= Solution
A donor star can feed a compact companion through <Roche-lobe overflow> near the inner <Lagrange point>, or through capture of a <stellar wind>. The transferred <gas> usually carries <angular momentum>; when its circularization radius exceeds the accretor's effective inner radius it forms an <accretion disc>. Outward <angular momentum transport> permits inward <mass> flow, while dissipation converts gravitational <binding energy> into heat and radiation. For a compact object with a surface $L\sim GM\dot M/R$; for a <black hole> write $L=\eta\dot Mc^2$, with efficiency determined by the flow and inner boundary. Optically thick disc regions emit a sum of thermal <radiation spectrum> components; a hot optically thin <accretion corona> can inverse-Compton scatter softer <photons> into a harder <X-ray> component. A <black hole> has no material surface on which to radiate a stellar boundary layer.
An explicit example is the <wind-fed black-hole binary> <Cygnus X-1>. Its massive stellar companion supplies <gas>, and the <accretion> flow produces strong <X-ray> emission.<Wind Accretion and State Transitions in Cygnus X-1 by D. R. Gies and others>[abstract, H-alpha wind monitoring and X-ray-state comparison]{ref} Compact-object evidence comes from orbital dynamics rather than <X-ray> brightness alone. The single-lined <binary mass function> constrains the unseen <mass>; inclination, donor properties and <distance> refine it. <Jerome A. Orosz> and collaborators combined optical photometry, <radial velocities>, rotation and a <distance> constraint to obtain a black-hole <mass> of $14.8\pm1.0M_\odot$ in their 2011 analysis. The inference depends on the stellar and orbital model, and that historical value should not be confused with a latest measurement.<The Mass of the Black Hole in Cygnus X-1 by Jerome A. Orosz and others>[abstract; dynamical modelling and observational constraints]{ref}
\b[Binary <accretion> converts orbital <mass> transfer into compact gravitational-energy release; a dynamical <mass> measurement identifies the accretor more securely than <luminosity> alone.]
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