Star formation is thought to involve both
gravitational infall and subsequent formation and evolution of a
proto-stellar disk. The kinematics of a proto-stellar disk can be
revealed by the gas motions. Low excitation gas in such a disk can be
mapped by emission in the CS J=0
1 line at 49 GHz. At
15K, the surface where the optical depth is unity in this molecule is
likely near 600 AU. For higher temperatures, this surface moves
inward, so that, for example, at 40 K it lies at 150 AU. Thus, the CS
molecule can provide a good probe of outer disk kinematics. To probe
the inner disk one needs a lower opacity transition. This can be
obtained with isotopic CS; using the 
isotope, for example, results
in a factor of 10-20 lower optical depth, providing a probe of the
inner disk.
CS emission could be imaged in a proto-stellar disk with the VLA with
high sensitivity and on arc-second scales; this cannot be easily
addressed with other instruments. Cyanoacetylene (HC
N) has lines
across the cm and mm bands which may also be used to probe disk
kinematics and chemistry. The 
7mm HCN line probes a
particularly interesting region, reaching optical depth unity at 2700
AU for a 40 K gas temperature. Although both of these lines may also
be imaged at millimeter wavelengths, the derivation of physical
conditions in the disk benefits from having images at several
transitions available. Also, the phase stability is better at
7mm than shorter wavelengths, and lower-J transitions will
have lower optical depth, providing a probe better suited to
high-opacity, inner-regions of the disk. Imaging of spectral lines
cannot currently be accomplished in a minimum solar-mass nebula as the
expected disk sizes are too small for the existing VLA. The enormous
improvement in 7mm sensitivity offered by the
VLA Development Plan could result in good images in a single
source transit time.
Formaldehyde (H
CO) may also be extremely useful for the study of
proto-stellar disks. For example, the IRAS4 region of NGC1333
contains two of the youngest stars, or protostars, known, the objects
IRAS4A and IRAS4B. Both still possess the massive disks which signal
ongoing accretion, as well as their infalling (outer) envelopes and
bipolar outflows. Recent observations of several millimeter-wave
transitions as well as VLA ammonia images
allow us to estimate the observability of the proto-stellar disks in
the system. The ortho-formaldehyde column density in the disk appears
to be about N
(o-HCO) = 
at a density of about 
. The warmer source 4A appears to have a disk temperature of
about 250 K, embedded in a less kinematically active core of kinetic
temperature about 100 K. In source 4B the disk appears cooler, about
85 K, while the envelope temperature is lower but poorly determined.
The dust blackbody temperatures of the two sources are 37 K and 27 K,
respectively. Under these conditions, a plot of line intensity
against the upper J quantum number peaks around J=3 or J=4 for the
K-doublet lines we are discussing. The size of the disk is on the
order of 2000 AU or less, necessitating arc-second resolution. The
brightness temperature of the 2cm formaldehyde line will be a
few K, completely beyond the reach of the VLA in any configuration
which will resolve the disk. The 48 GHz line should have a brightness
temperature perhaps 50% higher, however, and could be imaged in a
single transit by the VLA 45 GHz system once it has been installed on
all antennas. The 29 GHz line affords similar possibilities. These
observability estimates should apply to a large number of forming star
systems with proto-stellar disks.