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Polarimetry is a novel tool to detect and characterize exoplanets and theiratmospheres. Polarized scattered light from the non-transiting hot Jupiter$\upsilon$~And~b is measured to further constrain its orbit, mass, density, andgeometrical albedo. We obtained polarimetric measurements in the $UBV$ bandsover the orbital period and deduce an average peak-to-peak amplitude of $(49\pm 5)\times10^{-6}$ in both Stokes $q$ and $u$. From our data we evaluate theorbit inclination $i=111\degr\pm11\degr$, longitude of the ascending node$\Omega=236\degr\pm12\degr$ (or equivalently 56\degr), the effective size ofthe scattering atmosphere in the optical blue of $1.36\pm0.20$\,$R_{\rm J}$.These combined with spectroscopic measurements result in the planet mass$0.74\pm0.07$\,$M_{\rm J}$, mean density $0.36\pm0.08$\,g\,cm$^{-3}$, andsurface gravity $\sim10^3$\,cm\,s$^{-2}$, which favor a close similarity of$\upsilon$~And~b to other inflated hot Jupiters. We also significantly improvedthe periastron epoch $T_{\rm p}={\rm JD}2,450,032.451$, interior conjunctionepoch $T_{\rm t}={\rm JD}2,450,034.668$, and periastron longitude$\omega=279\degr\pm14\degr$. The latter indicates that the apsidal resonanceknown for planets c and d includes also planet b.  Obtained limits on the wavelength dependent geometrical albedo (average 0.35)indicate its similarity to Neptune with peak reflectivity in the blue.Combining all available measurements at various passbands, we construct aunified wavelength dependent albedo of an average hot Jupiter. It appears to belargely shaped by Rayleigh scattering in the blue and atomic and molecularabsorption in the optical and near infrared. Our findings demonstrate the powerof polarimetry for studying non-transiting exoplanets.

Upsilon Andromedae b in polarized light: New constraints on the planet size, density and albedo