The delicate balance of gravity is key to understanding binary stars
The Roche lobe is the teardrop-shaped region around a star in a binary system, within which gas is gravitationally bound to the star. But at the point between the two stars where the lobes meet – the inner Lagrangian point (L1) – gravity and centrifugal forces cancel out and the gas feels no net force. That is unless one of the stars has expanded to the point that it fills its Roche lobe. This happens in cataclysmic variable and many X-ray binaries. In these cases, the atmosphere of the lobe-filling star is pushed beyond the L1 point and flows towards and around the other star. As the escaping gas stream encircles the star it eventually loops around and collides with itself. This causes it to lose energy, spread out and form an accretion disc around the companion star.
Binary companion Inner Lagrangian point (L1) Star Roche lobe Accretion disc Gas stream from giant star escaping through L1 point Giant star which has expanded to fill its Roche lobe