Ah, gravity. It has so many tricks up its sleeve. This particular trick was discovered 90 years ago, but still is being investigated today. Take a look at the weird phenomenon known in which gravitational force, and possibly an exoplanet, gives a star a dark stripe around its middle.
Stars, with their constantly shifting surfaces, their central locations in solar systems, and their overwhelming brightness, often hide the fact that they’re spinning like tops in space. The spinning can have a noticeable effect. Stars are giant balls of gas and plasma, and so lack the solidity of, at least, the rocky planets. Their spin can sometimes radically alter their shape. Because the equator lines of these stars need to move faster than the poles in order complete every rotation, they’re thrown outwards due to centrifugal force. The star has a large bulge around its middle as it turns.
This middle bulge is exacerbated by gravity, which drops off at a rate proportional to the square of the distance from the center of the star. A little increase in the radius makes the gravity nose dive – so the relatively small increase in distance that centrifugal force adds will be compounded by the fact that the drop in gravity floats the equator region outwards even farther. Meanwhile, the poles are hugged closer to the center by gravity. The center is where the heat is generated, and so the poles light up, while the equator of the region darkens. This is referred to as gravity darkening. The gravity difference, and spin, of a star can change its color.
This can happen not only due to the spin of the star itself, but to a nearby planet. A planet orbiting a star will exert a gravitational pull on the star that will lift the central band of the star outwards – also cooling it. Astronomers might one day be able to find planets by the two-tone stars that we see around us.
But it will take a little tweaking. “Gravity darkening” is also called the “Von Zeipel theorem,” after Edvard Hugo von Zeipel. He came up with the equations meant to describe it over 90 years ago, and though his idea was correct, modern assessments of stars show that he was off in his calculations somewhere. Although the phenomenon exists, the temperatures aren’t quite adding up. Astronomers believe that von Zeipel didn’t consider the way that the stars' atmosphere flows and changes due to this difference in heat. So we'll have to figure out the numbers before we can use gravity darkening to hunt for other planets.