We present the results of a three-dimensional numerical simulation of the evolution of a doubly degenerate binary system in which the primary is a 1.2 M⊙ white dwarf and the Roche lobe filling secondary a 0.9 M⊙ white dwarf. The beginning of our simulation corresponds to the time at which the secondary fills its Roche lobe and mass transfer starts. No attempts have been made to include further loss of angular momentum due to gravitational wave radiation. The hydrodynamical equations were solved with a smooth particle hydrodynamics code using 7000 particles. Since the evolution of the system is determined mostly by angular momentum transport, we first present some tests to demonstrate that no spurious angular momentum transport occurs on a time scale corresponding to the simulation. The results show that in a little more than two orbital periods the secondary is completely destroyed and transformed into a thick disk orbiting about the primary. Since only a very small fraction of the mass (0.0063 M⊙) escapes the system, the evolution of the binary results in the formation of a massive object. This object is, however, not in a state of collapse. We show that it is roughly composed of three parts, the initial white dwarf primary, a very hot pressure-supported spherical envelope, and a rotationally supported outer disk. However, temperatures in the outer parts of the initial primary and in the envelope are very high, in fact, above carbon burning threshold. This suggests that further improvements in the physics included in this model are necessary to draw final conclusions about the structure of the merged object. The evolution of the system can, however, be understood in terms of a simple analytical model where it is shown that the angular momentum carried by the mass during the transfer and stored in the disk is a very important component which cannot be neglected. In fact the amount stored in the disk determines for a large part the evolution of the system.
