintegrating planetesimal. A cartoon schematic is shown below (paper here).