You made the comment that you don't see the sky darken when looking through a polarising filter. By viewing the coronal area using a linear polariser, and then presumably rotating the plane of polarisation and taking a series of pictures, and comparing this with images taken without a polarising filter, we can isolate the small fraction of light from around the Sun that is due to Thomson scattering in its corona. Thus we have a means of seeing a contrast between (polarised) light coming from the corona and (unpolarised) light coming from the sky in the same line of sight. In these circumstances the scattered light will be unpolarised. However, when we look at the sky right next to the Sun, then this will have been scattered through a very small angle. The polarisation effects of this scattering are almost identical in nature to that caused by Thomson scattering. In this case it is " Rayleigh scattering" from electrons that are bound into molecules and atoms in the Earth's atmosphere. The light we see from the daylight sky is also produced by scattering. The component of the acceleration along the line of sight does not cause any radiation to be emitted towards us. But the scattered light is polarised when it is scattered through a large angle, because we effectively can only "see" the electrons accelerating along a line that forms a tangent to the limb of the Sun. Such light accelerates the free electrons which re-emit light (this is what scattering is). The sunlight incident upon the electrons in the corona is unpolarised (that is, the electric field vector of the light is randomly oriented but at right angles to the direction of travel of the light). If we view the corona around the Sun (from our perspective), then the scattered light that reaches us has scattered through a large angle (roughly 90 degrees). When you look at the Sun in white (visible) light, what you see is actually sunlight that has scattered from free electrons in the solar corona.
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