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As they continue to gather mass from infalling interstellar cloud material, accretion disks surrounding protostars may often have the opportunity to become more massive than the central object which they each surround. It is not clear what physical processes are principally responsible for limiting the disk-to-central object mass ratio of such systems. Here we derive the conditions under which a massive disk may completely disrupt the nonrotating central star that it surrounds via a tidal process similar to that encountered in the classical binary Roche problem. We demonstrate that central stars with a polytropic index n greater than or equal to +3 or n less than 0 will never encounter runaway excretion, whereas in systems where tidal excretion has begun, central stars with 0.292 less than or equal to n less than 3 will always encounter runaway excretion. Although the disruption of a central star by a surrounding disk is possible in principle, we show that the mean temperature of the disk must always be higher than that of the central star in order for this to occur. Systems of this nature are unlikely to arise in normal astrophysical environments, including protostellar cloud core environments. We conclude, therefore, that the disk-to-central object mass ratio in protostellar systems is not likely to be limited by this tidal process.
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