
Evolutionary processes in binary star systems, including mass transfer and interactions.Binary stellar evolution covers the life cycles of stars that are gravitationally bound in pairs, where interactions such as mass transfer, common-envelope phases, and tidal effects dramatically alter their evolution compared to single stars. These processes produce exotic objects like X-ray binaries, millisecond pulsars, and merging black holes. The study of binary evolution is crucial for understanding stellar populations, supernova rates, and gravitational wave sources.
The theoretical framework was developed in the 1960s–1970s by researchers like Zdeněk Kopal and Bohdan Paczyński, with later refinements from observations of X-ray binaries and pulsars.
When a star in a binary expands (e.g., as a red giant), it can fill its Roche lobe, transferring mass to its companion. This mass transfer can spin up the companion, strip the donor's envelope, or lead to a common-envelope phase where the two stars spiral together. Magnetic braking and gravitational wave emission can also shrink the orbit, leading to eventual mergers or supernovae that kick the system.
Binary evolution models predict the rates and properties of gravitational wave sources (like black hole mergers) detected by LIGO and Virgo, and explain the formation of recycled pulsars used in precision timing arrays.
Some binary stars merge to form a single, rapidly rotating star that can mimic a young star, a phenomenon known as 'blue stragglers' in old clusters.
| \dot{\omega} | variable | rate of periastron advance — angular velocity radian per second |
| M | variable | total mass of the binary system — mass kilogram |
| a | variable | semi-major axis of the orbit — length metre |
| e | variable | orbital eccentricity — eccentricity |
| G | constant | Constant of universal gravitation. — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared |
| c | constant | Speed of light in vacuum. — speed of light = 299792458 metre per second |
| M | variable | Mass of the donor star — mass kilogram |
| M_dot | variable | Time derivative of the donor mass — mass loss rate kilogram per second |
| J | variable | Orbital angular momentum of the binary — angular momentum kilogram square metre per second |
| J_dot | variable | Time derivative of the orbital angular momentum — angular momentum loss rate kilogram square metre per second squared |
| zeta | variable | Mass-radius exponent of the donor star — mass radius exponent |
| zeta_L | variable | Mass-radius exponent of the Roche lobe — roche lobe mass radius exponent |
| \dot{J} | variable | Angular momentum loss rate — angular momentum loss rate kilogram metre squared per second square |
| \dot{M} | variable | Mass transfer rate — mass transfer rate kilogram per second |
| M_1 | variable | Mass of the primary star — mass kilogram |
| M_2 | variable | Mass of the secondary star — mass kilogram |
| a | variable | Orbital separation — length metre |
| P | variable | Orbital period — time second |
| q | variable | Mass ratio of the binary system — mass ratio |
| m_2 | variable | Mass of the secondary component — mass kilogram |
| m_1 | variable | Mass of the primary component — mass kilogram |


















