On the Orbits of Low-mass Companions to White Dwarfs and the Fates of   the Known Exoplanets
  The ultimate fates of binary companions to stars (including whether the companion survives and the final orbit of the binary) are of interest in light of an increasing number of recently discovered, low-mass companions to white dwarfs (WDs). In this Letter, we study the evolution of a two-body system wherein the orbit adjusts due to structural changes in the primary, dissipation of orbital energy via tides, and mass loss during the giant phases; previous studies have not incorporated changes in the primary's spin. For companions ranging from Jupiter's mass to ~0.3 Msun and primaries ranging from 1-3 Msun, we determine the minimum initial semimajor axis required for the companion to avoid engulfment by the primary during post-main-sequence evolution, and highlight the implications for the ultimate survival of the known exoplanets. We present regions in secondary mass and orbital period space where an engulfed companion might be expected to survive the common envelope phase (CEP), and compare with known M dwarf+WD short-period binaries. Finally, we note that engulfed Earth-like planets cannot survive a CEP. Detection of a first-generation terrestrial planet in the white dwarf habitable zone requires scattering from a several-AU orbit to a high-eccentricity orbit (with a periastron of ~Rsun) from which it is damped into a circular orbit via tidal friction, possibly rendering it an uninhabitable, charred ember. 
J. Nordhaus, D. S. Spiegel
astro-ph.SR astro-ph.EP