Exoplanet polarimetry astronomers will tell you one of the strengths of polarimetry is that it naturally nulls the starlight, so you know the signal you're getting is not from the star. However, they will also tell you this isn't true in every case. Stars themselves can produce polarised light signals from the Rayleigh scattering in their limbs (i.e. looking through the upper atmosphere at the edges of the star). This can produce a signal when their limbs are asymmetric either from being obscured by planets or star spots, or from rotational or tidal distortion which can distort the atmosphere through gravity darkening, essentially changing the distribution of the darkened regions.
Learning more about these exceptions to the rule is vital to the future of reliable exoplanet polarimetry and is inherently a fascinating way to learn about stars.
The reason most stars don't produce much polarised light from their own atmospheres has to do with the way we measure linearly polarised light (light whose electric field oscillates along a particular plane). The orientation of polarized light is denoted by “Stokes parameters”, Q and I are for linearly polarised light and are offset from each other by 45 degrees. They can be either negative or positive with the signs offset by 90 degrees.
You can imagine then, if the polarised light from a stellar limb is tangential to the surface that, taking the tangent as you move around a circle, the positive values in Q would be perfectly negated by the negative values a quarter of the way around from there. If it’s a perfect circle this works out perfectly giving you a net value of zero polarised light. In a case where there is substantial gravity darkening, as on a rapidly rotating star, those additional darkened regions produce a strengthened signal in polarised light. And since the darkening is spatially dependent---along the equator where a fast rotator will bulge out---it creates a polarised light signal.
Now we consider Regulus. Regulus is a multi-star system but the primary star, which we were observing, is a large blue-white star that rotates on its axis every 15.9 hours. That’s very fast, especially considering it’s a bigger, more extended star than our sun. Our own sun takes about twenty-four-and-a-half days to rotate and is much smaller. Regulus rotates so rapidly that it bulges in the middle as you might expect when picturing a centrifugal “force” acting on a body that would otherwise be ball-shaped. Planets like Jupiter also bulge in this way from spinning too fast.
McAllister et al 2005 took interferometric measurements of Regulus enabling them to infer the distortion, map the gravity darkening, and find the orientation of the star.
Long before that, Harrington & Collins 1968 predicted that distorted stars like these would produce a polarised light signal by the means I've just described.