Prediction of period gap around white dwarfs

Tides and Tidal Capture in post-Main Sequence Binaries: A Period Gap for Planets Around White Dwarfs
http://arxiv.org/abs/1002.2216

Abstract wrote:

The presence of a close, low-mass companion is thought to play a substantial and perhaps necessary role in shaping post-Asymptotic Giant Branch and Planetary Nebula outflows. During post-main-sequence evolution, radial expansion of the primary star, accompanied by intense winds, can significantly alter the binary orbit via tidal dissipation and mass loss. To investigate this, we couple stellar evolution models (from the zero-age main-sequence through the end of the post-main sequence) to a tidal evolution code. The binary's fate is determined by the initial masses of the primary and the companion, the initial orbit (taken to be circular), and the Reimer's mass-loss parameter. For a range of these parameters, we determine whether the orbit expands due to mass loss or decays due to tidal torques. Where a common envelope phase (CEP) ensues, we estimate the final orbital separation based on the energy required to unbind the envelope. These calculations predict a period gap for planetary companions to white dwarfs. The upper end of the gap is the shortest period at which a CEP is avoided. The lower end is the longest period at which companions survive their CEP. We predict a paucity of planetary companions with periods between $\sim130$ days ($\sim0.35$ AU) and $\sim250$ days ($\sim0.6$ AU) around white dwarfs. This is consistent with the tentative detection of an $\sim2$ $M_{\rm J}$ planet in an $\gtrsim 2.7$ AU orbit around GD66.