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During post-main-sequence evolution, radial expansion of the primary star,accompanied by intense winds, can significantly alter the binary orbit viatidal dissipation and mass loss. The fate of a given binary system isdetermined by the initial masses of the primary and companion, the initialorbit (taken to be circular), the Reimers mass-loss parameter, and the tidalprescription employed. For a range of these parameters, we determine whetherthe orbit expands due to mass loss or decays due to tidal torques. Where acommon envelope (CE) phase ensues, we estimate the final orbital separationbased on the energy required to unbind the envelope. These calculations predictperiod gaps for planetary and brown dwarf companions to white dwarfs. Inparticular, the lower end of the gap is the longest period at which companionssurvive their CE phase while the upper end of the gap is the shortest period atwhich a CE phase is avoided. For binary systems with 1 $M_\odot$ progenitors,we predict no Jupiter-mass companions with periods $\lesssim$270 days. Forbinary systems consisting of a 1 $M_\odot$ progenitor with a 10 Jupiter-masscompanion, we predict a close, post-CE population with periods $\lesssim$0.1days and a far population with periods $\gtrsim$380 days. These results areconsistent with the detection of a $\sim$50 $M_{\rm J}$ brown dwarf in a$\sim$0.08 day orbit around the white dwarf WD 0137-349 and the tentativedetection of a $\sim$2 $M_{\rm J}$ planet in a $\sim$4 year orbit around thewhite dwarf GD66.

Two Populations of Companions around White Dwarfs: The Effect of Tides and Tidal Engulfment