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The gravitational potential of a binary system is described by the Roche model where each star dominates the gravitational potential inside regions called Roche lobes.The two Roche lobes meet at the inner Lagrange point along the joining of the two stars. Figure 1 shows equipotential surfaces in the orbital plane for a binary system. As may be seen from Fig. 1, there are five equilibrium points( i.e. ∇φ = 0) three of which i.e., L1,L2,L3,are along the line centers. Two are peripheral to the masses and lie as the critical points along equipotentials that envelope both stars. two other points ,i.e., L4,L5 lie opposite to each other, perpendicular to the line of centers. These are quasi-equilibrium points for which local orbits are possible because of coriolis acceleration. If either star fills its Roche lobe, matter will stream from the Roche lobe filling star through the inner Lagrange point to the other star in a process known as Roche lobe overflow(RLOF). This actually occurs before the photosphere reaches the Roche lobe radius in the absence of magnetic fields or other constrains on the mass flow. This mass transfer affects both the evolution of the components of the binary as well as the binary properties such as orbital period and eccentricity. Roche lobe overflow can be triggered by the evolution of the binary properties or by evolution of the component stars. On the one hand, the orbital separation of the binary can change so that the Roche lobe can shrink to within the surface of one of the stars. On the other hand, stellar evolution may eventually cause one of the stars to expand to fill its Roche lobe. When both stars in the binary are main-sequence stars, the latter process is more common. Since the more massive star will evolve first, it will be the first to expand and fill its Roche lobe. At this stage, the mass exchange can be conservative (no mass is lost from the binary) or non-conservative (mass is lost). Depending on the details of the mass exchange and the evolutionary stage of the mass-losing star there are several outcomes that will lead to formation of a relativistic binary. The primary star can lose its envelope, revealing its degenerate core as either a helium, carbon-oxygen, or oxygen-neon white dwarf, it can explode as a supernova, leaving behind a neutron star or a black hole, or it can simply lose mass to the secondary so that they change roles. Barring disruption of the binary, its evolution will then continue. In most outcomes, the secondary is now the more massive of the two stars and it may evolve off the main sequence to fill its Roche lobe. The secondary can then initiate mass transfer or mass loss with the result that the secondary also can become a white dwarf (WD), neutron star (NS), or black hole (BH). The relativistic binaries that result from this process fall into a number of observable categories. AWD-MS or WD-WD binary may eventually become a cataclysmic variable once the white dwarf begins to accrete material from its companion. If the companion is a Main Sequence star RLOF can Davood Manzoori Department of Physics, University of Mohaghegh Ardabili, P. O.Box. 179, Ardabil Iran 8

Mass Transfer, and Effects of Magnetic Fields on the Mass Transfer in Close Binary System