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=01 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 (HCN) 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 (HCO) 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.