We present linear polarization measurements of nearby FGK dwarfs to parts-per-million (ppm) precision. Before making any allowance for interstellar polarization, we found that the active stars within the sample have a mean polarization of 28.5 +/- 2.2 ppm while the inactive stars have a mean of 9.6 +/- 1.5 ppm. Amongst inactive stars we initially found no difference between debris disk host stars (9.1 +/- 2.5 ppm) and the other FGK dwarfs (9.9 +/- 1.9 ppm). We develop a model for the magnitude and direction of interstellar polarization for nearby stars. When we correct the observations for the estimated interstellar polarization we obtain 23.0 +/-2.2 ppm for the active stars, 7.8 +/- 2.9 ppm for the inactive debris disk host stars and 2.9 +/- 1.9 ppm for the other inactive stars. The data indicates that whilst some debris disk host stars are intrinsically polarized most inactive FGK dwarfs have negligible intrinsic polarization, but that active dwarfs have intrinsic polarization at levels ranging up to ~45 ppm. We briefly consider a number of mechanisms, and suggest differential saturation of spectral lines in the presence of magnetic fields is the best able to explain the polarization seen in active dwarfs. The results have implications for current attempts to detect polarized reflected light from hot Jupiters by looking at the combined light of the star and planet.
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