The minimum mass ratio of W UMatype binary systems
Abstract
When the total angular momentum of a binary system J_{tot} = J_{orb} + J_{spin} is at a certain critical (minimum) value, a tidal instability occurs which eventually forces the stars to merge into a single, rapidly rotating object. The instability occurs when J_{orb} = 3J_{spin}, which in the case of contact binaries corresponds to a minimum mass ratio q_{min} ~ 0.0710.078. The minimum mass ratio is obtained under the assumption that stellar radii are fixed and independent. This is not the case with contact binaries where, according to the Roche model, we have R_{2} = R_{2}(R_{1}, a, q). By finding a new criterion for contact binaries, which arises from dJ_{tot} = 0, and assuming k^{2}_{1} ≠ k^{2}_{2} for the component's dimensionless gyration radii, a theoretical lower limit q_{min} = 0.0940.109 for overcontact degree f = 01 is obtained.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 June 2007
 DOI:
 10.1111/j.13652966.2007.11723.x
 Bibcode:
 2007MNRAS.377.1635A
 Keywords:

 instabilities;
 methods: analytical;
 binaries: close;
 blue stragglers