  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.
