Low Luminosity Companions to White Dwarfs
  This paper presents results of a near-infrared imaging survey for low mass stellar and substellar companions to white dwarfs. A wide field proper motion survey of 261 white dwarfs was capable of directly detecting companions at orbital separations between $\sim100$ and 5000 AU with masses as low as 0.05 $M_{\odot}$, while a deep near field search of 86 white dwarfs was capable of directly detecting companions at separations between $\sim50$ and 1100 AU with masses as low as 0.02 $M_{\odot}$. Additionally, all white dwarf targets were examined for near-infrared excess emission, a technique capable of detecting companions at arbitrarily close separations down to masses of 0.05 $M_{\odot}$.   No brown dwarf candidates were detected, which implies a brown dwarf companion fraction of $<0.5$% for white dwarfs. In contrast, the stellar companion fraction of white dwarfs as measured by this survey is 22%, uncorrected for bias. Moreover, most of the known and suspected stellar companions to white dwarfs are low mass stars whose masses are only slightly greater than the masses of brown dwarfs. Twenty previously unknown stellar companions were detected, five of which are confirmed or likely white dwarfs themselves, while fifteen are confirmed or likely low mass stars.   Similar to the distribution of cool field dwarfs as a function of spectral type, the number of cool unevolved dwarf companions peaks at mid-M type. Based on the present work, relative to this peak, field L dwarfs appear to be roughly 2-3 times more abundant than companion L dwarfs. Additionally, there is no evidence that the initial companion masses have been altered by post main sequence binary interactions. 
J. Farihi, E.E. Becklin, B. Zuckerman