Numerical stability of mass transfer driven by Roche lobe overflow in close binaries

Abstract

Numerical computation of the time evolution of the mass transfer rate in a close binary can be and, in particular, has been a computational challenge. Using a simple physical model to calculate the mass transfer rate, we show that for a simple explicit iteration scheme the mass transfer rate is numerically unstable unless the time steps are sufficiently small. In general, more sophisticated explicit algorithms do not provide any significant improvement since this instability is a direct result of time discretization. For a typical binary evolution, computation of the mass transfer rate as a smooth function of time limits the maximum tolerable time step and thereby sets the minimum total computational effort required for an evolutionary computation. By methods of ``Controlling Chaos'' it can be shown that a specific implicit iteration scheme, based on Newton's method, is the most promising solution for the problem.

6 pages, LaTeX, two eps figures, Astronomy and Astrophysics, accepted

References in corpus (3)

• AE Aquarii: how CVs descend from supersoft binaries
• Long-term evolution of compact binaries with irradiation feedback
• A Code for Stellar Binary Evolution and its Application to the Formation of Helium White Dwarfs

Cited by in corpus (7)

• The Evolution of Compact Binary Star Systems
• The Evolution of Compact Binary Star Systems
• A Binary Progenitor for the Type IIb Supernova 2011dh in M51
• Understanding the evolution of close binary systems with radio pulsars
• The Thermal Evolution of the Donors in AM CVn Binaries
• A theory of mass transfer in binary stars
• Astrophysics in 2006