Gravitational Potentials
How can matter be transferred from one star to the other in a binary system? To answer that question
we must consider the total gravitational force acting on a particle of gas in one of the stars.
Competing Forces
By the law of gravitation, every object attracts every other object in the
Universe. In a binary star system, if the masses are large enough and the
separations small enough,
a gas particle at a large radius in one star may feel a
gravitational force from the other star that is comparable to or even larger than
that from its "own" star. In that case, the gas particle is unstable against being
transferred from one star to the other. The diagram shown above illustrates the
competition between forces exerted on a gas particle by the two members of a binary.
Potential Energy Contours
This competition
can be understood by considering the total potential energy generated by the
gravitational fields of the two stars.
The adjacent figure plots contours of equal gravitational potential (all points on a given contour
correspond to exactly the same gravitational potential energy).
The center of mass is marked with an "x". The
point labeled as the inner Lagrange point is a
point where one unique potential energy contour intersects itself. If a star
expands sufficiently to place matter near the inner Lagrange point, accretion can
occur onto the other star. Astronomers commonly refer to the inner Lagrange point by the
shorthand designation L1.
