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The observational signatures of black holes in x-ray binary systems depend on their masses, spins, accretion rate, and the misalignment angle between the black hole spin and the orbital angular momentum. We present optical polarimetric observations of the black hole x-ray binary MAXI J1820+070, from which we constrain the position angle of the binary orbital. Combining this with previous determinations of the relativistic jet orientation, which traces the black hole spin, and the inclination of the orbit, we determine a lower limit of 40° on the spin-orbit misalignment angle. The misalignment must originate from either the binary evolution or black hole formation stages. If other x-ray binaries have similarly large misalignments, these would bias measurements of black hole masses and spins from x-ray observations.

We present novel calculations of the magnetic dichroism appearing in molecular bands in the presence of a strong magnetic field, which perturbs the internal structure of the molecule and results in net polarization due to the Paschen-Back effect. Based on that, we analyze new spectropolarimetric observations of the cool magnetic helium-rich white dwarf G99-37, which shows strongly polarized molecular bands in its spectrum. In addition to previously known molecular bands of the C2 Swan and CH A-X systems, we find a firm evidence for the violet CH B-X bands at 390 nm and C2 Deslandres-d'Azambuja bands at 360 nm. Combining the polarimetric observations with our model calculations, we deduce a dipole magnetic field of 7.5+/-0.5 MG with the positive pole pointing towards the Earth. We conclude that the developed technique is an excellent tool for studying magnetic fields on cool magnetic stars.