We obtained optical spectra of the counterpart of the ultraluminous X-ray source NGC 5408 X-1 using the FORS spectrograph on the Very Large Telescope. The spectra show strong high-excitation emission lines, He II λ4686 and [Ne V] λ3426, 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 × 1039 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 λ4686, and [Ne V] λ3426 fluxes are about 30% lower than in the other five observations. This implies that part of the line emission originates within 1 lt-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 ± 0.7) × 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. Based on observations collected at the European Organisation for Astronomical Research in the Southern Hemisphere, Chile (ESO Programme 69.A-0123(A)).
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