Exploring the Grain Properties in the Disk of HL Tau with an
  Evolutionary Model
  We model the ALMA and VLA millimeter radial profiles of the disk around HL
Tau to constrain the properties of the dust grains. We adopt the disk
evolutionary models of Lynden-Bell \& Pringle and calculate their temperature
and density structure and emission. These disks are heated by the internal
viscosity and irradiated by the central star and a warm envelope. We consider a
dust size distribution $n(a) da \propto a^{-3.5} da $, and vary the maximum
grain size in the atmosphere and the midplane, $a_{\rm max}=100\ \mu$m, 1 mm,
and 1cm. We also include dust settling and vary the dust-to-gas mass ratio from
1 to 9 times the ISM value. We find that the models that can fit the observed
level of emission along the profiles at all wavelengths have an atmosphere with
a maximum grain size $a_{\rm max} = 100 \ \mu$m, and a midplane with $a_{\rm
max}=1$ cm. The disk substructure, with a deficit of emission in the gaps, can
be due to dust properties in these regions that are different from those in the
rings. We test an opacity effect (different $a_{\rm max}$) and a dust mass
deficit (smaller dust-to-gas mass ratio) in the gaps. We find that the emission
profiles are better reproduced by models with a dust deficit in the gaps,
although a combined effect is also possible. These models have a global
dust-to-gas mass ratio twice the ISM value, needed to reach the level of
emission of the 7.8 mm VLA profile.
