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We obtained multi-epoch Very Large Telescope (VLT) optical spectroscopic datain 2011 and 2012 on the ultraluminous X-ray source (ULX) NGC 5408 X-1. Weconfirm that the HeII\lambda4686 line has a broad component with an averageFWHM of v=780\pm64 km/s with a variation of ~13% during observations spanningover 4 years, and is consistent with the origin in the accretion disc. Thedeepest optical spectrum does not reveal any absorption line from a donor star.Our aim was to measure the radial velocity curve and estimate the parameters ofthe binary system. We find an upper limit on the semi-amplitude of the radialvelocity of K=132\pm42 km/s. A search for a periodic signal in the dataresulted in no statistically significant period. The mass function andconstraints on the binary system imply a black hole mass of less than ~510M_sun. Whilst, a disc irradiation model may imply a black hole mass smallerthan ~431-1985 M_sun, depending on inclination. Our data can also be consistentwith an unexplored orbital period range from a couple of hours to a few days,thus with a stellar-mass black hole and a subgiant companion.

Towards a dynamical mass of the ultraluminous X-ray source NGC 5408 X-1