We present 50 nights of polarimetric observations of HD 189733 in $B$ band using the POLISH2 aperture-integrated polarimeter at the Lick Observatory Shane 3-m telescope. This instrument, commissioned in 2011, is designed to search for Rayleigh scattering from short-period exoplanets due to the polarized nature of scattered light. Since these planets are spatially unresolvable from their host stars, the relative contribution of the planet-to-total system polarization is expected to vary with an amplitude of order 10 parts per million (ppm) over the course of the orbit. Non-zero and also variable at the 10 ppm level, the inherent polarization of the Lick 3-m telescope limits the accuracy of our measurements and currently inhibits conclusive detection of scattered light from this exoplanet. However, the amplitude of observed variability conservatively sets a $3 sigma$ upper limit to the planet-induced polarization of the system of 58 ppm in $B$ band, which is consistent with a previous upper limit from the POLISH instrument at the Palomar Observatory 5-m telescope (Wiktorowicz 2009). A physically-motivated Rayleigh scattering model, which includes the depolarizing effects of multiple scattering, is used to conservatively set a $3 sigma$ upper limit to the geometric albedo of HD 189733b of $A_g < 0.37$. This value is consistent with the value $A_g = 0.226 pm 0.091$ derived from occultation observations with HST STIS (Evans et al. 2013), but it is inconsistent with the large $A_g = 0.61 pm 0.12$ albedo reported by (Berdyugina et al. 2011).
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