"Exocomet" is probably a new word to you. We know exoplanets as planets that revolve around stars outside our solar system. Exocomets are comets that revolve around stars outside our solar system. Astronomers assumed that they were out there somewhere, but only recently have we seen evidence of them. And like exoplanets, they are too far away to see, but we have evidence that comes from those far away stars themselves. One exocomet was detected around a star 815 light-years away, and another at 850 light-years away. So we at least have evidence that they were at those stars over 800 years ago. But how do we know they are comets?
The alien comets were found in data taken by the Kepler telescope, which spent several years staring at 150,000 stars in one spot in the sky. It was looking for exoplanet transits, a teeny dip in a star's light if an orbiting planet happened to pass directly between us and it. That only happens if the planet's orbit is almost exactly edge-on as seen from Earth, which is why it looked at so many stars. The more you look at, the more likely the geometry will work out.
Transits are detected by measuring the amount of light from a star, and when that light dips, it usually means a planet is transiting. But graphs of those transits show that light dips and then increases in a regular pattern. Some graphs showed an asymmetrical dip, which would have been caused by a comet's tail.
When this team of astronomers looked at the star KIC 3542116, though, they spotted decidedly asymmetric dips. Six of them, in fact! Three were about the same depth (about 0.1% of the star's light blocked), and another set of three a bit shallower (0.05% blocked).
As soon as they saw the fang-shaped profile, they knew they had something special. Still, first they made sure their data weren’t contaminated by the legion of issues that can mess of the observations: starspots (sunspots, but on another star), known stellar variability, camera detector issues, and more. Once they eliminated all the known potential problems, they were left with one conclusion*: exocomets.