Modelling the closest double degenerate system RXJ0806.3+1527 and its   decreasing period
  In the hypothesis that the 5.4m binary RXJ0806.3+1527 consists of a low mass helium white dwarf (donor) transferring mass towards its more massive white dwarf companion (primary), we consider as possible donors white dwarfs which are the result of common envelope evolution occurring when the helium core mass of the progenitor giant was still very small (~ 0.2Msun), so that they are surrounded by a quite massive hydrogen envelope (~1/100Msun or larger), and live for a very long time supported by proton--proton burning. Mass transfer from such low mass white dwarfs very probably starts during the hydrogen burning stage, and the donor structure will remain dominated by the burning shell until it loses all the hydrogen envelope and begins transferring helium. We model mass transfer from these low mass white dwarfs, and show that the radius of the donor decreases while they shed the hydrogen envelope. This radius behavior, which is due to the fact that the white dwarf is not fully degenerate, has two important consequences on the evolution of the binary: 1) the orbital period decreases, with a timescale consistent with the period decrease of the binary RXJ0806.3+1527; 2) the mass transfer rate is a factor of about 10 smaller than from a fully degenerate white dwarf, easing the problem connected with the small X-ray luminosity of this object. The possibility that such evolution describes the system RXJ0806.3+1527 is also consistent with the possible presence of hydrogen in the optical spectrum of the star, whose confirmation would become a test of the model. 
F. D'Antona, P. Ventura, L. Burderi & A. Teodorescu