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The SeBa stellar and binary evolution module
(page under development)
Evolution of single stars
The stellar and binary evolution package SeBa is fully
integrated into the kira integrator, although it can also be
used as a stand-alone module for non-dynamical applications.
Synchronous evolution of two stars
Stars are evolved via the time dependent mass-radius relations for
solar metallicities given by Eggleton
et al. (1989) with corrections by Eggleton
et al. 1990 and Tout
et al. 1997)
These equations give the radius of a star as a function of time and
the star's initial mass (on the zero-age main-sequence).
Neither the mass of the stellar core nor the rate of mass loss via a
stellar wind are specified in this prescription. However, both
quantities are important, both to binary evolution and to cluster
dynamics. We include them using the prescriptions of
Portegies Zwart & Verbunt (1996).
In the code the following stellar types are identified:
- proto star (0) Non hydrogen burning stars on the
- planet (1) Various types, such as gas giants, etc.; also
- brown dwarf (2) Star with mass below the hydrogen-burning limit.
- main sequence (3) Core hydrogen burning star.
- Hypergiant (4) Massive (m>25Msun) post main
sequence star with enormous mass-loss rate in a stage of
evolution prior to becoming a Wolf-Rayet star.
- Hertzsprung gap (5) Rapid evolution from the
Terminal-age main sequence to the point when the
hydrogen-depleted core exceeds the Schonberg-Chandrasekhar
- sub giant (6) Hydrogen shell burning star.
- horizontal branch (7) Helium core burning star.
- supergiant (8) Double shell burning star.
- helium star (9-11) Helium core of a stripped giant, the
result of mass transfer in a binary.
Subdivided into carbon core (9), helium
dwarf (10) and helium giant
- white dwarf (12-14) Subdivided into
carbon dwarf (12) , helium dwarf
(13) and oxygen dwarf (13).
- Thorne-Zytkow (15) Shell burning hydrogen
envelope with neutron star core.
- neutron star (16-18)
Subdivided into X-ray pulsar (16), radio
pulsar (17) and inert neutron (18)
- black hole (19) Star with radius smaller than the event
horizon. The result of evolution of massive
(m>25Msun) star or collapsed neutron
- disintegrated (20) Result of Carbon detonation to
Type Ia supernova.
Evolution of clusters of stars
Inerface with Kira
Due to the interaction between stellar evolution and stellar dynamics,
it is difficult to solve for the evolution of both systems in a
completely self-consistent way. The trajectories of stars are
computed using a block timestep scheme, as described earlier. Stellar
and binary evolution is updated at fixed intervals (every 1/64 of a
crossing time, typically a few thousand years). Any feedback between
the two systems may thus experience a delay of at most one timestep.
Internal evolution time steps may differ for each star and binary, and
depend on binary period, perturbations due to neighbors, and the
evolutionary state of the star. Time steps in this treatment vary
from several milliseconds up to (at most) a million years.
After each 1/64 of a crossing time, all stars and binaries are
checked to determine if evolutionary updates are required. Single
stars are updated every 1/100 of an evolution timestep or when the
mass of the star has changed by more than 1% since the last update.
A stellar evolution timestep is the time taken for the star to evolve
from the start of one evolutionary stage to the next.
After each stellar evolution step the dynamics is notified of changes
in stellar radii, but changes in mass are, for reasons of efficiency,
not passed back immediately (mass changes generally entail recomputing
the accelerations of all stars in the system). Instead, the
``dynamical'' masses are modified only when the mass of any star has
changed by more than 1%, or if the orbital parameters, semi-major
axis, eccentricity, total mass or mass ratio of any binary has changed
by more than 0.1%.