Evolution of a bi nary system.
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.
Figure 5: Cross section of equipotential surfaces in the orbital plane
of a binary with . The values of the potential surfaces are 5.0, 3.9075,
3.8, 3.559, 3.2, 3.0, and 2.8. The units have been normalized to the orbital
separation, so .
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.
More to come...
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