Binary evolution using the theory of osculating orbits

I. Conservative Algol evolution^⋆

¹ Institut d’Astronomie et d’Astrophysique (IAA), Université Libre de Bruxelles (ULB), CP226, boulevard du Triomphe, 1050 Brussels, Belgium
e-mail: pdavis@ulb.ac.be
² ESO Vitacura, avenue Alonso de Córdova 3107, Vitacura, Casilla 19001, Santiago de Chile, Chile

Received: 28 February 2014
Accepted: 20 August 2014

Abstract

Context. Studies of conservative mass transfer in interacting binary systems widely assume that orbital angular momentum is conserved. However, this only holds under physically unrealistic assumptions.

Aims. Our aim is to calculate the evolution of Algol binaries within the framework of the osculating orbital theory, which considers the perturbing forces acting on the orbit of each star arising from mass exchange via Roche lobe overflow. The scheme is compared to results calculated from a “classical” prescription.

Methods. Using our stellar binary evolution code BINSTAR, we calculate the orbital evolution of Algol binaries undergoing case A and case B mass transfer, by applying the osculating scheme. The velocities of the ejected and accreted material are evaluated by solving the restricted three-body equations of motion, within the ballistic approximation. This allows us to determine the change of linear momentum of each star, and the gravitational force applied by the mass transfer stream. Torques applied on the stellar spins by tides and mass transfer are also considered.

Results. Using the osculating formalism gives shorter post-mass transfer orbital periods typically by a factor of 4 compared to the classical scheme, owing to the gravitational force applied onto the stars by the mass transfer stream. Additionally, during the rapid phase of mass exchange, the donor star is spun down on a timescale shorter than the tidal synchronization timescale, leading to sub-synchronous rotation. Consequently, between 15 and 20 per cent of the material leaving the inner-Lagrangian point is accreted back onto the donor (so-called “self-accretion”), further enhancing orbital shrinkage. Self-accretion, and the sink of orbital angular momentum which mass transfer provides, may potentially lead to more contact binaries. Even though Algols are mainly considered, the osculating prescription is applicable to all types of interacting binaries, including those with eccentric orbits.