Modeling the closest double degenerate system RX J0806.3+1527 and its decreasing period

With the hypothesis that the 5.4 minute binary RX J0806.3+1527 consists of a low-mass helium white dwarf (donor) transferring mass toward its more massive white dwarf companion (primary), we consider as possible donors white dwarfs that are the result of common-envelope evolution, which occurs when the helium core mass of the progenitor giant is still very small (less than or similar to 0.2M(circle dot)), so that they are surrounded by a quite massive hydrogen envelope (similar or equal to 1/100 M-circle dot 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 of 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 it sheds the hydrogen envelope. This radius behavior, which is due to the fact that the white dwarf is not fully degenerate, has two important consequences for the evolution of the binary: (1) the orbital period decreases, with a timescale consistent with the period decrease of the binary RX J0806+15, and (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 an evolution describes the system RX J0806+15 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.