Orbital-phase-resolved infrared spectra of Cygnus X-3 in outburst and quiescence, including tomographic analysis, are presented. We confirm the phasing of broad He II and N V lines in quiescence, such that maximum blueshift corresponds to the X-ray minimum at Φ=0.00±0.04. In outburst, double-peaked He I structures show a similar phasing with two significant differences: (1) although varying in relative strength, there is continuous line emission in blue and red peaks around the orbit; and (2) an absorption component, ~(1)/(4) of an orbit out of phase with the emission features, is discerned. Doppler tomograms of the double-peaked profiles are consistent with a disk-wind geometry, rotating at velocities of 1000 km.s–1. Regrettably, the tomography algorithm will produce a similar ring structure from alternative line sources if contaminated by overlying P Cygni profiles. This is certainly the case in the strong 2.0587 µm He I line, leading to an ambiguous solution for the nature of double-peaked emission. The absorption feature, detected (1)/(4) of an orbit out of phase with the emission features, is consistent with an origin in the He star wind and yields for the first time a plausible radial velocity curve for the system. We directly derive the mass function of the system, 0.027 M☉. If we assume a neutron star accretor and adopt a high orbital inclination, i>60°, we obtain a mass range for the He star of 5 M☉≲MWR≲11 M☉. Alternatively, if the compact object is a black hole, we estimate MBH≲10 M☉. We discuss the implications of these masses for the nature and size of the binary system.
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