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The mass of the star that loses matter is
Accordingly, the mass of the accreting star is
where is the accretion rate of the captured matter.
For stages with no RL overflow, the accretion rate of the captured stellar wind matter is
At stages with RL overflow and both normal stars we will assume a mildly non-conservative mass transfer
This means that the evolution cannot be fully conservative as a rule, since during the first mass transfer episode the more massive star is usually characterized by a shorter thermal time-scale.
In the case of compact accretors, we require the rate of their mass increase to be limited by the accretion energy output equal to the critical Eddington luminosity
( is the Thompson cross-section) reached at the stopping radius for the accreted matter (see detailed discussion in Lipunov (1992)), which corresponds to a critical accretion rate
Thus, the mass of the accreting compact star at the end of the stage is determined by the relation