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The term mass transfer is used for the movement of material from one astronomical object to another, the term commonly used for that between members of a binary star. Members of a star system may be sufficiently separated that there is no mass transfer, or close enough to lead to sporadic or continuous mass transfer. Among the terms used for the two stars are the donor star and the accretor (i.e., recipient).
Mass transfer is presumed to underly characteristics observed in some stars. The consequences of sporadic mass transfer may underly brightness variation of a variable star, as can the shifting of the position of the mass transfer so as to hide and reveal it from our line of sight. The constituents of the stars revealed through spectrography may be other than that predicted by stellar evolution models of independent stars: examples of such unusual stars with binary companions are Algols and symbiotic binaries.
Either the donor or the accretor can be the more massive, the donor generally being a star that is physically large for its mass (often a giant star) and the accretor a star that is relatively small for its mass (often a white dwarf or other compact object). The large donor includes material that is far from its center, and is drawn away if/when it is beyond a volume of space surrounding its center termed its Roche lobe. Observed mass transfer is generally limited/stable, but also occurs as runaway processes (unstable mass transfer), in which case it can produce the conditions for explosive events such as novae and supernovae. The shifting mass from donor to accretor directly changes the donor's Roche lobe as well as indirectly changing it through modification of the orbit (i.e., the Roche lobe of the donor shrinks if the orbit shrinks, possibly shrinking enough to maintain or increase mass transfer), and theoretical analysis can determine conditions for runaway mass transfer. As a general rule, if the accretor is more massive than the donor, then the orbit will grow and runaway accretion will not occur and if it is sufficiently less massive than the donor, then the Roche lobe will shrink fast enough that runaway accretion occurs. Theory (i.e., application of Newton's laws) can produce more exact criteria.
A star capturing some of the stellar wind from its companion falls under the definition of mass transfer. This type would depend upon the conditions that produce the wind.