The VLA Nascent Disk And Multiplicity Survey of Perseus Protostars
  (VANDAM). IV. Free-Free Emission from Protostars: Links to Infrared
  Properties, Outflow Tracers, and Protostellar Disk Masses
  Emission from protostars at centimeter radio wavelengths has been shown to
trace the free-free emission arising from ionizing shocks as a result of jets
and outflows driven by protostars. Therefore, measuring properties of
protostars at radio frequencies can provide valuable insights into the nature
of their outflows and jets. We present a C-band (4.1 cm and 6.4 cm) survey of
all known protostars (Class 0 and Class I) in Perseus as part of the VLA
Nascent Disk and Multiplicity (VANDAM) Survey. We examine the known
correlations between radio flux density and protostellar parameters such as
bolometric luminosity and outflow force, for our sample. We also investigate
the relationship between radio flux density and far-infrared line luminosities
from Herschel. We show that free-free emission originates most likely from
J-type shocks; however, the large scatter indicates that those two types of
emission probe different time and spatial scales. Using C-band fluxes, we
removed an estimation of free-free contamination from the corresponding Ka-band
(9 mm) flux densities that primarily probe dust emission from embedded disks.
We find that the compact ($<$~1") dust emission is lower for Class I sources
(median dust mass 96 M$_{\oplus}$) relative to Class 0 (248 M$_{\oplus}$), but
several times higher than in Class II (5-15 M$_{\oplus}$). If this compact dust
emission is tracing primarily the embedded disk, as is likely for many sources,
this result provides evidence for decreasing disk masses with protostellar
evolution, with sufficient mass for forming giant planet cores primarily at
early times.
