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We present time-resolved optical spectroscopy of the counterpart to thehigh-inclination black hole low-mass X-ray binary Swift J1357.2-0933 inquiescence. Absorption features from the mass donor star were not detected.Instead the spectra display prominent broad double-peaked Halpha emission andweaker HeI emission lines. From the Halpha peak-to-peak separation we constrainthe radial velocity semi-amplitude of the donor star to > 789 km/s. Furtheranalysis through radial velocity and equivalent width measurements indicatesthat the Halpha line is free of variability due to S-wave components or disceclipses. From our data and previous observations during outburst, we concludethat long-term radial velocity changes ascribed to a precessing disc were oflow amplitude or not present. This implies that the centroid position of theline should closely represent the systemic radial velocity. Using the derivedsystemic velocity of -150 km/s and the best available limits on the sourcedistance, we infer that the black hole is moving towards the Plane in itscurrent Galactic orbit unless the proper motion is substantial. Finally, thedepth of the central absorption in the double peaked profiles adds support forSwift J1357.2-0933 as a high-inclination system. On the other hand, we arguethat the low hydrogen column density inferred from X-ray fitting suggests thatthe system is not seen edge-on.

VLT spectroscopy of the Black Hole Candidate Swift J1357.2-0933 in Quiescence