We present imaging circular polarimetry and near-infrared photometry of the suspected ultra-short period white-dwarf binary RX J0806.3+1527 obtained with the ESO VLT and discuss the implications for a possible magnetic nature of the white dwarf accretor and the constraints derived for the nature of the donor star. Our V-filter data show marginally significant circular polarization with a modulation amplitude of ~0.5% typical for cyclotron emission from an accretion column in a magnetic field of order 10 MG and not compatible with a direct-impact accretor model. The optical to near-infrared flux distribution is well described by a single blackbody with temperature kT_bb = 35000 K and excludes a main-sequence stellar donor unless the binary is located several scale heights above the galactic disk population.
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