Constraints on the HL Tauri protostellar disk from millimeter- and submillimeter-wave interferometry

Millimeter and submillimeter interferometry is used to probe the dusty accretion disks around young protostars. New 460 GHz (lambda = 650 mu m) data from the Caltech Submillimeter Observatory and the James Clerk Maxwell Telescope CSO-JCMT Interferometer are combined with previous 345 GHz (lambda = 870 pm) data from CSO-JCMT, 220 GHz (lambda = 1.4 mm) data from the Owens Valley Radio Observatory (OVRO) Millimeter Array, 110 GHz (lambda = 2.7 mm) data from the Berkeley-Illinois-Maryland Association Array (BIMA), and 43 GHz (lambda = 7 mm) data from the VLA, in order to constrain the nature of the protostellar disk around HL Tau on size scales of 50 AU and above. A power-law disk model is fitted directly to the measured visibility data, and probability distributions are derived for the parameters. The effects of instrumental uncertainties are included in a consistent way. The position angle of the major axis of the emission is determined to be 127 degrees +/- 5 degrees and the inclination 42 degrees +/- 5 degrees (where 0 degrees is face-on), assuming the disk is thin, flat, and circular. A strongly flared disk that is close to edge-on cannot be ruled out, however. The CSO-JCMT and OVRO data favor centrally concentrated distributions of the surface density Sigma, where Sigma chi r(-p), and p > 1. This is not compatible with the relatively large sizes measured at lower frequency by BIMA and the VLA. No simple power-law disk model can be found that reproduces all of the millimeter and submillimeter data well. Such a model, with radial power laws in the surface density and temperature, and a single dust component, is therefore unlikely to be a good representation of the actual disk structure. One possibility that would help to reconcile the model with the data is the existence of more than one dust component, i.e., a range of grain sizes or structures in the disk and no unique value of the emissivity index beta. Future models should allow for this as well as for disk geometries that are not thin and flat.