[Paper Review] Binary evolution using the theory of osculating orbits: conservative Algol evolution

Philip Davis, L. Siess+1 more|arXiv (Cornell University)|Aug 19, 2014

Stellar, planetary, and galactic studies4 citations

TL;DR

This paper introduces an osculating orbital formalism for modeling conservative mass transfer in Algol binaries, accounting for gravitational forces from the mass transfer stream and spin-orbit coupling. It shows that orbital shrinkage is significantly enhanced—by a factor of ~4—due to stream-induced torques and self-accretion, leading to shorter post-mass-transfer periods than predicted by classical models.

ABSTRACT

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 (RLOF). The scheme is compared to results calculated from a `classical' prescription. 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. 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.

Motivation & Objective

• To develop a physically consistent model of binary evolution that accounts for perturbing forces during Roche lobe overflow (RLOF), challenging the classical assumption of orbital angular momentum conservation.
• To investigate how gravitational forces from the mass transfer stream affect orbital evolution and stellar spins in Algol systems.
• To quantify the role of self-accretion (material returning to the donor) in enhancing orbital shrinkage during rapid mass transfer.
• To assess the impact of non-synchronous stellar rotation on orbital evolution and system stability.
• To provide a general framework applicable to all interacting binaries, including eccentric systems, beyond just Algol-type binaries.

Proposed method

• Uses the theory of osculating orbital elements to model time-varying orbital parameters under perturbing forces from mass transfer streams.
• Applies the restricted three-body equations of motion within a ballistic approximation to compute the velocity and momentum of ejected and accreted material.
• Calculates the gravitational force exerted by the mass transfer stream on each star, determining the resulting torque on the orbit via Eq. (63).
• Incorporates tidal torques and spin-orbit coupling, allowing for non-synchronous rotation of the donor star during mass transfer.
• Solves for the net change in orbital angular momentum using Eq. (66), which separates contributions from RLOF and mass loss.
• Compares results from the osculating formalism against the classical conservative mass transfer prescription, particularly in the limit of point masses and zero stream forces.

Experimental results

Research questions

• RQ1 How does the inclusion of stream-induced gravitational forces alter the orbital evolution of Algol binaries during conservative mass transfer?
• RQ2 To what extent does self-accretion (material returning to the donor) contribute to orbital shrinkage in systems with sub-synchronous rotation?
• RQ3 What is the impact of non-synchronous rotation on the orbital period evolution during rapid mass transfer?
• RQ4 Under what conditions does the classical assumption of angular momentum conservation break down in binary evolution?
• RQ5 How does the osculating formalism improve the prediction of post-mass-transfer orbital periods compared to classical models?

Key findings

• The osculating formalism predicts post-mass-transfer orbital periods that are typically ~4 times shorter than those from the classical model due to stream-induced torques.
• During rapid mass transfer, the donor star is spun down faster than tides can synchronize it, resulting in sub-synchronous rotation on a timescale shorter than the tidal timescale.
• Between 15% and 20% of the material leaving the inner Lagrangian point is accreted back onto the donor star, a phenomenon termed 'self-accretion'.
• Self-accretion and the sink of orbital angular momentum via the stream lead to enhanced orbital shrinkage, potentially increasing the formation rate of contact binaries.
• The classical assumption of angular momentum conservation fails unless the stars are point masses, the stream force is neglected, and the accretion velocity is exactly opposite to the orbital velocity.
• The formalism is general and applicable to all interacting binaries, including those with eccentric orbits, not limited to Algol-type systems.