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Roche-lobe overflow is mass transfer that begins when a donor star fills its Roche lobe. Gas near the inner Lagrange point can pass through the saddle in the rotating-frame effective potential toward the companion. Its orbital angular momentum can prevent direct radial infall and instead produce an accretion disk, depending on the geometry.

The process couples stellar evolution to orbital evolution. Losing mass changes the donor's stellar radius, while transferred or escaping matter changes the Roche lobe. Dynamical stability of binary mass transfer depends on which response dominates. Stable transfer can gradually strip an envelope; unstable interaction can lead to a common envelope. Case A mass transfer and Case B mass transfer distinguish the donor's nuclear state when overflow starts.

In stellar structure, stellar thermal equilibrium means that internal heating balances the surface luminosity and any energy loss through neutrinos, with negligible secular storage of thermal energy on the timescale considered. A star can satisfy this balance while its interior is hotter than its surface and heat flows outward. It is therefore different from equal-temperature thermal equilibrium between systems. Neglecting neutrino losses, the balance is $L_{\mathrm{surface}}=L_{\mathrm{heat}}$. In a slowly mass-losing donor star, a stellar thermal equilibrium radius sequence applies only when thermal adjustment is fast compared with the mass-loss timescale; rapid loss instead requires the adiabatic stellar radius response exponent.

An X-ray binary has a compact mass-gaining star or black hole accreting from a companion, so that much of its emitted power appears as X-rays. Gravitational binding energy supplies an accretion luminosity of order $GM\dot{M}/R$ when there is a surface or an appropriate inner disk radius. The donor star may feed an accretion disk through Roche-lobe overflow or a stellar wind.