A Binary Teetering on the Edge

We present a fully three-dimensional hydrodynamical simulation of Roche lobe overflow in a binary near the stability boundary. This boundary separates evolutionary branches that correspond to either an accelerating mass transfer rate leading eventually to merger through tidal instability or to a decaying mass transfer rate as the orbit expands. The binary begins with a mass ratio of 0.4 (ratio of donor to accretor mass) and is initially assumed to be rotating synchronously. We treat the stellar components as simple polytropic fluids characterized by a polytropic index, n = 3/2. As the donor overflows its Roche lobe, the mass transfer rate initially accelerates before stabilizing and eventually dropping over a timescale of tens of orbits. We also note that for this particular binary, the accretion stream impacts on the surface of the donor rather than forming an accretion disk. This simulation allows us to measure the efficiency with which the accretion stream spins up the accretor in this "direct impact" scenario and the degree to which angular momentum is transfered back to the binary orbit via the tidal field.