Context : Polarimetry is a novel tool to detect and characterize exoplanets and their atmospheres .
It provides unique constraints on the planet orbit parameters , such as its inclination , orientation in space and shape , as well as reflective properties and composition of the atmosphere .
These combined with spectroscopic and photometric measurements can fully characterize the planet with respect to its size , density , temperature , composition , etc. , even for non-transiting systems .

Aims : Polarized scattered light from the non-transiting hot Jupiter \upsilon And b is measured to further constrain its orbit , mass , density , and geometrical albedo .

Methods : We obtained polarimetric measurements in the UBV bands over the orbital period and deduce an average peak-to-peak amplitude of ( 49 \pm 5 ) \times 10 ^ { -6 } in both Stokes q and u .

Results : From our data we evaluate the orbit inclination i = 111 \degr \pm 11 \degr , longitude of the ascending node \Omega = 236 \degr \pm 12 \degr ( or equivalently 56° ) , the effective size of the scattering atmosphere in the optical blue of 1.36 \pm 0.20 R _ { J } .
These combined with spectroscopic measurements result in the planet mass 0.74 \pm 0.07 M _ { J } , mean density 0.36 \pm 0.08 g cm ^ { -3 } , and surface gravity \sim 10 ^ { 3 } cm s ^ { -2 } , which favor a close similarity of \upsilon And b to other inflated hot Jupiters .
We also significantly improved the periastron epoch T _ { p } = { JD } 2 , 450 , 032.451 , interior conjunction epoch T _ { t } = { JD } 2 , 450 , 034.668 , and periastron longitude \omega = 279 \degr \pm 14 \degr .
The latter indicates that the apsidal resonance known 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 .
Combinig all available measurements at various passbands , we construct a unified wavelength dependent albedo of an average hot Jupiter .
It appears to be largely shaped by Rayleigh scattering in the blue and atomic and molecular absorption in the optical and near infrared .

Conclusions : Our findings demonstrate the power of polarimetry for studying non-transiting exoplanets .