AMI-LA radio continuum observations of Spitzer c2d small clouds and
  cores: Serpens region
  We present deep radio continuum observations of the cores identified as
deeply embedded young stellar objects in the Serpens molecular cloud by the
Spitzer c2d programme at a wavelength of 1.8cm with the Arcminute Microkelvin
Imager Large Array (AMI-LA). These observations have a resolution of ~30arcsec
and an average sensitivity of 19microJy/beam. The targets are predominantly
Class I sources, and we find the detection rate for Class I objects in this
sample to be low (18%) compared to that of Class 0 objects (67%), consistent
with previous works. For detected objects we examine correlations of radio
luminosity with bolometric luminosity and envelope mass and find that these
data support correlations found by previous samples, but do not show any
indiction of the evolutionary divide hinted at by similar data from the Perseus
molecular cloud when comparing radio luminosity with envelope mass. We conclude
that envelope mass provides a better indicator for radio luminosity than
bolometric luminosity, based on the distribution of deviations from the two
correlations. Combining these new data with archival 3.6cm flux densities we
also examine the spectral indices of these objects and find an average spectral
index of 0.53+/-1.14, consistent with the canonical value for a partially
optically thick spherical or collimated stellar wind. However, we caution that
possible inter-epoch variability limits the usefulness of this value, and such
variability is supported by our identification of a possible flare in the radio
history of Serpens SMM 1.
