1. Mass Transfer in Close Binary Star Systems Isaac Schultz ME 547 Dr. Derek Tretheway June 4, 2015

2. The Algol Paradox Binary star systems were observed in which less massive star was further developed than more massive star The more mass a star has, the quicker it will evolve through its life cycle This observation presented a serious problem to scientists for many years 19 th century French astronomer Eduard Roche developed a model describing the mass transfer between binary stars More massive, younger star Less massive, older star

3. The Algol Paradox- Solved Roche found that the reason the less massive star was younger than its partner was that it had originally been more massive before mass transfer Mass transfer between two stars in a binary system allows for the originally more massive star to become less massive than its partner Roche developed a model for this unique mass transfer process starting from first principles

4. Close Binary Systems & Roche Lobes Any binary system in which the mass ratio of the stars will allow for mass transfer at some point in their lifetime is known as a “close binary system” Mass transfer in close binaries is mainly governed by gravity At some point in a stars life as it fuses through its fuel, pressure from the core will cause matter towards the surface of the star to be pushed into the surrounding space When mass from one star gets close enough to its partner star it will be pulled towards it, facilitating mass transfer

5. Assumptions in Modeling Roche Lobe Overflow Many assumptions need to be made in order to have any hope at modeling the processes involved in mass transfer in close binary systems Spherical orbits, the existence of a critical Roche lobe and Lagrangian points, conservation of mass and angular momentum

6. The Roche Model for Close Binary Systems Consider a test particle between two stars, with a coordinate system rotating with stars orbit The potential between the stars includes the gravitational potentials from each star in addition to the Coriolis force to account for any motion of the particle relative to the rotating coordinate system

7. Roche Equipotentials By setting the Roche potential equal to a constant, equipotential lines can be drawn When these equipotential lines meet, mass transfer can occur between the stars Whichever potential value results in intersecting equipotentials is defined as the critical Roche radius The size of the non-spherical Roche lobe is conveniently defined by a “Roche lobe radius” Critical Roche Surface and first two Lagrangian points

8. Critical Lagrangian Points in the Roche Potential Mass transfer will occur at critical points in the Roche radius, which occur at the solutions to Critical points in the Roche potential are called Lagrangian points and represent unstable equilibrium points in the space between the stars Any mass located near a Lagrangian point is subject to being transported between stars or being ejected from the system Stable equilibrium points Unstable equilibrium points

9. Predicting the Roche Radius Kobal tabulated the critical radius of some close binary systems in a 1959 journal article Pacyznski 1971 came up with a model to predict the critical radius based on the mass ratio Eggelton 1983 used a numerical method to arrive at a similar result to Pacyznski

10. Time scale of mass transfer between close binary stars Paczynski used 24 model close binary stars to determine time scales of the mass transfer in this process Initially, mass transfer between the stars is rapid and takes place on the Kelvin-Helmholtz time scale Kelvin-Helmholtz time scale represents the time it takes for a star to radiate away a large amount of its energy (≈30 million years for our sun)

11. What happens next? After mass transfer begins, the size of the Roche lobe will change due to the changing mass of the stars If the star looses mass too quickly, its Roche lobe will shrink faster than the physical star and the star may disintegrate If the star looses mass slowly, it will shrink down to a smaller size than its Roche lobe, ending mass transfer In order for steady mass transfer to occur the mass the size of the star must remain equal to its Roche lobe

12. Mass Transfer in Close Binary Star Systems Isaac Schultz ME 547 Dr. Derek Tretheway June 4, 2015