THE POSITION VELOCITY DIAGRAMS OF PROTOSTELLAR DISKS

We discuss the expected appearance of centrifugally supported astrophysical discs observed in optically thin line emission, with particular emphasis on the molecular line emission arising from protostellar discs. If spectra are taken along the (known) long axis of the projected disc, which is assumed to be unresolved perpendicular to this direction, then the resulting two-dimensional data set I(x, v), (the position-velocity, or l-v, diagram) describes the emission. Using a simple kinematic description of line formation in a rotating disc, we first present theoretical l-v diagrams and compare them with l-v diagrams recently reported in the literature which are claimed to represent rotating protostellar discs; the differences between the observed and predicted l-v diagrams are discussed. Since observations of the l-v diagrams of discs are an attractive way of studying disc structure, we go on to suggest methods of deriving the properties of discs (emissivity and mass as a function of radius) from the observed l-v diagrams; the emissivity distribution constrains the temperature structure in the disc. whilst the mass distribution (and hence also total disc mass) is a vital parameter in models of star formation. The performance of these inversion methods is investigated as a function of the signal-to-noise ratio and beamsize of the observations.