  We conducted a detailed radiative transfer modeling of the dust emission from
the circumstellar disk around HL Tau. The goal of our study is to derive the
surface density profile of the inner disk and its structure. In addition to the
Atacama Large Millimeter/submillimeter Array images at Band 3 (2.9mm), Band 6
(1.3mm), and Band 7 (0.87mm), the most recent Karl G. Jansky Very Large Array
(VLA) observations at 7mm were included in the analysis. A simulated annealing
algorithm was invoked to search for the optimum model. The radiative transfer
analysis demonstrates that most radial components (i.e., >6AU) of the disk
become optically thin at a wavelength of 7mm, which allows us to constrain, for
the first time, the dust density distribution in the inner region of the disk.
We found that a homogeneous grain size distribution is not sufficient to
explain the observed images at different wavelengths simultaneously, while
models with a shallower grain size distribution in the inner disk work well. We
found clear evidence that larger grains are trapped in the first bright ring.
Our results imply that dust evolution has already taken place in the disk at a
relatively young (i.e., ~1Myr) age. We compared the midplane temperature
distribution, optical depth, and properties of various dust rings with those
reported previously. Using the Toomre parameter, we briefly discussed the
gravitational instability as a potential mechanism for the origin of the dust
clump detected in the first bright ring via the VLA observations.
