We present new HST ACS observations and detailed models for a recently discovered edge-on protoplanetary disk around ESO H$alpha$ 569 (a low-mass T Tauri star in the Cha I star forming region). Using radiative transfer models we probe the distribution of the grains and overall shape of the disk (inclination, scale height, dust mass, flaring exponent and surface/volume density exponent) by model fitting to multiwavelength (F606W and F814W) HST observations together with a literature compiled spectral energy distribution. A new tool set was developed for finding optimal fits of MCFOST radiative transfer models using the MCMC code emcee to efficiently explore the high dimensional parameter space. It is able to self-consistently and simultaneously fit a wide variety of observables in order to place constraints on the physical properties of a given disk, while also rigorously assessing the uncertainties in those derived properties. We confirm that ESO H$alpha$ 569 is an optically thick nearly edge-on protoplanetary disk. The shape of the disk is well described by a flared disk model with an exponentially tapered outer edge, consistent with models previously advocated on theoretical grounds and supported by millimeter interferometry. The scattered light images and spectral energy distribution are best fit by an unusually high total disk mass (gas+dust assuming a ratio of 100:1) with a disk-to-star mass ratio of 0.16.
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