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How does one differentiate between an exoplanet orbiting in front of a distant sun and a large starspot traveling across that star’s disk?

Melvyn Goldberg, Toronto, Canada
Light-curve-exoplanet
The light curve of an exoplanet transiting its star (top) is different from that of a starspot traversing a star’s disk, so astronomers can tell the two signals apart. Astronomy: Roen Kelly
Astronomers had to resolve this question before NASA would deem the Kepler mission (which uses transits to search for terrestrial exoplanets) as feasible. Both transits and starspots will cause a dip in its star’s “light curve” (which plots its brightness vs. time). The dips can sometimes have similar depths.
 
Any likely transit of an exoplanet across its star lasts roughly 6 to 12 hours (due to planetary orbital speeds). Rotation periods of most solar-type stars are several weeks, so a starspot will take at least several days to rotate in and out of view. Thus we can distinguish a transit by the short duration of the dip.
 
There is a further difference: the shape of the dip. A planet doesn’t take long to go from being just off the disk’s edge to fully projected onto the star, so the onset and ending of a transit dip is sharp (short in time). For most of the transit, the planet blocks about the same amount of light, creating a fairly flat bottom to the dip. A star appears a little brighter in its disk’s center, so the dip of a transit is slightly “U-shaped” instead of having a completely flat bottom.

Starspot dips, on the other hand, will start off slowly because the spot we’re initially viewing is almost edge-on at the star’s limb. It doesn’t present as fully face-on until it is in the disk’s middle (halfway through its appearance). The shape of the starspot dip has gentle sides and looks more “V-shaped.” — Gibor Basri, University of California, Berkeley
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