# The stability of double white dwarf binaries undergoing direct-impact accretion

#### Abstract

We present numerical simulations of dynamically unstable mass transfer in a double white dwarf binary with initial mass ratio q = 0.4. The binary components are approximated as polytropes of index n = 3/2, and the initially synchronously rotating, semidetached equilibrium binary is evolved hydrodynamically, with the gravitational potential being computed through the solution of Poisson's equation. Upon initiating deep contact in our baseline simulation, the mass transfer rate grows by more than an order of magnitude over approximately 10 orbits, as would be expected for dynamically unstable mass transfer. However, the mass transfer rate then reaches a peak value, the binary expands, and the mass transfer event subsides. The binary must therefore have crossed the critical mass ratio for stability against dynamical mass transfer. Despite the initial loss of orbital angular momentum into the spin of the accreting star, we find that the accretor 's spin saturates and that angular momentum is returned to the orbit more efficiently than has been previously suspected for binaries in the direct-impact accretion mode. To explore this surprising result, we directly measure the critical mass ratio for stability by imposing artificial angular momentum loss at various rates to drive the binary to an equilibrium mass transfer rate. For one of these driven evolutions, we attain equilibrium mass transfer and deduce that, effectively, qcrit has evolved to approximately 2/3. Despite the absence of a fully developed disk, tidal interactions appear to be effective in returning excess spin angular momentum to the orbit. © 2007. The American Astronomical Society. All rights reserved.

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