The VLA Nascent Disk And Multiplicity Survey of Perseus Protostars
  (VANDAM). III. Extended Radio Emission from Protostars in Perseus
  Centimeter continuum emission from protostars offers insight into the
innermost part of the outflows, as shock-ionized gas produces free-free
emission. We observed a complete population of Class 0 and I protostars in the
Perseus molecular cloud at 4.1 cm and 6.4 cm with resolution and sensitivity
superior to previous surveys. From a total of 71 detections, 8 sources exhibit
resolved emission at 4.1 cm and/or 6.4 cm. In this paper we focus on this
sub-sample, analyzing their spectral indices along the jet, and their alignment
with respect to the large-scale molecular outflow. Spectral indices for fluxes
integrated toward the position of the protostar are consistent with free-free
thermal emission. The value of the spectral index along a radio jet decreases
with distance from the protostar. For six sources, emission is well aligned
with the outflow central axis, showing that we observe the ionized base of the
jet. This is not the case for two sources, where we note misalignment of the
emission with respect to the large-scale outflow. This might indicate that the
emission does not originate in the radio jet, but rather in an ionized outflow
cavity wall or disk surface. For five of the sources, the spectral indices
along the jet decrease well below the thermal free-free limit of -0.1 with
$>2\sigma$ significance. This is indicative of synchrotron emission, meaning
that high energy electrons are being produced in the outflows close to the
disk. This result can have far-reaching implications for the chemical
composition of the embedded disks.
