We expect comets to be a common feature of star formation, but that's mostly just guesswork. Their small size and mass have prevented definite detection. However, a study of the very Sun-like star KIC 3542116 has revealed dips in brightness consistent with the passage of comets across its face.
(For those struggling to remember stellar nomenclature, this is not KIC 8462852, better known as Tabby's Star, whose strange dimming has inspired many possible explanations, comets among them.)
The nucleus of a comet is city-sized, but the tail emitted on approach to the star can be enormous. The gas and dust liberated in this process is exceptionally diffused, but can still block a detectable amount of light. The pattern of dimming would be expected to have a steep start and more gentle finish compared to the U-shape produced by a passing planet.
This is exactly what Tom Jacobs saw when studying Kepler Space Telescope observations of KIC 3542116, a star about 815 light-years away. Six such transits were observed, three dimming the star by approximately 0.1 percent and three more subtly. Making some reasonable assumptions about cometary size, composition and lifetime, this is what we would expect from an object of similar size to Halley's Comet. Six individual objects appear more likely than repeated transits in the four years of observations.
With an F2V-type classification, KIC 3542116 is a little hotter and bigger than the Sun. The paper in the Monthly Notices of the Royal Astronomical Society in which Jacobs and scientists from MIT and the Harvard-Smithsonian Center for Astrophysics announced the find also reported a single very similar dip across another star viewed by Kepler, KIC 11084727. Jacobs examined lightcurves from 200,000 stars by eye alone to find these, but most comets would be missed if their orbits were in the wrong alignment between us and the star. Consequently, we still don't know how common comets are, although KIC 3542116 may be unusual in having so many large ones.
The authors consider a number of alternative explanations for the dips, such as sunspots and instrumentation errors, but rule each of these out as not fitting the pattern observed.
The smallest object previously detected around a Sun-like star is about a quarter the size of Earth, but an object the mass of the Moon has been found to be messing with the timing of a pulsar it orbits. Some probably smaller objects in the process of disintegration have also been detected by the dust they are trailing behind them, but their size is uncertain.
Meanwhile, we still don't know what is causing the changes to Tabby's Star, but if it is comets, they are operating on a scale hundreds of times as large as this.
[H/T: Bad Astronomy]