Scattering in a parabolic encounter of a single star with a circular binary

Abstract

Huang and Valtonen (1987) obtained an analytic expression for the energy transfer in a parabolic encounter of a single star with a circular binary keeping terms of the first order in a/q where a is the radius of the circular orbit and q is the distance of closest approach of the single star with respect to the centre of mass of the binary. They also obtained numerically the energy transfer and change in eccentricity of the single star for the case of mass of the binary equal to the mass of the single star. We extend their analytic treatment to obtain angular momentum transfer and change in eccentricity up to first order a/q and compare the change in eccentricity obtained by us with theirs. We find that our first order analysis is reasonable for Q=q/a > 2.5 for direct orbit and Q > 1.125 for retrograde orbit.