We perform deep 1.8 cm radio continuum imaging towards thirteen protostellar
regions selected from the Spitzer c2d small clouds and cores programme at high
resolution (25") in order to detect and quantify the cm-wave emission from
deeply embedded young protostars. Within these regions we detect fifteen
compact radio sources which we identify as radio protostars including two
probable new detections. The sample is in general of low bolometric luminosity
and contains several of the newly detected VeLLO sources. We determine the 1.8
cm radio luminosity to bolometric luminosity correlation, L_rad -L_bol, for the
sample and discuss the nature of the radio emission in terms of the available
sources of ionized gas. We also investigate the L_rad-L_IR correlation and
suggest that radio flux density may be used as a proxy for the internal
luminosity of low luminosity protostars.Comment: submitted MNRA