A Bayesian analysis of models for the dust cloud around Fomalhaut

We report on the results of modeling of the dust cloud around Fomalhaut to fit the existing far-infrared and submillimeter data from the Kuiper Airbor ne Observatory (KAO), IRAS, and the James Clerk Maxwell Telescope (JCMT). W e assumed an optically and spatially thin disk with the following free para meters: inner and outer radii, power-law surface-density gradient, and a si mple-grain model that characterized the emissivity as flat shortward of a t ransition wavelength and decreasing linearly with wavelength beyond that. W e also explored two other parameterizations of the models to try to find pa rameters that were better defined by the existing data. We analyzed the res ults of the modeling with Bayesian methods for deriving the probabilities o f the model parameters. We find that we can place significant constraints o n the location of the dust but, contrary to previous suggestions, not its d ensity gradient within the distribution. We confirm previous suggestions th at the dust must have an emissivity dependence that does not decrease signi ficantly with wavelength until longward of lambda similar to 80 mu m. The i nclination of the dust disk is moderately well constrained close to the ran ge previously suggested, theta = 65 degrees +/- 15 degrees. Our models also reproduce well the total submillimeter flux with the simple assumption of a lambda(-1) emissivity law in the submillimeter region.