We obtained multi-epoch Very Large Telescope ( VLT ) optical spectroscopic data in 2011 and 2012 on the ultraluminous X-ray source ( ULX ) NGC 5408 X-1 .
We confirm that the He ii \lambda 4686 line has a broad component with an average FWHM of v = 780 \pm 64 km/s with a variation of \sim 13 % during observations spanning over 4 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 \pm 42 km/s .
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 \sim 510 M _ { \odot } .
Whilst , a disc irradiation model may imply a black hole mass smaller than \sim 431 - 1985 M _ { \odot } , 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 .