The VLA Nascent Disk and Multiplicity Survey of Perseus Protostars
  (VANDAM). II. Multiplicity of Protostars in the Perseus Molecular Cloud
  We present a multiplicity study of all known protostars (94) in the Perseus
molecular cloud from a Karl G. Jansky Very Large Array (VLA) survey at Ka-band
(8 mm and 1 cm) and C-band (4 cm and 6.6 cm). The observed sample has a
bolometric luminosity range between 0.1 L$_{\odot}$ and $\sim$33 L$_{\odot}$,
with a median of 0.7 L$_{\odot}$. This multiplicity study is based on the
Ka-band data, having a best resolution of $\sim$0.065" (15 AU) and separations
out to $\sim$43" (10000 AU) can be probed. The overall multiplicity fraction
(MF) is found to be of 0.40$\pm$0.06 and the companion star fraction (CSF) is
0.71$\pm$0.06. The MF and CSF of the Class 0 protostars are 0.57$\pm$0.09 and
1.2$\pm$0.2, and the MF and CSF of Class I protostars are both 0.23$\pm$0.08.
The distribution of companion separations appears bi-modal, with a peak at
$\sim$75 AU and another peak at $\sim$3000 AU. Turbulent fragmentation is
likely the dominant mechanism on $>$1000 AU scales and disk fragmentation is
likely to be the dominant mechanism on $<$200 AU scales. Toward three Class 0
sources we find companions separated by $<$30 AU. These systems have the
smallest separations of currently known Class 0 protostellar binary systems.
Moreover, these close systems are embedded within larger (50 AU to 400 AU)
structures and may be candidates for ongoing disk fragmentation.
