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 Hyashi track
• planet (1) Various types, such as gas giants, etc.; also includes moons.
• 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 limit.
• 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 (11).
• 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) star (m<2Msun).
• black hole (19) Star with radius smaller than the event horizon. The result of evolution of massive (m>25Msun) star or collapsed neutron star.
• 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%.