The rate of mass transfer/loss from the Roche lobe filling star is governed by how the star’s radius changes in response to changes in its mass. Hjellming and Webbink  describe these changes and the response of the Roche lobe to mass changes in the binary using the radius-mass exponents, , for each of the three processes described in Equations (13, 14, 15) and defining.
Conservative mass transfer occurs when there is no mass loss from the system. During conservative mass transfer, the orbital elements of the binary can change. Consider a system with total mass and semi-major axis . The total orbital angular momentum
In non-conservative mass transfer, both mass and angular momentum can be removed from the system. There are two basic non-conservative processes which are important to the formation of relativistic binaries – the common-envelope process and the supernova explosion of one component of the binary. The result of the first process is often a short-period, circularized binary containing a white dwarf. Although the most common outcome of the second process is the disruption of the binary, occasionally this process will result in an eccentric binary containing a neutron star.
Common envelope scenarios result when one component of the binary expands so rapidly that the mass transfer is unstable and the companion becomes engulfed by the donor star. The companion then ejects the envelope of the donor star. The energy required to eject the envelope comes from the orbital energy of the binary and thus the orbit shrinks. The efficiency of this process determines the final orbital period after the common envelope phase. This is described by the efficiency parameter, and a discussion of the factors involved in determining is presented in Sandquist et al. .
The effect on a binary of mass loss due to a supernova can be quite drastic. Following Padmanabhan , this process is outlined using the example of a binary in a circular orbit with radius . Let be the velocity of one component of the binary relative to the other component. The initial energy of the binary is given by for a discussion), and that the primary has received no kick from the supernova (not necessarily a safe assumption, but see Davies and Hansen  or Pfahl et al.  for an application to globular cluster binaries). Since we have assumed that the instantaneous velocities of both components have not been affected, we can replace them by , and so
We have seen that conservative mass transfer can result in a tighter binary if the more massive star is the donor. Non-conservative mass transfer can also drive the components of a binary together during a common envelope phase when mass and angular momentum are lost from the system. Direct mass loss through a supernova explosion can also alter the properties of a binary, but this process generally drives the system toward larger orbital separation and can disrupt the binary entirely. With this exception, the important result of all of these processes is the generation of tight binaries with at least one degenerate object.
The processes discussed so far apply to the generation of relativistic binaries anywhere. They occur whenever the orbital separation of a progenitor binary is sufficiently small to allow for mass transfer or common envelope evolution. Population distributions for relativistic binaries are derived from an initial mass function, a distribution in mass ratios, and a distribution in binary separations. These initial distributions are then fed into models for binary evolution such as StarTrack  or SeBa [191, 168] in order to determine rates of production of relativistic binaries. The evolution of the binary is often determined by the application of some simple operational formulae such as those described by Tout et al.  or Hurley et al. . For example, Hils, Bender, and Webbink  estimated a population of close white dwarf binaries in the disk of the galaxy using a Salpeter mass function, a mass ratio distribution strongly peaked at 1, and a separation distribution that was flat in . Other estimates of relativistic binaries differ mostly by using different distributions [17, 119, 168, 167].
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