

4.1 Binary evolution
The evolution of a binary system of two main-sequence stars can
significantly affect the evolution of both component stars if the
orbital separation is sufficiently small. If the orbital period is
less than about 10 days, tidal interactions will have circularized
the orbit during the pre- and early main-sequence phase. [60, 167, 168] Both stars start
in the main sequence with the mass of the primary
, and the mass of the secondary
, defined such that
. The binary
system is described by the orbital separation
,
and the mass ratio of the components
. The
gravitational potential of the 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 line joining the two stars.
Figure 5 shows equipotential
surfaces in the orbital plane for a binary with
. 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 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 the 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, neutron star, or black
hole.
The relativistic binaries that result from this
process fall into a number of observable categories. A WD-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 be triggered by the
evolution of the companion. If the companion is another white
dwarf, then RLOF is triggered by the gradual shrinking of the orbit
through the emission of gravitational radiation. WD-WD cataclysmic
variables are also known as AM CVn stars. If the total mass of the
WD-WD binary is above the Chandrasekhar mass, the system may be a
progenitor to a type I supernova.
The orbit of a NS-MS or NS-WD binary will shrink
due to the emission of gravitational radiation. At the onset of
RLOF, the binary will become either a low-mass X-ray binary (if the
donor star is a WD or MS with
), or a
high-mass X-ray binary (if the donor is a more massive
main-sequence star). These objects may further evolve to become
millisecond pulsars if the NS is spun up during the X-ray binary
phase [34
, 134
]. A NS-NS binary
will remain virtually invisible unless one of the neutron stars is
observable as a pulsar. A BH-MS or BH-WD binary may also become a
low- or high-mass X-ray binary. If the neutron star is observable
as a pulsar, a BH-NS binary will appear as a binary pulsar. BH-BH
binaries will be invisible unless they accrete matter from the
interstellar medium. A comprehensive table of close binary types
that can be observed in electromagnetic radiation can be found in
Hilditch [74].
The type of binary that emerges depends upon the
orbital separation and the masses of the component stars. During
the evolution of a
star, the radius will slowly
increase by a factor of about two as the star progresses from zero
age main sequence to terminal age main sequence. The radius will
then increase by about another factor of 50 as the star transitions
to the red giant phase, and an additional factor of 10 during the
transition to the red supergiant phase. These last two increases in
size occur very quickly compared with the slow increase during the
main-sequence evolution. Depending upon the orbital separation, the
onset of RLOF can occur any time during the evolution of the star.
Mass transfer can be divided into three cases related to the timing
of the onset of RLOF.
- Case A:
- If the orbital separation is small enough
(usually a few days), the star can fill its Roche lobe during its
slow expansion through the main-sequence phase while still burning
hydrogen in its core.
- Case B:
- If the orbital period is less than about
100 days, but longer than a few days, the star will fill its Roche
lobe during the rapid expansion to a red giant with a helium core.
If the helium core ignites during this phase and the transfer is
interrupted, the mass transfer is case BB.
- Case C:
- If the orbital period is above 100 days,
the star can evolve to the red supergiant phase before it fills its
Roche lobe. In this case, the star may have a CO or ONe core.
The typical evolution of the radius for a low
metallicity star is shown in Figure 6. Case A mass transfer
occurs during the slow growth, case B during the first rapid
expansion, and case C during the final expansion phase. The nature
of the remnant depends upon the state of the primary during the
onset of RLOF and the orbital properties of the resultant binary
depend upon the details of the mass transfer.

