We obtained optical spectra of the counterpart of the ultraluminous X-ray source NGC 5408 X-1 using the FORS spectrograph on the VLT .
The spectra show strong high excitation emission lines , He ii \lambda 4686 and [ Ne V ] \lambda 3426 , indicative of X-ray photoionization .
Using the measured X-ray spectrum as input to a photoionization model , we calculated the relation between the He ii and X-ray luminosities and found that the He ii flux implies a lower bound on the X-ray luminosity of 3 \times 10 ^ { 39 } erg s ^ { -1 } .
The [ Ne v ] flux requires a similar X-ray luminosity .
After subtraction of the nebular emission , the continuum appears to have a power-law form with a spectral slope of -2.0 ^ { +0.1 } _ { -0.2 } .
This is similar to low-mass X-ray binaries where the optical spectra are dominated by reprocessing of X-rays in the outer accretion disk .
In one observation , the continuum , He ii \lambda 4686 , and [ Ne V ] \lambda 3426 fluxes are about 30 % lower than in the other five observations .
This implies that part of the line emission originates within one light-day of the compact object .
Fitting the optical continuum emission and archival X-ray data to an irradiated disk model , we find that ( 6.5 \pm 0.7 ) \times 10 ^ { -3 } of the total bolometric luminosity is thermalized in the outer accretion disk .
This is consistent with values found for stellar-mass X-ray binaries and larger than expected in models of super-Eddington accretion flows .
We find no evidence for absorption lines that would permit measurement of the radial velocity of the companion star .