Binary star is within its Roche lobe, i.e. the area where the gravitational pull of the star itself is larger than that of the other component. The stars have no major effect on each other, and essentially evolve separately. Most binaries belong to this class. "Semidetached binary stars" are binary stars where one of the components fills the binary star's Roche lobe and the other does not. Gas from the surface of the Roche-lobe-filling component (donor) is transferred to the other, accreting star. The mass transfer dominates the evolution of the system. In many cases, the inflowing gas forms an accretion disc
Star system even more complex dynamics of the large number of stars in star clusters and galaxies. In a "physical" triple star system, each star orbits the center of mass of the system. Usually, two of the stars form a close binary system, and the third orbits this pair at a distance much larger than that of the binary orbit. This arrangement is called "hierarchical". The reason for this is that if the inner and outer orbits are comparable in size, the system may become dynamically unstable, leading to a star being ejected from the system. Triple stars that are "not" all