The Geometric Crisis in Cygnus X-3: Limitations of Wind-fed Accretion and the Case for Roche Lobe Overflow

Abstract Cygnus X-3 is a Galactic X-ray binary with a 4.8 hr orbital period operating in the ultraluminous regime. Although the system is viewed at a relatively low inclination ( i ≈ 28°), it exhibits a deep orbital modulation. Recent IXPE observations show strong linear polarization orthogonal to the radio jet, indicating that the X-ray emission is dominated by reflection from the inner walls of a supercritical outflow funnel. We propose a “Hybrid” Roche lobe overflow scenario in which a massive Wolf–Rayet (WR) donor effectively fills its Roche lobe with a focused wind driving a super-Eddington accretion stream. Using a numerical synthesis of the folded light curve, we show that the modulation is reproduced when the central funnel is periodically occulted by a vertically extended, shock-heated “Turbulent Wall” formed by stream impact on the outer disk rim. This produces a phase lag (Δ ϕ ≈ 0.11) between X-ray minimum and binary conjunction, with extended attenuation by the WR wind defining a broader “Suppression Region.” This geometry explains the enhanced iron-line equivalent width during X-ray minimum via a coronagraphic effect. The large radial-velocity amplitude of Fe xxvi measured by XRISM ( K obs ≈ 430 km s −1 ) and its zero crossing at ϕ X = 0.0 arise naturally in the stream-impact region rather than from orbital motion of the compact object. Finally, we show that the observed secular orbital expansion ( P ̇ > 0 ) follows directly from highly nonconservative mass transfer with inner-disk mass loss, indicating that Cygnus X-3 is a stable, long-lived system in a supercritical accretion regime.