The sun not only brings us light and warmth, but it sometimes also brings us violent solar storms. Such storms can damage satellites and power grids, and are caused by magnetic explosions on the sun. Through polarization astronomers can now measure the magnetic fields on the sun, which helps us to understand and predict the explosive events on the sun.
Massive stars explode as a supernova at the end of their lives. How these violent explosions occur is not yet well understood. By measuring the polarization of the light that a supernova emits, astronomers can retrieve the intricate details of the explosion.
We know now that hundreds of stars are host to planets, just like the sun is the center to our solar system of planets. But for most of these planetary systems we only have indirect evidence: we have never seen the light from these planets, because they are very faint compared to their host star. Considering the fact that starlight is unpolarized and reflected light off the planet is very polarized, polarization measurements will allow astronomers to take pictures of exoplanets. Moreover, the polarization also holds clues about what the planet actually looks like.
The center of many galaxies contains a supermassive black hole. By nature, there is no light emerging from the black hole itself. But the light of the stuff around the black hole reveals a lot of information about how the black hole works. In particular, the polarization of this light allows astronomers to map the structure around the black hole.
It is very likely that life has developed on some of the billions of planets that exist in our Milky Way galaxy. This life is not necessarily intelligent, but may rather look like moss or bacteria, and will therefore be hard to see. However, it will likely consist of complex molecules that convert starlight into energy. Such molecules leave a small but distinct circular polarization imprint on this light, which constitutes one of the very few ways to detect life remotely.