Binary star origin of high field magnetic white dwarfs

White dwarfs with surface magnetic fields in excess of 1 MG are found as isolated single stars and relatively more often in magnetic cataclysmic variables (CVs). Some 1253 white dwarfs with a detached low-mass main-sequence companion are identified in the Sloan Digital Sky Survey (SDSS) but none of these is observed to show evidence for Zeeman splitting of hydrogen lines associated with a magnetic field in excess of 1 MG. If such high magnetic fields on white dwarfs result from the isolated evolution of a single star, then there should be the same fraction of high field magnetic white dwarfs among this SDSS binary sample as among single stars. Thus, we deduce that the origin of such high magnetic fields must be intimately tied to the formation of CVs. The formation of a CV must involve orbital shrinkage from giant star to main-sequence star dimensions. It is believed that this shrinkage occurs as the low-mass companion and the white dwarf spiral together inside a common envelope. CVs emerge as very close but detached binary stars that are then brought together by magnetic braking or gravitational radiation. We propose that the smaller the orbital separation at the end of the common envelope phase, the stronger the magnetic field. The magnetic CVs originate from those common envelope systems that almost merge. We propose further that those common envelope systems that do merge are the progenitors of the single high field magnetic white dwarfs. Thus, all highly magnetic white dwarfs, be they single stars or the components of magnetic CVs, have a binary origin. This hypothesis also accounts for the relative dearth of single white dwarfs with fields of 10⁴-10⁶ G. Such intermediate-field white dwarfs are found preferentially in CVs. In addition, the bias towards higher masses for highly magnetic white dwarfs is expected if a fraction of these form when two degenerate cores merge in a common envelope. Similar scenarios may account for very high field neutron stars. From the space density of single highly magnetic white dwarfs we estimate that about three times as many common envelope events lead to a merged core as to a CV.