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

We obtained multi-epoch Very Large Telescope optical spectroscopic data in 2011 and 2012 on the ultraluminous X-ray source NGC 5408 X-1. We confirm that the He ii lambda 4686 line has a broad component with an average full width at half-maximum of v = 780 +/- 64 km s(-1) with a variation of similar to 13 per cent during observations spanning over four years, and is consistent with the origin in the accretion disc. The deepest 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 of the binary system. We find an upper limit on the semi-amplitude of the radial velocity of K = 132 +/- 42 km s(-1). A search for a periodic signal in the data resulted in no statistically significant period. The mass function and constraints on the binary system imply a black hole mass of less than similar to 510 M-circle dot. Whilst, a disc irradiation model may imply a black hole mass smaller than similar to 431-1985 M-circle dot, depending on inclination. Our data can also be consistent with 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.